contentsstatphys22/abstractbook.pdfcontents 1 lectures by boltzmann award recipients 1 2 plenary...

Contents

1 Lectures by Boltzmann Award Recipients 1

2 Plenary Talks 3

3 Invited Talks 93.1 Topic 1 : Rigorous results and exact solutions; general aspects of statistical physics; thermodynamics. 93.2 Topic 2 : Phase transitions and critical phenomena (equilibrium and nonequilibrium) . . . . . . . . . . 113.3 Topic 3 : Nonequilibrium processes (transport theory, relaxation phenomena, random processes) . . . 133.4 Topic 4 : Pattern formation in systems out of equilibrium (growth processes, fracture, hydrodynamic

instabilities, chemical reactions, granular flows, etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.5 Topic 5 : Dynamical systems and turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.6 Topic 6 : Liquid matter (atomic, molecular and ionic fluids, freezing; metastable liquids; granular

matter) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.7 Topic 7 : Soft condensed matter (colloids, polymers, liquid crystals, microemulsions, foams, membranes,

etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.8 Topic 8 : Interfacial phenomena and wetting; surface effects and confined systems . . . . . . . . . . . 253.9 Topic 9: Quantum-mechanical problems (quantum phase transitions; strongly correlated fermions; Bose-

Einstein condensation; mesoscopic quantum phenomena, etc.) . . . . . . . . . . . . . . . . . . . . . . 273.10 Topic 10 : Disordered systems (random lattices, spin glasses, glass transition, localization, etc.) . . . 293.11 Topic 11 : Biologically motivated problems (protein-folding models, dynamics at the scale of the cell;

biological networks, evolution models, etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.12 Topic 12 : Other applications of statistical physics (networks, traffic flows, algorithmic problems, econo-

physics, astrophysical applications, etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Oral Presentations 394.1 Topic 1 : Rigorous results and exact solutions; general aspects of statistical physics; thermodynamics . 394.2 Topic 2 : Phase transitions and critical phenomena (equilibrium and nonequilibrium) . . . . . . . . . 464.3 Topic 3 : Nonequilibrium processes (transport theory, relaxation phenomena, random processes) . . . 574.4 Topic 4 : Pattern formation in systems out of equilibrium (growth processes, fracture, hydrodynamic

instabilities, chemical reactions, granular flows, etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.5 Topic 5 : Dynamical systems and turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.6 Topic 6 : Liquid matter (atomic, molecular and ionic fluids, freezing; metastable liquids; granular matter) 804.7 Topic 7 : Soft condensed matter (colloids, polymers, liquid crystals, microemulsions, foams, membranes,

etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.8 Topic 8 : Interfacial phenomena and wetting; surface effects and confined systems . . . . . . . . . . . 994.9 Topic 9 : Quantum-mechanical problems (quantum phase transitions; strongly correlated fermions;

Bose-Einstein condensation; mesoscopic quantum phenomena, etc.) . . . . . . . . . . . . . . . . . . . 1054.10 Topic 10 : Disordered systems (random lattices, spin glasses, glass transition, localization, etc.) . . . 1114.11 Topic 11 : Biologically motivated problems (protein-folding models, dynamics at the scale of the cell;



i

ii CONTENTS

5 Poster Presentations 1375.1 Topic 1 : Rigorous results and exact solutions; general aspects of statistical physics; thermodynamics . 1375.2 Topic 2 : Phase transitions and critical phenomena (equilibrium and nonequilibrium) . . . . . . . . . 1505.3 Topic 3 : Nonequilibrium processes (transport theory, relaxation phenomena, random processes) . . . 1855.4 Topic 4 : Pattern formation in systems out of equilibrium (growth processes, fracture, hydrodynamic

instabilities, chemical reactions, granular flows, etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2105.5 Topic 5 : Dynamical systems and turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2275.6 Topic 6 : Liquid matter (atomic, molecular and ionic fluids, freezing; metastable liquids; granular matter)2385.7 Topic 7 : Soft condensed matter (colloids, polymers, liquid crystals, microemulsions, foams, membranes,

etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2465.8 Topic 8 : Interfacial phenomena and wetting; surface effects and confined systems . . . . . . . . . . . 2805.9 Topic 9 : Quantum-mechanical problems (quantum phase transitions; strongly correlated fermions;

Bose-Einstein condensation; mesoscopic quantum phenomena, etc.) . . . . . . . . . . . . . . . . . . . 2875.10 Topic 10 : Disordered systems (random lattices, spin glasses, glass transition, localization, etc.) . . . 2995.11 Topic 11 : Biologically motivated problems (protein-folding models, dynamics at the scale of the cell;



Chapter 1

Lectures by Boltzmann Award Recipients

1.0.1 Wednesday 7 July 9:00-11:00 : Hall J

Boltzmann and Einstein: Statistics and Dynamics - An UnsolvedProblem

E.G.D.Cohen1

1The Rockefeller University, 1230 York Avenue, New York, NY 10021-6399

The struggle of Boltzmann with the proper description of the behavior of classical macroscopic bodies in equilibriumin terms of the properties of the particles out of which they consist will be sketched. He used both a dynamical and astatistical method. However, Einstein strongly disagreed with Boltzmann’s statistical method, arguing that a statisticaldescription of a system should be based on the dynamics of the system. This opened the way, especially for complexsystems, for other than Boltzmann statistics. The first non-Boltzmann statistics, not based on dynamics though, wasproposed by Tsallis. A generalization of Tsallis’ statistics as a special case of a new class of Superstatistics, basedon Einstein’s criticism of Boltzmann, is discussed. It seems that perhaps a combination of dynamics and statistics isnecessary to describe systems with complicated dynamics.

[email protected]

Correlated Randomness & Statistical Physics: Liquid Water,Economics, and Alzheimer’s Disease

H. Eugene Stanley1

1Physics Department, Boston University, Boston MA 02215, USA

We will offer a brief survey of the applications of statistical physics to other fields of science, emphasizing thosewhere the notion of correlated randomness is proving useful. We will then treat in some detail examples of threerecent applications. The first example will be the puzzling behavior of liquid water, a very complex fluid whoseunderstanding is important for biology and medicine. Here we shall sketch the degree to which the liquid-liquid phasetransition hypothesis unifies existing data, and we shall discuss recent experimental results germane to testing thishypothesis. The second example will be the puzzling behavior of economic fluctuations, where a number of phenomenaare describable by power laws with exponents that seem to be universal across different economic cycles and differentcountries. The third example will concern elucidating ”the first three minutes” of Alzheimer disease, namely thehypothesis that a peptide aggregation phenomenon triggers phenomena that ultimately result in this disease whoseincidence is reaching alarming proportions as life expectancy increases. This work was supported by NSF, NIH, andONR, and was carried out in collaboration with many graduate students, research associates, and faculty colleagues,

1

2 CHAPTER 1. LECTURES BY BOLTZMANN AWARD RECIPIENTS

with especial gratitude to L. A. N. Amaral, C. A. Angell, J. M. Borreguero, S. V. Buldyrev, M. Canpolat, L. Cruz-Cruz, P. Debenedetti, F. Ding, G. Franzese, X. Gabaix, A. Geiger, N. Giovambattista, P. Gopikrishnan, S. Havlin, B.T. Hyman, P. Kumar, E. La Nave, G. Malescio, K. Matia, M. Mazza, O. Mishima, S. Mossa, S. Peng, V. Plerou, P.H. Poole, S. Sastry, A. Scala, F. Sciortino, F. W. Starr, J. Teixeira, D. B. Teplow, B. Urbanc, and M. Yamada.

[email protected]

Chapter 2

Plenary Talks

2.1

2.1.1 Monday 5 July, 9:00-9:45 : Hall J

Statistical Mechanics of Complex Networks: From the topology of thewww to the cell’s genetic network

A L Barabasi1

1Department of Physics, University of Notre Dame, Notre Dame, IN, 46556

Networks with complex topology describe systems as diverse as the cell or the World Wide Web. In the past fewyears we have learned that their emergence is driven by self-organizing processes that are governed by simple butgeneric scaling laws. The analysis of the metabolic and protein network of various organisms shows that cells andcomplex man-made networks, such as the Internet or the World Wide Web, share the same large-scale topology. Iwill show that the scale-free topology of these complex webs have important consequences on their robustness againstfailures and attacks, with implications on drug design, the Internet’s ability to survive attacks and failures, and ourability to understand the functional role of genes in model organisms.

[email protected]

2.1.2 Monday 5 July, 9:45-10:30 : Hall J

The physics of active processes in living cells

Frank Julicher1

1 Max-PLanck Institute for the Physics of Complex Systems Nothnitzerstr. 38, 01187 Dresden, Germany

Living cells exhibit a remarkable variety of active behaviors. Material is transported within the cell, cells divideand many cells can swim or crawl along substrates. The molecular basis of such phenomena are specialized proteinmolecules which transduce the chemical energy of a fuel, ATP, to mechanical work and motion. A prototype systemfor force generation on the moleculer scale are motor proteins of the cytoskeleton which generate forces and motionalong linear filaments to which they bind specifically. Filaments together with motors and other elements can formcomplex networks and organized structures in the cell. Such systems represent complex active gel-like materials whichare very dynamic and can exhibit spontaneous motion and force generation. The mechanical properties of activecellular systems can be observed experimentally. I will give an overview over such phenomena and present theoreticalconcepts to describe the nonequilibrium physics of these systems. Theoretical descriptions for the energy transduction

3

4 CHAPTER 2. PLENARY TALKS

on the molecular scale capture the general properties of force generation which is stochastic in nature. Systemsinvolving a large number of active elements exhibit dynamic instabilities and bifurcations as a result of collectiveeffects. The generic properties of active gels on large scales are captured by a hydrodynamic theory which takes intoaccount viscoelasticity, the structural polarity of filaments and the generation of active stresses and flows in the system.Theoretical analysis shows that in many cases, mechanical oscillations occur in active cytoskeletal systems. Similaroscillations can also be observed in living cells and in some cases be related to the underlying cytoskeletal dynamics.Cells can use the complex dynamics of cytoskeletal structures for their function. For example, the proximity to a Hopfbifurcation can provide high sensitivity and frequency selectivity for mechanosensory cells.

[email protected]

2.1.3 Tuesday 6 July, 9:00-9:45 : Hall J

Sheared Solid Materials

Akira Onuki1

1Department of Physics, Kyoto University, Kyoto 606-8502, Japan

Nonequilibrium states realized under shear have been extensively studied for various complex fluids. However,not enough attention has yet been paid to such problems for metals and amorphous solids. In this talk I present atime-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. In this model the elastic energydensity is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With thisnew ingredient solving the equations yields formation of dislocation dipoles. In plastic flow high-density dislocationsemerge at large strains to accumulate and grow into shear bands where the strains are localized. The shear bandsin uniaxial deformation make angles of ±π/4 with respect to the stretched direction in the limit of weak elasticanisotropy. Furthermore, in addition to the displacement and the lattice velocity, we introduce an order parameter mrepresenting the local free volume in amorphous solids. For very small free volume the defect structures are metastableand long-lived due to the Peierls potential once they are created. However, with increasing the total amount of m,slow diffusive accumulation of m around defects breaks the Peierls potential leading to appreciable relaxations in thestress and the elastic energy even after the flow is stopped. Here the shear modulus is assumed to become small withincreasing m.

[email protected]

2.1. 5

2.1.4 Tuesday 6 July, 9:45-10:30 : Hall J

Theoretical Approaches to the Glass Transition in Simple Liquids

Chandan Dasgupta1

1Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore-560 012, India.

The first half of the talk will contain a review of analytical and computational studies of equilibrium and dynamicalproperties of simple supercooled liquids near the structural glass transition, with emphasis on analytic work basedon the analogy of the behaviour near the structural glass transition with that of a class of mean-field spin-glassmodels, and numerical work involving studies of the local minima of the potential energy (the “ potential energylandscape”) of simple model liquids. Both the successes of these approaches and some of the remaining problems willbe discussed. Other theoretical approaches in which the glass transition is viewed as a purely dynamical phenomenonwithout any underlying thermodynamic transition will also be described briefly. In the second half of the talk, Iwill summarize some of the results obtained by us from two approaches to this problem. The first approach involvesanalytic calculations using a combination of liquid-state theory and the replica method used in studies of systems withquenched disorder. In these calculations, the occurrence of one-step replica symmetry breaking, similar to that foundin mean-field spin-glass models exhibiting random first-order transitions, is assumed to represent a thermodynamicliquid-to-glass phase transition. The second approach is a numerical one, involving studies of the local minima of amodel free-energy functional for simple liquids. The “free-energy landscape” obtained from these studies exhibits, forappropriate parameter values, the presence of a large number of “glassy” local minima characterized by inhomogeneous,non-periodic distributions of the time-averaged local density. Various aspects of the behaviour of simple liquids nearthe glass transition may be understood in terms of the properties of these glassy minima and the free-energy barriersthat separate different minima. The results obtained from these two “mean-field” approaches to the structural glasstransition will be compared with each other and with the results of other studies. Finally, a few directions for furtherwork on this problem will be suggested.

[email protected]

2.1.5 Wedensday 7 July, 11:30-12:15 : Hall J

Fluctuations and Large Deviations in Non-equilibrium systems

Bernard Derrida1

1Laboratoire de Physique Statistique Dpartement de Physique - Ecole Normale Suprieure 24, Rue Lhomond 75230Paris Cedex 05 France

The exact solutions of simple models allow to obtain the large deviation functions of density profiles and of thecurrent through simple systems in contact with two reservoirs at different densities. These simple models show thatnon-equilibrium systems have a number of properties which contrast with equilibrium systems: phase transitions inone dimension, non local free energy functional, violation of the Einstein relation between the compressibility andthe density fluctuation, non-Gaussian density fluctuations. They also lead to a general expression for the currentfluctuations through a diffusive system in contact with two reservoirs.

References :[1] B Derrida, J L Lebowitz, E R Speer, Free Energy Functional for Nonequilibrium Systems: An Exactly SolvableCase, Phys. Rev. Lett. 87, 150601 (2001) and Exact Free Energy Functional for a Driven Diffusive Open StationaryNonequilibrium System, Phys. Rev. Lett. 89, 030601 (2002).[2] C. Enaud, B. Derrida, Large deviation functional of the weakly asymmetric exclusion process, J. Stat. Phys. 2004in press cond-mat/0307023.[3] B Derrida, B Doucot, P-E Roche, Current fluctuations in the one dimensional Symmetric Exclusion Process with


open boundaries, J. Stat. Phys. 2004.[4] T. Bodineau, B Derrida, Current fluctuations in non-equilibrium diffusive systems: an additivity principle, Preprint2004

[email protected]

2.1.6 Wednesday 7 July, 12:15-13:00 : Hall J

Phase Transitions, Interfacial Fluctuations and Hidden Symmetries forFluids near Structured Walls.

Andrew O. Parry1 and J. M. Romero-Enrique2

1,2Dept. Mathematics, Imperial College London, London SW7 2BZ, UK

Fluids adsorbed at micro-patterned and geometrically structured substrates can exhibit novel phase transitions andinterfacial fluctuation effects distinct from those characteristic of wetting at planar, homogeneous walls. We reviewrecent theoretical and experimental progress in this area paying particular attention to filling transitions pertinent tofluid adsorption near wedges, cones and apexes which have highlighted a deep connection between geometrical andcontact angles. We show that filling transitions are not only characterised by large scale interfacial fluctuations leadingto universal critical singularities but also reveal hidden symmetries with short-ranged critical wetting transitions andproperties of dimensional reduction.

[email protected]

2.1.7 Thursday 8 July, 9:00-9:45 : Hall J

Aspects of Dynamics in soft and Granular Systems

T.C. Lubensky1

1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104

Soft materials exhibit a rich and varied palette of dynamical behavior, ranging from simple hydrodynamical flowsto complex driven and nonequilibrium processes. After presenting a brief review of equilibrium hydrodynamics ofconserved and broken-symmetry variables with examples including nematic elastomers from liquid crystals, this talkwill focus on realizations of low-frequency, yet not quite hydrodynamical dynamical phenomena in soft and granularmaterials. It will consider, in particular, one- and two-point microrheology as a method of measuring the rheologicalresponse of small, inhomogeneous systems including highly-nonequilibrium ones like living cells, and it will presentphenomenological theories for the dynamics of granular matter including two-dimensional chiral granular gases.

[email protected]

2.1. 7

‘

2.1.8 Friday 9 July, 9:00-9:45 : Hall J

Critical Casimir forces and anomalous wetting

S. Balibar1,T. Ueno2,R. Ishiguro3,F. Caupin4,E. Rolley5 and T. Mizusaki6

1,3,4,5Laboratoire de Physique Statistique de l’Ecole Normale Superieure, Paris, France.2,6Department of Physics, Kyoto University, Kyoto Japan.

We review the present understanding of critical Casimir forces and wetting near a critical point, and compareavailable predictions to existing experimental results. Consider a binary liquid mixture below its critical temperatureTc: it is separated in two phases with an interface which may touch a wall with a non-zero contact angle q. As Ttends to Tc, q is expected to vanish. This phenomenon is called critical point wetting . It had been first predictedin a historical article by J.W. Cahn [1], confirmed by several theorists and osberved in every system up to now. Wehave discovered a first exception to critical point wetting in the physics of liquid helium mixtures [2] : a 3He-4Heinterface does not completely wet a sapphire wall, even close to the tricritical point where phase separation ( andsuperfludity) appear. We later explained [3] that this anomalous behavior could be a consequence of the existenceof critical Casimir forces . First predicted by M. Fisher and P.G. de Gennes [4], these long range forces originatein the confinement of critical fluctuations. In our system, we argued that the dominant effect is the confinement ofsuperfluidity in the 4He-rich film which exists between the wall and the 3He-rich bulk phase. Although the calcula-tion of critical Casimir forces has significantly progressed [5,6], it is not yet completed, especially below Tc and withthe boundary conditions corresponding to experiments [2,7]. Our measurements are now extended to the superfluidregion far below the tricritical temperature Tt. Our goal is to test the prediction by M. Kardar and R. Golestanianthat the confinement of Goldstone modes in superfluid films leads to an additionnal contribution to the Casimir force[8].

References :[1] J.W. Cahn, J. Chem. Phys. 66, 3667, 1977.[2] T. Ueno et al., J. Low Temp. Phys. 130, 543, 2003.[3] T. Ueno et al. Phys. Rev. Lett. 90, 116102, 2003.[4] M. Fisher and P.G. de Gennes, C.R. Acad. Sci. Paris, B 287, 209, 1978.[5] M. Krech and S. Dietrich, Phys. Rev. Lett. 66, 345, 1991 and J. Low Temp. Phys. 89, 145, 1992.[6] G. Williams, Physica B329, 204, 2003 and arXiv :condmat/0307125 (2003).[7] R. Garcia and M. Chan, Phys. Rev. Lett. 83, 1187, 1999.[8] M. Kardar and R. Golestanian, Rev. Mod. Phys. 71, 1233, 1999.

[email protected]


2.1.9 Friday 9 July, 9:45-10:30 : Hall J

Mathematical aspects of the scaling limit of 2-d critical systems

Wendelin Werner1

1Laboratoire de Mathematiques Universite Paris-Sud Batiment 425 91405 Orsay Cedex, France

It has been observed long ago that many systems from statistical physics behave randomly at macroscopic level attheir critical temperature. In two dimensions, these phenomena have been classified by theoretical physicists thanksto conformal field theory, that led to the derivation of the exact value of various critical exponents that describe thebehaviour of these systems near the critical temperature. In the last couple of years, combining ideas of complexanalysis and probability theory, mathematicians have constructed and studied a family a random fractals (called”Schramm-Loewner Evolutions” or SLE) that describe the only possible conformally invariant limits of the interfacesfor these models. This gives a concrete construction of these random systems, puts various predictions on a rigorousfooting, and leads to further understanding of the behaviour of these systems. The goal of this lecture will be tosurvey some of these recent mathematical developments (joint results with Lawler and Schramm, and also by Beffara,Rohde, Smirnov, etc.), and to describe their basic underlying ideas.

[email protected]

Chapter 3

Invited Talks

3.1 Topic 1 : Rigorous results and exact solutions; general aspects ofstatistical physics; thermodynamics.

3.1.1 Monday July 5 11:00-11:30 : Hall F

Recent results for the 6 and 8 vertex model at roots of unity and hardsphere virial coefficients

Barry McCoy1

1Institute for Theoretical Physics, State University of New York, Stony Brook, USA

For the 6 and 8 vertex model we present the newly discovered properties of 6 and 8 vertex models at roots of unityincluding the infinite dimensional loop algebra symmetry group, new functioal equations, fusion matrices, the solutionto the degeneracy problem of transfer matrix eigenvalues and new results on chains of odd length. For the hard spheregas we present new results for the virial coeffients through B10 for dimensions D=2,3,...,8 and use this to discuss theexistence of negative virial coefficients, the radius of convergence of the virial series and the freezing transition.

[email protected]

3.1.2 Thursday July 8 10:15-10:45 : Hall J

On the dynamical foundations of nonextensive statistical mechanics

C Tsallis1

1Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil and Santa Fe Institute, New Mexico, USA.

Ubiquitous artificial and natural systems exist which are not adequately tractable within Boltzmann-Gibbs (BG)statistical mechanical frame. A vast class of such systems appears to be appropriately handled within a gener-alization of the BG theory named nonextensive statistical mechanics. After a brief introduction of the formal-ism, we shall focus on the present status of its dynamical foundations. Bibliography: ”Nonextensive Entropy- Interdisciplinary Applications”, M. Gell-Mann and C. Tsallis (Oxford University Press, New York, 2004), andhttp://tsallis.cat.cbpf.br/biblio.htm

[email protected]

9

10 CHAPTER 3. INVITED TALKS


Inhomogeneous classical charge fluids at equilibrium

F. Cornu1

1 Laboratoire de Physique Theorique Laboratoire associe au Centre National de la Recherche Scientifique - UMR 8627Batiment 210, Universite Paris-Sud, 91405 Orsay, France

The structure of equilibrium density profiles in an electrolyte in the vicinity of an interface with an insulating orconductive medium is of crucial importance in chemical physics and colloidal science. Because of the difference betweenelectric permittivities on both sides of the interface, every charge in the electrolyte interacts with an electrostatic image,and the Boltzmann factor associated with the corresponding self-energy has an essential singularity over the lengthscale l from the wall. Besides Coulomb interactions, short-range repulsions must be taken into account in order toprevent the collapse between charges with opposite signs or between each charge and its image when the solventdielectric constant is lower than that of the continuous medium on the other side of the interface. For a dilute andweakly-coupled electrolyte, l is negligible with respect to the bulk Debye screening length ξD. In the framework ofthe grand-canonical ensemble, systematic partial resummations in Mayer diagrammatics allows one to exhibit that, inthis regime, the density profiles are eventually described by a mean-field theory, where the screened pair interactionobeys an inhomogeneous Debye equation. In the latter equation the effective screening length depends on the distancex from the interface: it varies very fast over the length l and tends to its bulk value over a few ξD’s. The equation canbe solved iteratively at any distance x, and the exact density profiles are calculated analytically up to first order in thecoupling parameter l/ξD. They show the interplay between three effects: the geometric repulsion from the interfaceassociated with the deformation of screening clouds, the screened interaction of each charge with its image on theother side of the interface, and the interaction between each charge and the potential drop created by the electriclayer which appears as soon as the fluid has not a charge-symmetric composition. Similar diagrammatic techniquesalso allow one to investigate other effects: the charge renormalization in the dipolar effective pair interaction along theinterface with an insulating medium, or screening in an electrolyte confined between two metallic electrodes submittedto a potential drop.

[email protected]

3.1.4 Friday July 9 15:45-16:15 : Hall E

Integral geometry in Statistical Physics: the shape of matter

Klaus Mecke1

1MPI for Metallforschung, Stuttgart

Spatially complex disordered matter such as foams, gels and porous media are of increasing technological importancedue to their shape-dependent material properties. But the shape of disordered structures is a remarkably incoherentconcept and cannot be captured by correlation functions alone which were almost a synonym for structural analysis inStatistical Physics since the very first X-ray scattering experiments. However, in the last 20 years numerous methodssuch as AFM and computer tomography have been developed which allow quantitative measurements of complexstructures directly in real space. Integral geometry furnishes a suitable family of morphological descriptors, known asMinkowski functionals, which are related to curvature integrals and do not only characterize connectivity (topology)but also size and shape of disordered structures. Furthermore, Minkowski functionals are related to the spectrum ofthe Laplace operator, so that structure-property relations can be derived for complex materials. Percolation thresholdsand fluid flow in porous media, for instance, can be predicted by measuring the Minkowski functionals of the porespace alone. Also, evidence was found in hard sphere fluids that the shape dependence of thermodynamic potentialsin finite systems can be expressed solely in terms of Minkowski functionals. Finally, a density functional theory isconstructed on the basis of Minkowski functionals which allows an accurate calculation of correlation functions andphase behavior of mesoscopic complex fluids such as microemulsions and colloids.

3.2. TOPIC 2 : PHASE TRANSITIONS AND CRITICAL PHENOMENA (EQUILIBRIUM ANDNONEQUILIBRIUM) 11

[email protected]


Laplacian growth

P. Wiegmann1

1James Franck Institute, Enrico Fermi Institute, Department of Physics of the University of Chicago, 5640 S. EllisAve, Chicago, IL 60637

Laplacian growth is an evolution of a plane interface between two immiscible phases, driven by a gradient of aharmonic field. Regardless of initial conditions an interface develops a complex unstable fingering pattern. A progressin this field has been driven by recently recognized connections between this class of phenomena and two branches ofmathematical physics: integrable (soliton-like) equations, and random matrix theory. I will review recent developmentsin the field and the current status of the problem.

[email protected]

3.2 Topic 2 : Phase transitions and critical phenomena (equilibrium andnonequilibrium)

3.2.1 Monday July 5 11:00-11:30 : Hall E

Viscoelasticity of Gels

A. Zippelius1

1Department of Physics, University of Goettingen, Bunsenstrasse 11, D-37073 Goettingen, Germany

We study shear relaxation and density fluctuations within simple dynamic models of randomly crosslinked macro-molecular networks. The sol phase is characterized by a stretched exponential decay of shear relaxation, which can betraced to the random connectivity of molecular clusters such that weakly connected regions dominate the relaxation ofshear. Anomalous time decays are also observed for density fluctuations. These can be related to a broad distributionof relaxation times, reflecting the corresponding cluster size distribution. The transition from the sol to the gel is- like the glass transition - characterized by a diverging static shear viscosity, if the transition point is approachedfrom the fluid side, respectively by a vanishing shear modulus, if the approach is from the amorphous solid side. Thecritical behaviour can be calculated exactly within the Rouse model, e.g. the critical exponent k of the static shearviscosity is shown to be k = (1 − τ + 2/ds)/σ. Here σ and τ are the exponents of the cluster size distribution ofpercolation theory and ds is the spectral dimension of the incipient percolating cluster. Coefficients of normal stresseshave also been computed and were shown to diverge even more strongly than the static shear viscosity. Hydrodynamicinteractions can be taken into account approximately within the Zimm model, for which we have analysed the scalingof the diffusion constant and the shear viscosity with cluster size. In the gel phase a finite fraction of particles, thegel fraction, is localised at random positions, resulting in a spontaneous breaking of the translational symmetry ofthe underlying model. Goldstone modes can be identified with long wavelength shear deformations, allowing for aderivation of the elastic free energy and the shear modulus within a microscopic model.

[email protected]


3.2.2 Tuesday July 6 15:45-16:15 : Hall E

Bulk and Boundary Critical Behavior at Lifshitz Points

H. W. Diehl1

1 Fachbereich Physik, Universitat Duisburg-Essen, Campus Essen, D-45117 Essen, Germany

Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulatedordered phase meet. Their bulk universality classes are described by natural generalizations of the standard φ4 model.Analyzing these models systematically via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of the 1970s. We survey the recent progress madein this direction, discussing results obtained via dimensionality and 1/n expansions, how they compare with MonteCarlo results, and open problems. These advances opened the way towards systematic studies of boundary criticalbehavior at m-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane isperpendicular to one of the m modulation axes or parallel to all of them. We show that the semi-infinite field theoriesrepresenting the corresponding surface universality classes in these two cases of perpendicular and parallel surfaceorientation differ crucially in their Hamiltonian’s boundary terms and the implied boundary conditions, and explainrecent results along with our current understanding of this matter.

[email protected]


Why you need a functional RG to survive in a disordered world

Kay Wiese1

1Institute of Theoretical Physics, University of California at Santa Barbara, Santa Barbara, USA

We discuss the behavior of an elastic manifold in a random potential, as a prototype for a disordered system. Thismodel describes physical systems as varied as charge density waves, domain walls in dirty magnets, directed polymers(equivalent to the KPZ-equation), the depinning of a contact-line, flux lattices in a superconductor, and many more.The theoretical challenge is that standard perturbation theory leads to absurd results. To escape this dilemma, onehas to follow the whole disorder distribution (functional renormalization). We describe recent results in perturbationtheory beyond one loop, both for equilibrium and depinning, which turn out to be in different universality classes. Wefinally compare to the variational replica method introduced by Mezard-Parisi, relying on replica symmetry breaking.

[email protected]

3.3. TOPIC 3 : NONEQUILIBRIUM PROCESSES (TRANSPORT THEORY, RELAXATIONPHENOMENA, RANDOM PROCESSES) 13

3.2.4 Thursday July 8 15:00-15:30 : Hall E

The analytic structure of lattice models

Anthony J. Guttmann1

1Department of Mathematics and Statistics The University of Melbourne Vic. 3010 Australia

Very few interesting lattice models are exactly solvable even in two dimensions, let alone three. The free-energyand spontaneous magnetization of the two-dimensional Ising model, and the specific heat of the 8-vertex model, aswell as certain properties of the hard hexagon model constitute the bulk of solved models in two dimensions. Modelssuch as the self-avoiding walk, percolation (both ordinary and directed), site (bond) trees, all remain unsolved. Inthree dimensions the list of solvable models is even shorter.We recently observed that most of the solved models were differentiably finite. That is, satisified a linear differentialequation with polynomial coefficients. We then proposed a numerical method for conjecturing which models are likelyto satisfy such a d.e. All the above-mentioned unsolved models appear not to be differentiably finite.More recently, Andrew Rechnitzer has shown how these conjectures can be made rigorous, and has proved that thegenerating function for self-avoiding polygons, directed bond animals, bond trees and general bond animals on thesquare lattice are all not differentiably finite. In all cases the generating function is shown to have a natural boundaryin the complex plane. The proofs can be extended to the hypercubic lattices.This feature is also shared by the susceptibility of the Ising model, though a polynomial time algorithm for thegeneration of the coefficients has been obtained by Orrick et. al.We will describe both the numerical and rigorous methods in this approach to lattice models.

[email protected]

3.3 Topic 3 : Nonequilibrium processes (transport theory, relaxationphenomena, random processes)

3.3.1 Monday July 5 15:45-16:15 : Hall J

Universal scaling for growth processes in one space dimension

Herbert Spohn1

1Department of Mathematics and Physics TU Muenchen, 85478 Garching, Germany

As known for almost 20 years, one-dimensional growth processes in the Kardar-Parisi-Zhang universality class havedynamical scale exponent z = 3/2. We report on novel techniques which, amongst other insights, yield the exact two-point function and certain universal probability distributions. The techniques are related to edge scaling in HermitianGaussian multi-matrix models. With this connection it can be seen that KPZ growth appears also in a purely staticcontext. E.g., the edge of an equilibrium facet has the same universal shape fluctuations as a growing droplet.

[email protected], [email protected]



Condensation Transitions in Nonequilibrium Systems

Martin Evans1

1School of Physics University of Edinburgh James Clerk Maxwell Building Mayfield Road EH9 3JZ Edinburgh UnitedKingdom

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium- forexample in phase transitions in one-dimensional systems. In this talk I will review several ‘condensation’ transitionsthat occur when a conserved quantity is driven through the system. Although the condensation is spatial, i.e. a finitefraction of the conserved quantity condenses into a small spatial region, useful comparison can be made with usualBose-Einstein condensation. Amongst some one-dimensional examples I will discuss the ‘Bus Route Model’ where thecondensation corresponds to the clustering together of buses moving along a bus-route. I will also discuss how, eventhough there is no free energy to describe nonequilibrium phase transitions, one can still formulate a general pictureakin to the Yang-Lee theory of equilibrium phase transitions. Finally I will discuss a curious situation wherein onany large finite system one sees apparently abrupt changes in behaviour as a control parameter is varied, yet in thethermodynamic limit one can show there is strictly no phase transition.

[email protected]


Nonequilibrium relaxation method - an alternative simulation strategy

Nobuyasu Ito1

1Department of Applied Physics School of Engineering The University of Tokyo Tokyo 113-8656, JAPAN

One well-established simulation strategy to study the thermal phases and transitions of a given microscopic modelsystem is so-called the equilibrium method, in which one firstly realizes the equilibrium ensemble of a finite systemand then extrapolates the results to infinite system. This equilibrium method traces over the standard theory of thethermal statistical mechanics, and over the idea of the thermodynamic limit. Recently, alternative simulation strategywas proposed. It analyzes the nonequilibrium relaxation(NER) process and it is called the NER method. There aresome advantages in the NER method over the equilibrium method. The NER method provides simpler analyzingprocedure. This implies the less systematic error which is inevitable in the simulation and provides efficient resourceusage. The NER method easily treat not only the thermodynamic limit but also other limits: for example, finite-timebehavior of infinite system. So the NER method cultivates the new fields of the statistical physics. Application ofthe NER method has been expanding to various problems: from basic first- and second-order transitions to advancedand exotic phases like chiral, KT spin-glass and quantum phases. From these studies, not only the improvementsin accuracy like better estimations of transition point and exponents, but also qualitative developments have beenprovided. For example, the universality class of random system, the nature of the two-dimensional melting and thescaling behavior of the spin-glass aging phenomena have been shown.References:N. Ito, Physica A 192 (1993) p.604, 196 (1993) p.569.N. Ito, T. Matsuhisa and H. Kitatani, J. Phys. Soc. Jpn. 67 (1998) p.1188.N. Ito, K. Hukushima, K. Ogawa and Y. Ozeki, J. Phys. Soc. Jpn. 69 (2000) p.1931.N. Ito and Y. Ozeki, Physica A 321 (2003) p.262 and references therein.

[email protected]



Interplay of Wetting and Phase Separation at Surfaces

Sanjay Puri1

1School of Physical Sciences Jawaharlal Nehru University New Delhi 110 067

We study a phase-separating mixture in contact with a surface which has a preferential attraction for one of thecomponents of the mixture. We clarify the complex interplay between two kinetic processes, viz., wetting at the surfaceand phase separation in the bulk. In particular, we demonstrate the sensitive dependence of the wetting kinetics on(a) the composition of the mixture, and (b) the relevance of hydrodynamic flow fields.

[email protected]

3.3.5 Friday July 9 11:00-11:30 : Hall F

Application of the density matrix renormalization group innon-equilibrium systems

T. Xiang1

1Institute of Theoretical Physics and Interdisciplinary Center of Theoretical Studies, Chinese Academy of Sciences,P.O.Box 2735, Beijing 100080, China

The density matrix renormalization group is a powerful and successful numerical method for studying stronglycorrelated systems. Recently we have extended this method for solving scattering equations. We have also proposeda new approach to calculate the time-dependent wavefunction of non-equilibrium systems at zero temperature usingthe DMRG. Our work provides a reliable framework for studying physical properties, especially long-time behaviors,of quantum many body systems out-of-equilibrium with the DMRG. We have applied these methods to a number ofnon-equilibrium mesoscopic systems, including a quantum dot and a tunneling junction between two Luttinger liquids,and compared the results with experiments

[email protected]


3.4 Topic 4 : Pattern formation in systems out of equilibrium (growthprocesses, fracture, hydrodynamic instabilities, chemical reactions,granular flows, etc.)


Length Scales and Time Scales in First-Passage Behavior of StepWandering on Solid Surfaces

Ellen D. Williams1

1Department of Physics And Institute for Physical Science and Technology University of Maryland College Park, MD20742

Structural fluctuations occur on solid surfaces at temperatures well below the melting point, and can be measuredboth spatially and temporally using real-space imaging tools such as LEEM, REM and STM. They couple to fieldgradients to create mass transport that can dramatically change the shape of the interface. For nanoscale structures,fluctuations may represent a significant fraction of the structural mass, and thus significantly influence the physicalproperties (e.g. catalytic, magnetic, electrical, optical) of interest. It is thus of interest to consider structural fluctua-tions not only from the traditional perspective of correlation functions, but also in terms of their stochastic variability.We have measured step fluctuations on a number of experimental systems using STM, over a wide temperature vari-ation in some cases. Analysis of the correlation functions shows that all systems fall into one of two classes for stepwandering, n=2 (non-conserved noise) or n=4 (conserved noise). The time constant for step wandering is strongly(Arrhenius) temperature dependent, but the correlation time is, surprisingly, temperature independent. This resultreveals interesting concepts about the effective system size for measurements of fluctuations. In addition, we haveanalyzed the First-Passage-related probability distributions, persistence and survival. We find the expected power-laws for persistence, with NO temperature dependence, and exponential decay (at late times) for survival with a timeconstant (and size issues) directly proportional to the correlation time. Supported by the NSF-MRSEC, Laboratoryfor Physical Science, NSF-NIRT and DOE-NNI.

[email protected]


Structure and cluster formation in granular media

Stefan Luding1

1Particle Technology, DelftChemTech, room 0.528 Julianalaan 136, 2628 BL Delft, The Netherlands

Granular Materials (GM) are an interesting and fascinating example for non-equilibrium many-particle systemswith a rich phenomenology, concerning their flow-behavior, their dynamics and their transport properties. Amongmany other, only partly understood, striking experimental observations are size-segregation, surface waves (oscillons),phase transitions, non-Newtonian flow behavior, and structure and cluster formation. The latter example is examinedmore closely using various methods from statistical physics, in both the free cooling and the driven case.The difference between GM and a conservative many-particle system (like a hard sphere fluid) is the fact that energyis dissipated at each conctact/collision of the particles, so that a balance between energy input and dissipation canbe achieved in a dynamic, non-equilibrium steady state (NESS) situation. Dissipation in granular media leads toa fluctuation driven clustering process of particles that is self enhanced and leads to large scale structures with aninteresting growth and flow dynamics.The freely cooling system is examined concerning the energy decay and the cluster/structure evolution and growth intime. The initial, homogeneous cooling state is properly described by Chapman-Enskog kinetic theory, whereas for

3.4. TOPIC 4 : PATTERN FORMATION IN SYSTEMS OUT OF EQUILIBRIUM (GROWTHPROCESSES, FRACTURE, HYDRODYNAMIC INSTABILITIES, CHEMICAL REACTIONS,GRANULAR FLOWS, ETC.) 17

the understanding of the cluster growth regime, other tools from statistical physics are used. Interesting parallels topercolation theory are obtained in three dimensions, and the cluster population dynamics is examined by means of amaster- equation approach.

[email protected]


Control of Spatio-temporal Disorder in Parametrically Forced SurfaceWaves

T. Epstein1 and Jay Fineberg2

1,2The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

The nonlinear interactions of parametrically driven surface waves have been shown to yield a rich family of nonlinearstates. When the system is driven by two commensurate frequencies, a number of interesting superlattice typestates are generated via a number of different 3-wave resonant interactions. They occur either as symmetry-breakingbifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the twoprimary unstable modes generated by the two forcing frequencies. Near the system’s bicritical point, there is a highlydisordered state, both in space and time, which we show results from competition between two different nonlinearsuperlattice states having different temporal and spatial symmetries. We will first characterize the type of spatial-temporal disorder that is embodied in the disordered state. We will then demonstrate that this highly disorderedstate can be rapidly stabilized to either of its neighboring nonlinear states by the application of a small-amplitudeexcitation at a 3rd frequency. We will demonstrate that the spatial symmetry of the selected pattern is determined bythe temporal symmetry of the 3rd frequency used. This technique can also excite rapid switching between differentnonlinear states.

[email protected]

3.4.4 Friday July 9 11:00-11:30 : Hall AB

Exact Nonstationary Probabilities in the Asymmetric Exclusion Processon a Ring

V. B. Priezzhev1

1Bogoliubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research, 141980 Dubna, Russia

The complete (nonstationary) solution of the master equation for a system of interacting particles of finite densityis presented. The system under consideration is the totally asymmetric exclusion process on a ring which is the wellknown model of growing interfaces, one-lane traffic, directed polymers in random media, etc. By using a new formof the Bethe ansatz, an exact expression for the probability of particle configurations is obtained for arbitrary initialconditions and time intervals.

[email protected]


3.5 Topic 5 : Dynamical systems and turbulence

3.5.1 Monday July 5 11:00-11:30 : Hall AB

Measurements of the Lagrangian Statistics in the Fully DevelopedTurbulence of Dilute Polymer Solutions.

Eberhard Bodenschatz1

1Laboratory for Atomic and Solid State Physics 618 Clark Hall Cornell University Ithaca, NY 14853-2501USA

It is well known that only a few parts-per-million by weight of long-chain flexible polymers dissolved in a fluidcan have huge effects on the properties of wall bounded turbulent flows. The observed drag reduction of up to 80%has been at the center of scientific inquiry for more than 50 years. The minute amounts of polymers have beenshown to change the structure of the turbulent boundary layer; however, the detailed mechanism is still unclear.In contrast, the bulk properties in the middle of a fully developed turbulent flow have received little experimentalattention. Experiments have been limited by the unavailability of suitable measurement techniques. Here, we reportmeasurements of Lagrangian statistics of dilute aqueous polymer solutions in bulk turbulence. The measurementshave been made possible by the development of high speed imaging systems that allow tracking passive tracers (smallparticles) in three dimensions at up to 70,000 measurements per second and at a spatial resolution of 1/5000. Wereport measurements of Lagrangian statistics, such as the acceleration distribution functions, the RMS accelerationand acceleration autocorrelation. We compare the results with those obtained for pure water at the same forcingand find that minute amounts of long-chained polymers have a huge effect on the observed quantities. This workis conducted in collaboration with Alice Crawford and Nicolas Mordant and is supported by the National ScienceFoundation under grants PHY9988755 and PHY0332405.

[email protected]


Pattern formations in chaotic extended systems

Hu Gang1

1Department of Physics Beijing Normal University Beijing China 100875

Pattern formations in chaotic extended systems modelled by chaotic coupled maps, coupled oscillators, and non-linear partial differential equations are discussed. The focus is on the motions and patterns at the onset of differentkinds of instabilities of synchronous chaos. The chaotic desynchronous patterns after instabilities can be generallydescribed by a universal form, including three parts: the synchronous chaos; a spatiotemporal pattern ordered in bothtime and space (of which the order is characterized by the unstable mode of the reference chaotic state); and chaoticvariation of the scale of the resulting patterns. Richpictures of temporally chaotic while spatially ordered patterns areshown and the mechanisms underlying the formation of these patterns are discussed.

[email protected]

3.5. TOPIC 5 : DYNAMICAL SYSTEMS AND TURBULENCE 19

3.5.3 Tuesday July 6 11:00-11:30 : Hall F

Universality in turbulence

Massimo Vergassola1

1Laboratoire GMP, Institut Pasteur Drtement de Biologie Mollaire25 rue du Dr Roux 75724 Paris Cedex 15 France

The dependence of the statistics of turbulent fields on large-scale features will be discussed. For passive transport,the finite-size effects induced by a large-scale shear on the scalar energy spectrum are derived. For active transport,scalar fields with different couplings to the advecting flow are analyzed. Finally, results for the decaying 3D Navier-Stokes equations will be presented.

[email protected]

3.5.4 Thursday July 8 10:15-10:45 : Hall F

Onsager and the Theory of Hydrodynamic Turbulence

Katepalli R. Sreenivasan1

1International Centre for Theoretical Physics, Trieste, Italy

Lars Onsager, a giant of the twentieth-century science and the 1968 Nobel-Laureate in Chemistry, made deep contri-butions to several areas of physics and chemistry. Perhaps less well-known is his ground-breaking work and life-longinterest in the subject of hydrodynamic turbulence. This talk will be a summary of Onsager’s published and unpub-lished contributions to hydrodynamic turbulence and an account of their place in the field as it has evolved throughthe years.

[email protected]



Aging dynamics at edge of chaos and intermittency at critical transition

Alberto Robledo1

1 Instituto de Fısica, Universidad Nacional Autnoma de Mexico,Apartado Postal 20-364, Mexico D .F., Mexico

The physical area of the nonextensive Tsallis statistics is probed by considering the dynamics near glass formationand at criticality in thermal systems. In both cases a connection is made with states in one-dimensional nonlinearmaps with vasnishing Lyapunov coefficients. (i) The dynamics of iterates at the transition to chaos in one-dimensionalunimodal maps is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation andaging [1]. The properties of the bifurcation gap induced by external noise, including a relationship between relaxationtime and entropy, are seen to be comparable to those of a supercooled liquid above a glass transition temperature.(ii) We put together two well-defined statistical-mechanical developments to show that the dynamics of the orderparameter at a thermal critical point is a reasonable application of the nonextensive statistics [2]. The first is thatcritical fluctuations are correctly described by the dynamics of an intermittent nonlinear map. The second is thatintermittency in the neighborhood of a tangent bifurcation in such map rigorously obeys Tsallis statistics. We commenton the implications of these results. [1] Robledo, A., ”Universal glassy dynamics at noise-perturbed onset of chaos. Aroute to ergodicity breakdown”, Physica A (in press) and cond-mat/0307285. [2] Robledo, A, ”Critical fluctuations,intermittent dynamics and Tsallis statistics”, Physica A (in press) and cond-mat/0401405.

[email protected]

3.6 Topic 6 : Liquid matter (atomic, molecular and ionic fluids, freezing;metastable liquids; granular matter)


“Strange” electrostatics in physics, chemistry, and biology

Yan Levin1

1 Instituto de Fısica, Universidade Federal do Rio Grande do SulCaixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil

Electrostatic correlations play important role in physics, chemistry and biology [1]. In plasmas they lead to thermody-namic instability similar to the liquid-gas phase transition of simple molecular fluids. For charged colloidal suspensionsthe electrostatic correlations are responsible for screening and colloidal charge renormalization. In biological systemsthe correlations are accountable for the organization of cytoskeleton and compaction of genetic material. In this talk Iwill demonstrate how the strong electrostatic correlation between multivalent counterions can lead to charge inversionin aqueous colloidal suspensions.1. Y. Levin, Rep. Prog. Phys. 65, 1577 (2002)

[email protected]

3.6. TOPIC 6 : LIQUID MATTER (ATOMIC, MOLECULAR AND IONIC FLUIDS, FREEZING;METASTABLE LIQUIDS; GRANULAR MATTER) 21


The Jamming Transition at Zero Temperature

Sidney Nagel1

1The University of Chicago, Chicago, USA

We have studied how systems made up of particles interacting with finite range, repulsive potentials jam (so thatthey develop a yield stress in a disordered state) at zero temperature and zero applied stress. For each configuration,there is a unique jamming threshold at which particles can no longer avoid each other. At this point the bulk andshear moduli simultaneously become non-zero. Essentially all configurations jam at the same packing fraction in thethermodynamic limit. The jamming threshold, Point J, occurring at zero temperature and applied stress has propertiesreminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scalingis found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure,shear modulus, and excess number of overlapping neighbors. However, Point J also differs from an ordinary criticalpoint: the scaling exponents do not depend on dimension but do depend on the inter-particle potential. As Point Jis approached from high packing fractions, the density of vibrational states develops a large excess of low-frequencymodes. Indeed, at Point J, the density of states is a constant all the way down to zero frequency. This last resultsuggests a natural explanation for the excess density of states seen in glasses at low temperatures and for the Bosonpeak.

[email protected]

3.6.3 Friday July 9 15:45-16:15 : Hall AB

Jamming patterns in two-dimensional hopper

Kiwing To1

1Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 115 R.O.C.

We report experimental studies of jamming phenomenon of mono-dispersed metal disks falling through a two-dimensional hopper when the hopper opening is comparable to the size of the disks. For each jamming event, theconfiguration of the arch formed at the hopper opening is studied. The statistical properties of the horizontal and thevertical components of the arch vector, which is defined as the displacement vector from the center of the first diskto the center of the last disk in the arch, will be discussed. Regarding the arch as a trajectory of a restricted randomwalker, we formulate an expression for the probability density function of forming an arch at the hopper opening, andits relation to the jamming probability will be derived.

[email protected]


3.7 Topic 7 : Soft condensed matter (colloids, polymers, liquid crystals,microemulsions, foams, membranes, etc.)


Non-linear Visco-Elasticity of Biopolymer Networks

Erwin Frey1

1Hahn-Meitner-Institut Berlin, Glienicker Str. 100, D-14109 Berlin

How polymers respond to external fields is of considerable importance for both the visco-elasticity of biopolymernetworks and a range of applications in micro- and nanofluidics. We present a unified theory for the non-linear responseof stiff biopolymers in solution to various external perturbations (mechanical excitations, electrical fields, temperaturequenches) that can be represented as sudden changes of ambient or boundary conditions. Intriguing new experimentalimplications are pointed out.

[email protected]


Depletion forces in colloidal mixtures

R. Roth1 and P.-M. Konig2

1,2Max-Planck Institut fur Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany1 Institut fur Theoretische und Angewandte Physik, Universitat Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart,

Germany.

Colloids can be found in many places in physics, chemistry and biology and they come in all kind of shapesand in a range of sizes between some nanometer up to some micrometer. In colloidal mixtures, which are studiedboth theoretically and experimentally with great interest, the size asymmetry of larger and smaller particles can besubstantial. In that case one can consider the larger particles to be in an effective background of the smaller ones byintegrating out the degrees of freedom of the smaller particles. This procedure leads to effective interactions amongbigger colloids and between walls and bigger particles. The entropic contribution of these effective interaction aredominating in many systems and if the bare interactions among all particles are hard they are of purely entropicorigin. These so-called depletion forces can be be measured directly using e.g. light scattering techniques and canbe calculated for simple geometries and systems in various ways. Here, however, we want to explore the effects ofparticle shape and the geometry of the wall on depletion forces using a novel treatment of non-spherical particles andcomplexly shaped wall geometries within the framework of density functional theory.

[email protected]

3.7. TOPIC 7 : SOFT CONDENSED MATTER (COLLOIDS, POLYMERS, LIQUID CRYSTALS,MICROEMULSIONS, FOAMS, MEMBRANES, ETC.) 23


Polymer mixtures in confined geometry: model systems to explorephase transitions

Kurt Binder1

1Institut fr Physik, Johannes Gutenberg Universitt Mainz 55099 Mainz, Staudinger Weg 7, Germany

While binary (A, B) polymer mixtures in three dimensions (d=3) in the symmetric case (chain lengths NA = NB =N) show an unmixing critical point that falls in the Ising universality class and crosses over to mean field behaviour forN , the situation is different for mixtures confined in thin film geometry. The critical behaviour then falls in the d=2Ising universality class for N irrespective of film thickness D. For N finite crossover to three-dimensional behaviouroccurs when the correlation length is less than D. Nevertheless the critical temperature Tc scales linear with N (witha nontrivial prefactor), irrespective of D, apart for strictly two-dimensional chains, for which Tc is proportional toN1/2. Monte Carlo simulation results are presented together with scaling considerations that illustrate these issues.When the walls of the thin film are not neutral, but preferentially attract one species, complicated phase diagramsoccur due to the interplay between capillary condensation and wetting phenomena. Particularly interesting are theinterface localization-delocalization transitions that occur for ”competing walls” (one wall prefers A, the other prefersB). A brief survey of these phenomena will also be given.

[email protected]


Colloidal interactions in nematic liquid crystals

M. M. Telo da Gama1

1Departamento de Fısica da Faculdade de Ciencias and Centro de Fısica Teorica e Computacional, Universidade deLisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal

Colloidal dispersions in nematic liquid crystals form a special class of colloids. The difference from ordinary col-loids arises from the long-range orientational order of the liquid crystal molecules, described by the so-called nematicdirector. Topological defects of the director field, additional long-range forces between colloidal particles, and, as aresult, supermolecular structures are phenomena specific of colloidal nematics. Colloidal nematics are usually preparedin the isotropic phase. To prevent flocculation due to attractive van der Waals forces, colloidal particles are treatedto induce electrostatic or steric repulsive interactions. After cooling to a temperature below the NI transition, thecolloids often segregate forming non-uniform clusters. In general, topological defects stabilize the dispersion although,in some cases, they may help flocculation by producing additional attractive interactions [1]. Here we review work oncolloidal interactions in 2D nematic liquid crystals under a variety of conditions: homeotropic and planar anchoringas well as the interaction of colloids with various NI interfaces.References:[1] “Colloidal Dipolar Interactions in 2D Smectic C Films”, P. Patrıcio, M. Tasinkevych and M. M. Telo da Gama,European Physical Journal E, 7, 117-122 (2002).[2] “Colloidal Interactions in Two Dimensional Nematics”, M. Tasinkevych, N. M. Silvestre, P. Patrıcio and M. M.Telo da Gama, European Physical Journal E, 9, 341-347 (2003).[3] “Forces between elongated particles in a nematic colloid”, D. Andrienko, M. Tasinkevych, P. Patrıcio, M. P. Allenand M. M. Telo da Gama, Physical Review E, 68, 051702 (2003).[4] “Colloidal disks in nematic liquid crystals”, N. M. Silvestre, P. Patrıcio, M. Tasinkevych, D. Andrienko and M. M.Telo da Gama, Journal of Physics: Condensed Matter, 16, S1921-S1930 (2004).[5] “Interaction of colloids with a nematic-isotropic interface”, D. Andrienko, M. Tasinkevych, P. Patrıcio, and M. M.Telo da Gama, Physical Review E, 69, 021706 (2004).


[6] “The key-lock mechanism in nematic colloidal dispersions”, N. Silvestre, P. Patrıcio, and M. M. Telo da Gama,Physical Review E, accepted for publication (2004).

[email protected]


Local simulation algorithms with Coulombic Interactions

A.C. Maggs1,L. Levrel2,J. Rottler3 and F. Alet4

1,2Laboratoire de Physico-Chimie Th’eorique, UMR CNRS-ESPCI 7083, 10 rue Vauquelin, F-75231 Paris Cedex 05,France

3PMI, Bowen Hall, Princeton University, Princeton, NJ 08544, USA4Theoretische Physik, ETH Zrich, CH-8093 Zrich, Switzerland

We consider a problem in dynamically constrained Monte-Carlo dynamics and show that this leads to the gener-ation of long ranged effective interactions. This allows us to construct a fast, local algorithm for the simulation ofcharged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simpleimplementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. They are bothbased on the constrained dynamics of an auxiliary vector field coupled to the physical charge density. There areanalogies between our formulation of electrostatics and the bosonic Hubbard model. Cluster methods developed forthis model further improve the efficiency of the electrostatics algorithm.


Knots in Polymers

Yacov Kantor1

1School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv, Israel

Knots and topological entanglements play an important role in the statistical mechanics of polymers. While topo-logical entanglement is a global property, it is possible to study the size of a knotted region both numerically andanalytically. It will be shown that long-range repulsive interactions [1], as well as entropy [2,3] favor small knots indilute systems. However, in dense systems and at theta-point the uncontracted knot configuration is the most likely[4].References :[1] P.G. Dommersnes, Y. Kantor, and M. Kardar Phys. Rev. E 66, 031802 (2002).[2] R. Metzler, A. Hanke, P. G. Dommersnes, Y. Kantor, and M. Kardar Phys. Rev. Lett. 88, 188101 (2002), andPhys. Rev. E 65, 061103 (2002).[3] R. Metzler, Y. Kantor, and M. Kardar Phys. Rev. E 66, 022102, 2002; O.Farago, Y. Kantor, and M. KardarEurophys. Lett. 60, 53 (2002).[4] R. Metzler, A. Hanke, P. G. Dommersnes, Y. Kantor, and M. Kardar Phys. Rev. E, in print (2004).

[email protected]

3.8. TOPIC 8 : INTERFACIAL PHENOMENA AND WETTING; SURFACE EFFECTS ANDCONFINED SYSTEMS 25

3.8 Topic 8 : Interfacial phenomena and wetting; surface effects andconfined systems

3.8.1 Tuesday July 6 11:00-11:30 : Hall AB

Structure and fluctuations of liquid surfaces

J. Daillant1,S. Mora2,D. Luzet3 and K. Mecke4

1,2,3SCM/LIONS, bat. 125, CEA-Saclay, F-91191 Gif-sur-Yvette cedex, France4MPI fur Metallforschung, Heiseinbergstrasse 1, D-70569 Stuttgart, Germany

Liquid-vapour interfaces were first described, in 1893 by van der Waals, as regions of continuous variation of densitycaused by density fluctuations within the bulk phases. In contrast, the more recent capillary-wave model (1965)assumes a step-like density profile across the liquid-vapour interface, whose width is the result of the propagation ofthermally excited capillary waves. The model has been validated for length scales of tens of micrometres and larger,but the structure of liquid surfaces on submicrometre length scales, where the capillary theory is expected to breakdown, remains poorly understood. Using grazing-incidence X-ray scattering, we have obtained the first completedetermination of the free surface structure and of the wavevector-dependent surface energy for water and organicliquids [1]. We observed a large decrease of the surface energy of sub-micrometer waves, which cannot be explained bythe phenomenological capillary theories, but is accurately described using a recent density functional theory (K. Meckeand S. Dietrich, Phys. Rev. E, 59, 6766-84, 1999). A quantitative agreement with the theory is obtained for Lennard-Jones liquids using literature values for the bulk correlation length and the Lennard-Jones potential parameters [2].Our data allow a precise discussion of bending energies. The most important point is that the local bending energy,Kq2 although formally determining the behavior q → ∞ is strongly reduced by the non-local contributions. Moststriking is that the total bending energy results from a partial compensation of the local contribution by the non-localcontribution. The same method has also been used to investigate Langmuir films at the water surface [3]. Beyondstructural parameters like the film thickness and density, diffuse scattering also gives access to phase transitions andelastic properties (surface tension and bending rigidity). We find that the surface tension measured with X-rays isconsistent with the Wilhelmy plate measurements, at least for tilted phases. The bending rigidity is found to be onthe order of 20-30 kT whatever the phase. None of the existing models seems to be able to capture the relevantmechanisms for those densily packed short chains. In fact, bending is always easier than predicted by the models.References:[1] C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke and J. Daillant, Reduction in thesurface energy of liquid interfaces at short length-scales Nature 403, 871 (2000).[2] S. Mora, J. Daillant, K. Mecke, D. Luzet, M. Alba, A. Braslau, B. Struth, An x-ray synchrotron study of liquid-vapor interfaces at short length-scales: effect of long-range forces and bending energies, Phys. Rev. Lett. 90, 216101(2003).[3] S. Mora, J. Daillant, D. Luzet, B. Struth, X-ray surface scattering investigation of Langmuir fims: phase transitionsand elastic properties, to be published in Europhysics Letters.

[email protected]


3.8.2 Thursday July 8 10:15-10:45 : Hall AB

The dynamics of droplets on chemically and topologically patternedsubstrates

A. Dupuis1 and J. M. Yeomans2

1,2The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, England

We develop lattice Boltzmann simulations to investigate the dynamics of micron-scale droplets spreading on chem-ically and topologically patterned substrates. For a substrate with lyophobic and lyophilic stripes of the same dimen-sions as the drop the final droplet shape is determined by the dynamic evolution of the fluid in a way which dependson the initial position and velocity. We compare the simulations to experiments and discuss how far a quantitativematch can be made. We also consider droplets moving on a substrate covered by an array of micron-sized posts,a geometry which leads to superhydrophobic behaviour. We show how the velocity on the posts is related to theunderlying geometry. The results are relevant to attempts to improve the quality of ink-jet printing.

[email protected], [email protected]


Fluctuation–Induced Interactions In and Out of Equilibrium

Ramin Golestanian1

1Institute for Advanced Studies in Basic Sciences, Zanjan, Iran

In a fluctuating medium of whether quantum, thermal, or non-thermal origin, an interaction is induced betweenexternal objects that modify the fluctuations. These interactions can appear in a vast variety of systems, leading toa plethora of interesting phenomena. Notable examples of these include: (1) like-charge attraction in the presenceof multivalent counterions, (2) Ludwig-Soret effect in charged colloids, (3) mass renormalization of moving defectsin a phononic background and moving metallic objects in EM quantum vacuum, and (4) dissipation due to motion–induced radiation. The fluctuation–induced forces are statistical in nature, and this could make their measurementvery difficult, because the actual value of the force might deviate most of the time from the predicted average value.

[email protected]

3.9. TOPIC 9: QUANTUM-MECHANICAL PROBLEMS (QUANTUM PHASE TRANSITIONS;STRONGLY CORRELATED FERMIONS; BOSE-EINSTEIN CONDENSATION; MESOSCOPICQUANTUM PHENOMENA, ETC.) 27

3.9 Topic 9: Quantum-mechanical problems (quantum phase transi-tions; strongly correlated fermions; Bose-Einstein condensation; meso-scopic quantum phenomena, etc.)


From Bose-Einstein Condensation of Molecules to BCS Pairing inUltra-Cold Fermi Gases

Christophe Salomon1

1Laboratoire Kastler Brossel, Ecole Normale Superieure - Departement de Physique

We will describe recent experiments aiming at studying superfluidity in ultra-cold Fermi gases. Because of the Pauliexclusion principle, cooling methods and analysis techniques developed for bosons must be modifed for fermions.Thanks to a resonance phenomenon in ultra-cold collisions, it is possible to adjust the sign and magnitude of theeffective interaction between trapped fermions and to enter in the strongly inteacting regime. Taking advantage ofthis tunability of interactions, it has been possible to produce for the first time Bose-Einstein condensates (BEC) ofmolecules and to study some of their properties. We will then present data recorded in the crossover region betweenBEC of molecules and the BCS regime of fermions with weak attractive interaction. Finally we will discuss a fewperspectives for this work at the interface between atomic physics and condensed matter physics.

[email protected]


Keldysh action for disordered superconductors

M. V. Feigel’man1,A. I. Larkin2 and M. A. Skvortsov3

1,2,3L.D.Landau Institute for Theoretical PhysicsKosygina 2 Moscow 117940 Russia

I will discuss Keldysh two-times representation for the action functional of disordered interacting quantum system,with particular emphasis on superconductive hybrid structures. A number of recently studied phenomena, which areall due to electron-electron interactions, will be presented: quantum phase transition from superconductive to normalstate, zero-bias anomalies in tunnelling conductance, current noise in superconductor-normal structures.

[email protected]



Interplay of interactions, disorder, and magnetic field in the 2DHubbard model

P.J.H. Denteneer1, R.T. Scalettar2, D. Heidarian3 and N. Trivedi4

1 Lorentz Institute, Leiden University, Leiden, The Netherlands2 Physics Dept, UC Davis, Davis, USA

3,4 Tata Institute, Mumbai, India

The effects of both interactions and Zeeman magnetic field in +disordered electronic systems are explored in theHubbard model on a square lattice. We investigate +the thermodynamic (compressibility, susceptibility) and transport(conductivity) properties using determinantal +quantum Monte Carlo [1] and inhomogeneous Hartree Fock techniques[2]. We find +that at half filling there is a novel metallic phase at intermediate disorder +that is sandwiched betweena Mott insulator and an Anderson insulator. This +metallic phase is highly inhomogeneous and coexists with antifer-romagnetic long +range order [2]. The metallic state can be destroyed by applying a Zeeman or +parallel magneticfield resulting in a magnetic field driven transition [3]. We discuss the implications of our results for experiments.References:[1] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, Phys. Rev. Lett. 83, 4610 +(1999); ibid 87, 146401 (2001).[2] D. Heidarian and N. Trivedi, to appear in Phys. Rev. Lett.[3] P.J.H. Denteneer and R.T. Scalettar, Phys. Rev. Lett. 90, 246401 (2003)

1 [email protected] ¡[email protected]

3.9.4 Friday July 9 15:45-16:15 : Hall F

A New Theory of Manganites Exhibiting Colossal Magnetoresistance

H R Krishnamurthy1

1Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India

Manganites of the La1−xCaxMnO3 family show a variety of novel and poorly understood electronic, magnetic andstructural effects. In this talk I discuss a new theory for these recently proposed by us*, where we argue that dueto strong Jahn-Teller(JT) coupling with phonons the twofold degenerate eg states at the Mn sites get dynamicallyreorganized into localized, JT polarons ` with exponentially small inter-site hopping, and band-like, nonpolaronicstates b, leading to a new 2-band model for manganites which includes strong Coulomb and Hund’s couplings. Ialso discuss results from a dynamical mean-field theory treatment of the model which explains quantitatively a widevariety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physicalconditions on the relative energies and occupation of the ` and b states. The microscopic coexistence of the twotypes of electronic states, and their relative occupation and spatial correlation is the key to manganite physics. *Work done in collaboration with T. V. Ramakrishnan, S R Hassan and G Venketeswara Pai; see Cond-Matt/0308376,Cond-Matt/0308396 and Cond-Matt/0309493.

[email protected]

3.10. TOPIC 10 : DISORDERED SYSTEMS (RANDOM LATTICES, SPIN GLASSES, GLASSTRANSITION, LOCALIZATION, ETC.) 29

3.10 Topic 10 : Disordered systems (random lattices, spin glasses, glasstransition, localization, etc.)


A sigma model approach to fluctuations in systems with glassy dynamics

L. F. Cugliandolo1 and C. Chamon2

1,2Laboratory of Theoretical Physics and High Energies, Paris Vi-vii, Jussieu, 4, Jussieu place; Turn 16, 1st stage,75232 Paris Cedex 05 - France

Mean-field disordered models, that are intimately related to self-consistent perturbative approaches (e.g. modecoupling), give a successful qualitative description of the glass transition and the dynamics of global observables aboveand below it. The picture that emerges has proven relevant to describe global properties of other systems with slowdynamics such as granular matter. However, many sharp features of this description, such as the mere existence ofa dynamic transition, are known to be smoothen by fluctuations that are specially important in glassy dynamics.Recently, we proposed to exploit the approximate asymptotic reparametrization invariance of the slow dynamics toconstruct a sigma model for the dynamic fluctuations. With this theory at hand, we derived several properties of localcorrelations and responses that we tested numerically in the 3d Edwards-Anderson model and a number of kineticallyconstrained spin systems. In this talk I shall review these theoretical ideas as well as their numerical examination. Ishall also briefly discuss some possible experimental tests.

[email protected]


Recent developments in the theory of spin glasses

Peter Young1

1Physics Department, University of California, Santa Cruz, CA 95064

An introduction to spin glasses will be given followed by a summary of some salient experiments, both equilibriummeasurements concerning the spin glass phase transition and non-equilibrium measurements in the low temperaturephase. Results of recent numerical studies of spin glasses using models with ”vector” spins will then be described.

[email protected]



Elastic and plastic depinning of driven disordered systems

M. Cristina Marchetti1

1Physics Department, Syracuse University , Syracuse, NY 13244, USA

Extended condensed matter systems, such as vortex lattices in superconductors and charge density waves, exhibit avariety of nonequilibrium phase transitions when driven through quenched disorder. These systems have mainly beenmodeled theoretically as elastic media that are distorted by disorder, but cannot tear. In this case the depinning atT=0 is a continuous phase transition, with universal critical behavior. Far less developed is the theoretical descriptionof systems that upon depinning exhibit plastic response. In this talk I will discuss various models of this more complexdriven dynamics. In one class of models plasticity is incorporated using non-convex interparticle interactions that allowfor phase slips. In a second class of models the coarse-grained degrees of freedom interact elastically in the directionparallel to the drive but are coupled by viscous forces in at least one of the directions transverse to the mean motion. Inthe infinite range limit these models exhibits a tricritical point separating a region where the depinning is continuous,in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collectivetransport models discussed in the literature are special cases of these two generic models.

[email protected]


Aging, rejuvenation and memory effects in glassy magnetic systems

E. Vincent1,F. Bert2,J.-P. Bouchaud3,V. Dupuis4,F. Ladieu5,D. Parker6 and J. Hammann7

1,2,3,4,5,6,7Service de Physique de l’Etat Condens’e, DSM/DRECAM, CEA Saclay (CNRS URA 2464) 91191 Gif surYvette Cedex, France

Spin glasses are magnetic systems in which the interactions are disordered and frus trated, due to a random di-lution of magnetic ions. Below their glass temperature Tg , the dynamic response to a smal l magnetic excitation isslow, and in addition depends on the time spent below Tg (aging). In contrast with st ructural and polymer glasses,aging in spin glasses is hardly influenced by the cooling rate. On the contrary, ea ch cooling step leads to a restart ofdissipation processes (rejuvenation), while the memory of previous a gings achieved at different temperatures duringcooling can be retrieved when re-heating [1]. It is possible to store independently the memory of several isothermalagings, which corresponds to imprinting the trace of v arious spin arrangements at well separated length scales thatare selected by temperature [2]. A comparison between an Ising spin glass and several Heisenberg spin glasses with various degrees of random anisotropy shows that the aging properties are quantitatively different in these systems, thememory effect being more pronounced in the Heisenberg case [3]. As the anisotropy decreases, the increased sharpnessof the memory effect points towards an increasingly fast separation of the active length scales with temperature. Ourresults underline the role of anisotropy in the nature of a spin-glass phase with Heisenberg spins. While glassinessis commonly observed in disordered and frustrated spin glasses, it can also be found in some disorder-free stronglyfrustrated antiferromagnets which, rather than condensing into a spin liquid state, undergo a freezing transition withspin-glass like properties. The aging properties of some disorder-free topologically frustrated antiferromagnets willalso be compared with those of conventional spin glasses [4].References:[1] E. Vincent, J. Hammann, M. Ocio, J.-P. Bouchaud and L.F. Cugliandolo, in Complex Behaviour of Glassy Systems,Springer Verlag Lecture Notes in Physics Vol. 492, M. Rubi editor, pp. 184-219 (pre print cond-mat/9607224).[2] J.-P. Bouchaud, V. Dupuis, J. Hammann and E. Vincent, Phys. Rev. B 65, 024439 ( 2002).[3] V. Dupuis, E. Vincent, J.-P. Bouchaud, J. Hammann, A. Ito and H. Aruga Katori, Phys. Rev. B 64, 174204(2001); F. Bert, V. Dupuis, E. Vincent, J. Hammann and J.-P. Bouchaud, e-print cond-mat/030 5088, to appear in

3.11. TOPIC 11 : BIOLOGICALLY MOTIVATED PROBLEMS (PROTEIN-FOLDING MODELS,DYNAMICS AT THE SCALE OF THE CELL; BIOLOGICAL NETWORKS, EVOLUTIONMODELS, ETC.) 31

Phys. Rev. Lett. 2004.[4] V. Dupuis, E. Vincent, J. Hammann, J.E. Greedan and A.S. Wills, J. Appl. Phys. 91, 8384 (2002); F. Ladieu, F.Bert, V. Dupuis, E. Vincent and J. Hammann, J. Phys.: Condens. Matter 16 (2004) S735-S741.

[email protected]

3.11 Topic 11 : Biologically motivated problems (protein-folding mod-els, dynamics at the scale of the cell; biological networks, evolutionmodels, etc.)

3.11.1 Tuesday July 6 15:45-16:15 : Hall J

RNA foding and large N matrix field theory

Henri Orland1

1Henri Orland Service de Physique Theorique, CE-Saclay, CEA 91191 Gif-sur-Yvette Cedex, France

In this talk, we show that the RNA folding problem can be mapped onto a large N matrix field theory. Secondarystructures of RNA are identified as the planar diagrams of the theory, whereas pseudo-knots are shown to be diagramsof higher topological genus. This allows for two different types of approaches: in one approach, we show how togeneralize the standard secondary structure recursion relations to include pseudo-knots of genus one. A secondapproach is discussed, based on a Monte Carlo method. In that case, the energy is the sum of the usual pairing orstacking energies, and a chemical potential for the genus of the diagram is added. Both methods allow to predictpseudoknots.

[email protected]



Modeling Information Networks

Kim Sneppen1

1Nordita and Niels Bohr Institute, Copenhagen

We suggest to classify scale-free networks by a hierarchical measure that characterize the extent to which thehighly connected hubs are positioned on the periphery of the networks. We find that the highly connected hubs areat the center of human communication networks, but at the periphery of molecular regulatory/signaling networks.This suggests that one should view scale-free features of molecular regulatory networks as a result of the property ofthe number of proteins needed to respond to various external perturbations. Also it suggest that one could modeldynamics of the regulation of the hub proteins by rather simple feedback mechanisms. We describe a few such ex-amples with quantitative biological examples of dynamics on localized hubs. In contrast to molecular networks, thescale-free communication networks of humans are related to local optimization. This can be quantified through anetwork economics model where links are traded between agents that each try to optimize their access to informationabout the other agents.

References: 1) S. Maslov & K. Sneppen, Specificity and stability in topology of protein networks, Science 296 910-

913, (2002).

2) S. Maslov, K. Sneppen & A. Zaliznyak Pattern Detection in Complex Networks: Correlation Profile of the Internet. Physica

A 333, 529-540 (2004).

3) A. Trusina, S. Maslov, P. Minnhagen & K. Sneppen, Hierarchy measures in Scale Free networks cond-mat/0308339. To

appear in Phys. Rev. Letters.

4) S. Bornholdt & K.Sneppen, “Robustness as an evolutionary principle”, Proc Roy. Soc. London, B (2000) 267 2281-2286

5) K.B. Arnvig, S. Pedersen & K. Sneppen ”Thermodynamics of Heat Shock Response”. Phys. Rev. Lett. 84 (2000) 3005-3008.

6) G. Tiana, M.H. Jensen and K. Sneppen. Time delay as a key to apoptosis induction in the p53 network. European Phys.

Journal B. 29 135 (2002).

7) M. Rosvall and K. Sneppen, “Modelling Dynamics of Information Networks”, Phys. Rev. Lett. 91, 178701 (2003).

[email protected]


On the Fusion of Biological Membranes

Michael Schick1

1Department of Physics, Box 351560, University of Washington, Seattle WA 98195-1560

Although membrane fusion is a fundamental biological process in fertilization, intracellular traffic, and viral infec-tion, its basic mechanism is not well understood. The biological community tends to focus on specific fusion proteinswhich, inter alia, ensure that only those membranes which should fuse get close enough to do so. There is muchevidence, however, that what happens after the membranes are brought close, such as the interuption of the integrityof the bilayers and the molecular reaarangements that lead to the formation of the fusion pore itself, depends only ongeneral properties of the molecules which make up the bilayer. As a consequence, these stages of fusion can be studiedin simple model systems, ones without proteins. For these, physicists have proposed scenarios of the fusion pathway. Ishall report results for model systems obtained from extensive Monte Carlo simulations and self-consistent field theorycalculations. They provide a view of the mechanism which is quite different from that commonly accepted. Results ofvery recent experiments support this view.

[email protected]



On the dynamics of the endemic process of tuberculosis in Olinda(Brazil): an interdisciplinary approach

Ana Amador1, Wayner Vieira de Souza2, Rita Maria Zorzenon dos Santos3, Silvina Ponce-Dawson4,and Maria de Fatima Militao de Albuquerque5

1 Departamento de Fisica-UBA, Buenos Aires, Argentina.2 CPqAM-Fiocruz, Recife (PE), Brazil.

3 Departamento de Fisica-UFPE, Recife (PE), Brasil.4 Departamento de Fisica-UBA, Buenos Aires, Argentina.

5 Departamento de Medicina Interna-UFPE, Recife (PE), Brasil.

Tuberculosis (TB) is one of the three most deadly infectious diseases, with approximately 30 % of the world populationcurrently infected. In Brazil one hundred thousand new cases appear per year. Here we analyze the spatio-temporaldistribution of TB cases per census tract (CT) observed in Olinda (town located in the northeast of Brazil) for theperiod 1996-2000. The CT is an administrative district corresponding to 300 households. Our aim is to extract infor-mation from the dynamics of the endemic process of TB that may be relevant to geographically based epidemiologicalsurveillance. Inspired in percolation concepts, for each year we obtain the connectivity distribution between neighborcensus tracts with at least one case of TB, as well as the connectivity distribution between the CTs that remainwith cases during five years and also between the ones that have a number of accumulated cases above the average.We compared these results with the density distribution function of socioeconomic indicators of 2000 census (lowschooling, low income and household density) obtained with a kernel estimator. While the late indicate risk regions,the physical approach localize the endemic foci in the regions of low schooling and low income and determine how aconnected path is formed between them, showing the role of high household density in transmitting and maintainingthe disease. We also discuss the results for 1991-1995 period.

1 [email protected] [email protected] [email protected] [email protected] [email protected]



Unzipping DNA

Somendra M. Bhattacharjee1

1Institute of Physics, Bhubaneswar 751 005, India

We discuss the nature of the unzipping phase transition of a double stranded DNA by a force. The phase diagramis obtained from an exactly solvable model. It shows the dependence of the phase diagram on the location of the pointof aplication of the force. The phase coexistence (Y-fork) during unzipping in appropriate ensemble is then used tostudy the propagaton of a helicase that opens a DNA.

[email protected]

3.11.6 Friday July 9 11:00-11:30 : Hall J

Free-energy recovery of RNA tertiary structures from irreversiblemeasurements of mechanical unfolding and refolding

Delphine Collin1, Felix Ritort2, Chris Jarzynski3, Steve Smith4, I. Tinoco5, and C. Bustamante6

1,4,5,6 University of California, Berkeley2Departament de Fisica Fonamental, Facultat de Fisica, Universitat de Barcelona Diagonal 647, 08028 Barcelona

(Spain)3 Los Alamos National Laboratory T-13 Complex Systems MS B213 Los Alamos, NM 87545 USA

Under appropriate conditions RNA folds into a three-dimensional functional structure. Its stability being determinedby the free-energy difference between the folded and the unfolded states and the presence of specific magnessium tertiaryinteractions. The knowledge of RNA folding-unfolding free energies is an important step towards the understandingof their biological function. Single molecule force measurements using optical tweezers can be used to determine themechanical work done upon a biomolecule in the unfolding process. If the process is quasistatic, then this work isequal to the free-energy change between the initial and final states, providing a method to determine free energies.However, high energy barriers usually impede the possibility to pull a biomolecule quasistatically. Therefore othermethods are required to recover free-energies from non-equilibrium measurements. In this talk I will report on newexperimental results that show how fluctuation theorems can be succesfully applied to recover free energies of RNAtertiary structures, beyond what current calorimetric techniques can provide.

1 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

3.12. TOPIC 12 : OTHER APPLICATIONS OF STATISTICAL PHYSICS (NETWORKS,TRAFFIC FLOWS, ALGORITHMIC PROBLEMS, ECONOPHYSICS, ASTROPHYSICALAPPLICATIONS, ETC.) 35

3.12 Topic 12 : Other applications of statistical physics (networks, traf-fic flows, algorithmic problems, econophysics, astrophysical appli-cations, etc.)


Evolution of scale-free random graphs: Potts model formulation

D.-S. Lee1,K.-I. Goh2,B. Kahng3 and D. Kim4

1,2,3,4 School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea

We study the bond percolation problem in random graphs of N weighted vertices, where each vertex i has aprescribed weight Pi and an edge can connect vertices i and j with probability PiPj (

∑Ni=1 Pi = 1). We show that the

problem is solved by the q → 1 limit of the q-state Potts model with inhomogeneous interaction strength Kij ∝ PiPj

for every pair ij. We apply this approach to the static model having Pi ∝ i−α(0 < α < 1) so that the resultinggraph is scale-free with the degree exponent γ = 1 + 1/α. The giant cluster size, the mean cluster size, and thenumber of loops are obtained as functions of p = L/N with L the number of edges, as well as the critical point pc

where the giant cluster first appears. Furthermore, their finite-size scaling behaviors are derived using the largestcluster size in the critical regime, which is calculated from the cluster size distribution, and checked against numericalsimulation results. We find in the static model that there are three regimes of α displaying different nature in formingthe giant cluster: (I) α < 1/3 : a giant cluster appears through an abrupt coalesce of small clusters at finite pc

given by pc = (1/2)(1− 2α)/(1− α)2 and the critical exponents associated with the giant cluster size, the cluster sizedistribution and so on are independent of α. The mean cluster size diverges at pc. (II) 1/3 < α < 1/2 : pc is stillfinite, but the critical exponents depend on α. (III) 1/2 < α < 1 : there is no percolation transition but the giantcluster is formed gradually without such an abrupt coalesce of small clusters as in (I) or (II). The mean cluster sizedoes not diverge at any value of p but shows double peaks.

[email protected]


Generalized Percolation for Complex Networks

Shlomo Havlin1

1Department of Physics, Bar Ilan University Israel

We show that scale free graphs which characterize many real world networks such as the Internet and social net-works can be regarded as a generalization of random graphs studied in mathematics or lattice networks studied inphysics. We find that scale free graphs have an ultrasmall diameter of loglog N compared with log N of random graphs[1]. We also developed a percolation approach for the behavior of generalized random graphs with a given degreedistribution of links, k, per node, P (k), under both random breakdown of nodes and intentional attack on the mosthighly connected nodes. We focus on scale free networks, where P (k) ∝ k−alpha. We show that scale free networkswith alpha¡3 are robust to random breakdown [2], but extremely fragile against intentional attack [3]. We also describethe behavior of the network near the percolation phase transition and show that the critical exponents are influencedby the scale free topology of the network. We propose an efficient immunization strategy for computer networks andpopulations [4].References:[1] Scale free networks are ultrasmall R. Cohen and S. Havlin Phys. Rev. Lett. 90, 058701 (2003).[2] Resilience of the Internet to random breakdown R. Cohen, K. Erez, D. ben-Avraham and S. Havlin Phys. Rev.Lett. 85, 4626 (2000).


[3] Breakdown of the Internet under intentional attack R. Cohen, K. Erez, D. ben-Avraham and S. Havlin Phys. Rev.Lett. 86, 3682 (2001).[4] Efficient immunization strategies for computer networks and populations, Reuven Cohen, Shlomo Havlin, andDaniel ben-Avraham Phys. Rev. Lett. in press (2003).

[email protected]


Statistical physics, Optimization and Coding Theory

Riccardo Zecchina1

1International Centre for Theoretical Physics (ICTP), Strada Costiera, 11 P.O.Box 586 I-34100 Trieste, Italy

The combinatorial problem of satisfying a given set of constraints that depend on N discrete variables is a funda-mental one in optimization and coding theory. Even for randomly generated problem instances, the question ”doesit exist an assignment to the variables that satisfies all constraints?” may become extraordinarily difficult to solve insome range of parameters where a glass phase sets in. We shall provide a brief review on the recent advances in thestatistical mechanics approach to these satisfiability problems and show how the analytic results help in the design anew class of message-passing algorithms – the Survey Propagation (SP) algorithms – that are able to solve efficientlysome combinatorial problems considered intractable. Applications to coding theory and to biologically motivatedproblems will be outlined. Open problems and perspectives will be given in the concluding remarks.

[email protected]


Phase Transition in m-ary Search Trees at m = 26

Satya N. Majumdar1

1 Directeur de Recherche, CNRS, Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud,Bat. 100, 91405 ORSAY cedex, FRANCE

A popular algorithm for storing data in a computer is to organize the data on a tree which has a fixed m number ofbranches. The case m = 2 corresponds to the simple binary tree. How many nodes of the m-ary tree are needed to storea random data of size N? We show that the statistics of the number of nodes needed has a peculiar phase transitionat m=26 ! We will employ techniques of statistical physics to understand the mechanism behind this peculiar phasetransition which will also reveal the mystery of the number 26! We show that this phase transition is actually quitegeneric and occurs in various other problems as well. In particular, for random vector data where each element is ad-dimensional vector, we show that a similar phase transition will occur at the critical dimension dc = 8.69363...

[email protected]



Crowds on the move

T. Vicsek1

1Department of Biological Physics Eotvos University Budapest Pazmany P. Stny 1A 1117 Hungary

The interpretation of collective human behaviour represents a great challenge for sciences. Here we discuss anemerging approach to this problem based on the quantitative methods of statistical physics. We demonstrate thatin cases when the interactions between the members of a group are relatively well defined (e.g, pedestrian traffic,network formation, synchronization, panic, etc) the corresponding models reproduce relevant aspects of the observedphenomena. In particular, people moving in the same environment typically develop specific patterns of collectivemotion including the formation of lanes, flocking or jamming at bottlenecks. We simulate such phenomena assumingrealistic interactions between particles representing humans. The two specific cases to be discussed in more detail arewaves produced by crowds at large sporting events and the main features of escape panic under various conditions.Our models allow the prediction of the main features of crowd behaviour even in cases when experimental methods areobviously not applicable and, thus, are expected to be useful in assessing the level of security in situations involvinglarge groups of excited people. * The above results have been obtained in collaboration with the following principalcollaborators: I. Farkas and D. Helbing.

[email protected]

Chapter 4

Oral Presentations

4.1 Topic 1 : Rigorous results and exact solutions; general aspects ofstatistical physics; thermodynamics

4.1.1 Monday 5 July, 11:30 - 11:45, Hall F

O(1) ground states, stochastic processes and fully packed loops

Jan de Gier1

1 Department of Mathematics and Statistics, The University of Melbourne, Parkville 3010, Australia

We will discuss the surprising conjecture that ground states of dense O(1) models may be obtained from the statisticsof fully packed loop (FPL) patterns on finite grids. Because of the integrability underlying the FPL patterns, thiscorrespondence has led to many exact expressions for finite size expectation values and correlation functions of thedense O(1) model. The O(1) ground states can be interpreted as stationary states of stochastic growth processes,and hence nontrivial exact results for a class of non-equilibrium models are obtained. Moreover, a connection is madebetween a non-equilibrium stochastic process, the thermodynamics of fully packed loops and the conformal field theoryunderlying the critical dense O(1) model.

1 [email protected]


Field theory for trees and forests

Jesper Lykke JACOBSEN1 and Hubert SALEUR2

1 LPTMS, Universite Paris-Sud, Orsay, France2 SPhT, CEA, Saclay, France

The number of spanning trees of a given graph is equal to the (regularized) determinant of the discrete Laplacian onthat graph, and thus can be written as a Gaussian Grassmann integral. We generalize this result by showing thatgenerating functions for forests can generally be written as Grassmann integrals with higher order interaction vertices.In the case of simple forests, we show that the corresponding fermionic model has a hidden OSP (1/2) symmetry, andcan be described by a supersphere sigma model in the continuum limit. This allows us to derive the phase diagram ofthis model.

1 [email protected] [email protected]

39

40 CHAPTER 4. ORAL PRESENTATIONS


Self-avoiding polygons, planar random loop boundaries, and the Airydistribution

Christoph Richard1

1 Fakultaet fuer Mathematik, Universitaet Bielefeld, Postfach 10 01 31, 33501 Bielefeld ,GERMANY

The Airy distribution, which was recently found to describe the area statistics of self-avoiding polygons in the limitof large perimeter, also describes the limiting area distribution of the boundary of planar random loops. We discussthese questions from the perspective of exactly solvable models of lattice polygons, present a Monte-Carlo analysis ofthe random loop model, and discuss the relation of the results to the probabilistic approach using stochastic Loewnerevolution (SLE).

1 [email protected]


The double fully packed loop (FPL2) model.

David dei Cont1 and Bernard Nienhuis2

1,2 ITFA, Valckenierstraat 65, Universiteit van Amsterdam, 1018 XE Amsterdam, Netherlands

The phrase fully packed loop (FPL) model has come to be used for statistical lattice models of which the configurationsconsist of (closed) paths on the lattice, which jointly visit all sites precisely once. On the honeycomb lattice and theManhattan lattice exact solutions are available and these are in different universality classes. On the square latticethe FPL model appears more complicated. At each vertex two occupied and two free edges come together. Thereforethe free edges form loops just as well as the occupied edges. There are thus two kinds of loops that are permittedto intersect members of the other kind only. Hence the FPL2 model, introduced by Jacobsen. Every configurationof the FPL model on the square lattice induces a configuration of the FPL2 model. In the generic case one givesan independent fugacity to both kind of loops. When these two fugacities are the same the model is integrable. Wefound the Bethe Ansatz equations, and from it we calculate both bulk properties and finite size corrections. Jacobsenand Zinn-Justin have found the R-matrix, which simplifies the calculations. We will discuss applications of the FPL2

model, its relation to other popular models and the results of the exact solution.


4.1. TOPIC 1 : RIGOROUS RESULTS AND EXACT SOLUTIONS; GENERAL ASPECTS OFSTATISTICAL PHYSICS; THERMODYNAMICS 41


New Results for Exactly Solvable Systems with Frustration

Jacques H. H. Perk1 and Helen Au-Yang2

1,2Department of Physics, Oklahoma State University, PS 145, Stillwater, OK 74078-3072, USA

In our recent works we have investigated several exactly solvable Ising models with quasiperiodic behavior in theircorrelation functions resulting in a diffuse scattering pattern with incommensurate peaks. Here we shall discuss certainfully-frustrated Ising models and present new results that show that these frustrated models exhibit no such aperiodicbehavior at all. Next, we shall discuss our results for more general models. Finally, we shall comment on the integrablechiral Potts model, which is the most natural generalization of Onsager’s two-dimensional Ising model to more thantwo states per spin.

[email protected]@okstate.edu


Applications of SLE to critical systems

Wouter Kager1 and Bernard Nienhuis2

1,2ITFA, Valckenierstraat 65, Universiteit van Amsterdam, 1018 XE Amsterdam, Netherlands

The stochastic Loewner evolution (SLE) is a family of stochastic processes parameterized by one real parameter κ,which is believed (and in a few cases known) to describe the scaling limits of a range of critical models, such aspercolation (κ=6) and q-state Potts models (κ ∈ [4, 8]). To connect SLE and these models, two main ingredients areused: (1) conformal invariance, and (2) a description of the model in terms of paths. These ingredients are commonto many well-studied models in statistical mechanics. We have considered the question if SLE could be applicableto a wider class of models than those considered so far. We shall explain why we believe that the answer to thisquestion is negative for a generic two-dimensional critical model. Our findings have reduced our ambitions to findwide applications for SLE. We do know, however, that for κ=6, SLE descibes the scaling limit of critical percolationand also that of the hull of a two-dimensional random walk. A model which interpolates between these, and maytherefore naively be expected to behave like SLE6 is a specific random walk sometimes known as the self-avoidingtrail. We will presents results on this model and its relation to SLE6.

[email protected]@science.uva.nl


4.1.7 Thursday 8 July, 11:15 - 11:30, Hall J

Existence of solution to the Bethe Ansatz equations for the onedimensional Hubbard model on a finite lattice

Pedro Goldbaum1

1 Jadwin Hall, Physics Department, Princeton University, Princeton, NJ 08544 USA

In this work, a proof of the existence of solutions to the Bethe-Ansatz equations for the one-dimensional Hubbardmodel on a finite lattice is presented, using a fixed point argument. The well known solution of the model in thethermodynamic limit, by E.H.Lieb and F.Y.Wu, requires the existence of this solution for finite systems. Continuityof the energy with respect to the interaction strength and other properties of the solution are also discussed.

1 [email protected]


The exact high-temperature expansion method for integrablelow-dimensional quantum spin systems and comparison with real

materials

N.Oelkers1,M.T.Batchelor2 and Xi-Wen. Guan3

1Department of Theoretical Physics and2Centre for Mathematics and its Applications,

3Institute of Advanced Studies,

Recent progress in the theory of integrable models has led to a new high-temperature expansion method, based ona set of coupled nonlinear integral equations, for thermodynamic properties [1]. Key ingredients are the QuantumTransfer Matrix method, T-systems and fusion hierarchies. This talk reviews the application of this approach to theintegrable family of su(N) models, specifically to the su(4) and su(3) cases. When combined with appropriate chemicalpotentials, it gives the magnetic and thermal properties of a number of real low-dimensional materials. Agreementwith experimental data for the specific heat, magnetisation and susceptibility is particularly good for the stronglycoupled spin ladders [2] and spin-1 compounds with single-ion and in-plane anisotropies [3]. In the latter case, strongsingle-ion anisotropy induced by orbital splitting can dominate the behaviour of compounds such as NENC, NBYCand the Nickel salts. [1] Z. Tsuboi, J.Phys.A 36 (2003) 1493 [2] M.T. Batchelor, X.W. Guan, N. Oelkers, K. Sakai, Z.Tsuboi and A. Foerster, Phys. Rev. Lett. 91 (2003) 217202 [3] M.T. Batchelor, X.W. Guan, N. Oelkers, A. Foersterand Z. Tsuboi, in preparation

[email protected]@[email protected]



Finite size corrections for the dimer model

Nickolay Izmailian1

1Institute of Physics, Academia Sinica, Taipei, Taiwan

We study the finite-size scaling properties of the dimers under different boundary conditions. We derive the exactasymptotic expansion of the logarithm of the partition function. In the case of infinitely long strip of finite oddwidth N we have found that critical properties of the dimer model crucially depends on the boundary conditions. Inparticular for free boundary conditions we get a conformal theory with central charge c = −2. In the case of periodicboundary conditions we get a conformal theory with central charge c = −1/2. And for twisted boundary conditionswe get a conformal theory with central charge c = 1 as in the case of the dimer model on an infinitely long strip offinite even width N .

[email protected]


A General Matriz Product Ansatz for Integrable Quantum Chains

Francisco C. Alcaraz1 and Matheus J. Lazo 2

1,2 Inst. Fisica, Univ. de Sao Paulo, CP 369, 13560-590, Sao Carlos, SP - Brazil

Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Betheansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonianare given by a sum of permutations of appropriate plane waves. In this paper, alternatively, we present a matrixproduct ansatz that asserts that those amplitudes are given in terms of a matrix product. The eigenvalue equation forthe Hamiltonian define the algebraic properties of the matrices defining the amplitudes. The existence of a consistentalgebra imply the exact integrability of the model. The matrix product ansatz we propose allow an unified and simpleformulation of several exact integrable Hamiltonians. In order to introduce and illustrate this ansatz we presentthe exact solutions of several quantum chains with one and two global conservation laws and periodic boundariessuch as the XXZ chain, spin-1 Fateev-Zamolodchikov model, Izergin-Korepin model, Sutherland model, t-J model,Hubbard model, etc. Formulation of the matrix product ansatz for quantum chains with open ends is also possible.As an illustration we present the exact solution of an extended XXZ chain with z-magnetic fields at the surface andarbitrary hard-core exclusion among the spins.



4.1.11 Friday 9 July, 16:45 - 17:00, Hall E

Non-dissipative transport and crossover phenomena in the spin-1/2XXZ chain

Andreas Klumper1,Kazumitsu Sakai2 and Stefan Glocke3

1,2,3Theoretical Physics, Wuppertal University, Germany

We present exact results on the spin and thermal conductivity of the one-dimensional spin-1/2 XXZ model in thegapless and the massive antiferromagnetic as well as ferromagnetic regimes. The thermal Drude weight is calculatedby a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy as well asanalytical results in the low and high temperature limits are presented. At finite temperature, the thermal Drude weightis finite and hence there is non-dissipative thermal transport even in the massive regimes. At low temperature, thethermal Drude weight behaves as Dth(T ) ∼ T in the gapless regime, and as Dth(T ) ∼ e−δ/T /

√T in the gapped regimes

where δ = δs/m is the one-spinon/one-magnon excitation gap. In the ferromagnetic regime we observe a crossover inthe low-temperature behaviour of the ratio of the thermal Drude weight and the specific heat Dth(T )/C(T ) from ∼ Tto ∼ T 3/2e−β(δm−δs) when changing from ∆ < 5/3 to ∆ > 5/3. Unlike the case of thermal conductivity, the state ofinvestigation of the spin conductivity of the XXZ chain is less complete if not controversial. Some of the controversiesare resolved by the observation of a strong variation of the energy level curvatures even within a microcanonicalensemble between “very similar states”.



Percolation Thresholds for Honeycomb, Kagome and Triangular Lattices

Motoo Hori1 and Kazuo Kitahara2

1 Kuriya 4-1-18, Tama-ku, Kawasaki 214-0039, Japan2 Department of Physics, International Christian University, Mitaka 181-8585, Japan

Exact equations satisfied by critical surfaces of mixed percolation on honeycomb, kagome and triangular latticeswith random sites, random bonds and closed faces are obtained. As consequences, the critical probability for thesite percolation on honeycomb lattice is given by rc = 1

(1−2 sin π18 )(3−

√1−2 sin π

18 )and the critical probability for the

bond percolation on kagome lattice is given by pc = 1−p03−2p0

+ 2(2−p0)3−2p0

sin[

13arcsin

(1− (3−2p0)

2[(3−p0)p20−1]

2p20(2−p0)3

)], where

p0 =√

1− 2 sin π18 . The critical equation for the triangular lattice with site probability r and bond probabilities p1,

p2 and p3 is given by r = 1p1+p2+p3−p1p2p3

.

1 none2 [email protected]



Structure Function of an Ising Model on a Penrose Tiling

Helen Au-Yang1 and Jacques H.H. Perk2

1,2 Department of Physics, Oklahoma State University, PS 145, Stillwater, OK 74078-3072, USA

We present our latest results on the Ising model with spins on every other vertex of a regular rhombus Penrosetiling and interactions along diagonals. We can exactly evaluate the pair-correlation functions combining quadraticrecurrence relations and Baxter’s Z-invariance. In order to use the results we need a reasonably efficient scheme toexactly evaluate joint probabilities on the Penrose tiling. We shall outline our most recent method for doing so. Withthis we can then perform a numerical Fourier transform of the pair-correlation function and obtain highly accurateresults for the wavevector-dependent susceptibility.



Universal size distribution of percolation

Robert M. Ziff1

1Michigan Center for Theoretical Physics and Dept. of Chemical Engineering, University of Michigan,Ann Arbor,MI 48109-2136 USA

The size distribution of clusters in percolation can be cast in a completely universal form (with no metric factors) isone characterizes the size by such measures as the outside dimension, the disk or sphere enclosing the cluster, or (intwo dimensions) the enclosed area. For the latter definition, we have shown (J. Cardy and R. Ziff, J. Stat. Phys. 2003)that the coefficient C that characterizes the size distribution can be calculated exactly for percolation as well as theq = 2 (ising), 3 and 4 state critical Potts’ models, which can be thought of as correlated percolation. The distributionis simply that the number of clusters whose enclosed area is greater than a value A equals CL2/A where L2 is thearea of the whole system. In this talk we extend these results to considerations away from criticality and discussthe form of the universal scaling relations, based upon numerical simulations of percolation on various lattices. Wealso discuss relations to other problems such as the orbit-size distribution of a particle scattering through randomlyoriented mirrors.

[email protected]



4.2.1 Cancelled

High precision Monte Carlo analysis of tails for the order-parameterdistribution of the two-dimensional Ising model

R. Hilfer1,B. Biswal2,H.G. Mattutis3 and W. Janke4

ICA-1, Universitat Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany and Institut fur Physik, UniversitatMainz, 55099 Mainz, Germany

2Department of Physics, Sri Venkateswara College, University of Delhi, New Delhi - 110 021, India3Tokyo University of Electro-communications, Dept. of Mechanical and Control Engineering, Chofu, Tokyo

182-8585, Japan4Institut f”ur Theoretische Physik, Universitat Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany

The tails of the critical order-parameter distribution of the two-dimensional Ising model have been investigated throughextensive multicanonical Monte Carlo simulation [1]. Results for fixed boundary conditions are reported here, andcompared with known results for periodic boundary conditions. Clear numerical evidence for “fat” stretched exponen-tial tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature.Our results suggests that, contrary to common belief, the true order parameter distribution at the critical temperaturemust be considered to be unknown at present. [1] R. Hilfer et al., Phys.Rev.E, 68, 046123 (2003)

[email protected]


4.2.2 Monday 5 July, 11:30 - 11:45, Hall E

Spontaneous Symmetry Breaking by Partial or Topological Fields

Masuo Suzuki1,Hidenori Suzuki2,Asuka Sugiyama3,Minoru Harabayashi4 and Shu-Chiuan Chang5

1,2,3,4,5Department of Applied Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601Japan

The first problem is to study such conditions on a partial field as make spontaneous symmetry breaking (SSB), namelyto clarify whether or not there exist lower dimensions (of the domain to which the field is applied) below which no SSBoccurs. The second problem is to evaluate explicitly the spontaneous magnetization at the boundary in the Ising modeland in the anisotropic XY - model using the topological perturbation method. Our main results are the following: (i)The total magnetization is proportional to the square of the spontaneous magnetization when a field is applied only toa finite region (an extension of C.N.Yang’s result, M = Nm2

s for a fixed single spin). A general formulation to calculatethe proportionality coefficient is given, and it is shown to vanish as the field goes to zero. This indicates no SSB in thissituation. (ii) On the other hand, if we apply partial fields to a d′-dimensional region and make them vanish, we findthat SSB occurs, at least, for d′ > d′c = β/ν. In the region 0 < d′ ≤ d′c, the situation is subtle. (iii) The spontaneousmagnetization at the boundary can be shown to be obtained from the free energy for a topological perturbation, namelyboundary-boundary interaction. For example, the spontaneous magnetization mb at the boundary in the square Isingsystem is derived exactly using the topological perturbation as m2

b = (cosh 2K2 − coth 2K1)/(cosh 2K2 − 1) withKi = Ji/kBT for the Ising interactions J1 and J2. This agrees with McCoy-Wu’s result. (iv) Similarly for theanisotropic XY - chain (1 ≥ γ > 0) at T = 0, we obtain m2

b,x = 4γ(1−h2)/(1+γ)2 for the interactions Jx,y = J(1±γ)with h = µBH/2J for a uniform magnetic field H in the z-direction. An exact scaling form is also obtained from theequation of state for a partial field obtained using the “ghost spin” by Suzuki and Griffiths.

[email protected]@[email protected]@[email protected]



Double Criticality and Density Anomaly in a Lattice Gas Model

Marcia C Barbosa1 and Vera Henriques2

1 Instituto de Fisica, UFRGS,Caixa Postal 15051,91501-970, Porto Alegre, RS, Brazil2 Instituto de Fisica, USP, Sao Paulo, Brazil

We present a simple lattice model for modeling structured liquids. Each occupied site can be in different statesrepresenting the molecule’s orientations. When two neighbor molecules are in complementary orientations, a bond isformed between them and the systems lower its energy. Each molecule can have a maximum of four hydrogen bond.As the chemical potential is increased a competition between the lattice gas interaction that tries to fill the lattice andthe hydrogen bond term that punishes molecules with more than four neighboors is stablished. At low temperaturesthis competition leads to the formation of two coexisting liquid phases at high chemical potential and a low densityliquid coexisting with a gas at a very low chemical potential. As the temperature is increased, the liquid-gas and theliquid-liquid phase transition end at two critical point. In the vicinity of the liquid-liquid critical point there is a lineof maximum densities.




Dominant Paths and the Bootstrap Transition: Reunification of Theoryand Simulations near the Arrest

Paolo De Gregorio1, Aonghus Lawlor2, Phil Bradley3 and Kenneth A. Dawson4

1,2,3,4 Irish Centre for Colloid Science and Biomaterials, Department of Chemistry, University College Dublin,Dublin, Ireland

The problem of bootstrap percolation has attracted considerable attention from a variety of scientific communities,including those interested in the dynamical arrest and glass transition, complex processor arrays, crack propogation,information flow, and many others. In essence it describes a system whose underlying dynamics is slowing, andfinally arresting when the bootstrap has a percolation transition. Broadly speaking, as a function of the underlyingrules the transition is known to pass from a continuous transition with universal critical exponents, to one with anessential singularity, more reminiscent of a non-equilibrium first-order kinetics of phase separation. There emerges along dynamical length originating in the fact that motion requires (diverging numbers of) concerted consecutive steps,as we approach arrest. In many studies, there has persisted a discrepancy between theory and simulation, despite thebelief that two-dimensional percolation transition can be treated exactly in the asymptotic regime. In a combinationof new theory and new simulations we have been able to resolve the discrepancy, explaining its origins in terms of thepaths that are explored as the system bootstraps near arrest. Using a new ’enrichment’ importance sampling methodin simulations we are able to explore length-scales far beyond those currently known. Besides this, the innovation isthat we are now able to solve the problem within controlled (and systematically improvable) approximations for alldensities, and identify the ’fluctuations’ captured there by the simulations, but not by the asymptotic theory. Thespirit of the theory is a new type of dominant paths (and fluctuations) approach (not unlike the instanton approachto phase-transition kinetics) that makes it possible to control the calcualtion on approach to the transiton. [1] Thecapacity to calculate in a controlled manner this diverging dynamical length is very promising, as may offer thepossibility to explain the onset of dynamical arrest, and the glass transition.[2] [1] Clarification of the BootstrapParadox, P. De Gregorio, A. Lawlor, P. Bradley, K. A. Dawson. - Preprint [2] Universality in Lattice Models ofDynamic Arrest: Introduction of an Order Parameter, A. Lawlor, D. Reagan, G. D. McCullagh, P. De Gregorio, P.Tartaglia and K. A. Dawson, Phys. Rev. Lett. 89, 245503 (2002)

1 [email protected] [email protected] [email protected] [email protected]


4.2.5 Monday 5 July, 12:15 - 12:30 Hall E

Critical Dynamics of Superconductors in the Charged Regime

Smitha Vishveshwara1,Courtney Lannert2 and Matthew P. A. Fisher3

1Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, IL 61801-3080,USA

2Department of Physics, Wellesley College, 106 Central St., Wellesley, MA 02481-8203, USA3Kavli Institute for Theoretical Physics,University of California,Santa Barbara,CA 93106-4030,USA

We investigate the finite temperature critical dynamics of three-dimensional superconductors in the charged regime,described by a transverse gauge field coupling to the superconducting order parameter. Assuming relaxational dynam-ics for both the order parameter and the gauge fields, within a dynamical renormalization group scheme, we find a newdynamic universality class characterized by a finite fixed point ratio between the transport co-efficients associated withthe order parameter and gauge fields, respectively. We find signatures of this universality class in various measurablephysical quantities, and in the existence of a universal amplitude ratio formed by a combination of physical quantities.


4.2.6 Tuesday 6 July, 16:15 - 16:30, Hall E

Phase Transitions in Parallel Computational Complexity in StatisticalPhysics

Jonathan Machta1

1 Department of Physics, University of Massachusetts, Amherst, MA, USA

Systems in statistical physics can be characterized by their depth. The depth of a system is the computational complex-ity of simulating its states on an idealized parallel computer or, alternatively, the minimum number of computationalsteps needed to generate typical system states from random bits. In systems with structural phase transitions theremay also be a phase transition in computational complexity. Two examples illustrate this phenomenon–percolationand growing networks. For percolation, depth has a logarithmic singularity at the percolation transition. For growingnetworks with attachment probabilities proportional to the degree of the node raised to a power α, depth has a dis-continuity at α = 1. For the sublinear case (α < 1), where there is a finite upper cut-off in the degree distribution,depth is logarithmic in the number of nodes. For the superlinear case (α > 1), where there is a “gel” node that almostall nodes attach to, depth is constant, independent of the number of nodes.

1 [email protected]



Going Extreme: Liquid Stability Limits and the Energy LandscapeApproach

Emilia La Nave1, Francesco Sciortino2 and Piero Tartaglia3

1,2,3 Dipartimento di Fisica, INFM UdR and Center for Statistical Mechanics and Complexity, Universita

Understanding the dynamic and thermodynamic properties of supercooled liquids is one of the more challenging tasksof condensed matter physics. Recent years have seen a strong development of numerical and theoretical studies ofsimple liquid models, attempting to develop a thermodynamic description based on formalisms which could be extendedto deal also with out-of-equilibrium (glassy) states. Among these formalisms, the study of the topological structure ofthe potential landscape (PEL) and the connection between the PEL properties and the dynamical behavior of glassforming liquids has become an active field of research. Properties of the PEL, such as depth, number and shape of thebasins of the potential energy surface are calculated and used in the evaluation of the liquid free energy in supercooledstate. We show that within the PEL approach it is possible to obtain an Equation of State (EOS) that allows us toextrapolate the thermodynamical properties of the liquid state below the lowest temperature at which equilibrateddata can be collected. The obtained EOS can help in the understanding of the physics of the liquid-liquid transitionand of density maxima observed in some complex liquids such as water by identifying the statistical properties of thePEL responsible for these anomalies. We also provide evidences of the connection between density anomalies and theliquid-liquid critical point. We then address the basic question of the liquid’s stability limits. We show how the PELapproach allows us to evaluate the Kauzmann locus, where the configurational entropy vanishes, and to investigatethe liquid phase diagram. In this framework, the boundary role of the Sastry density is also discussed.

1 [email protected] [email protected] [email protected]



Percolation of water in aqueous systems and its relation to phasetransitions

Ivan Brovchenko1, Alfons Geiger2 and Alla Oleinikova3

1,2 Physical Chemistry, University Dortmund, Germany3 Physical Chemistry, Ruhr-University Bochum, Germany

The percolation transition of physical clusters coincides with the thermodynamic critical point. Our studies of waterclustering in aqueous solutions suggest three different categories of behaviour at subcritical temperatures. In the caseof hydrophobic solutes a percolation transition is prevented by the formation of droplets when crossing the coexistencecurve. Two percolation transitions are observed in solutions with more hydrophilic solutes: quasi-2D percolationoccurs in the stable state region and a 3D percolating cluster appears close to the coexistence curve. In general,the liquid-liquid immiscibility appears to correspond to the concentration interval, where both components are abovetheir 3D percolation thresholds. We used these observations for the identification of water molecules with definitelocal order, which are responsible for the liquid-liquid phase separation in pure supercooled water. A study of thewater clustering near hydrophilic plane surfaces evidences a line of quasi-2D percolation transitions, which ends at thecritical point of a layering transition. This quasi-2D percolation is similar to that observed in aqueous solution withhydrophilic solutes. This finding suggests that the 2D percolation of water on protein surfaces, which is appearing inparallel to the onset of biological function of proteins, originates from a low temperature layering transition.




A New Kind of Monte Carlo Sampling in Statistical Physics

David P. Landau1, Fugao Wang2, Hwee Kuan Lee3 and Yutaka Okabe4

1,2 Center for Simulational Physics, The University of Georgia, Athens, GA 30602 U.S.A.3 Center for Simulational Physics, The University of Georgia, Athens, GA 30602 U.S.A. and Dept. of Physics,

Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo, Japan 192-03974 Dept. of Physics, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo, Japan 192-0397

Monte Carlo simulations [1] have become a powerful tool for the study of diverse problems in statistical/condensedmatter physics. Standard methods sample the probability distribution for the states of the system, most often inthe canonical ensemble, and over the past several decades enormous improvements have been made in performance.Nonetheless, difficulties arise near phase transitionsdue to critical slowing down near 2nd order transitions and tometastability near 1st order transitions, and these complications limit the applicability of the method. We shalldescribe a new Monte Carlo approach [2] (now generally termed Wang-Landau sampling in the literature) that uses arandom walk in energy space to determine the density of states directly. From this density of states all thermodynamicproperties can be calculated. This approach has been extended to multi-dimensional parameter spaces and is effectivefor systems with complex energy landscapes, e.g., spin glasses, protein folding models, etc. A Refined Wang-Landausampling method has also been devised in which the true density of states is estimated from the distribution determinedafter just a few stages of iteration and the histogram determined from the simulation. Advantages and limitations ofthe refined method will be discussed. [1.]A Guide to Monte Carlo Simulations in Statistical Physics, D. P. Landauand K. Binder (Cambridge U. Press, Cambridge, 2000). [2.] Fugao Wang and D. P. Landau, Phys. Rev. Lett. 86,2050 (2001); Phys. Rev. E64, 056101-1 (2001). * Research support in part by NSF



Phase transitions, the entropy function, and topology

Michael Kastner1

1 I.N.F.M. and Universita di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy

Beside the well-known canonical one, various non-standard approaches to phase transitions have received much at-tention recently. One of those, the microcanonical approach, has the microcanonical entropy as a starting point, andit has proved useful for certain applications. The second approach is a quite recent one, relating the existence of aphase transition to topology changes of a certain family of submanifolds of the phase space of the system. This latterapproach is interesting in particular from a conceptual point of view. Both approaches, the microcanonical and thetopological one, allow for ’natural’ generalizations of the definition of phase transitions to finite systems. Some newresults on the interrelation between these two approaches are presented. General statements about the properties ofthe microcanonical entropy are deduced, and conceptual questions are tackled.

1 [email protected]



Phase separation in binary mixtures: Oscillatory instabilities undercontinuous cooling or heating

G. K. Auernhammer1,J. Vollmer2 and D. Vollmer3

1,3Max Planck Institut for Polymer Research, Mainz, Germany2University of Marburg, Inst. of Physics, Germany

The kinetics of phase separation of binary mixtures under slowly ramping the temperature is discussed for systemsvarying significantly in their microscopic structure. For a broad range of compositions and heating rates pronouncedoscillations in the turbidity are reported. It hardly matters if phase separation is induced by cooling or heating, andwhether the liquids are of low molecular weight or if a polymer solutions are investigated. The origin of the oscillationsis discussed based on the non-linear advective diffusion equation for the transport of the microscopic constituents. Theyare caused by repeated cycles of nucleation and coarsening. Finally, the relation of these oscillations to oscillations inchemical systems and their relevance to rain-formation will be addressed.



Stochastic theory of Synchronization phase transitions

Miguel A. Munoz1 and Romualdo Pastor-Satorras2

1Universidad de Granada (Spain)2Universidad Politecnica de Catalunya (Spain)

We present a Langevin equation describing the universal properties of generic synchronization transitions in extendedsystems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits,depending on parameter values, either: i) a continuous transition in the bounded Kardar-Parisi-Zhang universalityclass, with a zero largest Lyapunov exponent at the critical point; ii) a continuous transition in the directed percolationuniversality class, with a negative Lyapunov exponent, or iii) a discontinuous transition. Cases ii) and iii) exhibitcoexistence of synchronized and unsynchronized phases in a broad region. This reproduces ALL the reported featuresand phenomenology described in the literature of synchronization transitions of coupled map lattices and other ex-tended models, providing a unified theoretical framework for the analysis of synchronization transitions in extendedsystems.

[email protected]@upc.es


4.2.13 Thursday 8 July, 15:30 - 15:45, Hall E

Correlated Acoustic Emission and Shape Memory Effect

G. Ananthakrishna1 and S. Sreekala2

1,2Materials Research Centre, Indian Institute of Science, Bangalore - 560012, India

Martensites are known to exhibit unusual features, for instance, the repetitive nature of acoustic emission (AE) signalswhen the system is cycled repeatedly in a restricted range of temperatures. This is correlated with the growth andshrinkage of martensitic domains and is directly linked to the shape memory effect. We report a numerical investigationof a recently introduced model for square-to-rectangle martensitic transformation to understand this old puzzle[1, 2].The model includes inertial effects, long-range interaction between the transformed domains, a dissipative term thatmodels the AE signals, and an inhomogeneous stress field to describe the effect of lattice defects which serve asnucleation centers. The rate of energy dissipated occurs in the form of bursts similar to the AE signals observed inexperiments. The model reproduces the repetitive nature of the AE signals when the system is cycled repeatedly ina restricted domain of temperatures after a few ’training’ cycles. Interestingly, the associated morphology shows acomplete reversal of the martensite domains during a stabilized cycle. The role of training cycles is shown to create adeeper set of metastable states for the system to circulate. The model provides insight into the shape memory effect.1. R. Ahluwalia and G. Ananthakrishna, Phys. Rev. Lett., vol.86, 4076 (2001). 2. S. Sreekala and G. Ananthakrishna,Phys. Rev. Lett., vol.90, 135501(2003).

[email protected]@mrc.iisc.ernet.in


Quantum spin chains and mass spectrum of the O(3) sigma model withtheta term

Giuseppe Mussardo1 and Davide Controzzi2

1,2SISSA,via Beirut 1 Trieste (Italy)

Quantum antiferromagnetic chains admit a continuum formulation in terms of O(3) non-linear sigma model withtopological θ term. The massive (θ = 0) or massless (θ = π) nature of this field theory is referred in the literatureas Haldane conjecture. In this talk, based on the paper published in Phys.Rev.Lett. 92 (2004) 021601, we study theevolution of the spectrum by varying θ. We show that the massless particles (spinons) present at θ = π get confinedonce θ moves away from this value and that the spectrum consists of a stable triplet of massive particles for all valuesof θ and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of θ close to πwhereas it becomes a resonance below a critical value θc.

[email protected]@fm.sissa.it



Anisotropic colloidal particles in critical fluids

Erich Eisenriegler1

1Institut fuer Festkoerperforschung, Forschungszentrum Juelich, D52425 Juelich, Germany

We consider anisotropic colloidal particles with dumbbell or lens shapes that are immersed in a critical binary fluidmixture. The orientation-dependent long ranged universal interactions mediated by the critical solvent between aparticle and a wall or between two particles are investigated for mesoscopic particle sizes small compared to thecorrelation length and inter-particle distances. Results are obtained from a Small Particle Operator Expansion inwhich the amplitudes of the isotropic and anisotropic operators depend on the size and aspect ratio of the dumbbell orlens and are determined by density profiles that arise in the Ising model at the critical point in a wedge geometry withsymmetry breaking fixed spin boundary conditions. Dumbbells and ellipsoids in a solution of nonadsorbing polymersare also considered.

[email protected]


Large scale numerical simulations of ”ultrametric” long-range depinning

Damien Vandembroucq1

1Unit Mixte CNRS/Saint-Gobain 39 Quai Lucien Lefranc 93303 Aubervilliers FRANCE

The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicableto crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing fora drastic reduction of the numerical complexity of the problem. Based on large scale simulations, two to three ordersof magnitude larger than previously considered, we obtain a very precise determination of critical exponents whichare shown to be indistinguishable from their Euclidean metric counterparts. Moreover the scaling functions (interfacewidth and depinning force distributions) are shown to be unchanged. The choice of an ultrametric distance thus doesnot affect the universality class of the depinning transition and opens the way to an analytic real space renormalizationgroup approach.

[email protected]



Surprises in driven diffusive systems with two species of particles

Gunter M Schutz1

1Institut fur Festkorperforschung, Forschungszentrum Julich, D-52425 Julich, Germany

It is by now well-known that driven diffusive systems with two species of particles cannot be understood by straight-forward generalization of the physical principles governing single-species systems. We show that bulk phase separation(which is unknown in one-dimensional single-species systems with local interactions and positive transition rates) canbe understood in terms of a current criterion. For systems with open boundaries we argue that there are two distinctmechanisms for broken ergodicity. One (which leads spontaneous symmetry breaking in the bridge model and itsvariants) can be explained only by introducing the notion of a “boundary defect”. The other – which occurs also insingle-species models – originates in a freezing of the position of macroscopic shocks through the introduction of extranoise which weakly violates the conservation law.

[email protected]


4.3.1 Monday 5 July, 16:45 - 17:00, Hall J

Mode-coupling theory of heat conduction in a chain

Jian-Sheng Wang1

1 Department of Computational Science and Singapore-MIT Alliance, National University of Singapore, Singapore117543

We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. Theparticles are connected by two-dimensional harmonic springs together with bending angle interactions. The problemis analyzed by mode-coupling theory and compared with molecular dynamics results. We find excellent agreement forthe damping of modes between mode-coupling theory and molecular dynamics. The theories predict generically thatthermal conductance diverges as N1/3 as the size N increases for systems terminated with heat baths at the ends.The N2/5 is also observed in molecular dynamics which we attributed to crossover effect.

1 [email protected]



Universal Distribution of Resistance Fluctuations in Highly DisorderedGranular Materials

Cecilia Pennetta1, Eleonora Alfinito2, Stefano Ruffo3 and Lino Reggiani4

1,2,4 Dip. Ingegneria, Univ. Lecce, Italy3 Dip. di Energetica , Univ. di Firenze, Italy

We study the distribution of resistance fluctuations in conducting thin films with granular structure. A film is modeledas a resistor network in a non-equilibrium steady state determined by the competition between two biased stochasticprocesses consisting in the breaking and recovery of elementary resistors [1]. A systematic investigation of the steadystates of the system is carried out by performing numerical simulations on systems of different sizes, with differentlevels of internal disorder and under different bias conditions [2]. The distribution of resistance fluctuations is found toexhibit relevant deviations from Gaussianity when the values of the external bias approach the threshold of electricalbreakdown. The magnitude of these deviations increases strongly at increasing the degree of internal disorder. We showthat this non-Gaussianity is in general related to the finite size of the system, thus vanishing in the thermodynamiclimit. However, in highly disordered materials, close to the critical point of the conductor-insulator transition, the non-Gaussianity persists in the large size limit. Remarkably, in this case we have found that the distribution of the resistancefluctuations follows the universal Bramwell-Holdsworth-Pinton distribution [3] within numerical uncertainty. [1] C.Pennetta et. al., Phys. Rev. E, 65, 066119 (2002). [2] C. Pennetta et al., Cond-mat/0401352 and Cond-mat/0310643.[3] S. T. Bramwell et al., Nature, 396, 552 (1998) and Phys. Rev. Lett., 84, 3744 (2000).



Segregation in diffusion-limited multispecies pair annihilation

Henk J. Hilhorst1, Olivier Deloubriere2, Mark J. Washenberger3 and Uwe C. Tauber4

1 Laboratoire de Physique Theorique, bat. 210, Universite de Paris-Sud, 91405 Orsay, France2,3,4 Dept. of Physics, Virginia Polytechnic Institute and state University, Blacksburg, Virginia 24060, USA

Particles of q different species diffuse on a d-dimensional lattice. When two unlike particles meet, they annihilate.This interpolates between the well-understood reactions A+B → 0 (the case q = 2) and A+A → 0 (the case q = ∞).For equal initial densities of the q species the the total particle density decays to zero as a power of time: ρ(t) ∼ t−α.During this process, depending on the values of q and d, there may or may not occur segregation, i.e. formation ofever growing single-species domains. We determine the conditions for segregation both above and below the criticaldimension dc = 2; in dimension d = 1 there appears to be segregation for all q. We derive the exponent α(q, d) of thedensity decay law.




Clustering of passive scalars advected by a 1-d noisy Burgers fluid

Apoorva Nagar1, Mustansir Barma2 and Satya N. Majumdar3

1,2 Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India3 Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris - Sud, Bat 100, Orsay, France

We study the clustering properties of advected, non-interacting, passive scalar particles in a Burgers fluid with noise,a problem which maps to that of passive sliding particles moving under gravity on a surface evolving through theKardar-Parisi-Zhang (KPZ) equation. We study a lattice version of the latter problem numerically in (1+1)-dimension.Our results show a strong tendency of the particles to cluster. We monitor two quantities: (i) the two-point correlationfunction CL(r) = 〈nini+r〉 where ni is the number of particles at site i and L is the system size, and (ii) the probabilitydistribution PL(ni). We find that CL(r) obeys the scaling form CL(r) ∼ L−1/2Y (r/L), with Y (y) ∼ y−3/2 for smallvalues of y; the divergence as r → 0 indicates strong clustering. Further, PL(n) scales as PL(n) ∼ L−2G(n/L). Inthe limiting case where the interface is frozen, the problem reduces to studying noninteracting random walkers on aSinai landscape. In this limit, we analytically determine the scaling functions and find Y (y) = [y(1 − y)]−3/2 andG(y) = e−yK0(y)/y where K0 is a modified Bessel function. Surprisingly, these scaling functions, derived for theequilibrium case with a frozen interface, continue to describe well the numerically determined CL(r) and PL(n), evenin the strongly nonequilibrium situation where the surface fluctuates rapidly.



Heat and Work Fluctuations in Small Driven Systems with a Heat Bath

Ramses van Zon1 and E.G.D. Cohen2

1,2 Theoretical Physics Lab, Rockefeller University, New York, USA

We consider the fluctuations in the work done on and in the heat produced in two different driven systems in contactwith a heat bath. The first is a Brownian particle dragged through water by a moving harmonic potential, thesecond is a parallel electric RC circuit with Nyquist noise and subject to a constant current source. In these typeof systems, potential energy can be temporarily stored. This in contrast to other non-equilibrium systems for whichit had been proved that any negative fluctuation −Q of the time averaged heat is exponentially suppressed in Qcompared to the positive fluctuation +Q; this is the fluctuation theorem. While in the two systems considered here,the work fluctuations do satisfy this same fluctuation theorem, the heat fluctuations satisfy a new relation. Accordingto this relation, large negative heat fluctuations (i.e. heat absorption) are suppressed only by a constant rather thanexponentially. In a small enough system, these negative heat fluctuations can be pronounced and might be importantfor its stability.




Irreversible transport in a fully Hamiltonian model

Carlos Mejia Monasterio1, Hernan Larralde2 and Francois Leyvraz3

1 Center for Nonlinear and Complex Systems, University of Insubria, Como, Italy2,3 Centro de Ciencias Fisicas, University of Mexico, Cuernavaca, Mexico

We study irreversible transport in a Lorentz gas with rotating scatterers connected to heat and particle baths at bothends of the system, which is a long and narrow channel. Apart from the baths at the ends, the system dynamics isfully Hamiltonian and reversible. We find normal heat transport, diffusion as well as a non-trivial coupling betweenmass and heat transport (thermodiffusion). The Onsager reciprocity laws as well as the Green-Kubo relations aresatisfied within numerical accuracy.



Force and Velocity Autocorrelation Functions of Liquid Metal

Puneet Sharma1, K. Tankeshwar2, K.N. Pathak3 and S. Ranganthan4

1,2,3 Department Of Physics, Panjab University, Chnadigarh -160014, India4 Department of physics, Royal Military College, Kingston, Ontario, Canada, K7K 7B4

Force and velocity autocorrelation functions of liquid rubidium at six thermodynamic states along liquid vapourco-existence curve have been studied by calculating time dependent contributions due to static pair, triplet andquadruplet correlations, separately. Binary contribution has been obtained using microscopic expression [1] basedon cluster expansion technique. The numerical calculations have been performed [2] using Monte-Carlo method ofmultiple integration and Verlet algorithm for evaluating time evolution of force. For interatomic potential, we have usedAshcroft pseudo-potential with Ichimaru screening and for static pair correlation function, we have used correspondingcomputer simulation data [3]. Time correlation function of force acting on a tagged particle has been written as atime series containing time dependent contributions due to two, three and four body cluster of particles. Three andfour body time dependent contributions have been estimated by phenomenological functions where parameters can bedetermined from contributions of three and four body static correlations’ to the sum rules of velocity autocorrelationfunction. It is found that close to the critical and at intermediate temperatures, contributions due to two and threebody static correlation are sufficient. However near the melting point, contribution due to four-body static correlationfunction is essential to explain velocity and force autocorrelation functions as has been judged by comparing our resultswith those obtained from computer simulation[3] and predictions of earlier theoretical investigation [4].References: [1] K.N. Pathak, S. Ranganathan and R. E. Johnson, Phys. Rev. E 50, 1135 (1994).[2] Puneet Sharma, K. Tankeshwar, K. N. Pathak and S. Ranganathan, Phys. Rev. E 68, 021202 (2003).[3] G. Kahl and S. Kambayashi, J. Phys.: Condens. Matter 6, 10897 (1994).[4] S. K. Sharma and K. Tankeshwar, J. Phys.: Condens. Matter 8, 10839 (1996).




On the Second Law of Thermodynamics and the Piston Problem

Christian Gruber1

1Ecole polytechnique federale de Lausanne Institut de theorie des phenomenes physiques CMST PHB - EcublensCH-1015 Lausanne

The so-called ”adiabatic piston problem” is a well-known and controversial problem of thermodynamics, In this talkwe shall discuss a very simple microscopic model describing this macroscopical sytem. In the first part we reviewthe results which have been obtained for the time evolution of the piston: two-time scale evolution, adiabatic anddeterministic motion vs conducting and stochastic motion, strong damping vs weak damping. In the second partwe present new results concerning the time evolution of the fluids separated by the piston in the case where thelength of the cylinder is infinite. We shall then show that, despite the fact that the particles of the fluid do notinteract, the hydrodynamical equations obtained from this microscopical model obey the two laws of non-equilibriumthermodynamics if the entropy is properly defined.

[email protected]


Flow-induced currents in nanotubes: a Brownian dynamics approach

Moumita Das1,Sriram Ramaswamy2,Ajay K. Sood3 and G. Ananthakrishna4

1,2,3Department of Physics, Indian Institute of Science, Bangalore 5600124Materials Research Centre, Indian Institute of Science, Bangalore 560012

Motivated by recent experiments reporting observation of flow-induced current and voltage generation in carbonnanotubes, we numerically study the effect, on overdamped, charged particles confined in a narrow channel, of aflow field applied on similar but slower particles in a reservoir in contact with the channel. For a suitable range ofshear rates, we find that the flow field induces a unidirectional drift in the confined particles, and is stronger fornarrower channels. The average drift velocity initially rises with increasing shear rate, then shows saturation for awhile, thereafter starts decreasing, in qualitative agreement with recent theoretical arguments (S. Ghosh, A.K. Sood,S. Ramaswamy and N. Kumar, submitted) based on Brownian drag and “loss of grip”. Interestingly, if the sign ofthe interspecies interaction is reversed, the direction of the induced drift remains the same, but the flow-rate at whichloss of grip occurs is lower, and the level of fluctuations is higher.

[email protected]@[email protected]@mrc.iisc.ernet.in



On the probability distribution of residence times of sandgrains insandpile models

Deepak Dhar1 and Punyabrata Pradhan2

1,2 Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

We study the steady state of a model sandpile, driven by adding a grain of sand at every time step. The residence timeof a grain is defined as the time spent by the grain in the pile. We study the probability distribution of residence times ofsand grains, and argue that for large system size this distribution can be expressed in terms of the survival probabilityof a single diffusing particle in a medium with space dependent diffusion co-efficient and absorbing boundaries. Wecheck these arguments by explicitly calculating the residence time distribution in 1-dimensional Bak-Tang-Wiesenfeldmodel of L sites, with grains added at one end. We derive the exact scaling function for the probability distributionof residence times when the grains are added randomly at either end. For sandpiles in any dimension and of arbitraryshape, with grains added everywhere with equal probability, we prove that for large L, the residence time distribution,Prob(T |L), that a randomly added grain has a residence time T tends to 1

MLexp(− T

ML). ML is the average mass of

the pile in the steady state. We also investigate the finite-size corrections to this function.


4.3.11 Friday 9 July, 11:30 - 11:45, Hall F

Asymmetric Random Average Processes

Andreas Schadschneider1

1 Institut fur Theoretische Physik, Universitat zu Koln, 50937 Koln, Germany

The Asymmetric Random Average Process (ARAP) describes an asymmetric transport of continuous masses on alattice through fragmentation and diffusion. It has various applications, e.g. for granular materials or traffic flow. Wederive the class of all ARAPs that are described exactly by a product-measure solution for the stationary state. Ageneralization of the matrix-product Ansatz for models with continuous state variables is proposed and applied to theARAP. Furthermore we study numerically and analytically variants of the model where the mass transfer is restrictedby a cutoff. Here two phases are found: a homogeneous phase and a condensed phase where a finite fraction of thetotal mass resides on one site. For small cutoffs both phases can coexist on a finite lattice. The lifetimes diverge inthe thermodynamic limit leading to a breaking of ergodicity. This might help to understand the unusual behaviourobserved in some models of traffic flow.

References:[1] J. Krug, J. Garcia: J. Stat. Phys. 99, 31 (2000)[2] R. Rajesh, S.N. Majumdar: J. Stat. Phys. 99, 943 (2000)[3] F. Zielen und A. Schadschneider: J. Stat. Phys. 106 , 173 (2002); J. Phys. A36, 3709 (2003); Phys. Rev. Lett.89, 090601 (2002)

1 [email protected]



Ab initio derivation of the hydrodynamic modes and entropy production

Pierre GASPARD1

1 Center for Nonlinear Phenomena and Complex Systems,

An overview is given of recent work on the construction of the hydrodynamic modes of relaxation toward the thermo-dynamic equilibrium from the underlying microscopic dynamics. The hydrodynamic modes have a fractal structurein relation to the chaotic property of the microscopic dynamics. In this framework, the nonequilibrium steady statesas well as the entropy production can be derived from the hydrodynamic modes. References: P. Gaspard, I. Claus,T. Gilbert, and J. R. Dorfman, The Fractality of the Hydrodynamic Modes of Diffusion, Physical Review Letters 86(2001) 1506-1509. J. R. Dorfman, P. Gaspard, and T. Gilbert, Entropy production of diffusion in spatially periodicdeterministic systems, Physical Review E 66 (2002) 026110 (9 pages); preprint nlin.CD/0203046.

1 [email protected]


Flow-induced current and voltage generation in carbon nanotubes

Shankar Ghosh 1, A.K. Sood2, Sriram Ramaswamy3 and N. Kumar4

1,2,3 Department of Physics, IIsc, Bangalore, 5600124 Raman Research Institute, C.V. Raman Avenue,Bangalore 560 080, India

New experimental and theoretical results are presented on the flow-induced current and voltage in single-walled carbonnanotube samples. In the experiments, the electrical response is found to be logarithmic in the flow speed over a widerange, and its direction can be controlled by electrical biasing of the nanotubes. A physically appealing Langevin-equation treatment of charge carriers in the nanotube interacting with the ions in the ambient fluid is shown to leadnaturally to a sublinear dependence on flow speed, and predicts a decreasing current at the highest flow-rates, througha “loss of grip” of the flow on the carriers in the nanotube.




Roughness of Sandpile Surfaces

J. G. Oliveira 1, J. F. F. Mendes2 and G. Tripathy3

1,2 Departamento de Fisica, Universidade de Aveiro, Aveiro, Portugal.3 Institute of Physics, Bhubaneswar, India.

We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncriticalvariants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface rough-ness yield different asymptotic scaling exponents. Using approximate analytical arguments and extensive numericalstudies we conclude that this counter-intuitive result is in fact a consequence of the special scaling properties of thenonlinear steady state surface. We also find that there is no such ambiguity for non-SOC models, although theremay be intermediate crossovers to different roughness values which need to be distinguished from the true asymptoticbehaviour.



Application of Dynamic density functional theory to steady statedistributions

F Penna 1 and Pedro Tarazona Lafarga 2

1,2 Facultad de ciencias c-V. Universidad Autnoma de Madrid. E-28049. Madrid.Spain

The deterministic Dynamic Density Functional (DDF) theory is an extension of the Density Functional (DF) formal-ism to off-equilibrium systems, which includes exactly the ideal gas and the external potential contributions and itrepresents the correlations out of equilibrium by those of an equilibrium system with the same density distribution.With this hypothesis, and the interpretation of the density ρ(r, t) as the average of the instantaneous density over therandom noise in the molecular Langevin dynamics, the theory enables the use of the well developed approximationsfor the equilibrium Helmholtz free energy in DF theory keeping the microscopic level of description of DF theoryneeded at high packing fractions. Using this theory we have studied the steady state density distribution of polymersin a light solvent created by a colloidal particle dragged at a constant rate c (e.g. by gravitation, electric or magneticfields, or by optical clamps). We present our result for the stationary state of 1D, 2D and 3D systems and comparedtheir with Brownian dynamics simulations (BDS). The good agreement between the BDS data and the DDF resultgives support to the DDF hypothesis.





Clustering in the inelastic gas

Srdjan Ostojic1, Bernard Nienhuis2 and Debabrate Panja3

1,2,3 ITFA, Valckenierstraat 65, Universiteit van Amsterdam, 1018 XE Amsterdam, Netherlands

The most popular model for granular kinetics is the inelastic gas. Already in one dimension the model exhibits non-trivial phenomena like clustering when the gas is left to cool under its own kinetics. The extreme case of completeinelasticity (the sticky gas) has been solved exactly in the seminal paper [Frachebourg, PRL 82, 1502 (1999)]. Ina study of the generic case we compared simulations of this model with a simplified version in which the positionalinformation is ignored except that the particles have a fixed order in space, invariant under the collision dynamics[Baldassarri e.a., Europhys.Lett.58, 12 (2002).]. In this model at each time step a pair of adjacent particles is chosenrandomly. If these particles approach each other they collide, updating their respective velocities. Surprisingly wefound that the velocity plotted versus sequence index develops the same structure (with a clear signal of clustering),as the full inelastic gas, with positions left intact. Not only does clustering still take place, the composition of theclusters, i.e. which particles make up a certain cluster, is the same between the two models. The late time compositionof the clusters depends only on the initial velocity configuration and not on the order of the collisions, nor on thecoefficient of restitution. These observation have strong implications beyond the simplified model for the true inelasticgas itself.




Network Formation of Cavity Regions in a Granular Material due toViscous Flow

Osamu Sano1 and Yoshifumi Kaneko2

1,2Dept.Appl. Phys.,Tokyo Univ.Agri.Tech., Koganei, Tokyo, Japan

Collapse of macroscopic cavity regions in an otherwise homogeneous granular material under viscous flow are investi-gated. The flow around a circular or slightly deformed cavity is analyzed on the basis of the Stokes equation and thegeneralized Darcy equation, inside and outside of the hole, respectively. The presence of a cavity enhances volume fluxand magnitude of velocity in the hole, which was verified experimentally. The locally enhanced flow destroys cavityboundary above a certain critical velocity, and the fluidized region develops towards upstream direction. This studyis extended to interaction of two equal-sized circular cavities exposed to uniform viscous flow at infinity, which revealthe presence of distances and orientations with highly increased volume flux and velocity. The experimental resultson the mechanism of the collapse are shown. Such an interaction suggests the lowering of critical fluidized velocity aswell as the configuration of cavities with fastest growth of the void region. In the case of many cavities, collapse andmerging of them lead to network formation of fluidized region, as well as macroscopic sheet-like void region, the latterof which is considered to be one of the mechanisms of the onset of landslide.

[email protected]


Persistence of Height Fluctuations in Radially Growing Surfaces

Subhendu B Singha1 and Deepak Dhar2

1,2 Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai - 400005, India

We study the temporal autocorrelations of height fluctuations in clusters growing radially in a plane. The surface of thecluster in this geometry is qualitatively different from that in the cylindrical geometry in that the surface width does notsaturate. For the Edwards-Wilkinson surface, we calculate the auto-correlation function C(t, t′) =< δr(θ, t)δr(θ, t′) >analytically, where δr(θ, t) is the fluctuation in the radial distance of the surface in the direction θ at time t, andsee that for t′ finite, t → ∞, C(t, t′) tends to a non-zero value. The normalized stochastic process δr(θ,t)√

<δr2(θ,t)>is

gaussian, whose correlation function C(t, t′) depends only on the ratio t/t′ for t, t′ À 1. Making a change of variableT = log t, this becomes a gaussian stationary process. The correlation function of this process decays exponentiallywith |T − T ′|. We determine the persistence exponent θ numerically, and also analytically approximately by using aperturbation theory about the gaussian Markovian process. We also argue, using some approximate phenomenologicalarguments, that these features persist even in the nonlinear case, as in the Kardar- Parisi- Zhang equation. This is ingood agreement with our simulations of growing Eden clusters in two dimensions.




Studying Infrequent Processes by Transition Interface Sampling

Titus Sebastiaan van Erp1

1 Laboratoire de physique/Centre Europeen de Calcul Atomique et Moleculaire (CECAM), Ecole Normale Superieurede Lyon (ENS-Lyon), Lyon, France

Many processes are dominated by infrequent transitions making them inaccessible for straight-forward MolecularDynamics (MD). As the timestep in a MD simulation is limited by the molecular vibration, it can take literally ages toobserve one single event. The standard approach to break this timescale problem is to use transition state theory andto determine a transmission coefficient. However, these methods fail to calculate reaction rates for high dimensionalcomplex systems that are not easily described by a single one-dimensional reaction coordinate. Typical examples arechemical reactions in solution, protein folding, or DNA denaturation. The transition path sampling (TPS) methodgenerates reactive pathways by a Monte Carlo (MC) scheme without the necessity of a reaction coordinate. Thismethod has shown to be very successful in various applications, but is, unfortunately, rather computer time consuming.The recently introduced transition interface sampling (TIS) technique, based on the measurement of effective fluxesthrough hypersurfaces in phase space, improves the TPS method considerably. After introducing the method, I willshow some possible extensions and applications of TIS, such as the denaturation of DNA in the Peyrard-Bishop modelthat is now being studied.

1 [email protected]


The Depletion Zone in Low-Dimensional Photobleaching TrappingReactions

Haim Taitelbaum1

1 Department of Physics, Bar-Ilan University, Ramat-Gan 52900, ISRAEL

The anomalous kinetics of the depletion zone around a single trap in low dimensions has been studied recently ina series of photobleaching trapping reactions in low-dimensional geometries produced by Hele-Shaw cells and flatcapillaries. The experimental results confirm earlier theoretical predictions for universal and nonuniversal kineticbehavior of the depletion zone. New segregation charactersitcs are revealed. In this talk we review the theoreticalresults and compare the predictions with the new experimental data. References: 1. Dynamics of the DepletionZone at a Finite-Sized Imperfect Trap in Two Dimensions: Photobleaching Experiments and Simulations H. Peng,S.H. Park, P. Argyrakis, H. Taitelbaum and R. Kopelman Phys. Rev. E 68, 061102 (2003). 2. Anomalous Growthof the Depletion Zone in the Photobleaching Trapping Reaction S.H. Park, H. Peng, R. Kopelman, P. Argyrakis andH. Taitelbaum Phys. Rev. E 67, 060103 (R) (2003). 3. Spatially and Temporally Resolved Studies of ConvectionlessPhotobleaching Kinetics: Line Trap S.H. Park, H. Peng, S. Parus, H. Taitelbaum and R. Kopelman J. Phys. Chem.A, 106, 7586 (2002). 4. Kinetics and Segregation at a Single Trap H. Taitelbaum and Z. Koza J. Mol. Liq. 86,305 (2000). 5. Nearest Neighbor Distances at an Imperfect Trap in Two Dimensions H. Taitelbaum Phys. Rev. A,43, 6592 (1991). 6. Statistical Properties of Nearest Neighbor Distances at an Imperfect Trap H. Taitelbaum, R.Kopelman, G.H. Weiss and S. Havlin Phys. Rev. A, 41, 3116 (1990).

1 [email protected]



Dislocation Formation in Phase-Separating Alloys

Minami Akihiko1 and Akira Onuki2

1,2 Department of Physics, Kyoto University, Kyoto 606, Japan

Proliferation of edge dislocations occurs around two-phase boundaries in deeply quenched binary alloys. The dynamicsis studied numerically using a nonlinear strain theory in which the elastic energy is a periodic function of the shear andtetragonal strains (a 2D or 3D generalization of the Frenkel-Kontrova model). We find that the dislocations appearin dipoles or quadrapoles near the interface and preferentially glide into the softer regions with smaller shear moduli.The multiple slips thus created result in coherency loss. We also study domain growth in the presence of dislocationsand mechanical response of the two-phase states against applied stress. Particularly, plastic flow in two-phase statesexhibits unique features. These effects are important in technology, but have rarely been studied theoretically.

1 minami [email protected] [email protected]


Patterns in Melting Snow and Vapour Deposited Layers

Ravi Mehrotra1 and Deepak Kumar2

1 National Physical Laboratory, K.S. Krishnan Marg, New Delhi-110012, India2 School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India.

We report an observation of a natural periodic pattern which occurs in the melting of snow lying on the groundunder certain atmospheric conditions. We explain this phenomenon by considering heat flow through this layer whichis coexistent in two phases ( snow and water). We develop a two-dimensional model involving two fields, that oftemperature and density. Our equations lead to quantitative understanding of the pattern observed, and also exhibita range of patterns depending on the average density. This range of patterns is strikingly similar to those observedin deposition of monolayers of Pb on heated PbCu substrates. We argue that the physics of the two phenomenon tobe similar. To our knowledge, this system is a unique one, in affording the study of a variety of patterns and theirrelative competition by variation of a controllable parameter.




Fast Crack Growth by Surface Diffusion

Robert Spatschek1 and Efim Brener2

1,2 Institut fuer Festkoerperforschung, Forschungszentrum Juelich, 52425 Juelich, Germany

Fracture is an intriguing irreversible phenomenon that plays an important role in our day-to-day-life. Crack propa-gation is responsible for the vast field of material failure but is also an interesting subject of physical research. Inparticular, it exhibits several peculiarities for higher propagation velocities. Here we present a continuum theory whichdescribes the fast growth of a crack by surface diffusion. By introducing a fully dynamical theory of elasticity, it ispossible to produce a self-consistent selection of the crack tip radius. This theory describes the complicated dynamicsof a crack tip, the saturation of the steady state velocity appreciably below the Rayleigh speed, and the blunting ofthe crack tip. Furthermore, it includes the possibility of a tip splitting instability for high applied tensions.



From Eden to Invasion: Field Induced Domain Growth inRandom-Field Ising Model

Ratnadeep Roy1 and Purusattam Ray2

1,2 The Institute of Mathematical Sciences, Taramani, Chennai - 600 113

We show that the zero temperature Glauber spin updating dynamics in the hysteretic response of a random-fieldIsing model is analogous, for bounded distributions of random fields, to the growth rules of a Eden model. In twodimensions, we show that for a uniform distribution of width ∆ of the random fields, the spin flip process interpolatescontinuously from a compact cluster (of flipped spins) growth at small values of ∆ (corresponding to a sharp firstorder magnetization reversal transition) to the cluster growth with trapped regions of strongly pinned unflipped spinsfor intermediate values of ∆ and finally to invasion growth at a critical value of ∆ = ∆c. ∆c marks the transitionfrom a system spanning cluster growth at a critical field for ∆ < ∆c to finite clusters growth with increasing field for∆ ≥ ∆c. We study the avalanche size distribution at ∆c.



4.4.10 Friday 9 July, 11:30 - 11:45, Hall AB

On the geometry of 2D networks patterns: soap froths, fractures and lefvenation

Steffen Bohn1 and Yves Couder2

1 Rockefeller University, 1230 York Avenue, New York, N.Y.100 21, USA2 Laboratoire de Physique Statistique, 24 Rue Lhomond, 75231 Paris cedex 05, France

A partition of a two-dimensional space into separate domains results from many physical phenomena. We will comparethree systems: two dimensional soap froths, fractures and the venation of plant leaves. The morphologies of thesethree systems will be characterised and their differences discussed. The main issue here will be the relation of thestructure with its history. Soap froths constantly reorganise so that their structure at a given time is not hierarchical.The resulting structure is formed of cells, which are, on the average, hexagonal as expected by the topology theoremdue to Euler. In contrast, the fractures observed in e.g. the glaze of a ceramics divide the space into domains, which,on the average, are quadrangles. We will show that this does not violate Eulers theorem and results from the hierarchyof fractures. They form successively, each one breaking an existing domain, and having no influence on the fracturesformed previously. We will discuss the leaf venation and its formation and show that it is an intermediate betweenthese two types of patterns as it has a strong hierarchy but allows for some reorganisation.



Anomalous impact of elastic materials

Kuninaka Hiroto1 and Hayakawa Hisao2

1 Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, JAPAN2 Department of Physics, Yoshida-South Campus, Kyoto University, Kyoto 606-8501, Japan

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional latticemodel for an elastic disk and an elastic wall, we demonstrate that the coefficient can exceed unity and have a peakagainst the incident angle. Finally we explain its mechanism based on a phenomenological theory of elasticity. Thepaper is based on H. Kuninaka and H. Hayakawa, cond-mat/0310058.




Statistical mechanics of jammed matter

Hernan A. Makse1,Chaoming Song2 and Ping Wang3

1,2,3Levich Institute and Physics Department, City College of New York, New York, USA

Jamming refers to a state which emerges when a many-body system is blocked in a static configuration far fromequilibrium. It has been postulated that the behavior of systems experiencing such a structural arrest can be describedby a statistical ensemble at a fixed total volume such that all microscopic jammed states are equally probable andbecome accessible to one another (the ergodic hypothesis) by the application of tapping or shear, just as thermalsystems explore their energy landscape through Brownian motion. Here we combine computational simulations andexperiments to explore this unifying thermodynamic framework. In particular we present recent results for jammedgranular materials and colloidal systems which support the thermodynamic approach by showing the existence of aneffective temperature to describe jammed matter.

[email protected] [email protected] [email protected]


Spatiotemporal Rheological Chaos in a Sheared Nematogenic Fluid

Buddhapriya Chakrabarti1, Moumita Das2, Chandan Dasgupta3, Sriram Ramaswamy4, and AjayK. Sood5

1 Department of Physics, University of Massachusetts, Amherst, MA 010032,3,4,5 Department of Physics, Indian Institute of Science, Bangalore 560012

Motivated by recent observations of rheochaos in sheared wormlike micelles, we study numerically the equations ofthe traceless symmetric order parameter for a sheared nematogenic system, measuring the alignment of the micellarworms, allowing for spatial variation. In a suitable parameter range where flow alignment does not occur, we findirregular, dynamic shear-banding and establish by decisive numerical tests that the chaos we observe in the model isspatiotemporal in nature. It is further seen that the system has a rich dynamical phase diagram, including a varietyof routes to chaos.




Steady states and pattern formation in vibrated granular materials

V. Kumaran1

1 Department of Chemical Engineering, Indian Institute of Science, Bangalore-12

The steady state density and temperature profiles for a vibrated granular material are determined as a function of therelative magnitudes of two length scales — the ‘density decay length’ (T0/g), and the ‘conduction’ length λ/(1−e)1/2.Here, T0 is the mean square velocity, e is the coefficient of restitution, and λ is the mean free path. It is found thatthe ratio of these lengths depends only on the number of monolayers at rest, and is independent of the driving. For(T0/g) ¿ λ/(1 − e)1/2, the system resembles a gas of elastic particles at equilibrium and the temperature is nearlya constant. The steady state, which is homogeneous in the horizontal direction, is found to be stable in this case.For (T0/g) À λ/(1 − e)1/2, there is a sharp decrease in temperature with height near the bottom. The steady stateis found to be unstable to perturbations, and the mechanism is similar to the Rayleigh-Taylor instability for fluidsheated from below. Simulation results are presented for the convection rolls that form after transition. Simulationsalso predict a ‘clustering’ instability in the limit of low density, which does not have an analogue in hydrodynamicstability theory.

1 [email protected]



4.5.1 Monday 5 July, 12:00 - 12:15, Hall AB

Multifractality in the Stochastically Forced Burgers Equation

Dhrubaditya Mitra 1, Jeremie Bec 2, Rahul Pandit3 and Uriel Frisch4

1,3 Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012,India

2,4 Dipartimento di Fisica, Universita La Sapienza, P.zzle Aldo Moro 2, 00185 Roma, Italy.4 Departement Cassiopee, Observatoire de la Cote d’Azur, BP4229, 06304 Nice Cedex 4, France

We revisit the problem of turbulence in the one-dimensional Burgers equation with a white-in-time, zero-mean, Gaus-sian random force that has a Fourier-space spectrum ∼ 1/k, where k is the wave number. Earlier numerical studies [1,2]indicate that this system displays a nonequilibrium statistical steady state in which order-p velocity u structure func-tions, Sp(`) ≡ 〈|u(x + `) − u(x)|p〉 ∼ `ζp show bifractal scaling;¿ ¿ i.e., the exponents ζp = p/3 for p ≤ 1, whichfollows from dimensional analysis; and ζp = 1 for p ≥ 3, the shock-dominated value. By using a very-high-resolutionnumerical simulation of the Burgers equation (two orders of magnitude better than earlier studies [1,2]) in the limitof vanishing viscosity, we have found strong evidence for multifractality of Sp(`), with substantial deviations from thesimple bifractal scaling described above. We also discuss possible artefacts that can make bifractal scaling appear likenontrivial multiscaling. Our study may cast new light on multiscaling in fluid turbulence, since the Burgers equationwe consider is perhaps the simplest nonlinear partial differential equation that has the potential to show such multi-scaling; and it can be studied much more carefully than the Navier-Stokes equation. References:[1] A. Cheklov and V. Yakhot, Phys. Rev. E 52, 5681 (1995).[2] F. Hayot and C. Jayaprakash, Phys. Rev. E, 56, 227 (1997); ibid, 4259 (1997).




Transport of passive scalars by three-dimensional chaotic flows

Jaan Kalda1

1 Institute of Cybernetics,Tallinn Technical University, Akadeemia tee 21, 12618 Tallinn, Estonia.

The chaotic transport of passive scalars is studied for three-dimensional smooth flows without coherent structures.The problem of the probability density function (PDF) of the tracer gradient reduces to the problem of the PDF of thestretching coefficients of infinitesimal fluid membranes. While the tracer gradients depend only on the stretching of themembrane surface area, the spatial pattern of the tracer field depends also on the stretching of the membrane width.Both stretching coefficients are described by a PDF, which evolves according to a simple one-dimensional convective-diffusive equation (in the case of the membrane height, the convective term is absent). The uneven stretching of thefluid membranes can be shown to lead (i) to multifractal tracer dissipation field, and (ii) to a power-law distributionof the tracer blobs. While the multifractality of the dissipation field is a well-known phenomenon which has beenaddressed both experimentally and (in the case of two-dimensional geometry) analytically, the power-law of the tracerblob distribution is a novel aspect. Finally, we discuss the relevance of the model of chaotic passive scalar transport tothe problem of intensity-distribution of speckles, created by waves propagating in continuously inhomogeneous media.

1 [email protected]


Statistical properties of driven Magnetohydrodynamic turbulence inthree dimensions

Abhik Basu1

1 Poornaprajna Institute of Scientific Research, Bangalore, India

We analyse the universal properties of nonequilibrium steady states of driven Magnetohydrodynamic (MHD) tur-bulence in three dimensions. We elucidate the dependence of various phenomenologically important dimensionlessconstants on the symmetries of the two-point correlation functions. We also explicitly calculate the multiscalingexponents of the even order magnetic field structure functions in the inertial range in the passive vector limit. Weuse renormalization group and operator product expansion techniques for our work. In one particular case, we findthat the multiscaling exponents vary continuously with the magnetic Prandtl number, and hence with the degree ofcrosscorrelations between the velocity and the magnetic fields. Our results suggest that the multiscaling universalityclass for MHD turbulence vary continuously with the degree of crosscorrelations between the velocity and the magneticfields. The experimental and theoretical implications of our results are discussed.

1 [email protected]


4.5.4 Tuesday 6 July, 11:30 - 11:45, Hall F

Power Laws, Precursors and Predictability During Failure

Rumi De1 and G. Ananthakrishna2

1 Materials Research Centre, Indian Institute of Science, Bangalore, India.2 Materials Research Centre, Indian Institute of Science, Bangalore, India. and Centre for Condensed Matter

Theory, IISc, Bangalore, India.

The impossibility of prediction of individual avalanches in power law state is a well known puzzle. This has triggeredconsiderable debate regarding earthquake predictability as seismically active faults systems are considered to be ina SOC state. However there are reports of enhanced precursory effects in earthquakes and related experiments onacoustic emission (AE) prior to failure. We address this question within the context of an extended Burridge-Knopoffmodel for earthquakes that includes a dissipative term which models the mechanism of AE. Apart from the fact thatthe amplitude of the energy dissipated follows a power law, interestingly, we find a precursor effect in the cumulativeenergy dissipated which allows for identification of large slip events. Further, we find a data collapse of the dissipatedenergy for several large slip events describable by a universal stretched exponential behavior with corrections in termsof time-to-failure. The model also explains many features of the statistics of AE signals observed in experiments suchas the crossover in the exponent value from a relatively small to larger amplitude regime (which has a parallel inearthquake magnitudes also), and their dependence on the pulling speed. The intervals between successive AE burstsand their duration also obey power laws consistent with recent experiments. Our results show that the SOC state, initself, does not preclude predictability.



Synchronization by Nonlinear Frequency Pulling

M. C. Cross1, A. Zumdieck2, Ron Lifshitz3 and J. L. Rogers4

1 Department of Physics 114-36, California Institute of Technology, Pasadena, California 911252 Max Planck Institute for Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden, Germany

3 School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel4 HRL, 3011 Malibu Canyon Road, Malibu, California 90265

We investigate a model for the synchronization of driven nonlinear oscillators with a distribution of natural frequencieswhere the synchronization arises from reactive coupling and nonlinear frequency pulling. We study the model for themean field case of all-to-all coupling, deriving results for the onset of synchronization from the unsynchronized stateas the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state in whichall the oscillators evolve with the same frequency. The model is motivated by the physics of arrays of nanomechanicalor micromechanical resonators.




Turbulent viscosity in Rayleigh-Benard convection

Hiroshi Shibata1

1 Department of General Education, Sojo University, Ikeda 4-22-1, Kumamoto 860-0082, Japan

The turbulent viscosity in the Rayleigh-Benard convection is studied on the basis of the theory for the molecularviscosity. The turbulent viscosity is calculated by the time integral of the two-time correlation function for themomentum flux. We find that the two-time correlation function for the momentum flux converges in a regime anddiverges at the transition point from soft turbulence to hard turbulence. This means that the viscosity coefficient ofthe turbulent viscosity diverges at the transition point. In addition, we propose the modification of the Navier-Stokesequation so that the viscosity coefficient satisfies the viscosity equation in order to explain the turbulent phenomenain the global scales.Refence [1]H.Shibata, Momentum flux in Rayleigh-Benard convection, Physica A 333C(2004)71-86.

1 [email protected]

4.5.7 Tuesday 6 July, 12:15- 12:30, Hall F

Instability of decelerating pipe flow

Kirti Chandra Sahu1 and Rama Govindarajan2

1,2 Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore560064

The laminar flow through a pipe is linearly stable for any Reynolds number, and it is well accepted that the transitionfrom laminar to turbulent flow is triggered by a nonlinear instability mechanism. The complete route to turbulence isstill a matter for debate, but it seems clear now that the spectrum of linear (stable) modes has some role to play viatransient algebraic growth of disturbances. Since the linear stability is described by a singular perturbation problem,a small deceleration/acceleration of the flow could have a large effect on the stability: this is known in boundarylayers and in channel flow. We use this idea to show here that a small local divergence in a pipe (even as low as 1degree) can cause linear modes to become unstable at surprisingly low Reynolds numbers. These results throw lighton the relative role of linear and nonlinear mechanisms in triggering transition to turbulence. The flow is computedby a multigrid Poisson solver, coupled with time marching for the vorticity. An extended eigenvalue problem for thestability of the spatially developing flow is solved.




Nonlinear dynamical systems with parametric modulation

Ramakrishna Ramaswamy1

1 School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067

Parametric modulation leads to a variety of novel bifurcations and dynamics in nonlinear dynamical systems.Quasiperiodic forcing gives rise to strange nonchaotic attractors, while with periodic modulation phenomena suchas bistability can arise from the creation of multiple coexisting attractors. Dynamical systems with feedback modula-tion exhibit enhanced stability: this is a novel method for chaos control. We study nonlinear mappings with parametricmodulation of several forms including periodic and quasiperiodic forcing, as well as pulsed dynamical systems. Thedifferent attractors and dynamical regimes are described. The synchronization properties of a coupled (nonlinear)map lattice under modulation are discussed with specific reference to strange nonchaotic dynamics. We show thatquasiperiodic forcing gives rise to an extended regime of synchronization when the basin of the synchronized attractorundergoes an abrupt expansion.

1 [email protected]


Kinetic theory of Turbulence: A Microscopic Derivation of SubgridModel

Santosh Ansumali1, Iliya V Karlin2 and Sauro Succi 3

1 Department of Energy Technology, ETH Zurich (Switzerland)2 Department of Materials, ETH, Zurich (Switzerland)

3 Istituto Applicazioni Calcolo, Roma Italy

The derivation of a tractable sub-grid scale hydrodynamic model from the Navier-Stokes equation is known to be adifficult challenge. In the present work, an alternate mean-field approach to derive sub-grid turbulence model from theBoltzmann equation will be presented. It will be demonstrated that the so called Smagorinsky type tensor-diffusivitymodel is the unique answer from such approach. A scaling of the coarse-graining length with the Reynolds numberwill be established. The physical meaning of this characteristic length will be explained.



4.5.10 Thursday 8 July, 11:15 - 11:30, Hall F

Statistics of unstable periodic orbits of a chaotic dynamical system witha large number of degrees of freedom

Mitsuhiro Kawasaki1 and Shin-ichi Sasa2

1Department of Materials and Science and Technology, Niigata University, Niigata 950-2181, Japan2Department of Pure and Applied Sciences, University of Tokyo, Tokyo 153-8902

Theoretical analyses for different kinds of dynamical systems with large degrees of freedom often fail with the samedifficulties, i.e., nonlinearity and a large number of degrees of freedom included in development equations of thesystems. In contrast, equilibrium statistical mechanics can succeed to overcome the difficulties and analyze macroscopicproperties of substances at equilibrium, which are in general dynamical systems with large degrees of freedom. Thereason for success is that analyses of nonlinear development equations can be skipped because only macroscopicproperties are of interests. In order to analyze the macroscopic properties, only an ensemble of states is requiredand the probability distribution to formulated the ensemble is not needed to be an accurate one, i.e., the naturalinvariant measure. It suggests that an ensemble formulated with an appropriate probability distribution can be apowerful tool to analyze theoretically dynamical systems with large degrees of freedom. An ensemlbe of unstableperiodic orbits (UPO) for a simple dynamical system with large degrees of freedom, a coupled map lattice (CML),is shown to be easily constructed by a Monte-Carlo simulation with the Metropolis method and expectation valuesof macroscopic quantities of the CML can be obtained from only one of almost any elements of the ensemble. Thismeans that te ensemble can be used as a statistical mechanical ensemlbe for the dynamical systems with large degreesof freedom. The result also provides one of possible understandings of a reason for success of UPO representation forsome turbulences (G. Kawahara and S. Kida, J. Fluid Mech. 449, 291 (2001); S. Kato and M. Yamada, Phys. Rev.E 68, 025302(R) (2003)).

[email protected]@jiro.c.u-tokyo.ac.jp


The Varieties of Dynamic Multiscaling in Turbulence

Dhrubaditya Mitra1 and Rahul Pandit 2

1,2 Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012,India

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to differentdynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponentsby different classes of bridge relations which we derive. We check this explicitly by detailed numerical simulations ofthe GOY shell model for fluid turbulence. Our results can be generalized to any system in which both equal-time andtime-dependent structure functions show multiscaling. We also discuss dynamic multiscaling effects in passive scalarturbulence.




Aging in Sub-Diffusion Generated by a Deterministic Dynamical System

Eli BArkai1 and Cheng Yuan-Chung2

1 251 Nieuwland Science Hall,University of Notre Dame, Notre Dame, IN 46556-5670, USA2 Massachusetts Institute of Technology,

77 Massachusetts Ave. Rm 6-230Cambridge MA 02139 USA

We investigate [1] aging behavior in a simple dynamical system: the Geisel–Thomae non-linear map. In the non agingregime this map is known to generates sub-diffusion deterministically. We show that the map exhibits aging behaviorwhen proper initial conditions are choosen. Asymptotic behaviors of the aging diffusion process are described usingthe stochastic framework of aging continuous time random walks [2]. We show numerically, how the deterministicaging process is described by an aging diffusion equation which is of fractional order. Our work demonstrates thataging behavior can be found in deterministic low dimensional dynamical systems. Interestingly, the aging behaviorwe obtain is similar to aging behavior found for random walks in random environments. [1.] E. Barkai Aging inSubdiffusion Generated by a Deterministic Dynamical System Phys. Rev. Lett. 90 104101 (2003). [2.] E. Barkai,Y. C. Cheng Aging Continuous Time Random Walks J. of Chemical Physics 118 6167 (2003).



Stabilization and destabilization of the synchronized state in coupleddynamical systems by varying coupling strengths

Govindan Rangarajan1, Yonghong Chen2 and Mingzhou Ding3

1 Department of Mathematics, Indian Institute of Science, Bangalore, India2,3 Centre for Complex Systems, Florida Atlantic University, Boca Raton, USA

In arbitrarily coupled dynamical systems (maps or ordinary differential equations), we consider the stability of syn-chronized states (including equilibrium point, periodic orbit or chaotic attractor) and pattern formation from loss ofstability of the synchronization. The eigenvalues of the coupling matrix determine the stability of the synchronizedstate, while the eigenvectors correspond to patterns emerging from desynchronization. Based on the stability re-gion/master stability function, we develop general approaches that yield constraints directly on the coupling strengthswhich ensure the stability of synchronized dynamics. We show how we can excite spatial patterns selectively by vary-ing the coupling strengths. We can also obtain interesting temporal evolution of the spatial pattern by choosing thestarting synchronized state appropriately. Conversely, given a desired spatiotemporal pattern, we are able to designcoupling schemes which give rise to that pattern as the coupled system evolves. Systems with specific coupling schemesare used as examples to illustrate our general methods.





Solid-fluid transition in a granular shear flow

Ashish V. Orpe1 and D. V. Khakhar2

1,2 Department of Chemical Engineering, Indian Institute of Technology - Bombay, Powai, Mumbai 400076, India

The rheology of a granular shear flow is studied in a quasi-2d rotating cylinder. Measurements are carried out nearthe midpoint along the length of the surface flowing layer where the flow is steady and non-accelerating. Streaklinephotography and image analysis are used to obtain particle velocities and positions. Different particle sizes androtational speeds are considered. We find a sharp transition in the apparent viscosity (η) variation with rms velocity(u). In the fluid-like region above the depth corresponding to the transition point (higher rms velocities) there isa rapid increase in viscosity with decreasing rms velocity. Below the transition depth we find η ∝ u−1.5 for all thedifferent cases studied and the material approaches an amorphous solid-like state deep in the layer. The velocitydistribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer.The observed transition appears to be analogous to a glass transition.



Space filling bearings in three dimensions

Hans Herrmann1 and Reza Mahmoodi-Baram2

1,2 Institute for Computer Applications 1, University of Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany

The existence of space filling bearings and the classification of all self-similar configurations with finite sized loopswas achieved 15 years ago. We will show the existence of such bearings in three-dimensions and prove that they rollwithout slip and that the points with twist lie on a set of measure zero. Also non-selfsimilar bearings will be discussed.The spontaneous appearance of bearings in monodisperse packings is shown numerically and implications on tectonicplate motion are discussed.




Simulation and theory of vibrational phase relaxation in the critical andsupercritical nitrogen: Origin of observed anomalies

Swapan Roychowdhury1 and Biman Bagchi2

1,2Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore - 560012, India

Vibrational phase relaxation of molecules near the gas-liquid critical point shows several highly interesting anomalousbehavior. We present results of extensive computer simulations and theoretical analysis of vibrational phase relaxationof a nitrogen molecule along the critical isochore and also along the gas-liquid coexistence. Dephasing time (τv ) andthe root mean square frequency fluctuation (∆) in the supercritical region are calculated. The principal importantresults are: (a) a crossover from a Lorentzian-type to a Gaussian line shape is observed as the critical point isapproached along the isochore (from above), (b) the root mean square frequency fluctuation shows non-monotonicdependence on the temperature along critical isochore and (c) along the coexistence line and the critical isochore thetemperature dependent linewidth shows a divergence-like λ-shape behavior. The origin of the anomalous temperaturedependence of linewidth can be traced to simultaneous occurrence of several factors, (i) the enhancement of negativecross-correlations between density and vibration-rotation (VR) contributions and (ii) the large density fluctuations asthe critical point (CP) is approached. The former makes the decay faster so that local density fluctuations are probedon a femtosecond time scale. A mode coupling theory (MCT) analysis shows the slow decay of the enhanced densityfluctuations near critical point. The MCT analysis demonstrates that the large enhancement of VR coupling near CParises from the non-Gaussian behavior of density fluctuation and this enters through a nonzero value of the tripletdirect correlation function.

[email protected]@sscu.iisc.ernet.in


Dynamics of drag and force distributions for projectile impact in agranular medium

Massimo Pica Ciamarra1,Antonio H. Lara2,Andrew T. Lee3,Daniel I. Goldman4 and Harry L.Swinney5

1Univerista’ di Napoli Federico II, Dipartimento di Scienze Fisiche, Complesso Universitario di M.S.A. Via Cintia,80126, Napoli, Italy

2,3,4,5Center for Nonlinear Dynamics, University of Texas at Austin, Austin, Texas, 78712

Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular mediumreveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, thetime taken for a projectile to decelerate to a stop is independent of its impact velocity. The simulations show thatthe probability distribution function of forces on grains is time-independent during a projectile’s penetration of themedium. At all times the force distribution function decreases exponentially for large forces.




Computer simulation of the phase diagram of water

Jose L. F. Abascal1, Eduardo Sanz2, Luis G. MacDowell3 and Carlos Vega4

1,2,3,4 Depto. Quimica-Fisica I, Univ. Complutense de Madrid

The phase diagram of water as obtained from computer simulations is presented by the first time for two of themost popular models of water, TIP4P and SPC/E. This work shows that the prediction of the phase diagram is anextremely stringent test for any water potential function, and that it may be useful in developing improved potentials.The TIP4P model provides a qualitatively correct description of the phase diagram, unlike the SPC/E model whichfails in this purpose. New behavior not yet observed experimentally is predicted by the simulations: the existence ofmetastable re-entrant behavior in the melting curves of the low density ices (I,III,V) such that it could be possible totransform them into amorphous phases by adequate changes in pressure.



Response of a Hexagonal Granular Packing under Localized ExternalForce

Debrabrata Panja1, Srdjan Ostojic2 and Bernard Nienhuis3

1,2,3 Institute for Theoretical Physics, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, TheNetherlands

In this work, we consider a theoretical statistical model of hexagonal close packing of hard spheres in two spatialdimensions. The problem is experimentally motivated: the experimental results demonstrate that when a downwardvertical external force is applied on such a granular packing, the vertical force per grain in any given layer hastwo peaks. These peaks lie on the two diverging lattice directions emanating from the point of application of thevertical force. Our model uses the microcanonical ensemble hypothesis for all possible force configurations in thepacking, and it yields symmetric double-peaked response just as one finds in the experiments. For massless grains,the peaks penetrate all the way to the bottom of the packing in the thermodynamic limit. For grains each of massm, the penetration depth of the peaks increases with F/mg, and the results for massless grains are approached forF/mg →∞. The responses of different system sizes also exhibit self-similarity. The results are robust under varyingboundary conditions, and the case for massless grains is theoretically exactly solvable.

Reference: D. Panja and S. Ostojic, e-print archive cond-mat/0403321, submitted to Phys. Rev. Lett.

[email protected]



Fluctuation and Response for a Granular Fluid

Aparna Baskaran1, James W. Dufty2 and J. Javier Brey3

1,2 Department of Physics, University of Florida, Gainesville, FL 32611, USA3 Fisica Teorica, Universidad de Sevilla, E-41080 Sevilla, Spain

A statistical mechanics for granular fluids is considered using a system of smooth, inelastic hard spheres. The linearresponse to initial and boundary perturbations, and to external forces is described from both the Liouville equationand the low density Boltzmann equation. The response functions for each type of perturbation are identified anddiscussed. Onsagers assumption on the regression of fluctuations is reformulated for granular fluids and the concept offluctuation dissipation relations is discussed. A specific example is provided for the mobility and diffusion of a taggedparticle[1]. [1] J. Dufty and V. Garzo, J. Stat. Phys. 105, 723-744 (2001).



Fragility of liquids or fragility of glasses?

Tullio Scopigno1

1 INFM Researcher, Physics Department - University of Roma 1, 00185 Rome - Italy

One of the most intriguing tasks of the physics of glasses is the understanding of how the interactions between theelemental constituents determine the phenomenology of the liquid-glass transition [1]. Approaching this transitionfrom the liquid side, different systems show qualitatively different temperature dependencies of the viscous flow.Accordingly, they have been classified by the useful concept of ”kinetic fragility” [1]: the more ”fragile” is a liquidthe faster is the change in its viscosity when approaching the glass transition temperature (Tg). We report here anew experimental observation relating the microscopic properties of the glassy phase to the kinetic fragility: we findthat the vibrational properties in the glass away from Tg are correlated to the viscous flow in the liquid approachingTg [2]. More specifically, we observe that in a number of glass forming systems the steepness of the non ergodicityfactor on approaching the T → 0 limit stands in a fashion similar to the Angell plot and, therefore, can be used topredict the kinetic fragility of the corresponding liquid. Consequently, we extend the fragility concept to the glassystate and indicate how to determine the fragility uniquely from glass properties far away Tg. Translated into the thelanguage of the Potential Energy Landscape, this finding establishes a correlation between the inter-basin dynam-ics of the supercooled liquid, and the dynamics proceeding within a single inherent structure visited in the glassy phase.

References:[1] L.-M. Martinez and C.A. Angell. Nature 410, 663-667 (2001).[2] T. Scopigno, G. Ruocco, F. Sette, and G. Monaco, Science 302, 849-852 (2003).

1 [email protected]



Bending and Buckling waves of Thin Granular Layer

Akiko Ugawa1 and Osamu Sano2

1,2 Dept. of Applied Physics, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan

An experimental study of the pattern formation is made on the granular layer of thickness h induced by verticalvibration with frequency f and amplitude a under atmospheric pressure. We used sesame of oval shape as well asdifferent sizes of spherical glass, lead, and steal particles. Irrespective of container size L, quasi-two dimensional waves,“ripples” are observed in a thin layer which consists of particles of spherical shape for relatively small accelerationof external forcing. “Undulations”, one of the global motion, depending on the system size are observed in a thickerlayer, which consists of sesame as well as spherical particles, for larger acceleration. Typical eigen modes are examined.The behavior of “undulations” seems to be explained by continuum theory on the bending wave of an elastic plate,irrespective of the material of the layer.

1 [email protected]


Intermediate range order and transport processes in multicomponentmelts: Computer simulation studies

Juergen Horbach1,Subir Kumar Das2,Hans Knoth3 and Kurt Binder4

1,2,3,4Institut fur Physik, Staudinger Weg 7, Johannes Gutenberg–Universitat, D–55099 Mainz, Germany

We use molecular dynamics (MD) computer simulations to investigate the atomic transport in multicomponent metallicand oxide melts. The detailed behavior as obtained by MD allows to elucidate the interplay between structure,dynamics, and phase behavior of liquid mixtures. We present simulation results for realistic models of ion-conductingalkali silicate melts and amorphous Al–Ni alloys with a glassy dynamics. These systems exhibit intermediate rangeorder that is reflected by prepeaks in static structure factors. In Al–rich Al–Ni melts a prepeak is found due to aninhomogeneous distribution of Ni atoms. This intermediate structure affects for instance the wavenumber dependenceof relaxation times. The intermediate range order in alkali silicates provides the presence of diffusion channels forthe fast ionic motion. The interplay of the latter channel structure with non-trivial transport phenomena such as themixed alkali effect is demonstrated. Moreover, we discuss the dynamics of the considered systems in the framework ofthe mode coupling theory of the glass transition.

[email protected]@uni-mainz.de



Effects of a metastable liquid-liquid critical point on the crystalnucleation

Giancarlo Franzese1, Sergey V. Buldyrev2 and H. Eugene Stanley3

1 Departament de Fisica Fonamental, Universitat de Barcelona, Barcelona, Spain2,3 Center for Polymer Studies and Physics Department, Boston University, Boston, MA

A metastable gas-liquid critical point enhances the crystal nucleation [1] in systems with short-range attraction,such as colloids or protein solutions with depletion [2]. For effective attractive interaction potentials, with soft-corerepulsion, simulations and theories predict [3] a liquid-liquid (LL) phase transition, as in experiments for phosphorous[4], and a LL critical point. For short-range attraction the LL critical point is metastable and we find that it affectsthe nucleation rate in a non-trivial way, showing two minima corresponding to two different temperatures and twodifferent nucleation mechanisms. This result could be relevant in systems such as star-polymers, protein solutions,DNA-coated colloids [5] or, to some extent, liquid metals. [1] P. Rein ten Wolde, and D. Frenkel, Science 277, 1975(1997); M. H. J. Hagen et al. Nature 365, 425 (1993). [2] S. Sanyal, N. Easwar, S. Ramaswamy, and A. K. Sood,Europhys. Lett. 18, 107 (1992). [3] G. Franzese et al. Nature 409, 692 (2001); Phys. Rev. E 66, 051206 (2002); A.Skibinsky et al. cond-mat/0309632. [4] Y. Katayama et al. Nature 403, 170 (2000); G. Monaco et al. Phys. Rev.Lett. 90, 255701 (2003). [5] D. B. Lukatsky and D. Frenkel, Phys. Rev. Lett. 92, 068302 (2004).



Quantum Effects on Melting

Charusita Chakravarty1

1 Department of Chemistry, Indian Institute of Technology-Delhi, Hauz Khas, New Delhi 110016, India.

Path integral simulations are used to study the changes in melting behaviour of solids as a function of the degreeof quantum delocalisation of the constituent particles. The parameters of the quantum Lennard-Jones system arechosen to provide a reasonable pseudo-atomic model for para-H2 and its isotopomers. Landau free energy curves areused to obtain solid-liquid coexistence conditions as well as to provide a rough estimate of the solid-liquid interfacialfree energy. Thermodynamic and structural properties of the two phases, specially the behaviour of the supercooledliquid, are studied and the results are compared with available experimental data.

References:[1] C. Chakravarty, Phys. Rev. B, 59, 3590 (1999).[2] C. Chakravarty and R. M. Lynden-Bell, J. Chem. Phys. 113, 9239 (2000).[3] C. Chakravarty, J. Chem. Phys., 116, 8938 (2002).[4] S. N. Chakraborty, N. Ghosh, P. Shah and C. Chakravarty (submitted).

1 [email protected]



Effective pair potential description of simple atomic fluids withthree-body interactions

Carlos F. Tejero1

1Departamento de Fisica Aplicada I, Facultad de Ciencias Fisicas, Universidad Complutense de Madrid, E-28040Madrid, Spain

The contribution of three-body interactions in simple atomic fluids is analyzed within an effective pair potentialdescription using Henderson’s theorem. It is shown that a unique state-dependent two-body potential generates boththe structural and thermodynamical properties. Since its analytical construction is unknown one needs to make aprescription for this pair potential. It is proved that, whatever the prescription, there is a unique procedure to obtainthe corresponding pair distribution function and all the thermodynamical properties in a self-consistent way. Thestructure and the thermodynamics resulting from a given prescription of the effective state-dependent pair potentialwould then be compared to simulations in order to assert its validity.

[email protected]


Statistics of power input into a vibrated granular system

Hongqiang Wang1,Klebert Feitosa2 and Narayanan Menon3

1,2,3Department of Physics, University of Massachusetts, Amherst, MA 01003, USA

We report an experimental and numerical study of the fluctuations in power input and energy dissipation in a sub-volume of a dilute systems of vibrated inelastic grains. The power fluctuations are in close accord with the relationregarding fluctuations in entropy production given by the Fluctuation theorem of Gallavotti and Cohen despite thefact that the system is open and the dynamics are not reversible. In making the correspondence between the measuredquantity and the entropy production, a temperature scale is left unspecified. We find that this effective temperaturedetermined from the distribution of power fluctuations is an intensive quantity, and is unchanged when the dissipation,the number density, or system size is changed while adjusting the driving intensity to keep the kinetic granulartemperature fixed.




Statistics of friction fluctuations at the liquid/solid granular phasetransition

Fergal Dalton1, Francis Farrelly2, Alberto Petri3, Luciano Pietronero4, Luca Pitolli5, and GiorgioPontuale6

1,2,3,5,6 IDAC, CNR Tor Vergata, Via del Fosso del Cavaliere 100, 00133 Roma, Italy.4 University of Rome ”La Sapienza”, Physics Department, Piazzale A. Moro 2, 00185 Rome (Italy)

We present results obtained from an experimental device which shears a granular medium in a shear ring geometry,via a torsion spring. Using the device we probe the statistical properties of the liquid/solid (metastable) state for thegranular medium. We investigate the fluctuations in the steady state torque and discuss the appearance, shape andfunctional dependence of its distribution, both for static and dynamic friction. The transition between the metastableand liquid phases is clearly marked by a change in the distribution’s properties; in particular the log-normal curvecharacteristic of a solid-like system changes to Guassian for the fluidised system. Additional results demonstrate avelocity-strengthening friction within a single experiment, which could be utilised to predict the transition point, andfurthermore we demonstrate that the initialisation of the medium can play an important role in the subsequent steadystate.





Polymer-colloid mixtures: the effects of polymer excluded volume

Ard A. Louis1, Peter G. Bolhuis2 and Jean-Pierre Hansen3

1,3 Dept. of Chemistry, Lensfield Road, Cambridge CB2 1HW, UNITED KINGDOM2 Dept. of Chem. Eng., Univ. of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam, NETHERLANDS

Upon addition of a polymer additive, a stable colloidal dispersion can be made to phase separate into a dense anda dilute phase. This problem has important applications in industry and biology (macromolecular crowding), andalso poses a classic multiple length scale problem: Whereas the colloids can easily be viewed as single ”giant atoms”,the polymers are typically modelled by hundreds or even thousands of small constituents, all strung together. Byperforming extensive Monte Carlo simulations on mixtures of self avoiding walks (SAW) and hard spheres, a basicmodel of these systems, we investigate the influence of polymer excluded volume interactions on the phase behaviour.For smaller polymers we solve the multiple length scale problem by a coarse-graining technique[1], and for the longerpolymers we use hyperparallel tempering[2]. The influence of polymer excluded volume interactions becomes increas-ingly important as the ratio of the polymer radius of gyration Rg to colloid radius Rc increases. For the ”proteinlimit”, where Rg/Rc >> 1, large qualitative deviations from ideal-polymer behaviour are observed. [1] P.G. Bolhuis,A.A. Louis, and J.P. Hansen, Phys. Rev. Lett. 89, 128302 (2002) [2] P.G. Bolhuis, E.J. Meijer, and A.A. Louis, Phys.Rev. Lett. 90 , 068304 (2003)




Long-lived Bound Pairs: Direct Evidence for Long-range AttractionBetween Like-Charged Colloids

B.V.R. Tata1, P.S.Mohanty2 and J. Yamanaka3

1,2 Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam - 603102, Tamil Nadu,India3 Faculty of Pharmaceutical Sciences, Nagoya City University, 1-3 Tanabe-dori, Mizuho, Nagoya 467 - 8603, Japan

Confocal laser scanning microscopy studies have been carried out in very dilute (volume fraction ∼ 0.0001) deionisedaqueous colloidal suspensions of highly charged polystyrene particles having a diameter d = 0.6 µm. Time series ofconfocal images recorded far away from the cover-slip clearly showed existence of bound pairs for several seconds.Stable three-particle and four-particle clusters are also observed. This observation is the first of its kind, and providedirect evidence for the existence of counterion mediated long-range attraction in the effective pair-potential U(r)of like-charged colloidal particles, which has been the subject of continuing debate. Pair-correlation function g(r)calculated from the confocal images clearly showed a single peak at an interparticle separation r/d = 1.38 . U(r)extracted from g(r) clearly showed an attractive minimum at r/d = 1.8 having a well depth of ∼ 2.2 kBT . Theseobservations provide unambiguous evidence against volume term theories proposed for describing the gas-liquid andgas-solid phase separation in bulk charged colloidal suspensions.



Mutual attraction of charged nanoparticles at interfaces

Martin Oettel1, Alvaro Dominguez Alvarez2 and Siegfried Dietrich3

1,2,3 Max-Planck-Institute for Metals Research, Heisenbergstr. 3, 70569 Stuttgart, Germany

The experimentally observed long–range attraction between like–charged colloids trapped at fluid interfaces (as re-ported, e.g., in [1]) can be explained by charge–induced capillary interactions. The short–ranged electrostatic stressesexerted by the colloidal particles on the interface lead to long–ranged capillary forces for which the capillary lengthor the finite system size are of crucial importance. This fact has been overlooked in previous treatments [2,3]. Forrealistic values of the characteristic parameters, the interface deformation induced by the charges is small enough toallow for a perturbative description leading to explicit expressions for the capillary interaction.[1] M. G. Nikolaides et al., Nature 420 (2002) 299.[2] M. Megens and J. Aizenberg, Nature 424 (2003) 1014.[3] L. Foret and A. Wurger, cond-mat/0310657.




Effect of quenched disorder on the elasticity of a smectic liquid crystal

Ranjini Bandyopdhyay1, Dennis Liang2, Ralph H. Colby3, James L. Harden4, and Robert L.Leheny5

1,2,5 Department of Physics and Astronomy, Johns Hopkins University, Baltimore MD 21218, USA3 Department of Materials Science and Engineering, Pennsylvania State University, State College, PA 16802, USA4 Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore MD 21218, USA

We report linear rheology experiments on the smectic elasticity of a thermotropic liquid crystal octylcyanobiphenol(8CB) confined in the pores of a silica gel (aerosil) network. The elasticity of the confined smectic shows an unex-pectedly strong temperature dependence and its frequency response indicates soft glassy behavior. The effect of thedefect density on the smectic elasticity is studied systematically by changing the concentration of the aerosil gel.



The Geometrical Structure of Disordered Sphere Packings

Tomaso Aste1, Mohammad Saadatfar2, Arthur Sakellariou3, Tim J. Senden4, and Tiziana DiMatteo5

1,2,3,4,5 Applied Mathematics, Australian National University, 0200 Canberra Australia

We present studies on very large samples of disorderly packed monosized spheres with the objectives of searchingfor signatures of disorder, exploring the local organization and the packing efficiency. Bead packs of up to 150,000mono-sized spheres with packing densities ranging from 0.58 to 0.64 have been studied by means of X-ray ComputedTomography. This study represents the largest and the most accurate empirical analysis of disordered packings at thegrain-scale ever performed. We discuss ways to characterize and classify these systems and the implications that localgeometry can have on densification dynamics. We investigate the local orientation order and test the idea that the localtendency to icosahedral arrangements is responsible for the formation of non-crystalline packings and glassy states.We discover that sphere-arrangements with high local densities (such as the icosahedral one) play no statisticallysignificant role in these disordered packings. On the other hand we identify the signature of a dynamical transitionsuggesting that at densities above 0.62 local rearrangements become increasely constrained leading the system to astructural arrest.




Equilibrium glassy phase in a polydisperse hard-sphere system

Pinaki Chaudhuri1, Chandan Dasgupta2, H.R.Krishnamurthy3 and Ajay K. Sood 4

1,2,3,4 Department of Physics, Indian Institute of Science, Bangalore, India

We report numerical results for the phase diagram of a polydisperse hard-sphere system in the density–polydispersityplane. These results are obtained from numerical minimization of the Ramakrishnan-Yussouff free energy functional forthis system. Using a discretized form of the free energy functional, we locate crystalline and glassy (inhomogeneous butaperiodic) local minima of the free energy as a function of the average density and the polydispersity. Our calculationshows that the free energy of the crystalline (fcc) minimum remains higher than that of the uniform liquid minimum atall densities if the polydispersity exceeds a critical value. We also find glassy local minima whose free energy is higherthan that of the crystalline minimum if the polydispersity is small. Most interestingly, the glassy minima are found tohave the lowest free energy at high densities if the polydispersity exceeds the critical value beyond which crystallizationdoes not occur. This suggests the occurrence of an equilibrium glassy phase in this system for sufficiently high valuesof the polydispersity.



The key-lock mechanism in nematic colloidal dispersions

N. M. Silvestre1, P. Patricio2 and M. M. Telo da Gama3

1,3 CFTC, Lisbon University, Lisbon, Portugal2 ISEL, Lisbon, Portugal

We consider the effect of planar or sculpted walls in two-dimensional colloidal dispersions in nematics. The behaviorof colloidal particles in a nematic matrix depends upon (i) the elastic constants of the nematic, (ii) the size of theparticle, and (iii) the boundary conditions at the particle and at the container. The elastic interaction between acolloidal disk and a flat wall, with homeotropic boundary conditions, is always repulsive. The repulsions are turnedinto strong attractions at structured or sculpted walls, with cavities that match closely the shape and size of thecolloids. This key-lock mechanism is analyzed in detail for spherocylindrical cavities of various length to depth ratios,by minimizing the Landau-de Gennes free energy functional of the nematic orientational order parameter. We findthat the attractions occur only for walls with cavities within a small range of the colloidal size and for a narrow rangeof orientations around the symmetry axis of the cavity.




Levy Flights in Viscoelastic Gels of Cylindrical Micelles: A DynamicLight Scattering Study

Rajesh Ganapathy1 and A. K. Sood2

1,2 Department of Physics, Indian Institute of Science, Bangalore 560012, India

We have used dynamic light scattering to study the dynamics of viscoelastic gels made from wormlike micellar solutionsof surfactant Cetyltrimethylammonium Tosilate (CTAT). The concentration of CTAT spans from 0.15wt% < c < 6wt%,covering the overlap concentration c∗ ≈ 0 .7wt%. We observe three modes in the decay of the intensity autocorrelationfunction: a fast gel mode associated with collective diffusion of the network followed by a Rouse mode and a viscoelasticmode. It is expected that the fast gel mode has relaxation rate Γ = D .qβ with β = 2 , implying normal diffusion (D- diffusion coefficient and q - wavevector). Most interestingly, our experiments reveal that for concentration c slightlyhigher than c∗, β is less than 2. A value of β < 2 implies enhanced diffusion (Levy flight) which gives mean squareddisplacement < ∆r2(t) >≈ t1+ε, where ε is positive. The exponent β ≈ 2 for c < c∗ and for c much greater thanc∗. The exponent is at its minimum value of 1.68 for a CTAT concentration of 2wt%. The reason for observing thesuper-diffusive gel mode may lie in the small breaking time of the cylindrical micelles.



Equilibrium phase behaviour of polydisperse hard spheres

Moreno Fasolo1 and Peter Sollich2

1,2 Dept of Mathematics, King’s College, University of London, Strand, Room 408, London WC2R 2LS, U.K

Many materials are polydisperse, comprising particles with properties (such as diameter or charge) that vary essentiallycontinuously. The resulting infinite number of distinguishable particle species makes the theoretical prediction of phaseequilibria highly nontrivial. In this study we calculate the equilibrium phase behaviour of polydisperse hard sphereson the basis of accurate free energy expressions, taking full account of fractionation and going beyond previous workon fluid-solid and solid-solid coexistence. Cloud and shadow curves are found exactly by the moment free energymethod, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier,simplified treatments we find no point of equal concentration between fluid and solid or reentrant melting at higherdensities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%). At sufficiently largepolydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations;we find, in addition, that coexistence of several solids with a fluid phase is also possible. We validate our theoreticalmethod against computer simulations at imposed chemical potential distribution and find excellent agreement.




Collective dynamics of relatively sheared soft monolayers:shear inducedmelting and re-entrance, and melting-freezing cycles

Moumita Das1, G. Ananthakrishna2 and Sriram Ramaswamy3

1,3 Department of Physics, Indian Institute of Science, Bangalore-560012, INDIA2 Materials Research Centre, Indian Institute of Science, Bangalore-560012, INDIA

We have studied the far-from-equilibrium dynamics of two crystalline two-dimensional monolayers driven past eachother using Brownian dynamics simulations. A dynamical phase diagram in the space of interlayer coupling anddrive is obtained. For low and high driving forces, we obtain macroscopically ordered, steadily drifting states. Ina suitable range of driving rates and inter-layer coupling, we see that the system switches between crystalline andliquid like states, with comparable residence times in each state. This phenomenon can be qualitatively understoodas a cooperative stochastic resonance (SR). Although there is no externally imposed time-periodic potential in oursystem, its role is played by the drive which shears the two layers past each other so that each moving layer providesa time-varying potential. To make the connection to SR more concrete, we have introduced a reduced model for thedynamics of the amplitude and phase of the order parameter variable, which mimics all features of the particle model,and also shows the main feature of SR namely the enhancement of signal to noise ratio for optimum values of noisestrength.




Study of Phase transformations via Anomalous Peak(s) Effects inWeakly Pinned Superconductors

A. D. Thakur1, D. Jaiswal2, S. Ramakrishnan3, M. J. Higgins4, and A. K. Grover5

1,2,3 Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research,Mumbai 400 005

4 NEC Research Institute, 4 Independence way, Princeton, NJ 085405 Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai

400 005

Weakly pinned vortex matter is a convenient medium to explore phase transformations arising out of competition andinterplay between interaction effects, quenched random disorder and thermal fluctuations. It is widely accepted thatthe critical current density Jc(H, T ) in a weakly pinned superconductor imbibes information on the spatial order offlux line lattice (FLL). The observation of the anomalous variation in Jc per se, therefore, imbibes information on thetransformation in the state of order in the vortex solid. The second magnetization peak (SMP) and the quintessentialPeak Effect (PE) are two well researched anomalous variations in Jc in conventional low Tc and Josephson CoupledLayered High Tc superconductors over last ten years. Their observation in a given isothermal scan in weakly pinnedsamples of high Tc Y Ba2Cu3O7 (for H‖c) and low Tc Ca3Rh4Sn13 had established the necessity to clearly distinguishbetween the physical basis of SMP and PE anomalies. Detailed re-investigations in a single crystal specimen of2H − NbSe2 have unraveled novel features, which help comprehend the wide variety in the thermomagnetic historyeffects and the temporal behavior in Jc(H) across the peak positions of SMP and PE anomalies in the pinned vortexmatter. A status report shall be presented and its consequence discussed as regards the determination of the vortexphase diagram in different systems.




A frustrated packing model for the B6-B1-B2 sequence of phasesexhibited by banana-shaped molecules

Arun Roy1 and N. V. Madhusudana2

1,2 Raman Research Institute, C.V. Raman Avenue, Sadashivanagar, Bangalore 560 080, INDIA

The most common sequence of phases exhibited as the chain length in a homologous series of banana-shaped moleculesis increased is the following: (i) The B6 phase has an intercalation of the molecules between successive layers with a layerspacing ≈ l/2, where l is the length of the long axis of the molecule. (ii) The B1 phase has a 2-dimensionally periodicstructure in which the arrow axes in near neighbour domains forming columns are oriented in opposite directions.(iii) In the B2 phase the molecules are again arranged in transversely polarized layers, without any intercalation ofthe molecules. The arrangements in the B6 and B2 phases are the only two possible types of efficient packing of themolecules in layers. We have developed a Landau theory by defining two coupled order parameters describing thesetwo packings, which also imply a polarization in each layer. We show that the B1 phase becomes stable in a parameterrange in which there is a frustration between the two types of packings. In the absence of the transverse polarization,the model reduces to that of frustrated smectics developed by Prost for highly polar compounds.



Structure of DNA-dendrimer Complex

Prabal Kumar Maiti1

1 Dept. of Physics, Indian Institute of Science, Bangalore, India, 560012

Recent in vitro transfection studies show that DNA can be efficiently compacted and transferred to the cell nucleus byPAMAM (Polyamidoamine) dendrimers [EDA (ethylene diamine) core)]. There is indication that very low toxicity andhigher transfection efficiency can be obtained by using complexes between DNA and PAMAM dendrimers. We haveused fully atomistic model of DNA and PAMAM dendrimer to study their complex in the presence of solvent using largescale Molecular dynamics simulation. We propose a molecular level structural model for the DNA-dendrimer complexand study the mechanism by which DNA condensed with dendrimer. Our simulation studies show how the stabilityand size of the dendrimer-DNA complex changes with dendrimer generation. To study the effect of solution pH wereport various structural and conformational properties of PAMAM-DNA complex at various dendrimer protonationlevels. Such study will aid the experimentalist to identify which generation and solution pH is most efficient for thegene delivery systems.

1 [email protected]



Screening of Spherical Colloids beyond Mean Field –A Local DensityFunctional Approach

Marcia C Barbosa1, Markus Deserno2, C. Holm3 and Rene Messina4

1 Instituto de Fisica - UFRGS, CP 15051, 91501-970, Porto Alegre, RS, Brazil2,3 Max-Planck-Institut fur Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany

4 Institut fur theoretische Physik II, Heinrich-Heine-Universitat Dusseldorf, Universitatsstr. 1, D-40225 Dusseldorf,Germany

We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of therecently developed Debye-Huckel-Hole-Cavity (DHHC) theory. This is a local density functional approach which incor-porates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the One ComponentPlasma. We compare the predictions for ion distribution and osmotic pressure obtained by the full theory and by itszero temperature limit with Monte Carlo simulations. They agree excellently for weakly developed correlations andgive the correct trend for stronger ones. In all investigated cases the DHHC theory and its computationally simplerzero temperature limit yield better results than the Poisson-Boltzmann theory.



Viscoelastic Phase Separation in Shear Flow

Akira Furukawa1 and Akira Onuki 2

1,2 Department of Physics, Kyoto University, Kyoto 605-8502, JAPAN

We investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landaumodel. (i) Even above the coexistence curve, phase separation occurs incompletely and two dynamic regimes emerge.In the linear regime γ < γnl the shear-induced fluctuations can be sustained only in the presence of the thermal noise,while in the nonlinear or chaotic regime γ > γnl dynamical steady states are realized due to the nonlinear interactionsamong the fluctuations. The crossover shear rate γnl is of order 0.2/τ where τ is the stress relaxation time. The lengthscale of the composition heterogeneities is also determined. (ii) Below the coexistence curve, unique two-phase statesare realized. There, the polymer-rich domains behave as gel-fragments undergoing continuous breakage but supportingmost of the applied stress, while the solvent regions behave as a lubricant being much deformed and supporting mostof the velocity gradient. The polymer-rich domains are connected and aligned perpendicularly to the flow directionon a characteristic scale ` in agreement with previous microscope observations. We calculate the rheology, the domainsize, and the structure factor with double peaks at ±2π/` along the flow direction.




Novel experiments lead to statistical measurements of jamming

Jasna Brujic1

1Biological Sciences, Columbia University, New York, USA

Jammed particulate matter is by its very nature impenetrable by observational techniques, thus prohibiting access toimportant characteristic features inside the bulk of the assembly of particles. Whereas numerous theoretical studiesand computer simulations have tackled problems such as the coordination number at the isostatic limit, the influenceof friction and polydispersity on the packing configuration and the fluctuations in particle density through the volumeof the ensemble, the experimental verification of all these properties has yet to be performed. The preparationof transparent samples of compressed emulsion droplets and colloidal particles at high volume fractions, combinedwith fluorescence mechanisms which provide the necessary contrast, allow for the full 3D characterisation in termsof the above parameters of the packing by the use of confocal microscopy. Furthermore, we present an analysisof the data based on the statistical mechanics introduced by Edwards and collaborators in which we investigatethe probability distribution of configurations and forces within the static packing of particles. The fluctuations inthe microstructure coupled with the stress fluctuations fully describe the particulate system, thus leading to themeasurement of macroscopic quantities such as the entropy and the ‘compactivity of a given static configuration.These experiments prove to be a powerful tool for the investigation of the thermodynamics of jamming.

[email protected]


The cone phase and the escape ”disclination” phase of liquid crystals.

Buddhapriya Chakrabarti1, Yashodhan Hatwalne2 and N. V. Madhusudana3

1 University of Massachusettes, Amherst, USA2,3 Raman Research Institute, Bangalore, India

We discuss the energetics and stability of the cone phase, and the escape “disclination” phase. The cone phase, whichoccurs near the nematic- smectic-C transition, is a hexagonal lattice of positive disclinations in the c-director as wellas the smectic layer normal. The escape “disclination” phase is composed of cylindrical escape configuration units,and intervenes the nematic-isotropic transition.




Lattice Dynamics of bcc and fcc Charged Colloidal Crystals

M.C. Valsakumar 1 and B. V. R. Tata2

1,2 Materials Science Division, IGCAR, Kalpakkam - 603102, India

Charged colloidal crystals (CCs) are known to exhibit body centered cubic (bcc) structure at low volume fractions (φ< 0.1) and face centered cubic (fcc) structure beyond this φ. Existing lattice dynamics calculations suffice to describethe dynamics in dilute CCs. We present a lattice dynamics calculation which incorporates harmonic interactions withall the neighbours (using Ewald summation technique) and the hydrodynamic interactions for arbitrary φ. Phonondispersion curves of longitudinal and transverse modes have been investigated as a function of φ and the surface chargeZe (on the particles) for both bcc and fcc structures. The decay rate Γ of the longitudinal mode showed occurrenceof bcc to fcc transition as a function of φ. Hardening of all the modes are observed as a function of φ and Ze. Thewavenumber q∗ at which overdamped transverse mode turn propagative is found to shift to higher q as φ and Ze areincreased. The calculation also suggests a linear instability for small q and large φ.





Interface Characteristics of Spreading Droplets

Avraham Beer1, Inbal Hecht2 and Haim Taitelbaum3,

1,2,3 Department of Physics, Bar-Ilan University, Ramat-Gan 52900, ISRAEL

The interface characteristics of spreading mercury droplets on thin metal films (silver and gold) have been studiedusing an optical microscope, Scanning Electron Microscope (SEM) and Atomic Force Microscope (AFM). The propa-gating interface has been digitized and analyzed in order to determine the roughness (α) and growth (β) exponents.New experimental results for these exponents have been obtained [1-3]. In particular, the result α = 0.66 ± 0.03,β = 0.46 ± 0.02, is the first experimental observation of a Quenched-KPZ universality class suggested by Hentscheland Family [4]. In this talk we present the experimental system and the various results obtained for the roughnessand growth exponents. We also suggest a new method for extracting system characteristics from the non-monotonicgrowth function of a single interface [5]. Finally we present a detailed study of a fluid invasion model, first suggestedby Cieplak and Robbins [6], from which we obtain insight on the dependence of the roughness exponent on thewetting properties of the spreading fluid [7].

References:[1] A. Be’er, Y. Lereah and H. Taitelbaum, Physica A, 285, 166-175 (2000).[2] A. Be’er, Y. Lereah, I. Hecht and H. Taitelbaum, Physica A, 302, 297-301 (2001).[3] A. Be’er, Y. Lereah, A. Frydman and H. Taitelbaum, Physica A, 314, 325-330 (2002).[4] H.G.E. Hentschel and F. Family, Phys. Rev. Lett. 66, 1982-1985 (1991).[5] A. Be’er, I. Hecht and H. Taitelbaum (submitted).[6] M. Cieplak and M.O. Robbins, Phys. Rev. Lett. 60, 2042-2045 (1988).[7] I. Hecht and H. Taitelbaum (submitted).

1 [email protected]

4.8.2 Tuesday 6 July, 11:30 - 11:45, Hall AB

Destruction of bulk ordering by surface randomness

Dima E. Feldman1

1 Physics Dept., Box 1843, Borwn University, Providence, RI 02906, USA

We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroyslong-range order in the bulk, and, instead, quasi-long-range order emerges. Correlation functions are calculated exactlyfor the two- and three-dimensional XY models with surface randomness via the functional renormalization group. Evenat strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughnessof a domain wall in the presence of surface disorder. [1] D. E. Feldman and V. M. Vinokur, Phys. Rev. Lett. 89,227204 (2002).

1 Dima [email protected]



Surface critical behaviour of one-component fluids near weaklyattractive substrates

Ivan Brovchenko1, Alfons Geiger2 and Alla Oleinikova3

1,2 Physical Chemistry, University Dortmund, Germany3 Physical Chemistry, Ruhr-University Bochum, Germany

The surface critical behaviour of water and LJ fluids is studied by analysing the density profiles of the liquid andvapour phases along the coexistence curve. The liquid-vapour coexistence curves of fluids between weakly attractiveplanar substrates were simulated in the Gibbs ensemble in a wide temperature range. The local critical behaviourwas analysed similarly to the bulk fluid, i.e. separating symmetric (order parameter) and asymmetric (coexistencecurve diameter) contributions to the local densities of the coexisting phases. The temperature dependence of thelocal order parameter near the surface is found consistent with the ordinary transition of Ising magnets and can bedescribed by a simple scaling law with a surface critical exponent of about 0.8. The temperature crossover from thebulk critical behaviour to the surface critical behaviour is studied as function of the distance from the surface. Theobserved intrusion of the surface critical behaviour into the bulk as well as the shape of the density profiles is found tobe governed by the bulk correlation length. The surface critical behaviour is found universal for both studied fluids.The influence of the fluid-surface interaction potential and the fluid density oscillations on the observed surface criticalbehaviour is discussed.



Interfacial structure at a two-dimensional wedge filling transition: Exactresults and a renormalization group study

Jose Manuel Romero-Enrique1 and Andrew O. Parry2

1,2 Department of Mathematics, Imperial College London, 180 Queen

Interfacial structure and correlation functions near a two-dimensional (2D) wedge filling transition are studied usingeffective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzerbinding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decayof the interfacial profile relative to the substrate and the correlations between interfacial positions above differentpositions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is relatedgeometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior isconsistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functionalrenormalization group scheme that keeps the geometry invariant.




The dynamics of wetting: some recent results.

De Coninck J1

1 University of Mons-Hainaut, 20 Place du Parc, Be-7000 Mons

This paper gives a review of the recent results devoted to the dynamics of wetting on different type of substrates: flatsurfaces, fibres, combining theoretical approach, experimental and numerical results. It stresses in particular thatseveral time scales are present within these phenomena.

1 [email protected]


Transport of Liquid Monolayers on Substrates with Chemical Patterns

M. N. Popescu1 and S. Dietrich2

1,2 M.P.I. fur Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, GERMANY

We have studied the transport of fluid monolayers being extracted form reservoirs in contact with a flat substrate onwhich domains of different affinity for fluid adsorption have been ”patterned” using a lattice gas model for the fluidand assuming that the difference in the affinity for fluid may be modeled in terms of different chemical potentials.Using kinetic Monte Carlo simulations we have analyzed the cases of stripes with different affinity oriented alongor perpendicular to the direction of flow and of a T-junction. Our results indicate that lateral confinement of flowalong high-affinity longitudinal stripes may be achieved at relatively low chemical potential differences, while for thecase of low-affinity stripes oriented transversally flooding of the stripe (eventually followed by rupture of the film)occurs even for very large chemical potential differences. For longitudinal stripes, the advancing edge of the monolayerfollows a square-root dependence on time, the prefactor depending on the width of the stripe. At long times andlarge spatial scales, this dependence is analyzed using a non-linear diffusion equation derived from the microscopicdynamics in the continuum limit. Ref.: M. N. Popescu and S. Dietrich, ”Model for Spreading of Liquid Monolayers”,cond-mat/0310768.




A new model for the velocity auto correlation function andself-diffusivity of inhomogeneous fluids

Krishnan S H1 and Ayappa K G2

1,2 Dept. of Chemical Engineering, Indian Institute of Science, Bangalore, India 560 012

We propose a new model for the velocity autocorrelation function of confined inhomogeneous fluids. The model hasbeen developed from the observation that the real lobe of the instantaneous normal mode spectrum follows a gammadistribution. The constants of the proposed model are obtained from the Einstein frequency and the fourth frequencymoment. Our model gives excellent agreement with molecular dynamic simulations for fluids confined in a sphericalpore at different densities and temperatures. By defining a relaxation time, an analytical expression for self-diffusivityhas been obtained in terms of the constants of the model. We have tested our model for dense fluids confined inslit shaped pores where the velocity autocorrelation function predicted by the model are compared with simulations.The self-diffusivity predictions are in closer agreement with the simulation results when compared with earlier modelsderived from analytical closure schemes of the memory equation.


4.8.8 Thursday 8 July, 11:15 - 11:30, Hall AB

Inhomogeneous hard-platelet fluids

L. Harnau1 and S. Dietrich2

1,2 Max-Planck-Institut fuer Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany, and Institut fuerTheoretische und Angewandte Physik, Universitaet Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

There is growing interest in properties of suspensions of platelike colloids like blood or clay sols because of possibleapplications in biomedicine and geophysics. Whereas the theoretical studies have focused on the understanding ofhomogeneous bulk fluids, experimentally it turns out that boundaries such as the walls of the sample container orcell membranes have a pronounced influence on the properties of the fluid. Here we study equilibrium properties ofinhomogeneous platelet fluids using density functional theory. Four examples of such suspensions are considered indetail, namely a fluid near a single planar wall [1], a binary platelet mixture confined in a slit pore [2], a fluid incontact with a curved substrate, and two hard spheres immersed in a solvent of platelets. Particularly, we compare theresults with the ones obtained for the corresponding hard-rod and hard-sphere fluids in order discuss the dependenceof equilibrium properties of inhomogeneous colloidal fluids on the shape of the fluid particles. [1] Fluids of platelikeparticles near a hard wall, L. Harnau and S. Dietrich, PRE 65, 021505 (2002). [2] Wetting and capillary nematizationof binary hard-platelet and hard-rod fluids, L. Harnau and S. Dietrich, PRE 66, 051702 (2002).




”Thermodynamic Casimir forces in 3He-4He mixture films near bulktricritical point.”

Anna Maciolek1 and Siegfried Dietrich2

1Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01224 Warsaw, Poland2Max-Planck-Institute fur Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany

Thermodynamic Casimir effect in films of 3He-4He mixture near their bulk tricritical point is studied within a latticemodel which takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom of4He. The effective force between the boundaries of a film arising from the confinement becomes long ranged nearthe tricritical point. This so-called Casimir force is calculated in the mean-field approximation as a function oftemperature at several concentrations close to the tricritical value. For nonsymmetric boundary conditions whichimpose a nontrivial concentration profile in the film the force is repulsive and exhibits a nonanalytic behavior at theλ-line. Its temperature variation across the tricritical point is similar to that obtained from the recent capacitancemeasurements of the equilibrium thickness of wetting films at solid substrates of 3He-4He mixtures.

[email protected]@mf.mpg.de


Pathways of dewetting of one-layer and two-layer films of soft matter

Thiele, Uwe1, Pototsky, Andrey2, Merkt, Domnic3 and Bestehorn, Michael4

1 Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Str. 38, D-01187 Dresden, Germany2,3,4 Lehrstuhl fur Theoretische Physik II, Brandenburgische Technische Universitat Cottbus, Erich-Weinert-Str. 1,

D-03046 Cottbus, Germany

We employ an evolution equation for the film thickness profile derived in long-wave approximation and incorporatinga disjoining pressure to study the competition of film rupture by nucleation and by surface instability for a one-layerfilm of soft matter. We then consider two stacked thin layers of different liquids on a solid substrate. Using long-wavetheory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linearanalyses show that depending on the long-range van-der-Waals forces and the ratio of the layer thicknesses, the systemfollows different pathways of dewetting. The instability may be dominated by varicose or zigzag modes and leads tofilm rupture either at the liquid-gas interface or at the substrate.




Predicting physical properties of disordered media from a singletomographic image

Christoph Arns1, Mark Knackstedt2 and Klaus Mecke3

1,2 Department of Applied Mathematics, ANU, Canberra, Australia3 MPI fr Metallforschung, D-70569 Stuttgart, Germany

The structure of a disordered material - an oil bearing rock, a piece of paper, a polymer composite - is a remarkablyincoherent concept. Despite this, scientists and engineers are asked to relate its properties to the “structure” of itsconstituent components. Integral Geometry provides a family of morphological functions Vν(r,Φ) for characterizingand reconstructing complex materials at porosity Φ by using parallel surfaces of distance r. Based on the morpholog-ical functions Vν(r,Φ) one can derive accurate expressions for percolation thresholds, transport properties and phaseequilibria in porous media . We illustrate this for conductivity and elasticity of complex model systems and experi-mental sandstone samples. In particular, for Boolean models Vν(r,Φ) is uniquely determined by its value at r = 0 atany porosity Φ0. Thus a single image is sufficient to estimate Vν(r,Φ) and physical properties such as permeabilitiesand elastic moduli.


4.9. TOPIC 9 : QUANTUM-MECHANICAL PROBLEMS (QUANTUM PHASE TRANSITIONS;STRONGLY CORRELATED FERMIONS; BOSE-EINSTEIN CONDENSATION; MESOSCOPICQUANTUM PHENOMENA, ETC.) 105

4.9 Topic 9 : Quantum-mechanical problems (quantum phase tran-sitions; strongly correlated fermions; Bose-Einstein condensation;mesoscopic quantum phenomena, etc.)


Superfluid, Mott-Insulator, and Mass-Density-Wave Phases in theOne-Dimensional Extended Bose-Hubbard Model

Ramesh V. Pai1 and Rahul Pandit2

1 Department of Physics, Goa University, Sub Postal Office Goa University, Goa 403 206, India2 Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012, India

We carry out the first comprehensive study the phase diagram of the one-dimensional extended Bose-Hubbard modelfor mean boson density ρ = 1. Our study uses the finite-size density-matrix renormalization-group method. In thepresence of repulsive onsite U and nearest-neighbour V interactions, we find a mass-density-wave (MDW) phase inaddition to the well-known superfluid (SF) and bosonic-Mott-insulator (MI) phases. The SF phase occurs at smallvalues of U and V ; as the interaction strength increases, the MI and MDW phase get stabilised. The former dominateswhen U is much larger than V whereas the latter dominates if U and V are both large and comparable. We determinethe phase boundaries as well as the natures of the quantum phase transitions between SF, MI, and MDW phases byusing finite-size scaling analysis. We show explicitly that the MI-SF phase boundary is in the Kosterlitz-Thouless(KT) universality class, whereas the MDW-SF phase boundary has both KT and two-dimensional-Ising character. Weshow further that, for large values of U and V , the direct MI-MDW transition is first order. The relevance of ourstudy to experiments on Bose-Einstein condensates in optical lattices is examined.




Ballistic resistivity in Al nanocontacts

A. Hasmy1, J.J. Palacios2, P. Garcia-Mochales3, J.L. Costa-Kramer4, M. Diaz5, and E. Medina6

1,5 Centro de Fisica, IVIC, Apdo 21827, Caracas 1020A, Venezuela2 Dpto de Fisica Aplicada, Univ. Alicante, Spain

3,7 ICMM-CSIC, Cantoblanco, Madrid, Spain4 IMM-CNM, CSIC, Tres Cantos, Madrid, Spain

6 Centro de Fisica, Caracas, Venezuela

Today, where manipulation of atoms is readily accessible, the lack of knowledge about the real efficiency of the electronicballistic transport at nanoscale limits innovations. The few studies available in the literature relate to the transportof single-atom contacts[1]. It has been evidenced that the only channel available for a single-atom gold contact has abetter electronic transmission performance than any single electronic channel, of the possible three, of the aluminumatom[1]. We show that the efficiency of ballistic conductivity can be quantitatively estimated through a transportparameter which, on average, does not depend on the contact neck thickness, for values smaller than the mean freepath of electrons. We perform Molecular Dynamics simulations of Al nanocontact ruptures computing simultaneouslythe evolution of the cross-section neck and the full quantum conductance, for more than thirty series of breakages(approximately 600 hundred Al nanocontact configurations). We demonstrate that, at atomic scale, the conductancebehaves as G = A/ρb, where A is the effective nanocontact cross-section area and ρb describes a phenomenologicalballistic resistivity for the energetically preferred Al nanocontact configurations[2,3]. Comparison of this quantity withthat of Au, allow to conclude that at the nanoscale, in contrast to the macroscale, Al contacts are better conductorsthan Au. [1] E. Scheeret al.Nature 394, 154(1998). [2] A. Hasmy et al.Phys. Rev. Lett. 86, 5574(2001). [3] E. Medinaet al.Phys. Rev. Lett. 91, 026802(2003).

1 [email protected]


Neutron Scattering Spectra of Alternating Spin-Chains

Weihong Zheng1, Chris J. Hamer2 and Rajiv R. P. Singh3

1,2 School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia.3 Department of Physics, University of California, Davis,CA95616, USA.

We consider a spin-half Heisenberg chain, where the exchange interactions alternate between the values of J and λJ,and present its complete dynamical structure factor, S(k, ω), by a high order power-series expansion in the variable λ.We analyze the frequency and wavevector dependence of the single-particle and two-particle spectral weights, whichmake up more than 99 percent of the contribution to S(k, ω) for the full range of parameters.




Quantum instanton approximation of the isotopic effects on the reactionrate constants

Jiri Vanicek1 and William H. Miller2

1,2 Dept. of Chemistry, U. of California, Berkeley, USA

We present a general quantum-mechanical method suitable for numerical evaluation of the isotopic effects on the rateconstants of chemical reactions. Our method is based on the quantum instanton approximation [1-4] and on the path-integral Metropolis Monte-Carlo evaluation of the Boltzmann operator matrix elements. The method is more accuratethan existing transition-state theory or semiclassical instanton method since we do not assume a single reaction pathand do not use a semiclassical approximation of the Boltzmann operator. In order to calculate the isotopic effect weuse a ”charging algorithm,” whereby the mass of the isotope is continuously changed from the initial to the final value.Direct calculation of the isotopic ratio turns out to be much more efficient than finding the absolute rate constantsfirst and then calculating their ratio. While the Monte-Carlo implementation should make the method accessibleto systems with a larger number of atoms, we present numerical results for the Eckart barrier and for the reactionsH + H2 → H2 + H and D + D2 → D2 + D.

1 [email protected]


Exact Solution For the Influence of Spectral Diffusion onSingle-Molecule Photon-Statistics

Eli Barkai 1 and Yong He 2

1,2 251 Nieuwland Science Hall, University of Notre Dame, Notre Dame, IN 46556-5670, USA

The stream of photons emitted from a single molecule source, itself embedded in a matrix exhibits in many casesquantum behaviors like sub-Poissonian statistics and anti-bunching. In many experimental situations single moleculesexhibit also spectral diffusion, where the absorption frequency of the molecule will randomly change due to differenttypes of interactions between the molecule and its environment. We investigate the distribution of number of photonsN emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave field(freq. ωL). Using a generating function formalism, exact analytical formulas for Mandel’s Q = N2−N

2

N− 1 parameter

and the line shape I(ωL) = limT→∞N/T are obtained in the limit of long measurement time T . The line shape exhibitsbehaviors predicted by the well known Kubo-Anderson stochastic theory of line shapes. The fluctuations described byQ exhibit transitions between: (i) Quantum sub-Poissonian and Classical super-Poissonian behaviors,and from (ii) fastmotional narrowing limit to slow modulation limit. The exact solution is valid for any laser field excitation strength.We show how to choose the Rabi frequency in such a way that the Quantum sub-Poissonian nature of the emissionprocess becomes strongest.




Renormalizing into the Quantum-Hall Insulator

Philipp Cain1 and Rudolf A Roemer2

1 Institut fuer Physik, Technische Universitaet, 09107 Chemnitz, Germany2 Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV4 9BU, United

Kingdom

Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantumHall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-spacerenormalization approach. Our results suggest that for a fully quantum coherent situation, the quantized Hall insulatorwith RH ≈ h/e2 is observed up to RL ∼ 25h/e2 when studying the most probable value of the distribution functionP (RH). Upon further increasing RL → ∞ the Hall insulator with diverging Hall resistance RH ∝ Rκ

L is seen. Thecrossover between these two regimes depends on the precise nature of the averaging procedure.



Existence of a Gapless line and a possible Lifshitz point for the Onedimensional quantum Axial Next Nearest Neighbour Ising (ANNNI)

chain

Amit Dutta1 and Diptiman Sen 2

1 Department of Physics, Indian Institute of Technology, Kanpur-208016, India2 Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560012, India

We study the one-dimensional transverse ANNNI chain using Bosonisation and the renormalisation group analysis.Using a Duality transformation, we map the model to an anisotropic XY model in a longitudinal field in the Xdirection. The Bosonisation study, which is valid for small anisotropy (a) and field (h), shows that the model hasa non-trivial fixed point at a certain value of a and h. Hence, there is a line of critical points in the (a,h) planeon which the system is gapless, even though the Hamiltonian does not have a continuous symmetry. This quantumcritical line corresponds to a spin-flop transition. Our study shows that the width of the modulated gapless region,separating the anti-phase and the disordered phase of the quantum ANNNI model, shrinks to zero in the limit whenthe (antiferromagnetic) next-nearest neighbour interaction is much larger than the (ferromagnetic) nearest neighbourinteraction. This indicates a possible existence of a novel Lifshitz point in the phase diagram where two gapped phasesmeet a gapless phase. The gapless line is also found in the case of an anisotropic XYZ model in a X field. Reference:A. Dutta and D. Sen, Phys. Rev. B 67 (2003) 094435




Semiclassical Foundation of Universality in Quantum Chaos

Sebastian Muller1,Stefan Heusler2,Petr Braun3,Fritz Haake4 and Alexander Altland5

1,2,4Fachbereich Physik, Universitat Duisburg-Essen, 45117 Essen, Germany3Fachbereich Physik, Universitat Duisburg-Essen, 45117 Essen, Germany; Institute of Physics, St Petersburg

University, 198504 St Petersburg, Russia5Institut fur Theoretische Physik, Universitat Koln, Zulpicher Str. 77, 50937 Koln, Germany

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical systemwith full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean levelspacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity,combinatorics and topology as agents determining the contributions of pairs of classical periodic orbits to the quantumspectral form factor. Bridges between classical orbits and (the non-linear sigma model of) quantum field theory arebuilt by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.



Frustration due to Exchange Anisotropy in Diluted MagneticSemiconductors

Chenggang Zhou1, Malcolm P Kennett2, Xin Wan3, Mona Berciu4, and R. N. Bhatt5

1,5 Dept of Electrical Engineering, Princeton University, Princeton, NJ 08544-5263, USA2 TCM, Cavendish Laboratory, University of Cambridge, Cambridge, UK

3 Physik Dept, Univ. Karlsruhe, Karlsruhe, Germany4 Dept of Physics and Astronomy, University of British Columbia, Vancouver, Canada

We study the effect of exchange anisotropy due to spin-orbit coupling in hole doped Diluted Magnetic Semiconductors(DMS), using a phenomenological effective spin model. The model incorporates both disorder in exchange (dueto positional disorder of the magnetic ion), and anisotropy in exchange (due to spin-orbit coupling effects in thesemiconductor valence band). We study the effect as a function of coordination number in short range models, andcompare with models having long range, power-law exchange couplings of the RKKY type. We find that disorder inthe sign, rather than the magnitude of exchange couplings is much more effective in reducing the low temperaturesaturation magnetization. Without antiferromagnetic couplings, the low temperature magnetization remains at a largefraction of the fully polarized ferromagnetic state. The possibility of spin-glass order is examined as well.




Generalized disorder measures and quantum entanglement

Raul D. Rossignoli1 and Norma B. Canosa2

1,2 Departamento de Fisica, Universidad Nacional de La Plata, C.C.67, La Plata (1900), Argentina

We discuss the fundamental properties of general non-additive entropic forms based on arbitrary concave functions,and their application to the detection of quantum entanglement in composite quantum systems [1]. It is shown thatin any separable state, the generalized entropy of the global system cannot be smaller than the local entropies. Thisprovides a general entropic criterion for separability that extends those based on the von Neumann and on the Tsallisentropies, and that is strictly equivalent to the most general disorder criterion when valid for any choice of entropicfunction. In entangled states however, the previous condition may be violated by a certain set of entropic forms,but not necessarily by all of them. A sufficient set of smooth entropic forms able to always detect such violations isprovided. These features are then illustrated in detail in different two-qubit and two-qudit systems.[1] R. Rossignoli, N. Canosa, Phys. Rev. A 66, 042306 (2002); Phys. Rev. A 67, 042302 (2003); Physica A 329, 371(2003).



A new look at the quantum phase transition in the 2D quantum Isingspin glass

Matthias Troyer1 and Prakash Dayal2

1,2 Department of Theoretical Physics, ETH, Zurich, Switzerland

A decade after the initial work by Rieger and Young [Phys. Rev. Lett. Vol. 72, Pg. 4141] we reinvestigate thequantum phase transition in the 2-dimensional Ising spin glass. Our work is triggered by the observation of activateddynamic scaling with an infinite dynamical exponent of the quantum phase transition in the random transverse fieldcase [cond-mat/9802108]. Large clusters of faster computers, combined with new Monte Carlo techniques, such asparallel tempering, allow us to extend the previous simulations to larger systems and to check whether there is evidencefor activated scaling also in the 2D quantum spin glass.





Onset temperature of slow dynamics and fragility in glass formingliquids

Srikanth Sastry1

1 Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bangalore 560064 India

Dynamic and thermodynamic aspects of glass forming liquids have recently been studied extensively through theanalysis of their potential energy landscape, specifically through the analysis of the statistics and properties of localenergy minima, or inherent structures. Recent results from such analysis are presented. One of the topics is thethermodynamic analysis of fragility. In previous work, a thermodynamic expression for fragility has been obtained,relying on the applicability of the Adam-Gibbs relation and relates parameters describing the energy landscape of aliquid to its fragility. Recent work addressing some open questions concerning such analysis will be described, includinganalysis of other model systems than previously studied. The other question that will be addressed is the onset of slowdynamics and its relation to changes in the energy landscape sampled by the liquid. Although empirical observationsclearly demonstrate a change in the sampled energy landscape across the onset temperature, a clear understanding,including its relationship to structural change and heterogeneous dynamics, is lacking. Results from recent analysis ofbehaviour near the onset temperature will be presented.

1 [email protected]


Fluctuating random solids in low dimensions

Paul M. Goldbart1, Swagatam Mukhopadhyay2 and Annette Zippelius3

1,2 Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois61801-3080, U.S.A.

3 Institut fuer Theoretische Physik, Universitaet Goettingen,37073 Goettingen, Germany

The amorphous solid state associated with the random localization of particles is examined with regard to the effects ofGoldstone fluctuations [1]. These long-wavelength, low-energy fluctuations dominate physical properties deep withinthe solid state, particularly in low dimensions. As such fluctuations are identified with shear deformations, theyfurnish an expression for the shear modulus in terms of the order parameter. In addition, Goldstone fluctuationsproduce a constant shift in the distribution of localization lengths, relative to the mean-field distribution. This shiftdiverges in two dimensions: thus fluctuations restore the broken translational symmetry and particles are no longertruly localized. Nevertheless, order-parameter correlations decay algebraically and the shear modulus remains finite,so that—as with crystalline solids—two-dimensional random solids exhibit quasi-long range, albeit random, order. [1]S. Mukhopadhyay, P. M. Goldbart, A. Zippelius, cond-mat/0310664.




Experimental study of the diffusion properties in a sheared granularmedia

Olivier Dauchot1 and Guillaume Marty2

1,2 CEA-Saclay, Group Instabilities and Turbulence; 91191 Gif sur Yvette; France

Granular media involve many particles, so that it is tempting to describe them thermodynamically. Unfortunately,energy is lost through friction and has to be brought by a non-thermal source. As a consequence, the dynamicalequations do not leave any obvious ensemble invariant. However it has been proposed that these systems could have astatistical mechanics of their own. Here, we present experimental results on the statistical properties of 2D disorderedgranular media under cyclic shear in an attempt to check the possibility of a thermodynamic construction for densegranular materials. Following tracers, we show that the particle motion is subdiffusive and that the trajectoriesexhibit strong cage effect of the kind observed in colloidal glasses. By direct visual observations, we investigate thecage properties (size, elapsed time in a cage...) in order to relate them to the global properties of the material. Furtherstatistical characterization of the motion are studied in an attempt to identify relevant lengthscales and ultimatelythe physical nature of a ”cage”. Finally, we expect to measure the response function to a small driving force in orderto investigate the fluctuation-dissipation relation and, eventually, measure an effective temperature.




Scale Invariance and Self-Averaging in Disordered Systems

Giorgio Parisi1,Marco Picco2 and Nicolas Sourlas3

1Dipartimento di Fisica, INFM, SMC and INFN, Universita di Roma em La Sapienza, P. A. Moro 2, 00185 Rome,Italy

2Laboratoire de Physique Theorique et Hautes Energies Boite 126, Tour 16, 1er etage 4 place Jussieu, F-75252 ParisCEDEX 05, France

3Laboratoire de Physique Theorique de l’ Ecole Normale Superieure 24 rue Lhomond, 75231 Paris CEDEX 05,France.

We study by large scale numerical simulations the long distance behavior of correlation functions in the randomfield Ising model (RFIM) in three dimensions and in random ferromagnetic Potts models in two dimensions in thedisordered phase. In both cases we find that the correlation length is not self-averaging near the critical temperatureTc while it is self-averaging far away from Tc. This is due to non perturbative phenomena, the formation of boundstates in the underlying field theory. These new phenomena can hardly be controlled in the renormalization group.It is not anymore obvious to us that the usual naive scaling arguments apply in the scaling region in the presenceof disorder, or if and how they should be modified. We argue that these non perturbative phenomena are at theorigin of the breaking of the perturbative renormalization group and dimensional reduction for the random field Isingmodel. We found that in the case or the random field Ising model the violation of self-averaging is maximal. Wealso observed similar phenomena for the random ferromagnetic Ising model in two dimensions, but in that case wecannot exclude a logarithmic cross-over to self-averaging. We expect also the possibility that these non perturbativephenomena invalidate other predictions of perturbative renormalization group (universality classes, critical exponentsetc).



Dualities in finite-dimensional Ising spin glasses

HIdetoshi Nishimori1 and Koujin Takeda2

1Department of Physics, Tokyo Institute of Technlogogy, Tokyo 152-8551, Japan2Department of Physics, Tokyo Institute of Technlogogy, Tokyo 152-8551, Japan

We have formulated duality transformations for finite-dimensional Ising spin glasses and their generalizations. Theresults are used to conjecture the exact location of the multicritical point in the phase diagram. In particular, theduality in three dimensions between the conventional +/-J Ising spin glass and the random-plaquette gauge modelis used to predict the value of error threshold of the toric code for quantum error correction. The resulting value isin good agreement with numerical simulations. We have thus established a route to connect symmetry arguments instatistical physics of disordered systems and explicit analytical results in quantum information.

[email protected]@stat.phys.titech.ac.jp



Glass transition in granular media

Marco Tarzia1, Antonio de Candia2, Annalisa Fierro3, Mario Nicodemi4, and Antonio Coniglio5

1,2,3,4,5 Dipartimento di Fisica, Universita degli Studi di Napoli “Federico II

In the framework of schematic hard spheres lattice models for granular media we investigate the phenomenon of the“jamming transition”. In particular, a system under gravity, made up of hard spheres with an internal degree offreedom, is studied on a 3D lattice under a Monte Carlo “tap” dynamics. A “jamming” transition similar to thatfound in real experiment is found. To understand the nature of such transition a simplified version of the model isalso studied in a mean field approximation, using the statistical mechanics approach a la Edwards. We derive thesystem phase diagram and show that “jamming” corresponds to a phase transition from a “fluid” to a “glassy” phase,observed when crystallization is avoided. Interestingly, the nature of such a “glassy” phase turns out to be the samefound in mean field models for glass formers.



Kinetically constrained models and glassy dynamics: analytical resultsfor the Kob-Andersen model

Cristina Toninelli1, Giulio Biroli2 and Daniel S.Fisher3

1 LPT, Ecole Normale Sup., 24 rue Lhomond F-75231 Paris France2 Service de Physique Theorique CEA/Saclay Orme des Merisiers F-91191 Gif-sur-Yvette Cedex France

3 Harvard Univ., Dep. of Physics Lyman 336, 17 Oxford Street, Cambridge MA 02138

After recalling kinetically constrained lattice gases and their relation with the dynamics of glass forming liquids, wefocus on the Kob-Andersen model. We prove that in the thermodynamic limit an ergodic/non-ergodic transitioncannot occur for this model in any finite spatial dimension. Then, we analyze dynamics in different density regimesfocusing on the self diffusion coefficient for a tagged particle, Ds: we prove that Ds cannot vanish at any finite densityand analyze its density dependence. At intermediate density, through percolation-type arguments, we predict a powerlaw behaviour. On the other hand, at high density a crossover occurs to a regime where relaxation takes place onlythrough the cooperative motion of large rare regions. The knowledge of the typical size and relaxation times of suchregions leads to a sharp prediction for the self diffusion coefficient, which vanishes faster than any power law of 1− ρfor ρ → 1. The predicted form is in very good agreement with numerical simulations.




Universality Near Dynamical Arrest, and the Glass transition

Aonghus Lawlor1, Paolo De Gregorio2, Phil Bradley3 and Kenneth A. Dawson4

1,2,3,4 Irish Centre for Colloid Science and Biomaterials, Department of Chemistry, University College Dublin,Belfield, Dublin 4, Ireland

There are many systems in nature where, instead of passing from one equilibrium phase to another, the systemdynamics arrests at a what is apparently a sharp ’transition’. Recent interest in such transitions has involved theliquid ’glass’ transition, and many more complex arrest phenomena in systems from colloidal particles, polymers,granular matter and others. Numerous models of such behavior exist, as well as some theoretical approaches that havehad some distinct success. Lacking, however, in these approaches, is the concept of an order parameter that makesdirect contact with dynamics of arrest, and that can be directly related to structural properties of the system. We haverecently introduced an order parameter, dynamically available volume (DAV) [1,2] that we believe is the simplest suchdescription, and tested the idea in a number of models. We have found that apparently quite different laws connectingtransport coefficients and particle density become quite universal when expressed in terms of this order parameter.In our original work on the Kob-Andersen and Biroli-Mezard models we have defined ’holes’ as vacancies into whichparticles can move, and continue to move up to the cross-over time in the mean squared distance travelled. Thishad involved, in some cases, removing certain holes that permit motion locally, but that are blocked on longer lengthscales (’rattlers’). Such holes may also be termed ’connected’, or ’disconnected’ depending on whether the particleswhich use them can access all or limited portions of the system. Subsequently we have made connection to otherprogress in the field in which the bootstrap length is used to describe the transport coefficients [3,4]. Remarkably,we have found that that our description of holes as being connected or disconnected is equivalent to these ideas ofthe bootstrap, and we now have a microscopic picture of how the connected holes enable transport on length scalesup to the crossover. That is, the typical distance between connected holes turns out to be the bootstrap length, andin developing an expansion near arrest in temrs of increasingly dilute holes (DAV) we are also making a connectionbetween bootstrap and transport. It also transpires that these ideas may be readily related to earlier concepts ofa long dynamical length [5,6]. Based on these new understandings, we have returned to develop the theory of theholes, and bootstrap length, and learned how to pose the problem in terms of dominant paths (closely analogous to’instanton’ approaches), both in theory and simulation. The resulting developments [7] enable us to compute, in arigorous and correctable manner, dynamical lengths much larger than have been possible in the literature before. [1]A. Lawlor, D. Regan, G. D. McCullagh, P. De Gregorio, P. Tartaglia and K. A. Dawson, ’Universality in LatticeModels of Dynamic Arrest: Introduction of an Order Parameter’, Phys. Rev. Lett., 89, 245503, (2002) [2] K. A.Dawson, A. Lawlor, P. De Gregorio, G. D. McCullagh, E. Zaccarelli, G. Foffi and P. Tartaglia, ’The nature of thecolloidal glass transition’, Faraday Discuss., 123/2, (2002) [3] J. Jackle and K. Kronig, ’A kinetic lattice-gas model forthe triangular lattice with strong dynamic correlations: I. Self-diffusion’, J. Phys.: Condens. Matter, 6, 7633-7653,(1994) [4] C. Toninelli, G. Biroli and D. Fisher, ’Spatial structures and dynamics of kinetically constrained modelsfor glasses’, cond-mat/0306746, (2003) [5] S. Franz, R. Mulet and G. Parisi, ’Kob-Andersen model: A nonstandardmechanism for the glassy transition’, Phys. Rev. E., 65, 021506, (2002) [6] W. Kob, C. Donati, S. J. Plimpton, P.H. Poole and S. C. Glotzer, ’Dynamical Heterogeneities in a Supercooled Lennard-Jones Liquid’, Phys. Rev. Lett.,79, 2827, (1997) [7] P. De Gregorio, A. Lawlor, P. Bradley, K. A. Dawson, ’Clarification of the Bootstrap PercolationParadox’, unpublished, (2004)




Sample to sample fluctuations in spin glasses

Matteo Palassini1

1 Laboratoire de Physique Theorique et Modeles Statistiques, Bat 100, Universite Paris-Sud, 94105 Orsay (France)

In disordered systems, thermodynamic variables fluctuate from a finite-volume sample to another, and, in certaincases, also in the infinite-volume limit. I will present the results of numerical investigations of these sample-to-samplefluctuations in Ising spin glasses. First, I will consider the ground-state energy in the Sherrington-Kirkpatrick model[1], showing that its fluctuations scale with the volume with an exponent inconsistent with the available theoreticalestimates. The full probability distribution is also investigated, in order to test for universality with respect to knownextreme-value distributions. I will then briefly discuss the fluctuations of the order parameter in three dimensions.Here, the numerical results [2] show convincingly that the fluctuations survive in the infinite-volume limit in theordered phase, and that they obey sum rules that appear naturally within the replica symmetry breaking picture ofspin glasses. [1] M.Palassini, cond-mat/0307713; [2] M.Palassini, F.Ritort, M.Sales, Phys. Rev. B 68, 224430 (2003).

1 [email protected]


Metastability and Supersymmetry in Disordered Systems

Andrea Cavagna1

1 Centre for Statistical Mechanics and Complexity - INFM Roma 1 and Universita

Metastable states are a key feature of disordered systems. Indeed, they are responsible for the sharp slowing downof the dynamics at low temperatures, which leads to the glass transition. Understanding the structure of metastablestates in the phase space, and what are the implications on the dynamics of a system, is thus of the utmost im-portance. The supersymmetry provides a powerful method for the study of metastable states in disordered systems,and in particular for the computation of their entropic contribution. Recent results show that different structures ofmetastable states, corresponding to different dynamical behaviours, may in fact be classified according to whether ornot the supersymmetry is broken. This suggests that spontanteous supersymmetry breaking is a new elegant way todescribe different dynamical behaviours in disordered systems.

1 [email protected]



Kac limit for finite range spin glasses

Silvio Franz1 and Fabio Lucio Toninelli2

1 ICTP Strada Costiera 11, 34100 Trieste Italy2 EURANDOM Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Nederland

We will report about some recent results (S. Franz and F.L. Toninelli PRL 92 (2004) 030602) on the Kac limit forfinite range spin glasses. We will consider spin glasses with interaction coupling decaying to zero on a distance γ−1.For γ → 0 we will show that for all temperatures, the free-energy and a local definition of the Parisi order parameterfunction P (q) tend to the ones of the long-range Sherrington-Kirkpatrick model. This analysis could represent a firststep toward an expansion around mean-field in spin glasses, which could shed some light on the nature of the spin-glassphase in finite range systems.



Complexity and supersymmetry in mean-field spin glasses

Luca Leuzzi1, Andrea Crisanti2, Giorgio Parisi3 and Tommaso Rizzo4

1,2,3,4 Department of Physics, Piazzale Moro 2, 00185 Rome, Italy

We perform the analysis of the number and the nature of metastable states in mean field spin glasses. Complexitycan be computed either as the quenched average of the logarithm of the number of states, or as the, sometimesexact, annealed average. When the complexity functional is expressed in terms of Grassmaniann variables it satifies aparticular supersymmetry. The explicit computation can lead both to a solution still satisfying this supersymmetry andto another one violating it. We analytically study different possible approaches and compare them in the Sherrington-Kirkpatrick model and in the p-spin interaction model when p > 2 in the whole frozen phase, with the aim of discussingthe extensivity of the complexity and to determine the nature of the stationary points that it counts in qualitativelydifferent models. We look at the limits of the definition of complexity as Legendre transform of the spin glass freeenergy functional and we deepen the study of the structure of the free energy landscape and the role of supersymmetry.




Gaussian density fluctuations, mode coupling theory, and all that

Grzegorz Szamel1

1 Department of Chemistry, Colorado State University, Fort Collins, CO 80523, USA

We consider a toy model for glassy dynamics of colloidal suspensions: a single Brownian particle diffusing amongimmobile obstacles. If Gaussian factorization of static density fluctuations is assumed, this model can be solvedwithout a factorization approximation for any dynamic correlation function. The solution differs from that obtainedfrom the ideal mode coupling theory (MCT). The latter is equivalent to including only some, positive definite termsin an expression for the memory function. An approximate re-summation of the complete expression suggests that,under the assumption of Gaussian factorization of static fluctuations, mobile particle’s motion is always diffusive. Incontrast, MCT predicts that the mobile particle becomes localized at a high enough obstacle density. We discuss theimplications of these results for models of glassy dynamics.

1 [email protected]


Cluster Coexistence, Memory Effects, and Energy Landscape in SpinModels with Competing Interactions and Bond Disorder

Kasturi Basu1, Sanjeev Kumar2, Chandra Shekhar Mohapatra3 and Pinaki Majumdar4

1 Dept. of Physics, University of Cambridge, Cambridge, U.K.2,4 Dept. of Physics, Harish-Chandra Research Institute, Allahabad, India

3 Dept. of Physics, Indian Institute of Technology, Kharagpur, India

We study the emergence of coexisting clusters of ferromagnetic and antiferromagnetic order by introducing weak bonddisorder in a model of competing ferromagnetism and (next nearest neighbour) antiferromagnetism. The specific formof the ferromagnetic coupling is chosen to mimic the ‘double exchange’ interaction in a classical Ising-like model. Thefirst order transition in the clean model gives way to a regime of meso/nanoscale cluster coexistence in the presence ofbond disorder. We map out the phase diagram in the space of couplings, bond disorder, and temperature, and estimatethe cluster dimension from an analysis of the magnetic structure factor. We also study the memory effects/glassinessin this model, by doing Monte Carlo runs for field cooling (FC) and zero field cooling (ZFC) and observe distinctlydifferent response below a characteristic temperature. We investigate the origin of this glassiness in terms of the‘energy landscape’ of the disordered model. This exploration of a disordered classical spin model is expected to throwsome light on the complex magnetic behaviour of the rare earth manganites.




TAP Complexity, the Cavity method and Supersymmetry

Tommaso Rizzo1

1 Physics Department, University of Rome ”La Sapienza”, Rome, Italy

We compute the TAP Complexity of the SK model through a generalized cavity method, showing that some essentialmodifications are needed with respect to the standard formulation. This allows to understand various features recentlydiscovered and to unveil the physical meaning of the parameters of the theory. We also reconsider the supersymmetricformulation of the problem showing that the SUSY relationships encode the physical meaning of the parameters.Applications to various models are discussed.

1 [email protected]


4.11.1 Tuesday 6 July, 16:15 - 16:30, Hall J

Genome Evolution by Substitutions, Duplications and Deletions

Yi Zhou1 and Bud Mishra2

1 Biology Department, New York University, 100 Washington Square East, New York, NY 10003, USA2 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA

Recently, statistical analyses of sequenced genomes have provided support for the “evolution-by-duplication” theoryoriginally proposed by Susumu Ohno in 1970’s. Based on this theory, several publications have appeared in theliterature proposing models of genome evolution that incorporate two basic processes: duplications and substitutions.We provide strong statistical evidences for the inadequacy of these models, and suggest a parsimonious model forgenome evolution incorporating an additional deletion process. In our model, genome evolution is described as adynamic process reminiscent of Polya’s Urn model with two free parameters. The evolution of the genome statisticalfeatures is summarized by a set of difference equations. Compared to the previous models, our model is able to fitthe distributions of genome elements (nucleotide or amino-acid words) from a much wider range of scale, and appliesequally well to prokaryotic and eukaryotic genomes. We also show that neither a reduction of duplication rate noran increase in substitution rate can completely replace the effect of deletions. We further present an analysis of theparameters of our model across species, leading to a better understanding of evolution modulation. Finally, we suggestseveral open problems focused on the statistical dynamics of evolution.




Self-organized Pattern Formation in Motor-Microtubule Mixtures

Gautam I. Menon1, Sumithra Sankararaman2 and P.B. Sunil Kumar3

1 The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600 113, India2 Department of Physics, University of Illinois at Chicago, 845 W taylor Street, Chicago, IL 60607-7059, USA

3 Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India

We model the stable self-organized patterns obtained in the non-equilibrium steady states of mixtures of molecularmotors and microtubules. In experiments [Nedelec et al. Nature, 389, 305 (1997); Surrey et al., Science, 292, 1167(2001)] performed in a quasi-two-dimensional geometry, microtubules are oriented by complexes of motor proteins.This interaction yields a variety of patterns, including arangements of asters, vortices and disordered configurations.We model this system via a two-dimensional vector field describing the local coarse-grained microtubule orientation andtwo scalar density fields associated to molecular motors. These scalar fields describe motors which either attach to andmove along microtubules or diffuse freely within the solvent. Transitions between single aster, spiral and vortex statesare obtained as a consequence of confinement, as parameters in our model are varied. For systems in which the effectsof confinement can be neglected, we present a map of non-equilibrium steady states, which includes arrangements ofasters and vortices separately as well as aster-vortex mixtures and fully disordered states. We calculate the steadystate distribution of bound and free motors in aster and vortex configurations of microtubules and compare these toour simulation results, providing qualitative arguments for the stability of different configurations. We also commenton the implications of our results for experiments.



Statistical Analysis of Bacillus Subtilis Protein-Protein InteractionNetwork

Olusola C. Idowu1, Steven J. Lynden2, Panayiotis Periorellis3, Malcolm P. Young4, and PeterAndras5

1,2,3,4,5 School of Computing Science, University of Newcastle upon Tyne, Newcastle, NE1 7RU, United Kingdom

Protein-protein interactions in a cellular system can be conceptualized as graphs of interacting nodes and edges inwhich the nodes represent proteins and the edges represent interactions between proteins. Analysing the topologicalproperties of these systems to detect their vulnerable components and their structural integrity can help in theprocess of identify potential new protein targets for the purpose of drug discovery. We analysed the protein-proteininteraction of the gram-positive bacteria bacillus subtilis using data from the Search Tool for the Retrieval of InteractingGenes/Proteins (STRING) database. We used different statistical algorithms (bottlenecks, hubs, elementary cycle) toanalyse the topological structures of the network and to derive a list of the most important proteins targets based onthe relative damaging potential of each individual protein within the protein network. We found that 40% of proteinstargets identified are encoded by genes that are known to be essential to the survival of bacillus subtilis.




Loop formation kinetics of single stranded DNA.

Anirban Sain1, Bae-Yeun Ha2, Heng-Kwong Tsao3 and Jeff Z.Y. Chen 4

1 Physics Dept., Indian Institute of Technology Bombay, Powai, Mumbai-400076, India.2,4 Dept. of Physics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

3 Dept. of Chemical Engineering, National Central University, Chung-Li, Taiwan 320, ROC

We develop a theoretical approach to hairpin-loop formation of single stranded (ss) DNA by treating the relativeorientations of the consecutive bases as two-state systems: the consecutive bases are either ”stacked” or ”unstacked”.The equilibrium kinetics of ssDNA looping is shown to be intrinsically different from that of a wormlike chain; for ashort strand, it is mainly controlled by stacking-breakage probability, not by the mean curvature of the loop. Thelooping kinetics is also highly sensitive to the composition of the strand as seen in recent experiments. Our estimateof the stacking energy for poly(dA), -3.9 kcal/mol, is consistent with known experimental results.


4.11.5 Moved to Poster Session 3.

Competitive Hybridization Model

Vera Cherepinsky1, Ghazala Hashmi2, Michael Seul3 and Bud Mishra4

1,4 Dept. of Mathematics & NYU Bioinformatics Group, Courant Institute of Mathematical Sciences, NYU, NewYork, NY, USA

2,3 BioArray Solutions, Inc., Warren, NJ, USA

Microarray technology allows one to gather abundance data for target DNA molecules and relies on hybridizingthe target to many short probe oligonucleotides arrayed on a surface. Subsequent analysis is based on the implicitassumption that the result of a given experiment is independent of whether it was conducted in isolation or in parallelwith many others. It’s been discussed in the literature that this assumption is frequently false, and its validitydepends on the types of probes and their interactions. To understand probe interactions in a multiplexed reaction, wepresent a detailed physical model of hybridization, formulated as a system of ODE’s describing kinetic mass action,with conservation-of-mass equations completing the system. We examine pair-wise probe interactions and present amodel of “competition” between the probes for the target. These effects are shown to be predictable from the affinityconstants for each of the probes, calculated from thermodynamic parameters such as the free energy of hybridization,computed according to the nearest neighbor model for each probe and target sequence. Simulations based on thecompetitive hybridization model explain the observed variability in the signal of a given probe when measured inparallel with different groupings of other probes or individually.




Do secondary structures play a role in messenger RNA processing? Astatistical study.

Thalmann Fabrice 1 and Herve Isambert 2

1 LDFC-CNRS and Universite L.Pasteur, Institut de Physique, 3 rue de l2 Institut Curie, UMR 168, 11 rue Pierre et Marie Curie, F-75231 Paris Cedex 05, France

Pseudoknots are crucial components of ribonucleic acids (RNA) secondary and tertiary structures. Their predictionis a difficult computational problem, both for algorithmic and physical reasons. We present here a statistical study ofthe E.Coli, Bac.Subtilis and Sac.Cerevisiae genomes, in order to determine whether pseudoknots in messenger RNAare likely to influence their biological role. We enumerate patterns which are all possible precursors in the primarystructure of pseudoknots, and analyse their statistical properties: number, stability, repartition. In a preliminary part,we focus on the distribution of inverted palindromes and find anomalies in their repartition, rendering the analysisof the statistics of pseudoknot patterns more difficult. We present a general methodology for detecting patterns withatypical and non-generic statistical properties, but we do not find strong evidence of anomalies in the statistics ofpseudoknot patterns.

1 [email protected]


Simulating the kinetics of a simplified polypeptide model: what can ittell us about cooperativity?

Michael Knott1 and Hue Sun Chan2

1,2 Department of Biochemistry, University of Toronto, Toronto, Canada

Many small globular proteins fold in an apparently two-state manner, displaying the experimentally observed propertiesof thermodynamic and kinetic cooperativity. We model these phenomena computationally, using Langevin dynamicssimulations to investigate the folding of a simplified atomic model of a 54-residue polypeptide which is designed tofold to a three-helix bundle. The model is continuous (off-lattice) and represents all the backbone atoms together withthe H and O side atoms attached, respectively, to the N and C′ backbone atoms; the side groups are represented assingle Cβ atoms. The potential energy function, which is non-Go-like (i.e., not biased towards the target structure),contains representations of hydrophobic and hydrogen bonding forces. To our knowledge, this is the first time thata protein model with this level of detail has been tested for kinetic cooperativity. The chevron plots for folding andunfolding display marked rollovers; this departure from kinetic cooperativity is consistent with the model’s relativelylow level of thermodynamic cooperativity. The simulation results lead us to a more general theoretical understandingof (i) the energetics that underlies thermodynamic and kinetic cooperativity, and (ii) the role that cooperativity oftenplays in the folding process of small globular proteins.




Dynamics of active fission-fusion on membranes : Trafficking networks

Madan Rao1

1 Raman Research Institute and National Centre for Biological Sciences, Bangalore, India

We study the large scale dynamics of morphology changes and compositional heterogeneity of membranal compart-ments subject to active fission and fusion processes. This involves an interplay between active protein machinery,composition and membrane deformation. Our study gives rise to a number of quantitative predictions which maybe tested in in-vitro experiments or cell-free extracts. We have also shown that such active fission-fusion processesmay induce a novel segregation in a two-component membrane compartment. We then extend our study to activeinteracting membranes trafficking material between themselves.

1 [email protected]


Formation and dynamics of membrane tubes

Imre Derenyi1, Frank Julicher2 and Jacques Prost3

1 Department of Biological Physics, Eotvos University, Pazmany P. stny. 1A, H-1117 Budapest, Hungary2 Max Planck Institut fur Physik komplexer Systeme, Nothnitzer Str. 38, D-01187 Dresden, Germany

3 Institut Curie, UMR 168, 26 rue d

Biological membranes often form highly dynamic tubular networks. Their exact role is not known, however, they aremost probably involved in the transport and sorting of proteins and lipids. We study the formation and dynamicsof membrane tubes, and their possible role in protein and lipid segregation. We show that (i) the force needed toform a tube changes non-monotonically with its length, (ii) the coupling between the concentration of the proteinsand the mean curvature of the membrane can lead to pearling instability along the tubes, (iii) the coupling betweenthe concentration and the Gaussian curvature is required to induce protein segregation, and (iv) a dynamic instabilitydue to segregation can lead to fission.

1 [email protected]



Functional modules of metabolic networks

Shalini1, Areejit Samal2, Nandula Raghuram3 and Sanjay Jain4

1,2 Department of Physics and Astrophysics, University of Delhi, Delhi, India3 Department of Biotechnology, G.G.S. Indraprastha University, Delhi, India

4 Department of Physics and Astrophysics, University of Delhi, Delhi, India, and Indian Institute of Science,Bangalore, India

We combine methods from statistical mechanics, graph theory and metabolic flux analysis to study the modularstructure of the metabolic network of Escherichia coli. We first compute the fluxes of all metabolic reactions in thisnetwork under different environmental conditions corresponding to different carbon sources available as inputs. Thisenables us to compute correlations between different reactions in the network in a manner analogous to correlationsbetween stocks computed from a time series of stock prices. This further enables us to obtain functional clusters withinthe metabolic network. We find a non-tree like decomposition of the network into inputs, outputs, core, and othermodules that perform specific tasks. This picture correlates well with modules already identified by biochemists, butalso provides new insight into mechanisms by which E coli optimizes its metabolism that is relevant for understandingthe origin and evolution of the metabolic network as well as for metabolic engineering.



Oscillating Gene Expressions in Regulatory Networks.

Mogens H. Jensen1, Kim Sneppen2 and Guido Tiana3

1,2 Niels Bohr Institute, Copenhagen, Denmark3 Milan University, Milan, Italy

We study oscillating genetic expressions in regulatory biological networks and have concentrated our effort on twosystems. The first is the Hes1 protein/hes1 mRNA feedback system which regulates timing in many cell types. Thesecond is the p53-mdm2 protein regulatory system which is important for cell control after DNA damage. In bothcases, we formulate sub networks of the full genetic network, by identifying the key players in the genetic regulation.We construct in each case differential equations of two variables and introduce, based on the biological properties, atime-delay in the equations in order to generate the oscillatory behavior [1,2]. The obtained results are in very goodagreement with the experimental measurements. [1] M.H. Jensen, K. Sneppen and G. Tiana, FEBS Letters 541,176-177 (2003). [2] G. Tiana, M. H. Jensen, K. Sneppen, Europ. Phys. J. B 29, 135 (2002).



4.11.12 Friday 9 July, 11:30 - 11:45, Hall J

Study of Diffusion and Chemotaxis in Cell Motion Using Cellular PottsModel.

Debasis Dan1 and James A. Glazier2

1,2 Department of Physics, Indiana University, Bloomington, USA.

Cell motion in fluid or cellular aggregates consists of both random and coherent components. In the presence ofchemical field it shows a highly adaptive response. We use Potts model to simulate these systems. Cellular large-QPotts model (CPM) is an energy minimization formalism to simulate the movement and properties of cells undergoingcytoskeletally driven fluctuations. One of our motivation lies in simulating the chemotactic movement of neutrophiltowards pathogenic bacteria. The hamiltonian in CPM consist of adhesive energy, i.e., cell dependent surface energy.This energy can be either positive or negative depending on the cell type. Since biological cells have fixed volume andsurface area, so we include volume and surface area constraints in the hamiltonian. We also include a chemical energyterm which incorporates the response of the cells to chemoattractant/repellant. Furthermore chemical diffusion andadvection of fluid is done within the framework of CPM. Temperature in our Potts model characterizes the fluctuationof cell membrane due to cytoskeleton activity. Using our model we characterize the mobility and diffusion of cells inthe presence/absence of morphogens. Our model reproduces the transient response to chemotactic stimuli in E-coli.Further work to simulate chasing of neutrophil towards bacteria pathogens (like staphylococcus aureus) in presence oferthrocytes is in progress.



Percolation and Burgers’ dynamics in a Model of Capillary Formation

A. Coniglio1, A. de Candia2, A. Gamba3 and S. Di Talia4

1,2 Dept. Physics, Naples3 Politecnico, Torino

4 Rockefeller, New York

Capillary networks are essential in vertebrates to supply tissues with nutrients. Experiments of ”in vitro” capillaryformation show that cells randomly spread on a gel matrix autonomously organize to form vascular networks. Wepresent a full characterization of a recently proposed model, which reproduces the main features of the biologicalsystem, focusing on its dynamical properties, on the fractal properties of patterns, and on the percolative phasetransition. We show that both the model and the real system exhibit a fractal behavior at small scales, due to theprocess of migration and dynamical aggregation, followed at large scale by a random percolation behavior due tothe coalescence of aggregates. The results are in good agreement with the analysis performed on the experimentaldata. We finally discuss the relevance of the model in relation with some experiments ”in vivo”, and with proposeddiagnostic methods based on the measurement of the fractal dimension of vascular networks.




Scaling with log-periodic oscillations in a null model for RNAinterference

Duygu Balcan1, Alkan Kabakcioglu2 and Ayse Erzan3

1,3 Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 34469, Istanbul,Turkey

2 Department of Physics, University of Padova, Padova, PD 35131, Italy

We have introduced[1] a simple model for gene interactions resulting in the regulation of gene expression. The model isa self-organizing null network upon which subsequent evolutionary pressures and genetic processes might have acted,to lead to present day regulatory systems. The adjacency matrix is based on a sequence matching condition on arandom bit-string representation of the chromosome, and results in a scale free, smallest world network of interactions.The envelope of the out-degree distribution exhibits power law decay with log-periodic oscillations, n(kout) ∼ (kout)−γ ,with γ ' 1 crossing over to ' 1/2, for larger values of kout. The in-degree distribution, on the other hand, is much morelocalized, a feature common to modern genomic systems. Here we will report both simulation results and analyticalcalculations which reproduce the log-periodic scaling behavior.

[1] D. Balcan and A. Erzan, “Random model for RNA interference yields scale free network,” q-bio.GN/0310027 andEur. Phys. Jr. B, to appear.



Stability, Dynamics and Rheology of Suspensions of Active Particles

Yashodhan Hatwalne1, Sriram Ramaswamy2, Madan Rao3 and R. Aditi Simha 4

1,3 Raman Research Institute, C.V. Raman Avenue, Bangalore 560 080 INDIA2 Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560 012

INDIA4 MPI-PKS, Noethnitzer Str. 38, 01187 Dresden, Germany

We present a set of coarse-grained equations governing the hydrodynamic velocity, concentration and stress fields ina suspension of active, energy-dissipating particles. We make several predictions for the mode-structure, stabilityand number fluctuations for ordered phases and for the linear and nonlinear rheology of the isotropic phase in suchsystems. These can be tested in experiments on bacterial suspensions, cell extracts with motors and filaments, orartificial machines in a fluid.




Chromatin dynamics and symmetry breaking during genomicregulation.

Graham Smith1, Andrei Zinovyev2 and Arndt Benecke3

1,2,3 Institut des Hautes Etudes Scientifiques - Bures-sur-Yvette - France

Chromatin is the proteo-nucleo domain orchestrated around the genome in eukaryotic nuclei. Its structure anddynamics have received over the last years increasing attention as being fundamentally involved in all DNA-basednuclear processes. Compelling evidence suggests a secondary regulatory code implemented by chromatin dynamicsestablishing a dynamic memory function. We have developed a mathematical model of chromatin dynamics based onreaction kinetics. The different nonlinearities associated with chromatin-coregulator interactions can thus be put for thefirst time on formal grounds. In absence of analytical solutions for the corresponding sets of differential equations, theresulting reaction kinetic graphs are being used for in silico numerical simulations from which characteristic parameterssuch as metabolic- and time-scales are obtained. Major efforts are devoted to the reduction of the parameter-spaceof these graphs. Resulting parameter-vectors can be confronted with corresponding in vivo values and used forhypothesis-driven experimentation. Based on the initial chromatin dynamics graphs we have furthermore developedreaction-kinetic models for both transcription and epigenetic regulation. The subsequent numerical simulations revealinteresting alternate mechanisms to, and divulge a unifying theme for initial symmetry breaking in both processes. Weare in the process to incorporate insights from non-linear thermodynamics to capture biased diffusion within the nuclearcompartment. The implications of chromatin-based dynamic memory for analyzing genomes of higher eukaryotesfor complex, composite regulatory networks are significant. Furthermore, the recent generation of systematic geneexpression information in response to specific cellular signals can be utilized within limitations as training data inmultiple-round feed-back optimization of these reaction kinetic models.





Self-organised pattern formation in a model of collective choicedynamics

Sitabhra Sinha1 and Raghavendra S.2

1 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, INDIA.2 Madras School of Economics, Gandhi Mandapam Road, Chennai 600025, INDIA.

In a society, an agent makes a choice based on its belief regarding the possible outcome of that choice, as well as theopinion of its neighbors regarding the expected quality of such a choice. The agent’s belief, in turn, need not be fixedin time, but will adapt with changing circumstances, based on the choices it has made previously, as well as whethersuch choices accorded with those of the majority (learning). Here we propose a model of collective choice which takesinto account the adaptive dynamics of beliefs, with individual agents opting for any one of two possible alternativesat a given time instant. We observe a phase transition in the behavior of the collective when learning is introduced.The system gets polarised into any one of the alternatives, although individuals may continue to alternate amongthe choices. This indicates the existence of long-range correlations among the beliefs of agents, and is observed in astriking manner as spatial patterns in the shape of vortices or spirals. Results of our model corraborate with empiricaldata on films, financial markets and voting behavior.




Transient Patterns and Traffic in Colonies of Organisms

Debashish Chowdhury1, Alexander John2, Ambarish Kunwar3, Katsuhiro Nishinari4, and AndreasSchadschneider5

1,3 PHYSICS Department, Indian Institute of Technology, Kanpur 208016, India2,5 Institute for Theoretical Physics, University of Cologne, 50923 Koln, Germany

3 PHYSICS Department, Indian Institute of Technology, Kanpur 208016, India4 Department of Applied Mathematics and Informatics, Ryukoku University, Shiga, Japan

Ant-trails are examples of self-organized patterns in colonies of organisms. On these trails, the spatio-temporalorganization appears very similar to those in vehicular traffic. We have developed discrete models of such trafficsystems using the so-called agent-based Lagrangian approach [1-4]. Each organism is represented by a “self-propelled”particle and the effects of their mutual interactions are captured through dynamical rules. One set of dynamicalvariables represents the presence (or, absence) of ants while the other set corresponds to that of pheromone. Thesemodels combine chemotaxis with totally asymmetric simple exclusion process and are closely related to a bus-routemodel. The pheromone-mediated interactions among the ants give rise to (a) non-monotonic variation of the averagespeed with the density of the ants on the trail (with periodic boundary conditions), (b) plateaus in the flow-densitydiagram of the model with bi-directional flow, and (c) systematic shifts of the phase boundaries with the rate ofpheromone evaporation (when open boundary conditions are imposed).Referencs:[1] D. Chowdhury, V. Guttal, K. Nishinari, A. Schadschneider, J. Phys. A, 35, L573 (2002).[2] K. Nishinari, D. Chowdhury, A. Schadschneider, Phys. Rev. E, 67, 036120 (2003).[3] A. John, A. Schadschneider, D. Chowdhury, K. Nishinari, submitted for publication.[4] A. John, A. Kunwar, K. Nishinari, A. Schadschneider and D. Chowdhury, to be published.




Optimal random searches of revisitable targets: crossover fromsuperdiffusive to ballistic random walks

M. C. Santos1, M. G. E. da Luz2, E. P. Raposo3 and G. M. Viswanathan4

1,2 Departamento de Fisica, UFPR, Curitiba, Brazil3 Departamento de Fisica, UFPE, Recife, Brazil4 Departamento de Fisica, UFAL, Maceio, Brazil

One of the most important aspects in the general search problem [1] of finding randomly located target sites is tocharacterize the role played by the nonrevisitability delay time τ during which a previously found target becomesunavailable to the searcher [2]. By using an appropriate parameterization of the number of random walk stepsundertaken between successive targets, as τ increases from τ → 0 to τ →∞, we show that the optimal search strategyshifts, respectively, from a superdiffusive to a ballistic strategy of essentially rectilinear motion between the targets,in the case of sparse randomly distributed sites. The crossover between these limiting regimes is a function of τ . Suchconclusions are shown to hold even if dissipative phenomena are considered in the searching dynamics [3]. We alsodiscuss the results in the context of their application to animal foraging. [1] G. M. Viswanathan, S. V. Buldyrev, S.Havlin, M. G. E. da Luz, E. P. Raposo, and H. E. Stanley, Nature 401, 911 (1999). [2] E. P. Raposo, S. V. Buldyrev,M. C. Santos, M. G. E. da Luz, H. E. Stanley, and G. M. Viswanathan, Phys. Rev. Lett. 91, 240601 (2003). [3] M.G. E. da Luz, S. V. Buldyrev, S. Havlin, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, Physica A 295, 89(2001).



Avalanche dynamics on complex networks

Byungnam Kahng1

1 School of Physics, Seoul National University NS50, Seoul 151-747

Recently the emergence of a power-law degree distribution in complex networks have attracted considerable attentions.Such scale-free (SF) networks are ubiquitous in nature. Due to the heterogeneity in degree, SF networks are vulnerableto attack on a few nodes with large degree. However, more severe catastrophe can occur, triggered by a small fraction ofnodes but causing a cascade of failures of other nodes. The recent blackout of power transportation in the northeasternUS and Italy is a typical example of such a cascading failure. Here, to study the avalanche dynamics, we investigatethe Bak-Tang-Wiesenfeld sandpile model on SF networks, a prototypical model exhibiting the avalanch dynamics.We obtain the avalanche size distribution analytically by using the branching process approach. Moreover, relatedproblems on various systems will be discussed.

1 [email protected]



Clustering and information in correlation based financial networks

Jukka-Pekka Onnela1, Kimmo Kaski2 and Janos Kertesz3

1,2 LCE Helsinki University of Technology, Finland3 Budapest University of Technology, Budapest and Helsinki University of Technology, Finland

Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to selectthe relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graphwith no edges where the vertices correspond to stocks. Then, one by one, we insert edges between the verticesaccording to the rank of their correlation strength, resulting in a network called asset graph. We study its properties,such as topologically different growth types, number and size of clusters and clustering coefficient. These properties,calculated from empirical data, are compared against those of a random graph. The growth of the graph can beclassified according to the topological role of the newly inserted edge. We find that the type of growth which isresponsible for creating cycles in the graph sets in much earlier for the empirical asset graph than for the randomgraph, and thus reflects the high degree of networking present in the market. We also find the number of clusters inthe random graph to be one order of magnitude higher than for the asset graph. At a critical threshold, the randomgraph undergoes a radical change in topology related to percolation transition and forms a single giant cluster, aphenomenon which is not observed for the asset graph. Differences in mean clustering coefficient lead us to concludethat most information is contained roughly within 10% of the edges.



Neural Cryptography

Wolfgang Kinzel1 and Ido Kanter2

1 Department of Physics, University of Wuerzburg, Germany2 Department of Physics, Bar Ilan University, Israel

Two neural networks which are trained on their mutual output bits show a novel phenomenon: The networks syn-chronize to a state with identical time dependent weights. It is shown how synchronization by mutual learning can beapplied to cryptography: secret key exchange over a public channel. The security of this novel statistical approach tocryptography is discussed. For publications and recent preprints see:http://theorie.physik.uni-wuerzburg.de/TP3

1 [email protected]



Modeling the evolution of the yeast protein interaction network in theframework of protein families

Kwang-Il Goh1, Byungnam Kahng2 and Doochul Kim3

1,2,3 School of Physics, Seoul National University, Seoul, Korea

Understanding of how protein interaction networks of living organisms have evolved or are organized can be the firststepping stone in unveiling how life works on a fundamental ground. Here we introduce an in silico evolution modelfor the protein interaction network in the framework of the protein families. The essential ingredient of the modelincludes the protein family identity and robustness under evolution, as well as the three previously proposed: geneduplication, divergence, and mutation. This model produces a prototypical feature of complex networks in a widerange of parameter space, following the generalized pareto distribution in connectivity. Moreover, we investigate otherstructural properties of our model in detail with some specific values of parameters relevant to the yeast Saccharomycescerevisiae, showing excellent agreement with the empirical data. Our model indicates that the physical constraintsencoded via the domain structure of proteins play a pivotal role in protein interactions.



Analysis and Comparision of Incomplete Enumeration Monte-Carloalgorithm for Linear and Branched Polymers

Sumedha1 and Deepak Dhar2

1,2 Dept. of Theoretical Physics,Tata Institute of Fundamental Research,Mumbai,India

Incomplete enumeration is a Monte-Carlo algorithm which can be used to generate an unbiased sample of configurationspace [Dhar and Lam, J. Phys. A 19 L1057(1986)]. In this work we make a systematic study of incomplete enumerationfor linear and branched polymers. We find that while the time to generate an independent sample of n sites for linearpolymers varies as n2, independent of dimension, for branched polymers the time for generation of an independentsample of n sites goes as exp(cnα), where 0 < α < 1. For branched polymers on Bethe lattice, the algorithm’s efficiencycan be studied analytically and we find α = 1/3.




The architecture of complex weighted networks

Alain Barrat1,Marc Barthelemy2,Romualdo Pastor-Satorras3 and Alessandro Vespignani4

1,4LPT, Universite2CEA-department de physique theorique et applique

3Deapartment de fisica y Enginyeria nuclear, Universitat politecnica de Catalunya, Barcelona, Spai

Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensityof the connections. These features, however, have mainly not been considered in past studies where links are usuallyrepresented as binary states, i.e. either present or absent. Here, we study the scientific collaboration network and theworld-wide air-transportation network, which are representative examples of social and large infrastructure systems,respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity orcapacity of the connections among the various elements of the network. We define new appropriate metrics combiningweighted and topological observables that enable us to characterize the complex statistical properties and heterogeneityof the actual strength of edges and vertices. This information allows us to characterize for the first time the correlationsamong weighted quantities and the underlying topological structure of the network. We also propose a model for thegrowth of weighted networks that couples the establishment of new edges and vertices and the weights’ dynamicalevolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting the statisticalproperties observed in several real-world systems.

[email protected]@[email protected]@th.u-psud.fr


Distribution of epicenters in the Olami-Feder-Christensen Model

Carmen P. C. Prado1 and Tiago P. Peixoto2

1,2 Depto FGE, Instituto de Fisica da USP, Sao Paulo, Brazil

We show that the well stabilished Olami-Feder-Christensen (OFC) model for the dynamics of earthquakes is able toreproduce a new striking property of real earthquake data (1). Recently, it has been pointed out by Abe and Suzuki(2) that the epicenters of earthquakes could be connected in order to generate a graph, with properties of a scale-freenetwork of the Barabasi-Albert type. However, only the non-conservative version of the model is able to reproducethis behavior. The conservative version, instead, behaves like a random graph. Besides indicating the robustness ofthe model to describe earthquake dynamics, those findingss reinforce that conservative and non-conservative versionsof the OFC model are qualitativelly different. Also, we propose a completely new dynamical mechanism that, withoutan explicit rule of preferential attachment, generates a free scale network. The preferential attachment is, in thiscase, a by-product of the long term correlations associated with the self-organized critical state. The detailed studyof the propertiies of this network can reveal new aspects of the dynamics of the OFC model, contributing to theunderstanding of self-organized criticality. (1) T. P. Peixoto, C. P. C. Prado, Phys. Rev. E 69 (2004) (2) S. Abe, N.Suzuki, Europhys. Lett 65, (2004)




First order phase transition in a simple social network dynamics

Matteo Marsili1, Frantisek Slanina2 and Fernando Vega-Redondo3

1 The Abdus Salam International Centre for Theoretical PhysicsStrada Costiera 11, 34014 Trieste Italy2 Institute of Physics Czech Academy of SciencesNa Slovance 2 CZ-182 21 Prague Czech Republic

3 Facultad de Economicas Universidad de Alicante03071 Alicante Spain

Social networks are important not only because their links are the support of profitable interactions between themembers of the community, but also because they allow information to disseminate briskly and broadly. This latterfunction is specially important if the environment is volatile so that individuals need to search continuously for freshopportunities. We present a model that captures this aspect in the simplest possible way. The model exhibits adiscontinuous phase transition, histeresis phenomena and a nono-trivial behavior in the dense phase. This explainsthe apparently paradoxical observation that although a networked society does not necessarily materialize even un-der favorable conditions it displays a significant resilience to deteriorating conditions. The phase transition is fullycharacterized within mean field theory. (appeared in PNAS February 10, 2004 vol. 101, p. 1439)



Productivity, Wealth and Scale-Free Networks

Tiziana Di Matteo1, Tomaso Aste2 and Stephen T. Hyde3

1,2,3 Applied Mathematics, Australian National University, 0200 Canberra Australia

Empirically it has been observed that the productivity of European firms is power-law distributed. Fat-tailed distribu-tions are also typically found in the wealth distributions (with different specific behaviours depending on the country);and similar behaviours characterize the distributions of other industrial dynamics indexes. The challenge to physicistsis to explain the origin of such power law tails. In the literature, this has been mimicked by multiplicative stochasticprocesses of exchanges among agents. We demonstrate that distributions with power law tails can emerge also fromadditive stochastic processes with interacting agents. In this case, we show that the network of connections amongagents plays a crucial role. Indeed, the resulting distributions are shaped directly by the degree distribution of thenetwork, and therefore Scale-Free Networks lead to power law-tailed distributions. Our original purpose was not toconstruct any realistic model; we planned only to demonstrate the possibility to obtain fat tails also without the useof multiplicative stochastic processes. Rather surprising we find that the results from such an additive process arein good qualitative agreement with the empirical data for the income distribution in Australia and explain well theproductivity distributions of European firms.




Searching good strategies in evolutionary minority game using variablelength genetic algorithm

Bing-Hong Wang1

1 Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

We propose and study a new adaptation minority game for understanding the complex dynamical behavior character-ized by agent interactions competing limited resource in many natural and social systems. We compare the strategyof agents in the model to chromosome in biology. In our model, the agents with poor performance during certaintime period may modify their strategies via variable length genetic algorithm which consists of cut and splice opera-tor, imitating similar processes in biology. The performances of the agents in our model are calculated for differentparameter conditions and different evolution mechanism. It is found that the system may evolve into a much moreideal equilibrium state, which implies much stronger cooperation among agents and much more effective utilization ofthe social resources. It is also found that the distribution of the strategies held by agents will tend towards a stateconcentrating upon small m region.

1 [email protected]


Intelligent Controlling Simulation of Traffic Flow at a Small CityNetwork

Mohmmad Ebrahim Fouladvand1

1 Dept. Physics, Zanjan University, P.O.Box 313, Zanjan , Iran.

We propose a two dimensional probabilistic cellular automata for description of traffic flow at a small city networkcomposed of two intersections. The traffic at the network is controlled by a set of traffic lights which can be operatedboth in fixed-time and traffic responsive manner. Vehicular dynamics is simulated and total delay experienced by thetraffic is evaluated within specified time intervals. We investigate both decentralized and centralized traffic responsiveschemes and in particular discuss the implementation of green-wave strategy. Our investigations prove that thenetwork delay strongly depends on the signalisation strategy. We show that in some traffic conditions, the applicationof green-wave scheme may destructively lead to increment of the global delay.

1 [email protected]

Chapter 5

Poster Presentations

5.1 Topic 1 : Rigorous results and exact solutions; general aspects ofstatistical physics; thermodynamics

5.1.1

The explanation of the mechanism of irreversibility in the frame of lawsof the classical mechanics

V.Somsikov1

1 Institute of Ionosphere,Almaty 480020, Kazakstan

Within the framework of laws of classical mechanics the mechanism of irreversibility is offered. Procedure of asubstantiation of the mechanism of irreversibility is consisting in the following. The closed nonequilibrium a hard diskssystem is prepared. Then it is splitting into interacting subsystems. The analysis of dynamics of one of subsystemsis carried out. For this analysis the generalized force, which resulting force of interaction of a subsystem with itsenvironment as a key parameter of dynamics is used. The analysis based on the generalized equations of Hamiltonand Liouville for the interacting subsystems. These equations were obtained with the help of the DAlambert equation.From conditions conservatism of all system and compatibility of dynamics of each of subsystems and system as a whole,with the help of generalized Liouville equation, the op-portunity of existence of two types of dynamics - irreversibleand reversible is obtained. Irre-versible dynamics is connected with the opportunity of decreasing of the generalizedforces, acting between subsystems. Reversible dynamics of nonequilibrium system is caused by existence of cyclic points(points of return) in phase space. Near to an equilibrium states at performance of linear ap-proach reversible dynamicsis possible only. The explanation of the mechanism of irreversibility for elastic disks is generalized all over again generalcase of potentially interacting elements. The connection between classical mechanics and thermodynamics is analyzed.

1 Mihailovich

137

138 CHAPTER 5. POSTER PRESENTATIONS

5.1.2

Investigations of energy and entropy of formation for AgxIn1-x liquidbinary alloys

G. M. Bhuiyan1,A. Z. Ziauddin Ahmed2 and M. D. Masud Rana3

1,2,3Department of Physics, University of Dhaka, Dhaka- 1000, Bangladesh

We have investigated the energy and entropy of formation for liquid AgxIn1-x binary alloys in the line of solid liquidphase separation and at an elevated temperature. A microscopic theory based on the first order perturbation hasbeen applied. This theory combines interionic interactions and a reference liquid as fundamental components. Theinterionic interactions and the reference liquid are described by a local pseudopotential and the effective hard sphereliquid, respectively. A new approach has been employed in the calculation of the entropy of formation. The results ofcalculations reveal a characteristic feature that the energy of formation in the phase separation line becomes minimumat the equiatomic composition, and thus indicates maximal miscibility and stability at this concentration. Takinginto account that we are calculating extremely small energy and entropy differences, the agreement with the availableexperimental data is good.KEY WORDS : Energy and entropy of formation, liquid binary alloys, line of phase separation, perturbation theory.

[email protected]

5.1.3

Morphological Thermodynamics: how do free energies depend onshape?

Peter Koenig1, Roland Roth2 and Klaus Mecke 3

1,2,3 Max-Planck-Institut fur Metallforschung, Stuttgart, Germany

We show that a thermodynamic potential of a fluid bounded by an arbitrarily shaped convex container can be calculatedfully from the knowledge of only four morphometric measures. This remarkable result is based on the assumption thata thermodynamic potential is an ”additive” functional which can be understood as a more precise definition for theconventional term ”extensive”. As a consequence, the surface tension and other thermodynamic quantities contain,beside a constant term, only contributions linear in the mean and Gaussian curvature of the container. Our findingsare tested numerically in the purely entropic system of hard spheres bounded by a hard wall and substantiated by thebehaviour of the density profile at the container wall.



5.1.4

Counting Multiple Solutions in Glassy Random Matrix Models

Nivedita Deo1

1 Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India

This is a first step in counting the number of multiple solutions in certain glassy random matrix models. We are ableto do this by reducing the problem of counting the multiple solutions to that of a moment problem. More precisely wecount the number of different moments when we introduce an asymmetry (tapping)in the random matrix model andthen take it to vanish. It is shown here that the number of moments grows exponentially with respect to N the sizeof the matrix. As these models map onto models of structural glasses in the high temperature phase (liquid) this mayhave interesting implications for the supercooled liquid phase in these spin glass models. Further it is shown that thenature of the asymmetry (tapping) is crutial in finding the multiple solutions. This also clarifies some puzzles raisedin literature.

1 [email protected]

5.1.5

The use of BurrXII and q-stretched exponential distributions foruniversality and selfsimilarity in complex systems.

F.Brouers1 and O.Sotolongo-Costa2

1 Institut de Physique,B5,University of Liege, 4000, Belgium.2 Department of Theoretical Physics, Habana UNiversity, Cuba.

For complex systems, many of the probability distributions used in physics, chemistry, biology, geology and socialand financial sciences belong to the domain of attraction of Levy stable distribution. Some of them have been derivedfrom the principle of maximum entropy (qmaxS) starting from the nonextensive form proposed by Tsallis. We showusing examples in various fields of natural and social sciences that the q-stretched exponential and more generally theBurrXII distributions obeying the qmaxS principle appear to be useful distribution functions to express universality,self-similarity and scaling laws in complex systems.

1 [email protected]


5.1.6

Study of thermodynamic properties of Sodium carbonate, Na2CO3

Mala N. Rao1 and S.L. Chaplot2

1,2 Solid State Physics Division, BARC, Mumbai-400085

Sodium carbonate (Na2CO3) has a couple of unique structural phase transitions with temperature. At high temper-atures (T¿760 K), the a phase is hexagonal with space group P63/mmc. With decrease in temperature, at T=760 K,through a process of lattice melting [1-4] Na2CO3 transforms to the b-phase, which is monoclinic (space group C2/m).Lattice melting is a phenomenon where long-range order is reestablished on cooling below the transition tempera-ture, by a process of continuous recrystallization. Currently, Na2CO3 is the only known example in nature, in whichthis phenomenon occurs. We have studied the lattice dynamical and thermodynamic properties of sodium carbonatethrough a combination of inelastic neutron scattering experiments and potential model calculations. We carried outinelastic neutron scattering studies at Dhruva reactor, Trombay, to determine the phonon density of states of theexternal modes of polycrystalline sodium carbonate Na2CO3 at room temperature and pressure. The experimentalresults have been analyzed on the basis of a lattice dynamics computation employing a rigid molecular ion model [5].The parameters were optimized to the available experimental phonon dispersion curves of calcite and then transferredto sodium carbonate. The computed values of lattice parameters and the computed phonon density of states are infairly good agreement with experimental data. Also, the calculated diffuse scattering corresponding to the soft modein the high temperature a phase is consistent with published experimental observations that suggest lattice meltingat the a-b phase transition. [1] M.J. Harris et al., Phys. Rev. Lett. 71 (1993) 2939; ibid. 79 (1997) 4846. [2] M.J.Harris et al., Phys. Rev. B51 (1995) 6758. [3] I.P. Swainson et al., J. Phys. Condens. Matter 7 (1995) 4395. [4]M.J.Harris et al., J. Phys. Condens. Matter 8 (1996) 7073. [5] K.R. Rao et al., Phys. Chem. Miner. 16 (1988) 83.


5.1.7

Space Groups and Galois Coverings in Two-Dimensional Lattice Models

Masafumi Fujimoto1

1 Kashihara, Nara 634-8521, JAPAN

Recently it was pointed out that the anisotropic correlation lengths of two-dimensional lattice models are representedby the use of simple algebraic curves [1-2]. In this paper we show that the representation is directly derived fromsymmetries of lattice models. The analyses of the eight-vertex model in [1-2] are extended. The eight-vertex modelis defined on the square and Kagome lattices rotated through an arbitrary angle ϕ with respect to the coordinateaxes. We exactly calculate eigenvalues of transfer matrices acting on zigzag walls. For each of the two lattices we findthe following properties: (i) the correlation function is expressed in terms of differential forms on Riemann surfacesof genus 1 [3]; (ii) analyticity of eigenvalues plays an important role to connect calculations for various angles ϕ; (iii)there is a one-to-one correspondence between the point group and a Galois covering of a suitable Riemann surface[4]. The properties (i-iii) are expected to be quite general. Using (i-iii), we can determine the anisotropic correlationlengths for a wide class of lattice models including unsolvable ones. [1]. M. Fujimoto, Physica A 233:485-502 (1996).[2]. M. Fujimoto, J. Stat. Phys. 90:363-388 (1998). [3]. M. Fujimoto, J. Phys. A:Math. Gen. 35:7553-7557 (2002).[4]. M. Namba, Branched Coverings and Algebraic Functions (Longman).

1 [email protected]


5.1.8

Statistical Mechanics in the Extended Gaussian Ensemble

Ramandeep S. Johal1, Antoni Planes2 and Eduard Vives3

1,2,3 Dept. of ECM, University of Barcelona, Diagonal 647, 080028 Barcelona, Spain

We introduce the extended gaussian ensemble (EGE),as a generalization of the canonical ensemble. The new ensembleis an extension of the Gaussian ensemble introduced previously by J. H. Hetherington [J. Low Temp. Phys. 66, 145(1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finitereservoir and from the Maximum Statistical Entropy Principle. The probability of each microstate depends on twoparameters β and γ which allow to fix, independently, the mean energy of the system and the energy fluctuationsrespectively. We establish the Legendre transform structure for the generalized thermodynamic potential and proposea stability criterion. As an example, an application to a system with few independent spins is presented.


5.1.9

Anomalous Distribution and Superstatistics

F.Brouers1, O.Sotolongo-Costa2 and A.Gonzalez3

1 Institute of Physics, B6, University of Liege, 4000, Belgium2 Department of Theoretical Physics, Chair Henri Poincare, University of Havana, Cuba.

3 Department of Physics, Matanza University, Cuba.

We show how anomalous distributions encountered in physical, chemical, biological economical and social complexsystems can arise from superstatistics concepts. In particular we show how the Singh and Maddala distribution usedfor more than three decades to fit income and other economical data can be used successfully in a variety of complexdynamical and non-equilibrium systems.

1 [email protected]


5.1.10

The Universal Evolution Criterion Fails on Chaotic Strange Attractors

Ladislav G. Andrey1

1 Department of Nonlinear Dynamics, Institute of Computer Science, Academy of Sciences, Prague, Czech Republic

In the analogy with the Prigogine’s nonequilibrium thermodynamics the so called universal evolution criterion ofGlansdorff-Prigogine is formulated for the celebrated dynamical Lorenz system, generating the deterministic chaos.Then it is shown in detail numerically that such criterion fails on the Lorenz strange attractor. From this it can bededuced that the evolution criterion of Glansdorff-Prigogine is not universal in this sense. Suggestions are made how toanswer a natural question what would be possible evolutionary principles gowerning a behaviour of such systems. Alas,in general the question still remains very open. This research was partly supported by the grant GACR 305/02/1487A.

1 [email protected]

5.1.11

Canonical ensemble in a generalized thermostatistics

Jan Naudts1

1 Physics Department, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen Belgium

In systems with many degrees of freedom the choice of equilibrium probability distribution of a canonical ensemble isnot very critical because, due to the entropy effect, only microstates with approximately the right energy contributeto ensemble averages. Hence the Boltzmann-Gibbs (BG) distribution is a convenient choice. In open systems witha limited number of degrees of freedom energy can fluctuate strongly and distributions other than BG are relevant.In [1,2,3] a formalism has been developed in which the form of the equilibrium distribution, determined by thechoice of entropy functional, is not specified in advance. It is shown that equilibrium distributions still reproducethe basic thermodynamic relations and satisfy thermodynamic stability. As an application it is shown how Tsallis’thermostatistics, with some slight modifications, fits into the general theory. [1] J. Naudts, arXiv::cond-mat/0211444,Physica A332, 279-300 (2004). [2] J. Naudts, arXiv::cond-mat/0311438, to appear in Physica A. [3] J. Naudts,arXiv::math-ph/0402005.

1 [email protected]


5.1.12

Complex Networks: state of the art

Jose Fernando Ferreira Mendes1

1Physics Department, University of Aveiro, Aveiro, Portugal

Significant research efforts have recently been made in the study of complex networks. I will review some of theimportant results on this field. I will also present some recent studies about the spectra of the adjacency/transitionmatrices of correlated and uncorrelated random Bethe lattices. Exact equations will be presented. Together, a simpleapproximation will be used to calculate the spectra of random and scale-free graphs. The results will be comparedwith previously obtained (numerical, simulations and empirical) results.

[email protected]

5.1.13

Statistical transport in Hamiltonian systems

Madalina Vlad1 and Florin Spineanu2

1,2 National Institute of Laser, Plasma and Radiation Physics, Magurele, Bucharest, Romania

Test particle motion in stochastic velocity fields is a generic problem in various topics of fluid and plasma turbulenceor solid-state physics. In this context, the stochastic motion in 2-dimensional divergence-free velocity fields is a specialcase that cannot be studied by means of the existing methods. This is a consequence of the Hamiltonian nature of theequation of motion that leads to trajectory trapping. A new method that is able to describe this process of dynamicaltrapping and to yield the statistical characteristics of the trajectories is presented. It applies to homogeneous stochasticfields with Gaussian distribution, either static or time dependent with stationary Eulerian correlation function. Wehave shown that the statistical behaviour of the trapped trajectories is completely different from that of the freetrajectories. The trapped trajectories have a quasi-coherent behaviour. Their average displacement, dispersion andprobability distribution function saturate. Their clump lifetime is very large compared to the time of flight. Thisshows that these trajectories form structures similar with fluid vortices. The trajectories contained in such structuresdo not contribute to the large time diffusion coefficient. The later is determined by the free trajectories, which havea continuously growing average displacement and dispersion. The probability distribution function for each type oftrajectories is non-Gaussian. The general conclusion of this work is that the Hamiltonian evolution equation determineslong-time correlations (memory effects) and coherence (trajectory structures) in the stochastic motion.



5.1.14

Integrable vertex models with general boundary conditions

Marcio J. Martins1

1 Universidade Federal de Sao Carlos, Departamento de Fisica, Sao Carlos, Brazil

We formulate the algebraic Bethe ansatz solution of a variety of isotropic vertex models with general non-diagonaltoroidal boundary conditions. This includes the systems basead on mixed representations of the SU(N) symmetry andthe infinite dimensional representation of the non-compact SU(1,1) Lie algebra. The structure of the transfer matrixeigenvectors consists of multi-particle states and the corresponding eigenvalues depend crucially on the boundarymatrix eigenvalues. We also discuss the peculiar case of twisted boundaries associated to singular matrices.

1 [email protected]

5.1.15

Decomposition of Levy stable self-similar processes

Aleksander Weron1 and Krzysztof Burnecki2

1,2 Hugo Steinhaus Center, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland

We employ ergodic theory to demonstrate the foundations of ubiquity of Levy stable self-similar processes in physicsand present a catalog of models for nonextensive diffusion defined by the Tsallis q-entropy and the anomalous diffusionphenomena in the Langevin equation framework. We construct the canonical decomposition of all such processes andidentify the three components with mixed fractional motion, harmonizable and evanescent processes, respectively.The first process corresponds to a dissipative part and two other to a conservative part of the dynamics. Thepresented complete description of all Levy stable and self-similar process could provide new insights into the mechanismunderlying a range of self-similar natural phenomena. Our results answer the question how rich is the class of all self-similar models driven by Levy stable noise.



5.1.16

Topological Perturbation in Transverse Ising chain and XY -chain

Asuka Sugiyama1,Hidenori Suzuki2 and Masuo Suzuki3

1,2,3Department of Applied Physics, Tokyo University of Science 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601Japan

We study the spontaneous magnetization at the boundary in the transverse Ising chain and in the anisotropic XY -chain using the topological perturbation method. We apply the topological perturbational interaction J2 betweenboundary spins. The interaction J2 changes the topology of the chains. The correlation function C between boundaryspins can be derived from the derivative −∂f2/∂J2, where f2 is the free energy for the topological perturbation. Inthe case of a non-vanishing J2, C becomes a short-range correlation function, whereas it reduced to the long-rangecorrelation function at J2 = 0. The correration function C becomes zero at finite temperatures in both chains. AtT = 0, C is expressed as 2(1−h2)/[h(h2 + γ2− 1)1/2−h2 + γ +1] in the anisotopic XY -chain, where Jx,y = J1(1± γ)is the interaction and h = µBH/2J1 (H is a uniform magnetic field in the z-direction). In the transverse Ising chain,C becomes 1− h2, namely the square of the spontaneous magnetization at the boundary.


5.1.17

Entropy changes in the cosmological many body problems: A statisticalmechanical approach

Naseer Iqbal1

1Department of Physics, University of Kashmir, Srinagar - 190 006 (J and K),India

The entropy changes in the large scale structure of universe on the basis of statistical mechanics is studied by startingwith the grand canonical partition function ZG of particles (galaxies) in an ensemble of universe. Different entropycontours for different values of numberdensity n and temperature T are analytically derived and the behaviour isstudied as a function of the measuring correlation parameter b (0 - 1). The results of both point mass particles(galaxies) and extended mass particles (galaxy) are compared and in the limit of point masses, the results reducedexactly to previous results derived from thermodynamical arguments. Thus providing a new mode fundamental basesfor the earlier results. Key words: Cosmology: theory - galaxies: clusters: general - gravitation- large scale structureof universe

1dr [email protected]


5.1.18

Expansion around mean field in quantum magnetic systems

Ferdinando de Pasquale1 and Salvatore Marco Giampaolo2

1Physics department University ”La Sapienza” P.le Aldo Moro 5, 00185 Roma (Italy)2Physics department University di Salerno I-84081 Baronissi (Sa) Italy

We introduce a new definition of ordered phase in a magnetic system based on properties of the local spin stateprobability. A statistical functional associated to this quantity depends both on amplitude and direction of the localmagnetization. We show that it is possible to introduce an expansion at fixed magnetization amplitude in the inverse oflattice coordination number if the direction is selected by an extremum condition. In the limit of infinite coordinationnumber we recover the mean field results. First order corrections are derived for the Ising model in the presence of atransverse field and for the xy. Our results concerning critical temperature and order parameter compare favorablywith other approaches.

[email protected]@sa.infn.it

5.1.19

Mixed integrable vertex models with arbitrary twists

Giuliano Augustus Pavan Ribeiro1 and Marcio Jose Martins2

1,2 Departamento de Fisica, Universidade Federal de Sao Carlos, Sao Carlos, Brasil

We formulate the quantum inverse scattering method for integrable vertex models with non-diagonal toroidal boundaryconditions based on higher spin representation of SU(2), for the non-compact symmetry SU(1, 1) and for the vectorand dual representations of SU(N). We exhibit explicitly the eigenvectors and the eigenvalues of the respectivetransfer matrices in terms of the Bethe ansatz roots. We also discuss an approach to related the eigenvectors of thetransfer matrix with non-diagonal twists and standard periodic boundary conditions which became fundamental tosolve general singular boundaries.



5.1.20

Topological Perturbation and Spontaneous Symmetry Breaking inTwo-Dimensional Ising Model

Hidenori Suzuki1, Shu-Chiuan Chang2 and Masuo Suzuki3

1,2,3 Department of Applied Physics, Tokyo University of Science 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601Japan

Using the topological perturbation method, we study the boundary spontaneous magnetization of the square latticeIsing model with the periodic boundary condition in the horizontal direction and free boundary condition in the verticaldirection. The topological perturbational interaction J ′ between the free boundaries changes the topology of the lattice.The correlation function C between oppsite boundary spins can be derived from the derivative −∂f(J ′)/∂J ′, wheref(J ′) is the free energy for the topological perturbation per boundary site. In the case of a non-vanishing J ′, C denotesshort-range correlation, whereas it becomes the long-range correlation at J ′ = 0. Below the critical temperature, thecorrelation function C at J ′ = 0 becomes non-zero even in the thermodynamic limit, and we derive exactly that C issquare of the boundary spontaneous magetization obtained by McCoy and Wu.



5.1.21

The Anisotropic XY-Model on the 1D Inhomogeneous Periodic Lattice

Tayroni Francisco de Alencar Alves1,Lindberg Lima Goncalves2 and Jose Pimentel de Lima3

1,2Departamento de Fisica, Universidade Federal do Ceara, Campus do Pici, CP 6030, 60451-970 Fortaleza, Ceara,BRAZIL

3Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina, Piaui, BRAZIL

The static and dynamic properties of the anisotropic XY-model (s = 1/2) on the inhomogeneous periodic chain(composed of N segments with n different bonds) in a transverse field h are obtained exactly at arbitrary temperatures.They are determined by introducing the generalized Jordan-Wigner transformation and by reducing the problem toa diagonalization of a finite matrix [2] of n-th order. The diagonalization procedure is discussed in detail and thecritical behaviour induced by the transverse field, at T = 0, is presented. The quantum transitions are determinedby analising the behaviour, as functions of the field, of the induced magnetization

⟨SZ

j,m

⟩(where j denotes the

segment and m the site within the segment) and the correlation⟨SX

j,mSXl,r

⟩for large spin separations. These results,

which are obtained for infinite chains, correspond to an extension of the ones obtained by Zhong and Tong[3] forfinite chains. The dynamic correlations,

⟨SZ

j,m(t)SZl,r

⟩, and the dynamic susceptibility χZZ

Q (ω) are also obtained atarbitrary temperatures. Explicit results are also presented in the limit T = 0, where the critical behaviour occurs, forthe static susceptibility χZZ

Q (0) as a function of the transverse field h, and for the frequency dependency of dynamicsusceptibility χZZ

Q (ω).

References:[1] E. Lieb, T. Schultz, D. Mattis, Ann. Phys. (NY) 407 16 (1961).[2] J. P. de Lima and L. L. Goncalves, J. Magn. Magn. Mater. 226-230, 650 (2001).[3] P. Tong and M. Zhong, Physica B 304 91 (2001) Work partially financed by the Brazilian Agencies CNPq, Capesand Finep.


5.1.22

Gap distributions in competitive two species adsorption

Maria R. D’Orsogna1 and Tom Chou2

1Dept. of Chemical Eng. Caltech2Dept. of Biomathematics UCLA

We consider the successive adsorption of different-sized molecules on a one-dimensional lattice. We compute the gapdistribution remaining after the first species of segments have been deposited. A second, shorter segment is thenallowed to bind, and their adsorption inetics are computed using the gap distribution left by the first, longer segments.The cases of freely sliding and fixed (random sequential adsorption) initial and final particles are considered. Ourasymptotic results are compared with Monte Carlo simulations.

[email protected]@ucla.edu


5.1.23

A Unified System of Quantum Stochastic Differential Equations forBoson and Fermion

T. Arimitsu1, T. Hayashi2 and A.E. Kobryn3

1,2 Institute of Physics, University of Tsukuba, Ibaraki 305-8571,3 Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan

A unified canonical operator formalism for quantum stochastic differential equations, including the quantum stochasticLiouville equation and the quantum Langevin equation both of the Ito and the Stratonovich types, is presentedwithin the framework of Non-Equilibrium Thermo Field Dynamics (NETFD). It is performed by introducing anappropriate martingale operator in the Schrodinger and the Heisenberg representations with fermionic and bosonicBrownian motions. In order to decide the double tilde conjugation rule and the thermal state conditions for fermions,a generalization of the system consisting of a vector field and Faddeev-Popov ghosts to dissipative open situations iscarried out within NETFD. NETFD is a unified formalism, which enables us to treat dissipative quantum systemsby the method similar to the usual quantum mechanics and quantum field theory, which accommodate the conceptof the dual structure in the interpretation of nature, i.e. in terms of the operator algebra and the representationspace. See A.E. Kobryn, T. Hayashi and T. Arimitsu, Annals of Physics 308/2 (2003) 395–446 [math-ph/0304023]Quantum Stochastic Differential Equations for Boson and Fermion Systems — Method of Non-Equilibrium ThermoField Dynamics and the references therein.


5.1.24

R-matrices and Spectrum of Vertex Models based on Super Algebras

Wellington Galleas1 and Marcio Jose Martins2

1,2 Universidade Federal de Sao Carlos, Departamento de Fisica, C.P. 676, CEP 13565-905, Sao Carlos (SP),Brazil

We investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariantrelative to q-deformed superalgebras sl(c2)(r|2m), osp(c1)(r|2m) and osp(c2)(r = 2n|2m) with Coxeter automorphismscl. The R-matrices are presented in terms of the standard Weyl basis and the corresponding transfer matrices arediagonalized by means of the quantum inverse scattering method.



5.1.25

Nonequilibrium steady states and thermodynamically equivalentequilibrium models

R. A. Blythe1

1Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK

The equilibrium Lee-Yang theory of phase transitions has recently been shown to apply to nonequilibrium steadystates. An intriguing result is that the microscopic transition rates used to define the model seem to play the roleof fugacities. In this poster, this observation is elucidated by establishing the thermodynamic equivalence of theasymmetric exclusion process (ASEP) with various microscopic update rules and equilibrium random walks on thelattice. In the latter picture, one finds the transition rates are fugacities. Further, one gains an additional insight intothe robustness of the ASEP phase diagram to changes of the updating scheme.

[email protected]


5.2.1

A Model for Ferromagnetic Martensites

S. Sreekala1 and G. Ananthakrishna2

1,2 Materials Research Centre, Indian Institute of Science, Bangalore -560012, India

We consider a recently introduced 2-D square-to-rectangle martensitic model that explains the power law behaviorof the acoustic signals and the shape memory effect[1] to study the ferromagnetic martensites. The original modelincludes inertial effects, long-range interactions, dissipation and inhomogeneous stress field to mimic nucleation atdefect sites . The strain order parameter is coupled to the magnetic order parameter through a 4-state clock model. Ingeneral, as both the austenite and martensite phases have their own curie temperatures, TC

A and TCM respectivley,

six different orderings are possible among TCA, TC

M and the austenite - martensite transformation temperatureTM−A, of which two are discussed here: a)TC

M < TM−A < TCA and b) TC

A < TCM < TM−A. For both cases, we

observe change in orientation of the magnetic order parameter as one crosses the marensite- martensitic interface ormartensite- austenite interface. We find that the magnetic orientation is along the short axis of the rectangular variantin 2-D and does not depend on the size of the martensitic domains. In general the contribution to the magnetizationis due to both the growth of martensite domains and the lowering of temperature. The model shows a subtle interplaybetween the growth of strain order parameter (martensitic domains) and magnetic order parameter with decrease intemperature, a feature that cannot be captured in earlier models. The magnetization curves obtained from the modelare similar to that predicted earlier. Reference 1)R. Ahluwalia and G. Ananthakrishna, Phys. Rev. Lett., vol 86, 4076(2001), S. Sreekala and G. Ananthakrishna, Phys. Rev. Lett., vol 90, 135501(2003).



5.2.2

The fluctuation-dissipation relation in phase-ordering systems

Federico Corberi1,Claudio Castellano2,Eugenio Lippiello3 and Marco Zannetti4

1,3,4Dipartimento di Fisica “E. R. Caianiello2Dipartimento di Fisica, Universita

The integrated response function in phase-ordering systems with scalar, vector, conserved and non conserved orderparameter is studied at various space dimensionalities. Assuming scaling of the aging contribution χag(t, tw) =t−aχw χ(t/tw) we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing

the dimensionality dependence of aχ in all cases considered. The primary result is that aχ vanishes continuouslyas d approaches the lower critical dimensionality dL. This implies that i) the existence of a non trivial fluctuationdissipation relation and ii) the failure of the connection between statics and dynamics are generic features of phaseordering at dL.

[email protected]@[email protected]@na.infn.it


5.2.3

Phase equilibria in laser matrix YLiF[sub4]: a computer simulationstudy

A. Sen1,S. L. Chaplot2 and R.Mittal3

1Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India

Ternary halide YLiF4 displays several structural phase-transitions upon compression[1,2], which turns out to be uniquein comparison of isostructural CaWO4[3]. While the latter has a scheelite(I41/a,Z=4) to wolframite(P21/c,Z=4)sort of high-pressure phase transformation, the former shows in addition an intermediate fergusonite-like phase,associated with a soft phonon mode[1]. Recently, the post-fergusonite phase of YLiF4 has been predicted aswolframite-like monoclinic one[2,4]. Interestingly, the axial ratio in both the compounds evolves in a differentway under the effect of pressure[3]. A possible phase diagram of YLiF4 is drawn to understand the underlyingphysics at the microscopic level. We make use of constant-temperature and constant-pressure molecular dynamicssimulations that are further complemented by quasi- harmonic lattice dynamical calculations[5]. A comparison of therespective Gibbs free energies allows us to account for the relative stability of several structural modifications in YLiF4.

References:[1] A. Sen et al, J. Phys.: Condens. Matter 14, 975(2002); F. J. Manjon et al, Phys. Rev. B64,235108(2002); A.Grzechnik et al, Phys. Rev. B65,104102(2002).[2] A. Sen et al, Phys. Rev. B68,134105(2003).[3] D. Errandonea et al, J. Solid State Chem.(2004).[4] Sa Li et al, J. Phys.: Condens. Matter 16,1(2004).[5] A. Sen et al, Phys. Rev. B64,024304(2001).



5.2.4

Multiply reentrant liquid-liquid phase transitions in ethanol-watermixture induced by ions

Debjani Bagchi1, Anil Kumar2 and Reghu Menon3

1,3 Department of Physics, Indian Institute of Science, Bangalore - 560012. India.2 (deceased)Department of Physics, Indian Institute of science, Bangalore - 560012, India.

Liquid alcohol(e.g, methanol, ethanol)-water mixtures have attracted considerable attention recently because of thepresence of ordered structures in these systems [1] . Controlled addition of certain electrolytes causes the mixtureto phase separate. We have observed that a mixture of ethanol + water + sulphate salt shows four liquid-liquidphase transitions on monotonically varying a single field variable (temperature) at a fixed mixture composition. Thisrich and unique phase behaviour could be a result of subtle interplay of entropy and short-range interactions likeH-bonding, ion-dipole and Van der Waals interactions. The multiplicity of reentrance can be tuned by changing thesize of the ions of the electrolyte added. A prominent feature of the phase diagram is the presence of two specialcritical points - Critical Double Point (CDP) and Double Critical Point (DCP) (critical exponents double at thesepoints) formed by the merger of two ordinary critical points. Triple reentrance exists in a very narrow range ofsalt concentrations (0.0005 weight fraction), which necessitates a high degree of accuracy and resolution for dataacquisition. This range shrinks on decreasing the salt concentration and a limiting case is the merger of the CDP andthe DCP leading to the Critical Inflection Point (theoretically, there could be a tripling of critical exponents at thispoint). This is the first experimental observation of a systematic merger of these two special critical points. Thesefeatures make this system potentially significant for studying the role of electrolytes in modifying the ubiquitous 3DIsing behavior [2], to elucidate the role of supramolecular structures in modifying the criticality, and to interpretprotein liquid-liquid phase transitions. *This work is dedicated to the memory of Late Prof. Anil Kumar.

References:[1] J.H. Guo et al, Phys. Rev. Lett. 91 157401(2003).[2] H. Weingartner, W. Schroer, Adv. Chem. Phys. 116, 1(2001).


5.2.5 Poster 5.2.5 moved to the Oral Section.


5.2.6

Monomer-Monomer Reactions on a Two-Dimensional RandomCatalytic Substrate

G. Oshanin1, M. N. Popescu2 and S. Dietrich3

1 Laboratoire de Physique Theorique des Liquides, Universite Paris 6, FRANCE2,3 M.P.I. fur Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, GERMANY

We present a model of a monomer-monomer reaction A + B → ∅ on a two-dimensional inhomogeneous, catalyticsubstrate and study the equilibrium properties of the two-species adsorbate. The substrate is modeled as a regularlattice of adsorption sites and contains randomly placed catalytic bonds of mean density q which connect neighboringadsorption sites. The interacting A and B species undergo continuous exchanges with corresponding adjacent gaseousreservoirs. An instantaneous reaction A+B → ∅ occurs when A and B particles occupy sites connected by a catalyticbond. For annealed disorder in the placement of the catalytic bonds, the model is mapped onto a classical spin modelwith spin values S=-1,0,+1. In a particular case, it reduces to an exactly solvable Blume-Emery-Griffiths model, whichallows us to derive analytically the pressure of the adsorbate. We show that at equal partial vapor pressures of the twospecies the coverage exhibits a second-order phase transition which reflects a spontaneous symmetry breaking withlarge fluctuations and progressive covering of the entire substrate by either one of the species. Ref.: G. Oshanin, M. N.Popescu, and S. Dietrich, ”Exactly Solvable Model of Monomer-Monomer Reactions on a Two-Dimensional RandomCatalytic Substrate”, cond-mat/0311618.


5.2.7 Poster 5.2.7 moved to the Oral Section.5.2.8

Directed percolation process with a long-term memory

Hyunggyu Park1,Heung Sik Park2,Sungchul Kwon3 and Meesoon Ha4

1,4School of Physics, Korea Institute for Advanced Study, Seoul, Korea2Department of Physics, Inha University, Inchon, Korea

3ITF, Forschungszentrum, Juelich, Germany

The pair contact process with diffusion (PCPD) has attracted considerable interest recently, due to a possibilityof a new universality class distinct from well-established directed percolation (DP) and directed Ising (DI) classes.Although various scenarios are suggested based on numerical and field theoretical results, its critical properties havenot been clarified yet. A few years ago, one of us pointed out that the long-term memory in the PCPD model isthe main source of this new universality class and suggested a possibility of continuously varying critical exponentsdepending on the memory strength. In this study, we set up a DP-based cyclically coupled model where we candirectly control not only the memory strength but also its power-law tail exponent. Our numerial simulation resultsstrongly support our previous claim in the PCPD model.

[email protected]@[email protected]@kias.re.kr


5.2.9

Quasiaverages and equilibrium states of condensed media withspontaneously broken symmetry

Anatoly Petrovich Ivashin1, Michail Yurievich Kovalevsky2 and Lyubov Viktorovna Logvinova3

1 Akademicheskaya str.,1. National Science Centre ”Kharkov Institute of Physics and Technology”, kharkov,Ukraine, 61108

2,3 Pobedy str.,85, Belgorod State University, Belgorod, Russia, 308007

The classification of equilibrium states of condensed media with spontaneously broken symmetry is carried out in viewof possible nonuniform structure. The used approach is founded on the quasiaverages concept [1]. The symmetryproperties of equilibrium state are defined from requirements of the residual and spatial symmetry. This approachis founded on the representation of the residual symmetry of the degenerated equilibrium state as a subgroup of anormal phase symmetry. The states with singlet and triplet pairing in superfluid liquid [2], the states of superfluidnuclear matter with d-pairing [3], liquid crystal states of matter are considered in this report. Admissible conditionsof the spatial symmetry and the general structure of the corresponding generator are found. For above-mentionedstates the explicit form of residual symmetry generator is fined and the corresponding equilibrium structures of orderparameter are obtained. The requirement of residual symmetry is expanded on the inhomogeneous equilibrium states,the relation to the homogeneous case has been found. 1. N.N. Bogolyubov. // Proceedings of the Steklov Institute ofMathematics, Iss. 2, 1988. 2. M.Yu. Kovalevsky, S.V. Peletminsky. // Physics of Particles and Nuclei, Vol. 33, N 6,2002. 3. A.P. Ivashin, M.Yu. Kovalevsky, N.N. Chekanova. // Fiz. Nizk. Temp., Vol. 6, 2004.


5.2.10

Phase transitions in periodically driven macroscopic systems

Sreedhar B. Dutta 1

1 Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005,INDIA

We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain rangeof the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is thatof certain other equilibrium systems. We then illustrate with a few examples how the conventional knowledge of theequilibrium systems can be made use in choosing the driving fields to engineer new phases and to induce new phasetransitions.

1 [email protected]


5.2.11

The eigenvalue distribution of the time-evolution operator ofnon-equilibrium systems

Yuichi Nakamura1 and Naomichi Hatano2

1 Department of Physics, University of Tokyo, Tokyo, Japan2 Institute of Industrial Science, University of Tokyo, Tokyo, Japan

We propose a new algorithm of analyzing the phase transition of a non-equilibrium system with a flow. The phasetransition manifests itself in the eigenvalue distribution of the time-evolution operator. We discuss two deterministicone-dimensional cellular automata, the rule184 and the EBCA1 (the extended Burgers cellular automaton 1), as adiscrete traffic-flow model. Under the periodic boundary condition, we can have the free phase and the congestedphase. We use a new time-evolution operator with the flow operator incorporated as a perturbation. Specifically, wegeneralize the matrix elements corresponding to the flow of a specific car from unity to eg. This technique was firstintroduced to an electron system to discuss the localization of electrons in a random potential, namely the Andersonlocalization, by making the transfer energy asymmetry [1]. We here apply it to classical systems. Consequently, theeigenvalue distribution of the new time-evolution operator shows a remarkable difference between the free phase andthe congested phase. We can thus regard the congested phase as a localized state and the free phase as an extendedstate. Furthermore, the distance of the eigenvalues from the origin is related to the average velocity and the flux. [1]N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996); Phys. Rev. B 56, 8651 (1997)


5.2.12

Universality of the diluted two-dimensional Ising model

Paulo Henrique Martins1 and Joao Antonio Plascak2

1Universidade Federal do Tocantins, Caixa Postal 111, 77001-970, Palmas, TO - Brazil2Departamento de F

Magnetic materials are, in real life, very different from that pure idealized systems. Usually, they have defects andnon-magnetic impurities. A fundamental question about these systems (so-called diluted magnets) concerns theiruniversality classes. According to Harris criterion, the critical behavior of the pure system is (not) affected by dilutionif the specific heat critical exponent αpure is positive (negative). If αpure = 0, as the two-dimensional Ising model, thiscriterion is inconclusive. Several theoretical and simulational works have attempted to determine the universality classof this model. Actually, there are two main scenarios: the strong universality, that claims the diluted system belongsto the same class of the pure one, and the weak universality, in which the critical exponents vary continuously withdilution. In this work we evaluate the order parameter probability distribution function for different spin concentrationsp on square lattices, by using extensive Monte Carlo simulations (up to 9.0 × 107 MC steps per spin). Our resultsstrongly show that the universality class of the two-dimensional Ising model is in fact independent of the amount ofdilution. Nevertheless, the correction to s caling exponent is found to be sensible to dilution.

[email protected]@fisica.ufmg.br


5.2.13

Experimental investigation of disorder-influenced first order transition

M. A. Manekar1, M. K. Chattopadhyay2, K. J. S. Sokhey3, S. B. Roy4, and P. Chaddah5

1,2,3,4,5 Low Temperature Physics Laboratory, Centre for Advanced Technology, Indore 452013, India

The actual composition in any alloy or doped compound may vary around some average composition simply due to thedisorder that is frozen in as solid crystallizes from the melt. It was proposed earlier that such static, quenched-in, purelystatistical compositional disorder can under certain circumstances introduce a landscape of transition temperature ina system undergoing first order transition. Such disorder-influenced first order transition appears to be the commonunderlying physics in many novel materials of current interest namely, CMR manganites, magnetocaloric materials,shape memory alloys, relaxor ferroelectrics and vortex matter. We highlight the generality of this phenomenon, withour experimental studies performed on a test bed magnetic material both as a function of temperature and magneticfield. We identify certain experimental features mainly based on phase-coexistence and metastability, which can beused as characteristic features of a disorder-influenced first order transition process. In addition we show that in manyof these systems there is kinetic arrest of first order transition process in certain region of the field-temperature phasespace, giving rise to interesting glassy behaviour.


5.2.14

Critical Dynamics: theory for time-dependent intensity correlationsmeasured by X-ray microdiffraction

Klaus Mecke1, Cristian Mocuta2 and Harald Reichert3

1,3 Max-Planck-Institut fur Metallforschung, Stuttgart, Germany2 ESRF, Grenoble, France

We studied the dynamics of critical fluctuations in Fe3Al, which exhibits an order-disorder phase transition (DO3-B2,TC =780 K). In the experiments we used a well focused beam to probe a sub-micron sized single crystalline sample,so that the size of fluctuating domains is large compared to the probed volume due to the diverging correlation lengthclose to TC . Pronounced effects on the time-course of the intensity of a superstructure peak (characteristic for thechemical order) were measured. Starting from a stochastic Langevin equation for the fluctuations of a non-conservedorder-parameter (model A) the four-point structure function can be calculated and directly related to the measuredtime-dependent intensity-intensity correlation function. The analytical expression fits very well the experimental datasets fixing the correlation time τ as only free parameter of the theory. We find a strong dependence on temperature, inparticular an increase of τ close to the critical point. The agreement of theory and experiments - even for various spatialand time resolutions - demonstrate the potential of partially coherent x-ray microbeams for the direct observation ofdynamical phenomena at critical phase transition.

1 [email protected]


5.2.15

Monte Carlo Study of the Anisotropic Three-Dimensional HeisenbergModel in a Crystal Field

Rodrigo Teixeira Santos Freire1, Joao Antonio Plascak2 and Bismarck Vaz da costa3

1,2,3 Departamento de Fisica - ICEx - Universidade Federal de Minas Gerais. Belo Horizonte - Brazil

We study the phase diagram of the three-dimensional classical ferromagnetic Heisenberg model with an easy-plane crys-talline anisotropy and an easy-axis exchange anisotropy through Monte Carlo simulations. We employ the Metropolisalgorithm together with single-histogram techniques in order to characterize the transitions in each region of the phasediagram. Our results reveal, besides the disordered phase, the existence of Ising-like and XY-like ordered phases whichare separated by a first-order transition line.


5.2.16

Two-dimensional O(n) model in a staggered field

Dibyendu Das1 and Jesper Lykke Jacobsen2

1 Physics Department, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India2 Laboratoire L.P.T.M.S., Universite Paris-Sud, Batiment 100, F-91405 Orsay, France

Nienhuis’s truncated O(n) model gives rise to a model of self-avoiding loops on the hexagonal lattice, each loop havinga fugacity of n. We study such loops for a particular kind of staggered field w, which for n →∞ has the geometricaleffect of breaking the three-phase coexistence, linked to the three-colourability of the lattice faces. Via the Coulombgas formalism, an exact mapping, and transfer matrix studies, we have established the full phase diagram with thecritical branches and renormalization group flows in the (T, w, n) parameter space. One particularly interesting resultis that at T = 0, for w > 1, the model flows to the ferromagnetic q−state Potts model with q = n2 states. We also havenew results on the Benjamini and Schramm’s RGB loops on triangular lattice (namely that their fractal dimensionDf = 3/2), and its variants with a staggered field. Our paper reference is J. Phys. A: Math. Gen. 37(2004)1− 35 (toappear).



5.2.17

Instability threshold in a 1D driven diffusive system: ASEP withnonlocal hopping

Meesoon Ha1 and Hyunggyu Park2

1,2 School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea

We study the instability threshold of nonlocal hopping in a one-dimensional driven diffusive system with a 1D parkinggarage model [PRE 66, 036118 (2002)]. Nonlocal hopping of cars, controlled by probability P , promotes clustering andcoarsening towards a phase-ordering state. As a result, a new phase, namely Fully-Condensed (FC) phase, appears andthe system undergoes nonequilibrium phase transitions from the FC phase to the conventional condensed, maximal-current, and normal phases at finite P . We determine the value of the instability threshold Pc by the mean-fieldtheory and numerical simulations. Above Pc, all three conventional phases become unstable against the FC phasewhich occupies the whole phase space, while, below Pc, they become stable and manifest simultaneously in the phasediagram. We give an intuitive argument on the nature of the phase transitions at the instability threshold, which isnumerically confirmed.


5.2.18

Deposition and evaporation of hard rods in two dimensions : Static anddynamic orientational correlations

M. D. Khandkar1 and Mustansir Barma2

1,2 Dept. of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai-400 005

Deposition and evaporation of hard rods in two dimensions is studied using Monte Carlo simulations. The ratio κof deposition and evaporation rates controls the equilibrium density ρ of rods, and increasing κ beyond κc leads toa transition to a nematic phase characterised by algebraically decaying orientational correlations. We monitor thecorrelation functions g`(r, t) = 〈cos[`(θ(r, t) − θ(0, 0))]〉 for l = 2 and 4, where θ denotes the orientation of the rods.We find g`(r, 0) ∼ r−η` and g`(0, t) ∼ t−β` for both ` = 2 and 4, where both η` and β` vary continuously with κ.Our results for the static case agree with those for a conserved number of rods [1]. An effective phenomenologicaldescription of the non-conserved orientational field is given by ∂tθ = D∇2θ + ξ. Here ξ denotes white noise andD is expected to depend upon κ. This equation predicts an algebraic decay of g`(r, t) and the relations η2 = η4/4and β2 = β4/4 . These are borne out by our numerical results. For κ close to κc , we find η2 ' 0.22 close to theKosterlitz-Thouless value 0.25. [1] D. Frenkel and R. Eppenga, Phys. Rev. A, 31, 1776 (1985).



5.2.19

Cross-over behavior of fiber bundle model under mixed-mode(ELS+LLS) load sharing scheme

Srutrshi Pradhan1, Bikas K. Chakrabarti2 and Alex Hansen3

1,3 NTNU, Trondheim, Norway2 SINP, Kolkata, India

We introduce mixed-mode load sharing rule in a loaded fiber bundle model. This model reduces exactly to ELS ansLLS models at the two extreme conditions of the load sharing rule. We identify two distinct regions: (a) Mean-fieldregion where ELS mode dominates and (b) Short range region dominated by LLS mode. The avalanche size statisticsand the cluster analysis help to locate the cross-over point of these regions exactly. Also different exponent values ofsusceptibility and relaxation time characterizes the two regions uniquely. We thus conclude that even in one dimension,fiber bundle models show cross-over behavior from mean-field to short range interactions.


5.2.20

First-order Synchronization Transition in Locally Coupled Maps

Pradeep Kumar Mohanty1

1Phys Complex Sys, Weizmann Institute of Science, Rehovot, 76100. ISRAEL

We study a family of diffusively coupled chaotic maps on periodic d-dimensional square lattices. Even and odd sub-lattices are updated alternately, introducing an effective delay. As the coupling strength is increased, the systemundergoes a first order phase transition from a multi-stable to a synchronized phase. Further increase in couplingstrength shows de-synchronization where the phase space splits into two ergodic regions. We argue that the de-synchronization transition is discontinuous for piece-wise linear maps, and is continuous for non-linear maps which aredifferentiable.

[email protected]


5.2.21

Shear thinning in a critical viscoelastic fluid

Palash Das1 and Jayanta K. Bhattacharjee2

1,3 Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur,Kolkata-700032,India

Viscoelasticity and shear thinning occur near the consolute point of a binary mixture. The long relaxation timesof near critical fluctuations make this possible even when the molecules are much smaller than polymers. Similarrheological behaviour occurs near the liquid-vapour critical point of a pure fluid as simple as xenon. Prompted by therecent zero gravity measurents of dynamic critical properties, we have undertaken the study of shear thinning in acritical viscoelastic fluid. The competition between finite shear and finite frequency effects are studied near the criticalpoint. A scaling function describing the crossover between various zones is suggested.


5.2.22

Laser induced phase transitions in two- dimensional hard disks from anumerical renormalization group study.

Debasish Chaudhuri1 and Surajit Sengupta 2

1,2 Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Calcutta - 700098.

Colloids trapped within crossed laser beams show the remarkable phenomenon of re-entrant laser-induced freezing intwo dimensions (Q.-H. Wei et. al. Phys. Rev. Lett. 81, 2606, (1998)). This phenomenon was earlier predicted bydensity functional theory and later by a dislocation mediated melting calculation of Frey et. al. (Phys. Rev. Lett. 83,2977 (1999)). Here, we study laser induced freezing using a different approach allowing numerical comparison withFrey et. al.. We first obtain precise values for the ’bare’ dislocation fugacities and elastic moduli of the 2-d hard disksystem from a Monte Carlo simulation constrained in a manner such that only configurations without dislocations aresampled. These ’bare’ quantities were then used as inputs to the renormalization equations of Frey et. al. to obtainthe equilibrium phases. Our calculations show that (1) re-entrance is built into the bare quantities themselves for allvalues of the density (2) cross-over effects from the zero laser field KTHNY melting transition are, however, substantialat small values of the laser potential and (3) the renormalization flow equations need to be correct at least upto secondorder in the dislocation fugacity to be accurate in predicting non-universal quantities like the phasediagram.



5.2.23

Hull Properties of Directed Spiral Percolation Clusters

S. B. Santra1 and S. Sinha2

1,2 Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam India

The external perimeters or hulls of directed spiral percolation (DSP), percolation under both directional and rotationalconstraints, are studied on the square and triangular lattices of size 211×211 in two dimensions (2D). It has already beenfound that the DSP model belongs to a new universality class than that of ordinary, directed and spiral percolation.It has also been found that the values of the critical exponents of the DSP clusters are considerably different onthe square and triangular lattices in 2D. The DSP model then exhibits a breakdown of universality in the clusterproperties between the square and triangular lattices in 2D. The hull dimension dH and some of the critical exponentsassociated with the different moments of hull size distribution are calculated. It is found that the values of thehull critical exponents and the hull dimension are the same on the square and triangular lattices within error bars,unlike the cluster properties. Thus, the hulls of the DSP clusters do not exhibit breakdown of universality betweenthe square and triangular lattices. The hull dimension is found to be dH = 1.31 ± 0.01 for the square lattice anddH = 1.43± 0.01 for the triangular lattice. Both the values of dH is close to 4/3, the exact result of hull dimension ofordinary percolation clusters. The same value of dH is also obtained for the hull of spiral percolation clusters. Thus,the hull dimension remains invariant under different external constraints on the percolation model whereas the clusterproperties differ from model to model. Directed spiral percolation is expected to occur in disordered systems whenboth rotational and directional force fields are present.


5.2.24

Chirality discrimination via chemical stochasticity and diffusion

V.S. Gayathri1 and Madan Rao2

1 Raman Research Institute , C.V. Raman Avenue, Sadashivanagar, Bangalore 560080, India2 Raman Research Institute, C.V. Raman Avenue, Sadashivanagar, Bangalore 560080, India and National Centre

for Biological Sciences, UAS-GKVK campus, Bellary Road, Bangalore 560065, India

How does molecular homochirality emerge globally in a perfectly unbiased world ? In this study we show that enan-tiomeric selectivity can arise from dynamical equilibrium fluctuations in completely symmetric autocatalytic chemicalreactions without specific antagonism. While a mean field description does not break chiral symmetry, incorporatingstochasticity via a Gillespie algorithm leads to chirality discrimination and amplification beyond a time scale τ , witha mean that scales as the total number of reactants. Introducing spatial heterogeneity and diffusive transport of thechemical reactants, we establish a “phase-diagram” exhibiting global chirality discrimination; a novel realisation ofdynamical fluctuation induced growth of spatial order in chemical reactions.

1 [email protected] [email protected], [email protected]


5.2.25

A multicanonical Monte Carlo study of the liquid-solid phase transitionof Lennard-Jones fluids

Chizuru Muguruma1, Yuko Okamoto2 and Masuhiro Mikami3

1 Faculty of Liberal Arts, Chukyo University, Toyota, Aichi 470-0393, Japan2 Department of Theoretical Studies, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan

3 Research Institute for Computational Sciences, National Institute of Advanced Industrial Science and Technology,Tsukuba, Ibaraki 305-8568, Japan

The multicanonical (MUCA) algorithm has been introduced as one of the method to overcome multiple-minimaproblem and has been proven to be very efficient in studying first-order phase transitions. In the present study, weconsidered that the phase transition of the bulk system can be discussed with the MUCA algorithm, and applied themulticanonical Monte Carlo (MUCAMC) method to the bulk argon system. We put 108 argon particles in periodiccubic cell so that the density of the system is 1.65 g/cm3 and performed the MUCAMC simulation under constantvolume. Time series of total potential energy and the probability distribution obtained by the long production runshow that the weight factor is reliable from 60 to 250 K. Averaged thermodynamic properties such as potential energy,pressure, entropy and free energy show discontinuous changes around 150 K. Those results are the characteristics ofthe first-order phase transition and suggest that the transition temperature is around 150 K. We are also investigatingthe size effect in the first-order phase transition of the bulk L-J fluid system.


5.2.26

Critical Dynamics of the One Dimensional Ising Model with InverseSquare Interaction

Shyamal Biswas1, Amit Dutta2 and J. K. Bhattacharjee3

1,3Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur,Kolkata-700032,India

2Department of Physics, Indian Institute of Technology,Kanpur-208016, India

We study the critical dynamics of the one dimensional Ising model with inverse square interaction.Using the techniqueof Bary, who studied the Langevin equation for a logarithmic potential in two dimension to discuss the Kosterlitz-Thouless transition,we expliot the one dimensional logarithmic potential to explore the persistence effects in the inversesquare Ising model. The existence of a phase with infinite static suscepbility over a finite range of temperature leadsto rich varity of dynamical behaviour



5.2.27

Longitudinal and transverse correlation functions and critical exponentsin ϕ4 model

J. Kaupuzs1

1 Institute of Mathematics and Computer Science, University of Latvia, 29 Rainja Boulevard, LV-1459 Riga, Latvia

We have studied the transverse G⊥(k) and the longitudinal G‖(k) correlation functions in ϕ4 (n-component vector)model below the critical point in presence of an infinitesimal external field h within the framework of our reorganizeddiagrammatic perturbation theory [1]. Our method allows a qualitative analysis not cutting the perturbation series.The long–wave limit k → 0 has been studied, showing that G⊥(k) ' a k−λ⊥ and G‖(k) ' b k−λ‖ with exponentsd/2 < λ⊥ < 2 and λ‖ = 2λ⊥ − d is the physical solution of our equations at the spatial dimensionality 2 < d < 4,which coincides with a non–perturbative renormalization group (RG) analysis. We disprove the conventional statementof the perturbative RG theory that λ⊥ = 2 is the exact result. The exponents, as well as the ratio bM2/a2, includingthe magnetization M , are universal. We have made Monte Carlo (MC) simulations in 3D XY model to verify ourconclusion that M(h)−M(+0) ∝ hρ holds at h → 0 with 1/2 < ρ < 1, the value ρ = 1/2 of the Gaussian spin wavetheory (and the perturbative RG) being wrong. The numerical estimates ρ = 0.705(9) and ρ = 0.728(25) confirm ourstatement. We have made also MC simulations in 3D Ising model for system sizes up to L = 410 to show that thewidely believed critical exponents are only effective, whereas the asymptotic values could be those given in [1]. [1]

J. Kaupuzs, Ann. Phys. (Leipzig) 10 (2001) 299

1 [email protected]

5.2.28

Renormalization Group Transformations and Extensions of EllipticFunction Fields

Masafumi Fujimoto1

1 Kashihara, Nara 634-8521, JAPAN

For two-dimensional lattice models it was shown that the correlation function is expressed in terms of differential formson Riemann surfaces of genus 1 [1]; we can choose a suitable Riemann surface to find a one-to-one correspondencebetween the point group and a Galois covering [2]. Here, we assume the square (respectively triangular) lattice; thepoint group is C4v (respectively C6v). Using the fact that C4v (or C6v) is a solvable group, we construct a Galoisextension of an elliptic function field. It is found that the same extension appears in a renormalization group (RG)approach for the Ising models in [3]. We point out a close relation between the Galois extension derived from C4v (orC6v) and the RG transformation. [1]. M. Fujimoto, J. Phys. A:Math. Gen. 35:7553-7557 (2002). [2]. M. Namba,Branched Coverings and Algebraic Functions (Longman). [3]. H. J. Hilhorst et al., Phys. Rev. B 19:2749-2763 (1979).

1 [email protected]


5.2.29

Discrete folding in three dimensions:Density-matrix-renormalization-group study

Yoshihiro Nishiyama1

1 Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530,Japan

Folding of the triangular lattice in a discrete three-dimensional space (Bowick-Di-Francesco-Golinelli-Guitter model)is investigated by means of the density-matrix-renormalization-group method. The model reduces to a two-componentIsing model on the hexagonal lattice. Our data for the transfer-matrix-strip lengths up to L = 29 indicate that thecrumpling transition is discontinuous. The amount of the latent heat appears to be considerably large q = 0.365(5).Our estimate for the folding entropy S = 0.378(2) lies within the exact bound 0.361 ≤ S ≤ 0.463 obtained previouslyvia combinatorics argument.

1 [email protected]

5.2.30

High pressure phase stability in LuPO[sub4]

R. Mittal1, S. L. Chaplot2 and N. Choudhury3

1,2,3 Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India

The combination of physical and chemical properties of orthophosphates such as high melting point, structural andchemical stability and long term corrosion resistance makes them possible candidates as media for the storage andpermanent disposal of nuclear waste materials. LuPO[sub4] has the zircon structure at ambient pressure and showeda reversible phase transition [1] at 22 GPa in Raman scattering experiments carried out at Trombay. Scheelite isa likely high pressure structure for similar compounds. We have carried out lattice dynamical calculations of thestructure, dynamics and thermodynamic properties of LuPO[sub4]. The lattice dynamical model has been validatedby the polycrystalline and single crystal inelastic neutron scattering data of LuPO[sub4] available in the literature.We have calculated free energy in zircon and scheelite phases of LuPO[sub4] which shows that zircon and scheelitephases are stable below and above 13 GPa respectively.

References:[1] Rekha Rao, T. Sakuntala, R. Mittal, S. K. Deb, S. L. Chaplot, N. P. Karanjikar and A. P. Roy, ”Internationalconference on Raman scattering, Cape Town, South Africa (1998)”.



5.2.31

The Role of Topological Defects In The Phase Transitions In TwoPlanar Lattice Models

Subhrajit Dutta1 and Soumen Kumar Roy2

1,2 Department of Physics, Jadavpur University, Kolkata - 700 032, India

The role played by the topological charges in the phase transitions exhibited by planar lattice models with nearestneighbour interactions −P2(Cosθ) and −P4(Cosθ) have been studied using the standard Metropolis algorithm. In theP2 model the stable topological defects are disclination points of strength 1/2 where as in the P4 model the stabledefects are those of strength 1 and 1/2 [E. Mondal and S.K. Roy, To appear in PLA, 2004]. On suppressing the1/2-defects in the P2 model the normally present second order phase transition disappears, while in the P4 modelwhich has a strong first order phase transition, suppression of the 1/2-defects leads to a change in the nature andthe temperature of the phase transition. This too disappears on suppressing the 1 defects. These results indicate thenecessity of the topological excitations in the phase transitions exhibited by these models. We have also shown thatthe nature of the phase transition in the P4 model changes to second order on suppressing the 1/2-defects.The finitesize scaling method was used to estimate the critical exponents and the transition temperature of this new transition.The exponents are found to obey the scaling laws.


5.2.32

Percolation with correlated bonds: a model of gas diffusion through apolymer film

Manoj Gopalakrishnan1, Beate Schmittmann2 and R. K. P. Zia3

1,2,3 Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

We study bond percolation in a two-dimensional L × L square lattice, where the bonds are occupied by N non-interacting `-mers. We investigate percolation of free bonds in this system at (i) fixed monomer density ρ = N`/L2

and varying `, and (ii) fixed polymer length ` and varying ρ. In the first case, we show that, for fixed ρ and L, linkingup monomers to form `-mers reduces (enhances) the percolation probability at low (high) ρ. In the second case, asharp transition is found at a critical monomer density ρc(`) as L → ∞. The fraction of free bonds pc(`) at thepercolation threshold is also determined via finite size scaling. Applications to a simple model of gas diffusion througha polymer film is discussed.



5.2.33

A sandpile through dissipative topplings

Chai-Yu Lin1 and Chien-Fu Chen2

1,2 Department of Physics, National Chung Cheng University, Chia-Yi, Taiwan 66117

A sandpile model with a losing probability f for that an unstable site transfers a grain to one of its neighbors but thisneighbor site does not receive any grain is studied. In such a dissipative system, we find that the critical exponent oftoppling size for all waves with different f is identical to the original BTW sandpile with open boundary condition.However, the exponents of dissipative and last waves are dependent on the value of f . We also derive analyticexpressions for dissipative and last exponents and numerical simulations show that they are consistence.

1 [email protected]

5.2.34

Collective phase synchronization in locally-coupled limit-cycle oscillators

Hyunsuk Hong1, Hyunggyu Park2 and Moo Young Choi3

1,2 School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea3 Department of Physics, Seoul National University, Seoul 151-747, Korea

We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on d-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to d = 4. Onthe other hand, numerical investigation for d = 5 and 6 reveals the emergence of the synchronized (ordered) phasevia a continuous transition from the fully random desynchronized phase. This demonstrates that the lower criticaldimension for the phase synchronization in this system is dl = 4.



5.2.35

Critical exponents in the planar Lebwohl-Lasher model

Enakshi Mondal1 and Soumen Kumar Roy2

1,2 Department of Physics, Jadavpur University, Kolkata, India

The two-dimensional Lebwohl-Lasher model, where three dimensional spins located at the sites of a square lattice ofsize LXL interact with the nearest neighbours via an interaction which goes like −P2(Cosθij), P2 being the secondLegendre polynomial and θij is the angle between the nearest neighbours i and j, is known to possess a second orderphase transition driven by the condensation of topological defects. We have performed a Monte Carlo simulation inthis model using lattices of size ranging from L=10 to 240 using periodic boundary conditions. The cluster algorithmof Wolff along with the histogram reweighting technique of Ferrenberg and Sweendsen has been used and about 10to 14 temperatures close to the transition for each lattice were chosen to obtain results with good statistics. Theauto-correlationtime for all temperatures and lattice sizes were determined using the method of Madras and Sokal.The finite size scaling technique like the data collapse for scaled specific heat, susceptibility and auto-correlation timehas been used to obtain the critical exponents and the thermodynamic limit of the critical temperature. These resultsseem to be the best estimates of these parameters available so far.


5.2.36

Phase diagrams in the lattice RPM model: from order-disorder togas-liquid phase transition

Alexandre Diehl1 and Athanassios Z. Panagiotopoulos2

1 Departamento de Fisica, Universidade Federal do Ceara, Caixa Postal 6030, Fortaleza, Brazil2 Department of Chemical Engineering, Princeton University, Princeton NJ 08544

The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range(SR) interactions has been studied by grand canonical Monte Carlo simulations. Systems with both SR attractionand nearest-neighbors repulsion have been investigated. The results reveal a great variety of behaviors as the SRstrength is varied for these two types of potentials. For weak or vanishing SR attraction only order-disorder phasetransitions and a tricritical point are found, while for strong SR interactions the high-density ordered phase becomesincommensurate with the lattice structure and only a gas-liquid coexistence and a critical point are observed. For acertain range of SR strength between these two limits both the critical and the tricritical points can become stable.For a SR nearest-neighbors repulsion we found a phase diagram very similar to the continuum RPM model as theSR strength increases. For the low density region we found a gas-liquid phase separation with an Ising critical point,while for the high density region only first-order liquid-solid transition appears. We discuss how the line of continuousorder-disorder transitions present for the low SR strength changes into the continuum-space behavior as one increasesthe SR strength.



5.2.37

Novel universality classes of coupled driven diffusive systems

Abhik Basu1 and Erwin Frey2

1 Poornaprajna Institute of Scientific Research, Bangalore, India2 Hahn-meitner-Institut, Berlin, Germany

Motivated by the phenomenologies of dynamic roughening of strings in random media and magnetohydrodynamics, weexamine the universal properties of driven diffusive system with coupled fields. We demonstrate that cross-correlationsbetween the fields lead to amplitude-ratios and scaling exponents varying continuosly with the strength of these cross-correlations. The implications of these results for experimentally relevant systems are discussed.


5.2.38

Numerical Study of Phase Transition and Shock Formation in anInteracting Particles System

Farhad H Jafarpour1

1 Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5531, Tehran, IRAN

A one-dimensional branching-coalescing model is considered on a chain of length L with reflecting boundaries. Westudy the phase transitions of this model in a canonical ensemble by using the Yang-Lee description of the non-equilibrium phase transitions. Numerical study of the canonical partition function zeros reveals two second-orderphase transitions in the system. Both transition points are determined by the density of the particles on the chain.In some regions the density profile of the particles has a shock structure.

1 [email protected]


5.2.39

A Procedure for Obtaining General Nonlinear Fokker-Planck Equations

Fernando Dantas Nobre1,Evaldo Mendona Fleury Curado2 and George Rowlands3

1,2CBPF - Rua Xavier Sigaud 150, Urca, 22290-180, Rio de Janeiro, Brazil 3Department of Physics,The Universityof Warwick,Coventry CV4 74L United Kingdom

A procedure for deriving general nonlinear Fokker-Planck equations (FPEs) directly from the master equation ispresented. The nonlinear effects are introduced in the transition probabilities, as general powers of the probabilitiesfor finding the system in a given state. It is shown that the FPEs, obtained from master equations describing transitionsamong discrete and continuous sets of states, are identical. Within such a procedure, we construct a nonlinear FPEthat appears to be very general. Our general FPE recover, as particular cases, nonlinear FPEs investigated previouslyby many authors, introduced on a purely phenomenological basis, and leads to the possibility of more complete andcomplex diffusive equations.


5.2.40

Depressed magnetic phase transition and field-tunable rigidity inelastomagnetic compounds

Giancarlo Franzese1 and Lucilla de Arcangelis2

1 Departament de Fisica Fonamental, Universitat de Barcelona, Barcelona, Spain2 Department of Information Engineering, Second University of Naples, Naples, Italy

Elastomagnetic compounds –new materials, suitable for ”intelligent” devices– are made of magnetic nonoparticlesdispersed in an elastic matrix. We study the magnetic phase transition and the response to external deformations ofthese materials, by introducing a model and finding its mean field solution. We investigate the dense case that wasnever considered in experimental realizations. We find that the magnetic critical phase transition under deformationhas a novel feature: below the ordering temperature the magnetization has a deformation-dependent plateau (depressedmagnetic phase transition). Moreover, the rigidity in an external magnetic field increases for decreasing temperatureand increasing field. Recent experiments verify our predictions [1]. Therefore, 1) the changes in the macroscopicmagnetic order can reveal microscopic mechanical deformations and 2) the rigidity of these materials can be tuned byan external magnetic field. [1] L. Lanotte et al. in preparation



5.2.41

Spinodal Decomposition for Phase Transitions under Off-EquilibriumConditions

Bernd A.Berg1, Urs M.Heller2, Hildegard Meyer-Ortmanns3 and Alexander Velytsky4

1 Department of Physics, Florida State University, Tallahassee, FL 32306, USA2 American Physical Society, One Research Road, Box 9000, Ridge, NY 11961, USA

3 SES, International University Bremen, P.O.Box 750561, D-28725 Bremen, Germany4 CSIT, Florida State University, Tallahassee, FL 32306, USA

Motivated by the rapid crossover between QCD-phases, we study phase conversion in 2d-Potts models. Using hysteresismethods, we find spinodal decomposition as the dominating conversion mechanism due to off-equilibrium conditions,even where one would expect nucleation for an adiabatic heating or cooling across the transition temperature.


5.2.42

Ageing in the Contact Process

Jose J. Ramasco1, Malte Henkel2, Maria A. Santos3 and Constantino A. da Silva Santos4

1,3,4 Centro e Departamento de Fisica do Porto, Facludade de Ciencias, Universidade do Porto, R. Campo Alegre687, P-4169-007 Porto Portugal.

2 Laboratoire de Physique de Materiaux, Universite Henri Poincare Nancy I, F-54506 Vandoeuvre-les-Nancy Cedex,France.

In this work, we present a study on the temporal evolution of a model without detailed balance, the contact process.This model belongs to the Directed Percolation universality class, which represents the paradigm of the non equilibriumphase transitions with an absorbing state. We estimate the two time correlations functions and the response to anexternal field at the critical point, both by direct Monte-Carlo numerical simulations in 1D and 2D and by mean fieldcalculations. Our results show that the definition of an effective temperature is not possible for this system in contrastto what has been recently found for other non equilibrium models with additional symetries such as the voter model.

1 [email protected]


5.2.43

Lee-Yang circle theorem, boundary condition, and new phase insemi-infinite systems

Ming-Chang Huang 1 and Tsong-Ming Liaw2

1 Department of Physics, Chung-Yuan Christian University, Chung-Li 320, Taiwan2 Computing Centre, Academia Sinica 11529, Taipei, Taiwan

Effect of boundary condition on the distribution of partition function zeros for infinitely long Ising strip with finite widthis analysed in the context of Lee-Yang circle theorem. The scaling laws of the zeros and the corresponding exponentsfor periodic boundary condition are determined rigorously. The zeros distribution for antiperiodic boundary conditioncontains the bulk critical point but with different singular property. The singularity is realized as the discontinuityat the bulk critical point for the derivative of free energy with respect to temperature to any order. The critical gapsquantifying the discontinuities in internal energy and specific heat are given. Numerical evidence from Monte Carlosimulations for this new phase is also presented.


5.2.44

Harmonic oscillator with multiplicative noise

M. Gitterman1

1 Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel

Harmonic oscillator with random frequency has long been a subject of study.We found (PRE, 67, 057103,2003) that suchoscillator subject to a periodic force shows nonmonotonic dependence on the strength and the rate of dichotomous noise(stochstic resonance)with no resonance for white noise. We consider also the underdamped oscillator with fluctuatingdamping parameter (PRE, in press), where in the absence of an external force the noise of a sufficiently large strengthleads to an instability. In this case stochastic resonance exists for white noise as well.

1 [email protected]


5.2.45

Spin model for inverse melting and inverse glass transition

Nadav Shnerb1 and Nurith Schupper2

1,2 Department of Physics, Bar-Ilan University, Ramat-Gan 52900 Israel

An interacting spin system that yields inverse melting is presented and analyzed. The Blume-Capel model, for spin-one particles with low-energy inert (zero) state and exchange interactions, is extended to include many |S| = 1 statesfor each spin. The larger entropy associated with the paramagnetic phase yields an (first and second order) inversemelting transition, with a phase diagram that resembles the experimental results. Motivated by the appearance ofa reversible thermogelation in Methyl-Cellulose solution, the model is considered for random exchange interactionsusing the replica trick. The results are shown to differ qualitatively from those obtain by Ghatak and Sherrington,and inverse freezing of various types is exhibited.


5.2.46

The role of driving in single species reaction-diffusion systems withabsorbing states

Park, Su-Chan1 and Park, Hyunggyu2

1,2 Korea Institute for Advanced Study, Seoul 130-722, Korea

We study branching annihilation random walks (BAW) and pair contact process with diffusion (PCPD) under theinfluence of external driving (biased diffusion). BAW models are robust against the driving, regardless of the parityconservation. However, the driving is relevant for the PCPD and changes the universality class. Since the field theoryof single species predicts that the driving is irrelvant in general, we conclude that the PCPD is generically a two-speciesmodel and a field theory of two species is required. Our result provides a clue that the PCPD does not belong todirected percolation universality class which can be described by a single-species field theory.



5.2.47

Pseudospin description of intrinsic inhomogeneities in models ofstructural transitions

Turab Lookman1, Subodh R. Shenoy2 and Avadh Saxena3

1,3 Los Alamos Natl. Lab.2 ICTP, trieste, Italy

Nonlinear Landau free energies for ferroelastic structural transitions can be mapped onto effective pseudospin mod-els with anisotropic long-range interactions. In particular, at the first-order transition a scaled temperature takes auniversal value, with a scaling choice of the order-parameter strain magnitude and energy density, causing the degen-erate minima to fall on a ‘unit-sphere’ in scaled order parameter space. These discrete minima suggest ’clock-type’pseudo spin models that can yield complex, textured equilibrium states that are relevant to the physics of multiferroicmaterials such as martensites, cuprates and manganites. We show the results of Monte Carlo simulations and localmeanfield approximations in two dimensions on the simplest pseudo spin model which corresponds to the square torectangle tansformation.



5.2.48

Synchronization phenomena and Generalization of doubleintegrate-and-fire neuron model

Yasuomi Daishin Sato1

1 Department of Applied Physics, Faculty of Science, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku,Tokyo, 152-0033, Japan

We propose a new type of neuronal firing model. We assume that the firing occurs when its membrane potential crossesthe threshold θ1 (> Xr) to jump up to the value of Xu (> θ1) and then it decays to the threshold θ2 (θ1 < θ2 < Xu) tobe subject to abruptly reset to Xr. Accordingly, the new model is obtained by adding the standard integrate-and-fire(IF) model to the equation that describes the firing process and thakes the form:

dx

dt= F (x) + Isyn(t), (5.1)

F (x) =

X1 − γ1x, for x ∈ [θ2 ,∞],X0 − γ0x, for x ∈ [−∞, θ1 ],

where x is an activation variable like membrane potential. γ0 and γ1 (> 0) are the relaxation rates for the dynamicsof a non-firing and a firing. X0 (> θ1) and X1 (< θ2) are the values of x that the activation variable x would approachwithout the restrictions, θ1 and θ2. The regimes of x [θ2,∞] and [−∞, θ1] show the active and silent phases respectively.Here F (x) for the regime θ1 < x < θ2 does not have to be defined if we don’t set up with the initial state of x in theregime, because x can not enter the regime θ1 < x < θ2 for continuous trajectories of x. In what follows, we call thenew type of model the double integrate-and-fire (d-IF) model. The d-IF neuron model contains fundamental firingcharacteristics (i.e., the threshold for a firing and an absolute refractory period), which are possessed in physiologicallyrelevant neuron models as well as theoritically tractable ones. In various types of previously proposed neuron models(except for the IF model), their time evolutions of a membrane potential can be numerically simulated. However ithas been extremely difficult to understand inituitively how the width of an action potential is characterized by theirparameters and variables. The d-IF model allows us to overcome such difficulties and easily calculate the width ofan action potential. Moreover, if the firing duration is extremely short, the d-IF model becomes precisely equal tothe IF model. By using the singular perturbation approach, the d-IF model can be compared with the FitzHugh-Nagumo (FHN) and piecewise-linear (PL) models. The FHN model is originally described as dV

dt = −V 3

3 + V −W

and dWdt = ε(V + a− bW ). By piecewise-linearizing the right hand side of the dV

dt equation, we obtain the PL neuronmodel with a small time scale parameter (ε (> 0)): dV

dt = − 43V + |V +1|− |V −1|−W and dW

dt = ε(V +a− bW ) whereV is the excitable variable, that being the membrane potential. W is the recovery variable. a and b are constants.Changing the time scale to τ = εt and taking the limit of ε → 0, the PL model is simplified as a one dimensionaldifferential equation of the V -variable. For the uncoupled neuron model, the simplified PL model is then identicalto the DIF one. On the other hand, if Isyn(t) is involved in the righthand of the equation of the W -variable of thePL model and then the equation is transformed into a one-dimensional differential quation of the V -variable, theobtained model becomes just identical to Eq.(1). Therefore, since the d-IF model contains all firing properties of theoriginal IF, FHN and PL models even though they have the synaptic interactions, it enables us to qualitatively andanalytically clear up the relationship between the IF and FHN models. In addition we expected that the d-IF modelmakes it possible to reproduce synchronous behaviors in more realistic neuron models coupled via chemical synapses.Consequently, it becomes apparent that the d-IF model is a more beneficial when synchronization phenomena arequalitatively explained by focusing on obvious firing properties.

1 [email protected]


5.2.49

Recent Progress on Nonequilibrium Relaxation Method

Yukiyasu Ozeki1, Nobuyasu Ito2 and Katsumi Kasono3

1 Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguroku, Tokyo 152-8551, JAPAN2 Department of Applied Physics, The Tokyo University, Bunkyo-ku, Hongo, Tokyo 113-8656, JAPAN

3 Department of Physics, Jikei University School of Medicine, Kokuryo, Chofu, Tokyo 182-8570, JAPAN

It has been shown that the nonequilibrium relaxation process is useful to study phase transitions and critical phe-nomena. Observing relaxation of physical quantities, one can locate the critical point finely and estimate criticalexponents accurately. The advantage of the method originates in the facts that the behavior in the thermodynamiclimit is observed more easily.Since the equilibration is not necessary, it is appropriate much to study systems withslow dynamics such as frustrated and/or random systems. The application is expanding to wide variety of statisticalmodels. For the KT transitions, the finite-time scaling analysis is useful to estimate the transition point and criticalexponents. The 2D fully-frustrated XY models and the gauge glass models are analyzed and some conclusive resultsare presented for controversial problems. For the first-order transition cases, the mixed phase initialization overcomesthe difficulty of metastable states, and reveals an accurate estimation of transition temperatures.



5.2.50

Static and Dynamic Properties of the XXZ chain with long-rangeInteractions

Lindberg Lima Goncalves1,Lenilson Pereira dos Santos Coutinho2 and Jose Pimentel de Lima3

1,2Departamento de Fisica, Universidade Federal do Ceara, Campus do Pici, CP 6030,60451-970 Fortaleza, Ceara,BRAZIL

3Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina, Piaui, BRAZIL

The one-dimensional XXZ MODEL (s=1/2) in a transverse field, with uniform long-range interactions among thetransverse components of the spins, is studied. The model is exactly solved by introducing the Jordan-Wigner trans-formation and the integral gaussian transformation [1]. The complete critical behaviour of the system is determinedand the critical surface for the quantum and classical transitions, in the space generated by the transverse field andthe interaction parameters, are presented. The crossover lines for the various classical/quantum regimes are also de-termined exactly, and it is shown that, besides the tricritical point associated to the classical transition, there are alsotwo quantum critical points, namely, a bicritical one where the classical second order critical line meets the quantumcritical line and a transition one where the classical first order transition line also meets the quantum critical line.It is also shown that the phase diagram for the first order classical/quantum transitions presents the same structureas the one for the second order classical/quantum transitions. The critical classical and quantum exponents are de-termined, and the internal energy, the specific heat ch and the isothermal susceptibility χzz

T are presented for thedifferent critical regimes. The two-spin static and dynamic correlation functions, < Sz

jSz

l >, are also presented andthe dynamic susceptibility χzz

q (ω) is obtained in closed form. Explicit results are presented at T = 0 and it is shownthat the isothermal susceptibility χzz

T is different from the static one χzzq (0). [1] L. L. Goncalves, A. P. Vieira and L.

P.S. Coutinho, J. Magn. & Magn. Mater 226-230, 613 (2001). Work partially financed by the Brazilian agenciesCNPq,Capes and Finep.

[email protected]@ufpi.br


5.2.51

Abelian and non-abelian spin models with P4-interaction in twodimensions.

Ana Isabel Farinas-Sanchez1,Ricardo Paredes2 and Bertrand Berche3

1,2 Laboratorio de Fısica Estadıstica de Sistemas Desordenados. Centro de Fısica. Instituto Venezolano deInvestigaciones Cientıficas. Apartado Postal 21827, Carac as 1020A. VENEZUELA

3 Laboratoire de Physique des Materiaux. Faculte des Sciences. Universite Henri Poincare - Nancy I. BP 239, 54506Vandœuvre Les Nancy Cedex. FRANCE

Simulations of nematic-isotropic transition of liquid crystals in two dimensions may be performed using O(n) vectormodels. Among them, XY and Heisenberg models are well known. The first one has an abelian symmetry andpresents a topological transition, while the second one has a non-abelian symmetry and does not have any transitionat finite temperature in d = 2. It is interesting to extend these models by a generalization of the spin interaction.In the present work we make a detailed comparison of the critical behaviour between two models with the same spininteraction but with two different symmetries, one of them with an abelian symmetry [O(2)] and the other one witha non-abelian symmetry [O(3)]. In both models the spin interaction is governed by the fourth Legendre polynomialP4 which is relevant to explain some properties of liquid crystals. We compare the thermodynamic behaviour, studiedthrough finite-size scaling methods, and the behaviour of the correlation function, studied with conformal invariancemethods.



5.2.52

Relative stability of the α and Cmcm phases in AlPO4 : Afirst-principles study

L.M. Ramaniah 1,S.M. Sharma 2,K. Kune 3 and M.Laghate 4

1,2,4Synchtrotron Radiation Section, Physics Group, Bhabha Atomic Research Centre, Trombay, Mumbai 400085.3 CNRS and University of P. and M. Curie, T13-C80, 4 Pl. Jussieu, Paris.

5Computer Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085.

Berlinite, α-AlPO4, belongs to a class of iso-structural compounds MXO4 (M=Si,Ge,Al,Ga.. and X=Si,Ge,P,As...)which crystallise, at ambient pressures, in the trigonal phase (space group P312 1), adopting structures made up ofMO4 and XO4 tetrahedra. Several of these compounds are believed to amorphise at pressures of around 20 GPa.AlPO4 had long been believed to undergo a reversible amorphisation transition at ≈ 15 GPa, with both experimentalevidence[1] and theoretical support[2] for this widely-held view. However, some recent experiments[3] have suggestedthat it transforms to a crystalline phase at these pressures. This was confirmed by recent synchrotron x-ray diffractionexperiments[4], which also identified the crystalline phase as Cmcm. Recent molecular dynamics (MD) simulations[5]using classical pair potentials, but a much larger simulation cell than used in previous simulations, have failed toreproduce a transition from the α to the Cmcm phase. In order to better understand and clarify the picture regardingthe high-pressure behaviour of α-AlPO4, we have undertaken a first-principles study of this problem[6]. In thispaper, we present the results of our optimization calculations of the α and Cmcm phases of this material. We workwithin the framework of density-functional theory, using the generalised gradient corrections to the local densityapproximation[7] exchange and correlation energy proposed by Becke[8] and Lee, Yang and Parr[9] (BLYP). Onlyvalence electrons are treated explicitly and their wave-functions are expanded in plane-waves with an energy cut-offof 70 Ryd, while core-valence interactions are described by Troullier-Martins norm-conserving pseudopotentials[10].Most ground-state properties may be obtained from the total energy and its derivatives. Hence, the total energy ofthe crystal as a function of different supercell volumes is calculated for each phase, and the E(V ) phase diagram isconstructed. Optimisation of the atomic positions in the supercell is performed by employing ab-initio moleculardynamics[11]. Our calculations of the equations of state and of the enthalpies show clearly that, the crystallineCmcm phase is indeed energetically favoured over the α phase at pressures above about 9.5 GPa, in agreementwith the recent synchrotron x-ray diffraction experiments. The computed fractional atomic coordinates are also ingood agreement with available experimental results. Interestingly, they are also in agreement with those obtainedfrom the earlier classical MD simulations. Further, the difference in enthalpies between the two phases is also verysimilar in our ab-initio calculations and earlier classical MD simulations, over the entire pressure range of interest.These two comparisons thus seem to validate the classical potentials, and lead us to deduce that they are able tocorrectly capture the physics of the problem. Our study suggests therefore that the non-appearance of the Cmcmphase in classical MD simulations is not due to a limitation of the classical potentials; but, very probably, due toproblems inherent in MD simulations[12] (time-scale limitations, suppression of heterogeneous nucleation due tothe use of periodic boundary conditions) in correctly describing experimental phase transitions. Evidence from theexperiments (a sluggish phase transition, the possibility of non-hydrostatic stresses) supports this view. Furtherdetailed investigations of the nature of the kinetic barrier in AlPO4 would be very useful, providing as they may richinsight into this and other similar transformations in the iso-structural compounds.

References :[1] M. B. Kruger and R. Jeanloz, Science 249, 647 (1990).[2] J. S. Tse and D. D. Klug, Science 255, 1559 (1992).[3] P. Gillet, J. Badro, B. Vasel, P.F. Macmillan, Phys. Rev. B 51, 11262 (1995).[4] S.M.Sharma, N. Garg and S.K. Sikka, Phys. Rev. B 62, 8824 (2000).[5] N. Garg and S.M Sharma, J. Phys. Cond. Matt. 12, 6683 (2000).[6] L. M. Ramaniah, S. M. Sharma, K. Kunc, N. Garg and M. Laghate, Phys. Rev. B 68, 14119 (2003).[7] D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980).[8] A.D. Becke, Phys. Rev. A 38, 3098 (1988).[9] C. Lee, W. Yang, and R.G. Parr, Phys. Rev. B 37, 785-789 (1988).[10] N. Troullier and J.L. Martins, Phys. Rev. B 43, 1993 (1991).[11] CPMD Version 3.4.0, J. Hutter, A.Alavi, T.Deutsch, W.Silvestri, Max–Planck–Institut fur Festkorperforschungand IBM Research Laboratory.[12] R. Martonak, L. Colombo, C. Molteni and M. Parrinello, J. Chem. Phys. 117, 11329 (2002).

[email protected]


5.2.53

Calculations on solvent dispersions of carbon nanotubes

Francisco Torrens1

1 ICMol-Universitat de Valencia

The aqueous solubility Sw and 1-octanol- (Po), cyclohexane- (Pch) and chloroform- (Pcf) water partition coefficientsare calculated. The properties of single-wall carbon nanotubes (SWNT) are related to the indices (n,m) designating thechiral vector. SWNTs are classified in zigzag (n,0), armchair (n,n) and chiral (n,m). The properties allow classifyingSWNTs according to (n,m). A recommended periodic table (PT) format is discussed. The relationships that anySWNT (n,m) has with its neighbour (n-1,m+1) are approximately repeated for each period. Correlations between(n2+nm+m2) power (1/2), log Sw, log Po, log Pch and log Pcf show that (n,m) are adequate indices. (10,10) isthe most favourite, presenting consistency between great kinetic stability, small Sw and great Po,Pch,Pcf. The room-temperature solubility of SWNTs is investigated in a variety of solvents, finding a class of non-hydrogen-bondingLewis bases that provide good solubility. The investigated solvents are grouped in three classes. Five solvents, allfeaturing high electron-pair donicity (BETA) and low hydrogen-bond parameter (ALPHA) demonstrate the ability toreadily form stable suspensions. SWNTs in some organic solvents are positively charged, while in water/Triton X arenegatively charged. This is explained on the basis of permittivity and electron affinity.

1 [email protected]

5.2.54

Anomalous scaling along a renormalization group flow line in thecontact process

Heungsik Park1, Jae Woo Lee2 and Hyunggyu Park3

1,2 Department of Physics, Inha University, Inchon 402-751, Korea3 School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea

We investigate a scaling property of the contact process along a singular dynamic path approaching the critical point.The creation probability p of a particle varies with time t as p = pc + ct−α, where pc is the critical probability. Apath with α > 1/ν|| (ν||: relaxation exponent) is asymptotically equivalent with the c = 0 path and the directedpercolation (DP) exponents are recovered. For α < 1/ν||, the dynamic scaling behavior is masked in an expected andsimple way. Along a renomalization group flow line (α = 1/ν||), we find an anomalous scaling behavior characterizedby a c-dependent finite-size-scaling exponent, although the early time dynamic scaling still belongs to the DP class.The origin of this anomalous scaling is suggested.



5.2.55

Vortices in Layered Superconductors with Columnar pins: Liquids,Crystals, Glasses, and Melting.

Oriol T. Valls1 and Chandan Dasgupta2

1 School of Physics and Astronomy and Minnesota Supercomputer Institute, Minneapolis MN 55455 USA2 Department of Physics, Indian Institute of Science, Bangalore 560012, India

We have extensively studied the melting of the superconducting vortex system in layered superconductors, in thepresence of a small concentration of columnar pins. Our method uses large scale numerical minimization of theappropriate free energy functional. The results are very different depending on whether the pins are distributedperiodically or randomly. In the former case, the first order melting transition becomes continuous at a criticalvalue of the pin concentration. In the latter case the low temperature Bragg glass phase and the high temperatureinterstitial liquid can be separated by an intermediate Bose glass phase. The method yields detailed results forthe density structure of each of the phases, which allows for their thorough characterization and for study of theirproperties.


5.2.56

Folding of RNA in the Presence of Solvated Ions

Yeugeni Shamil Mamasakhlisov1, Shura Hayryan2, Vladimir Fedor Morozov3 and Chin-Kun Hu4

1,3 Dep of Physics, Yerevan State University, Al. Manukian str. 1, Yerevan 375025, Armenia2,4 Inst of Physics, Academia Sinica, Nankang 11529, Taipei, Taiwan (ROC)

We use the replica approach for quenched disordered systems to study the thermodynamics of a large random RNA-likemolecule in the solvent containing solvated ions. In our calculations we don’t assume any prescribed order of RNAfolding and don’t prohibit forcibly the emergence of the pseudo-knots. We show that under realistic environmentalconditions RNA molecule undergoes a phase transition into thermodynamically dominant folded conformation withfrozen tertiary and secondary structures. The melting temperature and the freezing temperature are calculated andtwo basic results are obtained: (i) the melting temperature and the freezing temperature depend on the solute chargeconcentration logarithmically, (ii) the folding rate of RNA is lower than that predicted by hierarchical models. Theresults obtained are consistent with experimental observations.



5.2.57

Possibility of d-wave superconductivity in LaAg1-xMnx alloys

S. N. Kaul1,S. Kumar2,J. Rodrguez Fernndez3,L. Fernndez Barqun4 and A. Seas5

1School of Physics, University of Hyderabad, Hyderabad - 500 046, India and CITIMAC, University of Cantabria,39005 Santander, Spain

2School of Physics, University of Hyderabad, Hyderabad - 500 046, India3,4,5CITIMAC, University of Cantabria, 39005 Santander, Spain

Addition of Ag to La in the equiatomic proportion (resulting in the for mation of the intermetallic compound LaAg,which crystallizes in the CsCl struct ure) brings down the superconducting transition temperature (Tc) of the double-hexagonal-close-packed (dhcp) phase of La from Tc ≈ 5K[1]toTc ≈ 1K[2]. If Ag in LaAg compound is partially replacedby a magnetic 3d-transition metal (TM), while retaining the CsCl structure, which is one of the most unfavourablestructures [3] for the occurrence of superconduc tivity (SC), it is expected that even a small concentra-tion of TMatoms should suffice to destroy the conventional phonon-mediated SC in this compound and when a certain thresholdTM concentra-tion is reached, the LaAg1−xTMx alloy should enter into a spin-glass (SG) state. Of particular interestis the concentration regime in which SC is on the verge of disappearing and SG behaviour just sets in. This rationaleprompted us to synthesize, for the first time, the ternary alloy LaAg1−xMnx with x = 0, 0.025, 0.05, 0.1, 0.2 and 0.3in the polycrystall ine form. Detailed microprobe analysis demonstrated that the actual composition of the grains(major phase) in the alloys with x = 0.1, 0.2 and 0.3 is x = 0.05(1), 0.08(1) and 0.09(1) and that of the minorgrain-boundary phase is La1−xAg1−xMn2x with ix = 0.2, 0.3 and 0.4, respectively, while in the remaining alloys theactual composition matches the nominal one. Extensive x-ray diffraction [4] , ac susceptib-ility [4] with and withoutsuperposed dc field (χac(T, H)), dc magneti-zation (M(T, H)), and susceptibility (χdc(T )) [4], electrical resistivity(ρ(T )) and magnetoresistivity (ρ(T, H)), ’zero-field’ and ’in-field’ specific heat (Cp(T, H)) measurements down to 1.7K reveal the following. (i) The CsCl structure of the parent compound LaAg is retained even in the alloy with thehighest Mn concentration and the lattice parameter a increases linearly with the actual Mn concentration x. (ii)Contrary to the above expectation, Tc rises steeply beyond x = 0.025 and attains a value close to 6.2 K for x = 0.09(1).(iii) M(T, H), χdc(T ) and ρ(T ) data indicate the existence of strong antiferromagnetic spin correlations in that (a)M increases with H with no sign of saturation even in fields as high as 9 Tesla, (b) the characteristic temperatureΘ, deduced from the Curie-Weiss behaviour, χdc(T ) = [C/(T + Θ)] + χ0, scales with x as Θ sim(x − xc)2/3 withxc = 0and (c) ρ(T ) ∼ T 3/2 over a certain temperature range for T Θ. (iv) Cp(T ) neither goes through a peak atany temperature including T = Θ (indicating absence of long-range an tiferro-magnetic order) nor exhibits a jumpat Tc. (v) The coefficient γ of the term linear in T, signifying the electronic contribution to Cp(T ), or equivalentlythe density of states at the Fermi level, for Mn concentration in the range 0.05 ≤ x ≤ 0.09, has a value that is 5times larger than that in LaAg whereas the Mn substitution leaves the Debye temperature of the parent compoundunaltered (indicating that Mn sub stitution has no effect on the phonon spectrum of LaAg). The observations (i) -(v) make a strong case for the antiferromagnetic spin-fluctuation-mediated singlet even-parity pairing (gapless d-wave)superconductivity in the ternary LaAg1−xMnx alloys. [1] D. K. Finnemore et al., Phys. Rev. 137, A 550 (1965). [2]C. C. Chao et al., J. Phys. Chem. Solids 27, 1555 (1966). [3] B. T. Matthias et al., J. Less-Comm. Metals 46, 339(1976). [4] S. N. Kaul and S. Kumar, J. Magn. Magn. Mater. at press.

[email protected] & [email protected]@[email protected]@[email protected]


5.2.58

Self-organization in an irreversible stochastic model

Leonardo Crochik1 and Tania Tome2

1,2Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Sao Paulo, Brazil

We analyse the steady states of a nonequilibrium Ising system defined in an bipartite square lattice in contact with aheat bath and external sources of energy and particles. The system evolves in time according to a sthocastic dynamicsconstituted by two subprocess: (i) a Kawasaki dynamics which simulates the contact of the system with a heath bathand (ii) a dynamics that simulates the flux of particles into the system. This dynamics places particles with a a givenprobability into one of the sublattices and take out particles from the other sublattice. Using Monte Carlo simulationswe verify that the system maintains a self-organized pattern of particles in space, even for very high temperatures.

[email protected]@if.usp.br

5.2.59

Fully frustrated Josephson junction arrays with modulated couplings:Effects of disorder in the Ising and Kosterlitz-Thouless phase transitions

Veronica I. Marconi1 and Daniel Domınguez2

1 The Abdus Salam International Centre for Theoretical Physics, Condensed Matter Group, Strada Costiera 11,34014 Trieste, Italy.

2 Centro Atomico Bariloche, 8400 San Carlos de Bariloche, Rio Negro, Argentina.

We study the Berezinskii-Kosterlitz-Thouless (BKT) and Ising phase transitions as a function of the amount of disorderin square Josephson Junction Arrays (JJA) with full frustration (f = 1/2) and modulated couplings. We obtain aphase diagram as a function of the disorder in the Josephson currents. For small amount of disorder strength, ∆,we find two clearly separated transitions: the Ising transition at T = TIsing and the BKT transition at T = TBKT,with TIsing(∆) < TBKT(∆). As disorder is increased, TBKT(∆) decreases with increasing ∆, while TIsing(∆) is almostconstant. For very strong disorder, ∆ = 0.8, the Ising transition disappears abruptly and only a BKT phase transitionis observed.



5.2.60

Monte Carlo simulation to study stress driven transition in Cu-Au Alloy

Umesh Gupta1 and S.K. Ghoshal2

1,2Department of Applied Physics, Guru Jambheshwar University, Hissar, (Haryana)-125001, India

To investigate the exact transition temperature accurately at the onset of structural phase transition of the Cu-Aualloy a Monte Carlo (MC) simulation using Effective Medium Theory (EMT) has been performed for three differentphases Cu-Au, Cu3Au and CuAu3. The simulation is performed on a 8x8x8 box with periodic boundary conditionsusing the Kawasaki kinetics with three different changes i.e. box breathing, diagonal and the free change applied tothe system similar to that of the dynamics of real systems. These alloys show first order transition from FCC to FCTphase in which some of the important properties exhibit abrupt jump (e.g., axial ratio, short ranged order and longranged order) at the onset of transition and they are very important for understanding the phenomena. This paperfocuses on the variation of two such important issues i.e. Long Range Order and the Stress-Strain relationship neartransition temperature for the Cu-Au alloy. Both Long Range order and the ! stress-strain curve show a jump at thetransition point exhibiting the relationship between the above properties and the structure of the alloy. MC resultsfor the stress driven transition for both compression and the expansion shows different transition temperature leadingto the hysteresis in the stress-strain curve. These results are further used as input in the extended lattice gas densityfunctional theory (ELG-DFT) to predict of the accurate transition temperature of the Cu-Au alloy theoretically. EMTbased simulation being a realistic one can give accurate estimate compare to other studies.

[email protected]@postmark.net



5.3.1

Environment Dependent Transport in Classical Ratchets

Marcus Werner Beims1,∗ and Jane Rosa 1

1 Universidade Federal do Parana, Departmento de Fisica, Curitiba - PR, Brazil

The classical transport of particles in multiple asymmetric well potentials, called stochastic ratchets1, is studiedthrough numerical integration of equations of motion. The motivation in studying such ratchets comes from molecularbiophysics where ratchet-like mechanisms have been proposed to explain nature’s efficiency in transporting largemolecules in the absence of obvious appropriate potentials or thermal gradients. Ratchets can also be used to modelbiological motor proteins2 or even to study the effect of laser fields on electron transport through molecular wires3.The problem considered here is an one-particle system in a multiple asymmetric well potential coupled to harmonicoscillators (the environment) and subjected to an external time-dependent field. Energy flow between system andoscillators is discussed and the transport is analyzed as a function of coupling strength and number of oscillators. It isshown that by increasing the coupling strength or the number of oscillators, the transport process can be destroyed 4.1 M. O. Magnasco, Phys. Rev. Lett. 71 (1993) 1477. 2 J. M. Scholey, Mobility Assays for Motor Proteins (Academic,New York, 1993). 3 J. Lehmann, S. Kohler, P. Hanggi and A. Nitzan, Phys. Rev. Lett. 88 (2002) 228305. 4 J. Rosaand M. W. Beims, submitted.

∗ [email protected]

5.3.2

Relaxation between hot electrons and surface-phonons in small metalparticles

Navinder Singh1

1 Raman Research Institute, Bangalore-560080, India

The relaxation of hot electrons is considred in a small metal particle. When the particle size is of the order of electronmean free path, the main channel of hot electron energy loss is through electron surface-phonon generation, ratherthan bulk phonon generation. The calculation for the present nonequilibrium situation between hot electrons andthe surface-phonons, assumes that electrons and surface-phonons are described by their fermi and bose distributionfunctions . The assumption is valid because time required to establish equilibrium in the electron gas is much less thanthe time for achieving equilibrium between the electrons and the surface-phonons. The expressions obtained for lowtemperature and high temperature regimes are inversly proportional to the radius of the particle. This shows that sizedependency of electron surface-phonon energy exchange is purely a geometric effect and is the primary factor. Theelectron phonon screening reduction due to spell-out of electron wave functions( electron number density reduction)and hence the energy exchange rate acceleration from the particle surface is another factor.

1 [email protected]


5.3.3

Approach to equilibrium in adiabatically evolving potentials

Himadri Shekhar Samanta1, Jayanta Kumar Bhattacharjee2 and R. Ramaswamy3

1,2 Department of Theoritical Physics,Indian Association for the Cultivation of Science,Jadavpur,Calcutta 700032,India

3 School of Physical Sciences,Jawaharlal Nehru University,New Delhi 110 067,India

For a potential function (in one-dimension) which evolves from a specified initial form, Vi(x), to a different Vf (x)asymptotically, we study the evolution of an initial probability density to its final equilibrium. There can be unexpectedeffects that can arise from the time dependence. For a choise of time variation, we show that in particular, if theevolution is adiabatic, this results in a decrease in Kramers’ time characteristic of Vf (x): thus the time dependencemakes diffusion over a barrier more efficient. There can also be interesting resonance effects that arise from thecoincidence of the intrinsic time-scale characterising the potential variation and the Kramers’time.


5.3.4

Transfer-matrix DMRG for the dynamics of stochastic systems

Andreas Schadschneider1, Andreas Kemper2, Andrej Gendiar3 and Tomotoshi Nishino4

1,2 Institut fur Theoretische Physik, Universitat zu Koln, 50937 Koln, GermanyKobe University, Rokkodai 657, Japan

3,4 Department of Physics, Faculty of Science, Kobe University, Rokkodai 657, Japan

Most numerical studies of stochastic systems rely on Monte-Carlo simulations. For one-dimensional quantumsystems the so-called DMRG method that combines exact diagonalizations with a renormalization approach allowsan extremely accurate determination of the energy spectrum. We propose a variant of the DMRG that allows toinvestigate the dynamics of stochastic systems. The new technique treats the thermodynamic limit and sampleaverages exactly and does not need random numbers. We show that it provides a general and very efficient methodfor 1D stochastic problems which can compete with Momte-Carlo results. As an example the Domany-Kinzel cellularautomaton and two reaction-diffusion models are discussed.

References :[1] A. Kemper, A. Schadschneider und J. Zittartz, J. Phys. A34, L279 (2001)[2] A. Kemper, A. Gendiar, T. Nishino, A. Schadschneider, J. Zittartz, J. Phys. A36, 29 (2003).



5.3.5

Non-stationary Similarity Solutions and Power-law Tails in StochasticProcesses with Multiplicative Interactions

Akihiro Fujihara1, Toshiya Ohtsuki2, Hiroshi Yamamoto3 and Satoshi Tanimoto4

1,2,3,4 Graduated School of Integrated Science, Yokohama City University, Kanazawa-ku, Yokohama 236-0027, Japan

Stochastic processes with asymmetrically multiplicative interactions are investigated analytically and numerically. Inthe model, two particles of positive quantities x, y(> 0) interact and quantities x, y convert into x′, y′ as

(x′

y′

)=

(c(1− a) cb

da d(1− b)

) (xy

)(x ≥ y) (5.2)

where c, d ≥ 0 and 0 ≤ a, b ≤ 1 are interaction parameters and two particles are selected randomly. Similatiry solutionsand power-law tails of the probability density function(PDF) of this model can be dealt with analytically in a similarway as in inelastic Maxwell models[1-3]. First, the Fourier transform of the master equation is performed. Secondly,moment equations are derived on the assumption that similarity solutions exist. Finally, transcendental equationswhich determine the growth rate γ and the power-law exponent s of the tail are obtained. The resulting equations ofthis model read:

γ =12[c(1− a + b) + d(a + 1− b)] +

12(c− d)(1− a− b)A− 1, (5.3)

A ≡∫∞0

dξ2

∫∞ξ2

dξ1(ξ1 − ξ2)Ψ(ξ1)Ψ(ξ2)∫∞0

dξξΨ(ξ), (5.4)

γs = c(1− a)s + das − 1 (s > 1) (5.5)

where Ψ(ξ) is PDF rescaled by the scaling variable ξ = xe−γt. In the case c = d or a + b = 1, the value of the growthrate γ and power-law exponent s can be obtained analytically because the equation for the first moment is closed. Itshould be emphasized that the power-law exponent s is independent of the parameter b when c = d. Transcendentalequations are formally same as those for symmetric interactions (c=d, a=b)[4]. However, the physical meaning of theparameters is completely different. In the other case c 6= d and a + b 6= 1, on the contrary, the value of γ is unableto be calculated analytically because the first moment equation is not closed. Then numerical simulations have beenperformed. Good agreement is achieved for both γ and s. The effect of randomness in stochastic processes withsymmetric interactions is also studied. In this case, c = d ≡ p + q and a = b ≡ p/(p + q) are random parameters withprobability distribution ρ(p, q)[5]. The transcendental equations determining the growth rate γ and the power-lawexponent s are

γ = p + q − 1, (5.6)γs = ps + qs − 1 (s > 1) (5.7)

where bars denote average over ρ(p, q). Generally, randomness results in decrease of s and γ. Explicit calculations areperformed for two examples: uniformly distributed and two peaked systems. Significant influence is demonstratedwhen a bare growth rate is low and coupling is weak. It should be emphasized that even the sign of the growth ratecan be changed from positive to negative growth.

References:

[1] A. V. Bobylev, J. A. Carrillo, and I. M. Gamba: J. Stat. Phys. 98 (2000) 743-773.[2] M. H. Ernst and R. Brito: J. Stat. Phys. 109 (2002) 407-432.[3] E. Ben-Naim and P. L. Krapivsky: Phys. Rev. E66 (2002) 011309.[4] D. ben-Avraham, E. Ben-Naim, K. Lindenberg, and A. Rosas: Phys. Rev. E68 (2003) R050103.[5] T. Ohtsuki, A. Fujihara, and H. Yamamoto: cond-mat/0312357.



5.3.6

Hysteresis in Anti-Ferromagnetic Random Field Ising Model

Prabodh Shukla1 and L Kurbah2

1,2 Physics Department, North Eastern Hill University, Shillong-793022, India.

We present an exact solution of the zero temperature hysteresis in the one-dimensional anti-ferromagnetic randomfield Ising model in the case of an unbounded continuous distribution of quenched random fields. Our work generalizesan earlier result that was restricted to a rectangular distribution of fields of width 2∆, ∆ ≤ |J |, where J is the nearestneighbor exchange. The unbounded distribution presents new complexities in the kinetics of the model that are tackledin the present work.

1 [email protected]

5.3.7

Hysteresis in Ferromagnetic Random Field Ising Model

Prabodh Shukla1 and R S Kharwanlang2

1,2 Physics Department, North Eastern Hill University, Shillong-793022, India.

We consider hysteresis at zero temperature in the ferromagnetic random field Ising model on a Bethe lattice, andpresent an exact expression for the hysteresis loop in the case when a fraction of spins (randomly dispersed in thesystem) are quenched. Our result generalizes an earlier solution when all spins were free to flip but the initial statewas restricted to all spins pointing in the same direction. The effect of random initial states on the nonequilibriumcritical behavior of the model is discussed.

1 [email protected]


5.3.8

Persistence with Synchronous Dynamics

P. Shukla1, G. I. Menon2 and P. Ray3

1 Department of Physics, North Eastern Hill University, Shillong-793022, India.2,3 The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai-600113, India.

We study Ising and Potts chains evolving under synchronous dynamics at zero temperature. At each time step, a spinis aligned along the net field at its site, and if the net field happens to be zero, it is flipped from its previous statewith probability p. Persistence in the system is determined by the diffusive motion of zero-field sites (sites where thenet field is zero). For p = 1/2, two consecutive zero-field sites that constitute a domain wall move independently ofeach other. In this case, the system comprises two independent reaction-diffusion sub-systems and the persistenceprobability P (t) ≈ t−θ decays with the exponent θ = 3/4. Any other value of p leads to a dynamic coupling betweenthe two sub-systems; p < 1/2 corresponds to attraction, and p > 1/2 corresponds to repulsion between the pair ofzero-field sites along a domain wall. We show that the cases for p > 1/2 and p < 1/2 are dual to each other, anddiscuss the effect of coupling between the two sub-systems on persistence in each sub-system.


5.3.9

Persistence in Transport Processes

Devashish Sanyal1

1 Department of Theoretical Physics,Indian Association for the Cultivation of Science,Calcutta-700032,India

Persistence is of importance in non-equilibrium processes for it brings out the hidden temporal correlations. In thepresent paper persistence has been studied analytically in both diffusive as well as advective systems. Persistenceexponent for the diffusive system, as defined in the paper, comes out to be d/4 under certain conditions. The theoryhas further been extended to develop a renormalised theory for the calculation of persistence in the advective systemdriven by a gaussian velocity field.

1 [email protected]


5.3.10

Exact result for nonreciprocity in one-dimensional wave transmission

Onuttom Narayan1 and Abhishek Dhar2

1 Department of Physics, University of California, Santa Cruz, CA 950642 Theoretical Physics Group, Raman Research Institute, Bangalore 560080

Wave propagation in nonlinear media plays an important role in science and technology, but its understanding iscomplicated by the fact that even for monochromatic radiation, the medium generates all higher harmonics, couplingan infinite number of frequency channels together. Here we devise a new approach to this problem by applyingmonochromatic filters to the ends of a one dimensional system. We have discovered an exact identity, relating thenonreciprocity — the difference in transmitted power with the source to the left or right — to the net power flowingwith equal strength sources at both ends. Thus nonreciprocity has an unanticipated link to an apparent violation ofthe second law of thermodynamics; this violation is only apparent because of a subtle dependence on the (arbitrarilysmall, but non-zero) bandwidth of the filters. This identity has the unexpected feature that it breaks down whenthe incident power is large, with a nonperturbative transition to a noisy state. Apart from the theoretical insightgained by putting in the filters, not contaminating other frequency channels has advantages from a communicationsperspective.


5.3.11

Brownian dynamics simulations of polyelectrolytes in a flashing ratchet

Heiner Linke1, Martin Zuckermann2, Erin Craig3 and Michael Plischke4

1,3 Physics Dept., Univ. Oregon, Eugene, USA2,4 Physics Dept., Simon Fraser Univ., Vancouver, Canada

Within the ratchet and Brownian motor community, increasing attention is currently being paid to coupled motors,that is, ratchet effects for coupled particles. One of the easiest ways of realizing a coupled motor experimentallywould be to mechanically link a number of single particles. For instance, one could use a polymer to link chargedbeads, and expose the system to an electrostatic flashing ratchet, that is, a periodic, asymmetric potential whosestrength is periodically varied as a function of time. A ”natural” system where many charged particles are linkedtogether are polyelectrolytes such as DNA. We present molecular dynamics simulations of such a system. Focusing onexperimentally realizable physical conditions, we model the behavior of a freely-jointed chain model of a polyelectrolyte.For the driving force, we use a realistic, time-dependent electrostatic potential as it would be created by an asymmetric,interdigitated electrode pattern on a silicon chip. A Brownian dynamics algorithm is used and results for the kineticbehavior of the motors will be presented, with particular attention to qualitative differences between the behavior ofthe coupled motors as compared to single motors.



5.3.12

Multifractality in the Interaction of Ballistic Particles with IrregularSurfaces

S. B. Santra1 and B. Sapoval2

1 Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam India.2 Laboratoire de Physique de la Matiere Condensee, Ecole Polytechnique, 91128 Palaiseau Cedex, France.

Ballistic particles interacting with irregular surfaces are representative of several physical problems in the Knudsendiffusion regime like catalytic efficiency, Knudsen diffusivity, and chaos. The distribution of the collisions of ballisticparticles interacting with irregular surfaces, modeled by a quadratic Koch curve, are studied here numerically in 2dimensions. The q moments of the spatial distribution of collision numbers µ(x) are characterized by a sequence of“collision exponent” τ(q). The measure µ(x) is found to be multifractal even when a random micro-roughness (orrandom re-emission) of the surface exists. The dimensions f(α), obtained by a Legendre transformation from τ(q),consist of two parabolas corresponding to a trinomial multifractal. This is demonstrated for a particular case byobtaining an exact f(α) for a multiplicative trinomial mass distribution. The trinomial nature of the multifractalityis related to the type of surface macro-irregularity considered here, independently of the incidence angle and micro-roughness which however influence the values of αmin and αmax. The information dimension DI increases significantlywith the micro-roughness of the surface. Interestingly, in contrast with this point of view the surface seems to workuniformly. This would correspond to a possible absence of screening effects in Knudsen diffusion.


5.3.13

Kink diffusion in open boundary ASEP

Tetsuya Mitsudo1, Shinji Takesue2 and Hisao Hayakawa3

1,2,3 Department of Physics, Kyoto University, Yoshida-Nihonmatsu-Cho,Kyoto 606-8501,Japan

Asymmetric Simple Exclusion Process(ASEP.) is known as a simple model of the transport phenomena,whosestationary state is solvable. In these days, we have recognized possibilities to apply ASEP to many related fields suchas traffic flows, granular flows and biological transport problems In the study of traffic flow and granular flow, it isknown that the power spectrum of the particle density in the congested flow obeys a power low as f−a where f is thefrequency. We studied the power spectrum in the ASEP with an open boundary condition. The congestion on ASEPis undestood as a Brownian motion of the domain wall. Based on this kink diffusion picture we have confirmed thatthe exponent a should be a = 3/2 [1]. We also check that the kink corresponds to the zero eigenfunction and try toderive the kink diffusion from ASEP. We also try to extend the model to a two-lane model. We want to show someresults about interaction between kinks in the both lanes.

[1] S.Takesue,T.Mitsudo and H.Hayakawa,Phys.Rev.E68(2003)015103(R)

1 [email protected]


5.3.14

A Statistical Mechanics Model for Fracture in Glassy Materials

Pier Giuseppe Gabrielli1 and Simone Gabrielli2

1 UTS Materiali CR Casaccia ENEA2 Physics Department Universit di Roma LaSapienza

The motion of a planar crack front in a solid can be thought as an elastic manifold pulled through a quenched randommedium by an applied force F: when F is increased through a critical value Fc the manifold exhibits, in the absenceof thermal fluctuations, a sharp transition from a pinned phase to a moving phase (this behavior is common toothers system like vortex lines in type II supercondunctor, charge density waves or between oppositely magnetizedferromagnetic domains). This model proposes to explain the dissipative behavior of the system by the competitionbetween an elastic restoring force and a non linear, randomly distributed, time-independent pinning force: in the caseof crack front the pinning force is due to local fracture toughness, and the elastic restoring force is a result of the linetension of the front due to bulk elasticity of the medium (in brittle materials). In the case of strong pinning it is wellknown that, when subjected to an external driving load, the crack front displays local instabilities that force it toadvance quasistatically. This property makes it difficult to handle the problem in the continuum approximation. Infact, in the non-equilibrium stationary regime, the main contribution to the global displacement is from jumps of localparts of the chain resulting from these instabilities: near the depinning transition, the dynamics is very jerky withsegments of the manifold spending most of their time stationary or almost so, but occasionally getting unpinned by theforces from other segments and moving forward only to get pinned again by combination of the newly explored randomforces and the elasticity. This evolution can be effectively described by an extremal model: only the site closest toits instability threshold advances. . All the information in this dynamics is contained in a space-time ”cracking plot”of where the front is active at every instant of time: most of the relevant information is contained in the probabilitydensity function (PDF) of this plot. If the PDF is an exponential distribution, the probability that at every instanttime the weakest site ”jumps” is a double-exponential function: in other words, the extreme-value statistics is of theGumbel class equivalent to the one-step replica symmetry breaking (RSB) univer-sality class. We develop and applya specific release of such a model to the fracture mechanics of a glassy (disordered) material.

5.3.15

Condensation in a two species zero-range process

Tom Hanney1 and Martin Evans2

1,2 School of Physics, University of Edinburgh, Edinburgh, UK

Condensation phenomena and phase separation are observed in a variety of physical systems. A generic mechanism forunderstanding these phenomena is provided by condensation transitions in the zero-range process — a model of manyinteracting particles which move on a lattice. In the condensate phase, a finite fraction of particles accumulate at asingle site. We consider a generalisation of the zero-range process to include two species of particles, and investigatehow the interaction of the two species of particles can lead to new mechanisms of condensate formation. The steadystate of the model is exactly soluble and we exploit this to derive the phase diagram for a quite general choice ofdynamics. In particular, we find a novel phase in which a condensate of one of the particle species is sustained by a‘weak’ condensate of particles of the other species.



5.3.16

Nonlinear mechanical responses of a collapsed polyelectrolyte

Hirofumi Wada1, Yoshihiro Murayama2 and Masaki Sano3

1,2,3 Department of physics, University of Tokyo, Tokyo, Japan

Collapse of a charged macromolecule due to counterion condensation is one of the most striking phenomena in awide range of polyelectrolyte systems such as DNA solutions. Thus it is also expected that ionic effects can modifyelastic properties of polyelectrolyte chains drastically. In this work, we describe preliminary results of the Browniandynamics simulations on the stretching of single polyelectrolyte condensates. The present simulation covers only asalt-free system, but the counterions are taken into account explicitly in the strong electrostatic coupling limit. Inthe simulations, an initially collapsed polyelectrolyte is stretched by pulling its one end at a constant speed, whilethe other end is fixed in a position. The force-extension curves obtained at low temperature shows either plateausor stick-release patterns depending on the strength of the electrostatic coupling, which may reflect a series of partialmelting of the solid-like structure of the ionic condensate. We note that qualitatively similar force profiles are alsofound in the several force-measuring experiments of collapsed single DNA molecules by multivalent cations.

1 [email protected]

5.3.17

Fluctuation Statistics in Networks: a Stochastic Path Integral Approach

Eugene Sukhorukov1

1 Department of Theoretical Physics, University of Geneva, Geneva, Switzerland

We investigate [1] the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. Thenodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to findthe time evolution of the probability distribution of charges in the network. The building blocks of our theoreticalapproach are (1) known probability distributions for the connector currents, (2) physical constraints such as localcharge conservation, and (3) a time-scale separation between the slow charge dynamics of the nodes and the fastcurrent fluctuations of the connectors. We integrate out fast current fluctuations and derive a stochastic path integralrepresentation of the evolution operator for the slow charges. The statistics of charge fluctuations may be foundfrom the saddle-point approximation of the action. Once the probability distributions on the discrete network havebeen studied, the continuum limit is taken to obtain a statistical field theory. We find a correspondence betweenthe diffusive field theory and a Langevin equation with Gaussian noise sources, leading nevertheless to non-trivialfluctuation statistics. To complete our theory, we demonstrate that the cascade diagrammatics, recently introducedby Nagaev, naturally follows from the stochastic path integral. By generalizing the principle of minimal correlations, weextend the diagrammatics to calculate current correlation functions for an arbitrary network. One primary applicationof this formalism is that of full counting statistics (FCS), the motivation for why it was developed in the first place.We stress however, that the formalism is suitable for general classical stochastic problems as an alternative approachto the traditional master equation or Doi-Peliti technique. The formalism is illustrated with several examples: bothinstantaneous and time averaged charge fluctuation statistics in a mesoscopic chaotic cavity, as well as the FCS andnew results for a generalized diffusive wire.Reference:[1] A.N. Jordan, E.V. Sukhorukov, S. Pilgram. cond-mat/0401650.

1 [email protected]


5.3.18

Anomalous Diffusion and Complexity: New lights at an old problem

Fernando A. Oliveira1, Ismael Costa2 and Rafael Morgado3

1,2,3 Institute of Physics and International Center of Condensed Matter Physics, Universidade de Brasilia, Brasilia,Brazil

Since its formulation by Boltzmann 1 the ergodic hypothesis (EH) has attracted the attention of the scientificcommunity. As well the Kubo’s Fluctuation-Dissipation theorem (FDT) has fundamental rule in non-equilibriumstatistical mechanics. In this seminar we show how to classify diffusion, the limits of FDT and EH, and how it canbe used in systems, such as glass, fluid polymers, and many kinds of complex fluids. In short, we expect that thoseworks may help us understand the way complex systems approach an equilibrium 2.

References :[1] Boltzmann L. “On the evolution of Methods of Theoretical Physics in Recent times” (1899).[2] I. V. L. Costa, R. Morgado, M. V. B. T. Lima, and F. A. Oliveira, Europhysics Lett. 63, 173 (2003); R. Morgado,F. A. Oliveira, G. G. Batrouni, A Hansen, Phys. Rev. Lett. 89, 100601 (2002).


5.3.19

Coherent fluid flow generation via sphaleron transitions

Florin Spineanu1 and Madalina Vlad2

1,2 National Institute of Laser, Plasma and Radiation Physics, Magurele, Bucharest, Romania

The linkage of two lines of flow (and analogously of two magnetic field lines in plasma, or two polymers) can bedescribed by the Gauss invariant or by the Chern-Simons topological charge. Extending to continuum, in a volume offluid the helicity is distributed continuously and can be described as a density of the Chern-Simons current of chargeand expressed by a magnetic potential. When the boundary conditions are not fixing the helicity content in the volumeit exists the possibility that a certain amount of helicity is transformed in ordered, large scale flow (and analogously inmagnetic field, the alpha-dynamo). It is possible to express the magnetic potential of the Chern-Simons action as theprojection along the third direction in the isospin space of the bosonic field of a Non-Abelian Yang-Mills-Higgs theory.In this theory there exist sphaleron solutions connecting vacua of distinct topological classes, with the energetic barrierbeing traversed at finite temperature, i.e. in the presence of fluctuations. We propose the model where the change ofhelicity in the fluid volume is represented as the real-space projection of the sphaleron transitions in the Non-Abelianmodel. The rate of modification of the topological degree can be estimated on the base of the sphaleron rate. Whenthe sphaleron rate saturates to a very low value the regular large scale flow is also saturated meaning that not all thehelicity content is available for transformation.



5.3.20

Spatial Field Correlations in Quasi-one-dimensional systems

Gabriel Cwilich1, Luis S. Froufe Perez2 and Juan Jose Saenz3

1 Department of Physics, Yeshiva University, New York, USA2,3 Departamento de Fisica de la Materia Condensada, Universidad Autonoma de Madrid, Madrid, Spain

When a wave propagates coherently through a disordered medium, the correlations between the transport coefficientsproduce long-range effects that appear in the intensity-intensity correlations. These correlations have been studiedexperimentally in the spatial domain in microwaves in a quasi one-dimensional geometry, in the diffusive regime byP. Sebbah, et al. (Phys. Rev. Lett. 88, 123901, (2002)). Interesting symmetries between the roles of sources anddetectors were found. It was shown that all contributions can be expressed in terms of a single function, the field-fieldcorrelation. We show that those results can be obtained from Random Matrix Theory (RMT) applied to coherenttransport in quasi one-dimensional cavities. The structure of the correlations follows from the isotropy hypothesis ofthe statistical distribution of the transmission eigenvalues, which is shown to be independent of the specific transportregime, extending the range of validity of the results obtained by Sebbah et al. beyond the diffusive regime. Thesource-detector symmetries arise from general properties of the eigenfunctions corresponding to the geometry of anypropagating cavity. The experimental results are recovered in the large-N (number of propagating channels) limit inRMT. New results on the scaling of the correlations with the size of the system will be discussed.


5.3.21

Study of stochastic phenomena in vertical cavity lasers

Giovanni Giacomelli1

1 Istituto Nazionale Ottica Applicata, largo E. Fermi 6, 50125 Firenze (Italy)

The vertical cavity laser may operates in a bistable regime where two linear polarizations of the emitted field aresustained. Noise-induced switchings between the two polarizations are observed, ruled by the Kramers statistics. Inthis regime, evidence has been given of several stochastic phenomena, including Standard and Aperiodic StochasticResonance, Noise-Induced Phase Synchronization and Vibrational Resonance. Thanks to the combination of fasttime scales and stability of the setup, the system allows for detailed experimental investigations. Moreover, themeasurement parameters can be calibrated in order to compare the results with the predictions of the theory. Anoverview of the experimental results is given, together with the comparison with the theory and some perspectives forfuture investigations.

1 [email protected]


5.3.22

Macroscopic fluctuation theory for stochastic and deterministic particlesystems

Lamberto Rondoni1, Andrea Gamba2, Claudio Giberti3 and Cecilia Vernia4

1,2 Politecnico di Torino - Italy3 Univ. della Insubria - Italy

4 Universita‘ di Modena - Italy

Recently, a fluctuation theory for stationary states of stochastic nonequilibrium systems has been proposed by Bertini,De Sole, Gabrielli, Jona-Lasinio and Landim. The aim of the theory is to extend the Onsager-Machlup fluctuationtheory for equilibrium systems to nonequilibrium steady states. The result is the introduction of a term in the”adjoint” hydrodynamic equations (the equations which describe the evolution of the fluctuations away from thenonequilibrium steady state), which has no counterpart in the usual hydrodynamic equations (the equations whichdescribe the relaxation back towards the nonequilibrium steady state). This term breaks the symmetry between theadjoint hydrodynamic and the usual hydrodynamic equations. We check numerically the applicability of this theoryon simple deterministically thermostatted systems, in nonequilibirum steady states. The dynamics of these systemsare not stochastic, but they are chaotic, which makes them very close to that of a stochastic process.

1 [email protected]

5.3.23

Stochastic W.Z.N.W. model and stochastic Chern-Simons theory

Leandre R.1

1 Departement de Mathematiques. Faculte des Sciences. 21000. Dijon (France) (After 26-01-2004)

We define a measure over the maps from a surface into a group, and we define the stochastic Wess-Zumino termassociated. The theory satisfies the glueing property of Segal’s axioms of conformal field theory, by using the Markovproperty of the random field. We define, by using a Gaussian regularization, a measure on the set of connections on a3 dimensional manifold. The theory which is got satisfies one of Atiyah’s axioms of topological field theory, by usingMarkov property on the field.

1 [email protected]


5.3.24

Constitutive relations and linear stability of sheared granular flows

V. Kumaran1

1 Department of Chemical Engineering, Indian Institute of Science, Bangalore-12

The constitutive relation for the granular flow of smooth and rough, nearly elastic particles is derived in the ‘adiabatic’limit, where the length scale for conduction is small compared to the macroscopic scale. In this case, there is a balancebetween the rate of production (due to the shear) and the rate of dissipation (due to inelastic collisions). The stresstensor is used to obtain analytical expressions for the growth rates of the hydrodynamic modes in a linear shearflow in the limit where the wavelength is long compared to the length scale of conduction. The results show thatt is perturbations are unstable in the vorticity direction, and that the Navier-Stokes approximation is not adequateto capture the leading behaviour in the small wave number limit, and dominant terms in the growth rates of thetransverse modes depend on the Burnett coefficients. When the wave length is small compared to the conductionlength, the stable hydrodynamic modes for a gas or elastic particles are recovered. The transition between thesetwo regimes is examined for a dilute granular flow. The analysis indicates that the minimal model which accuratelycaptures the dynamics in both limits is one in which the constitutive relation for the stress incorporates the strainrate dependent Burnett terms in the stress equation, and the constitutive relation for the heat flux is the Fourier lawfor heat conduction.

1 [email protected]

5.3.25

Bethe Ansatz and Random Matrices

Attila Rakos1 and Gunter M. Schutz2

1,2 Institut fur Festkorperforschung, Forschungszentrum Julich, Julich, Germany

For many surface growth models of the KPZ universality class the distribution of the height at late times was calculatedand it was shown that this relates to the Tracy-Widom distribution of the largest eigenvalues of some Gaussian randommatrix ensembles. We study how this result can be derived from the Bethe Ansatz solution of this type of systemsand in particular of the asymmetric exclusion process. The Bethe Ansatz does not require the use of combinatorialarguments including the statistics of increasing subsequences in random permutations, but is straightforward to applyto integrable systems.



5.3.26

Fluctuation-Dissipation Dispersion Relation for Slow Processes

Viatcheslav V. Belyi1

1Theoretical Department, IZMIRAN, Troitsk, Moscow region, 142190, Russia

A generalization of the Callen-Welton formula for systems with slowly varying parameters is given. Using the mo-mentum method and the time multiscale technique, it is shown that not only the dissipation but also the dispersivecontributions determine the spectral function of the fluctuations in these systems. The general formalism is illustratedfor an oscillation electrical circuit, and the influence of the dispersion contributions on the quality factor of the systemis discussed.

[email protected]

5.3.27

Delay Langevin equations and its functional approach

Manuel O. Caceres1 and Adrian A. Budini2

1Centro Atomico Bariloche, Argentina2Max Planck Institute, Dresden, Germany

We present an exact functional characterization of linear delay Langevin equations driven by any noise structure definedthrough its characteristic functional. This method relies on the possibility of finding an explicity analytical expressionfor each realization of the delayed stochastic process in terms of those of the driving noise. General properties of thetransient dissipative dynamics are analyzed. The corresponding interplay with a color Gaussian noise is presented. Asa full application of our functional method we study a model for population growth with non-Gaussian fluctuations:the Gompertz model driven by multiplicative white shot noise.

[email protected]@mpipks-dresden.mpg.de


5.3.28

Hyperbolic fluctuating phenomena in the framework of path integrals

Federico Vazquez1, Alan McKane2 and Miguel A. Olivares-Robles3

1,3 Physics Department, Morelos State University, Cuernavaca, Mexico2 Physics and Astronomy Department, Manchester University, Manchester, UK

In this work we focus on the mesoscopic formulation of thermodynamic fluctuating phenomena by using path-integralmethods which have shown to be a powerful tool to perform calculations in a variety of physical situations. Wefirstly generalize the formulation of stochastic differential equations in terms of path functionals to the case of singulardiffusion matrices which are encountered when one of the equations does not possess a stochastic term. This is thecase in Linear Irreversible Thermodynamics and Extended Irreversible Thermodynamics, specifically the equation formass density, which is a conserved property of the system. Our method is applicable away from equilibrium. Thenwe consider simple case to illustrate this, namely, the case of a fluid with a temperature gradient due to a steady,non-zero, heat flux which is of considerable experimental interest. We finally investigate the application of the generalformalism for non-Markovian processes to the study of hyperbolic phenomena when they are described at the level ofLIT where irreversible processes with thermodynamic inertia are well described by hyperbolic type transport equationsof the Maxwell type.


5.3.29

New results in the study of metastable states of Markovian systems.

Gabriella Baez Juarez1, Francois Leyvraz Waltz2, Hernan Larralde Ridaura 3 and Rafael MendezSanchez4

1 Laboratorio de Sistemas Dinamicos, Departamento de Ciencias Basicas, Universidad AutonomaMetropolitana-Azcapotzalco, AP 21-267, Coyoacan 04000, Mexico D.F., MEXICO.

2,3,4 Centro de Ciencias Fisicas UNAM, AP 48-3, 62210, Cuernavaca, Morelos, MEXICO.

We assume that the metastable state of Markovian systems, satisfying detailed balance, can be described by a superpo-sition of the ground and first excited states of the correspondent master equation. Then, we show that an appropiatelyfluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for timesshorter than the nucleation time of such systems. We corroborate this results numerically for the metastable states ofa two-dimensional Ising model and q-exponential behaviour is observed in the magnetization correlation function.



5.3.30

Approach to equilibrium in shape-changing potential

Himadri Shekhar Samanta1,Jayanta Kumar Bhattacharjee2 and Ram Ramaswamy3

1,2Department of theoritical physics,Indian Association for the Cultivation of Science,Jadavpur,Kolkata-700 032,India3School of Physical Sciences,Jawaharlal Nehru University,New Delhi-110 067,India

For potential function (in one-dimension) which evolves from a specified initial form, Vi(x) asymptotically, we studythe evolution of an initial probability density to its final equilibrium. There can be unexpected effects that can arisefrom the time dependence. For a choise of the variation, we show that in particular, if the evolution is adiabatic, thisresults in a decrease in the Kramers’ time characteristic of Vf (x): thus the time dependence makes diffusion over abarrier more efficient. There can also be interesting resonence effects that arise from the coincidence of the intrinsictime-scale characterising the potential variation and the Kramers’ time.


5.3.31

Monte Carlo Simulations of the Magnetic Reversal for Nano-particles

Hwee Kuan Lee1, Yutaka Okabe2, Xingzhi Chen3 and Mansoor Bin Abdul Jalil4

1,2 Department of Physics, Tokyo Metropolitan University, Tokyo, Japan3,4 Department of Electrical and Computer Engineering, National University of Singapore, Singapore

Dynamics in magnetic reversal plays an important role in the design of magnetic recording devices, in particular in thelong time scale limit. In addition to long time scale, microscopic effects such as the entropic effect become importantin magnetic nano-scale systems. Unfortunately, many advanced simulation methods were either incapable of reachinglong time scales or unable to accurately model the microscopic effects of nano-scale systems. We devised a new MonteCarlo method for calculating the dynamics of magnetic reversal. This method is based on microscopic interactionsof many constituents and the magnetic probability distribution function is obtained symbolically; Thus enabling usto model magnetic reversal effects of nano-particles to arbitrarily long time. Actual calculations were done up to1e50 Monte Carlo steps per-site. Our method involves solving the Markov Chain Master Equation using arbitraryprecision calculations from equilibrium probability distributions. This method requires a constant computationaltime for evaluating the magnetic properties of nano-particles at arbitrary physical time. In contrast, most advancedsimulation methods requires computational time proportional to the simulated physical time.



5.3.32

The kinetic ising model on the periodic inhomogeneous AB2 and A2b2chains

Lindberg Lima Goncalves1, Andre Pinho Vieira2, Mariano Lopez de Haro3 and Julia TaguenaMartinez4

1 Departamento de Fisica, Universidade Federal do Ceara, Campus do Pici, CP 6030, 60451-970 Fortaleza, Ceara,BRAZIL

2 Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 05315-970 Sao Paulo, BRAZIL3,4 Centro de Investigacion en Energia, UNAM, Temixco, Morelos, 62580, MEXICO

The kinetic Ising model on inhomogeneous periodic linear chains, which are composed of N segments with n differentAB2 or A2B2 structures, is considered. Each AB2 structure is composed of a loop built with two decorated bonds,where the connecting sites are occupied by ions A, the decorating sites by ions B. In the A2B2 structure, the loopsare connected by a single bond whose vertices are occupied by ions A. The model is studied within the restricteddynamics[1] introduced by us for the description of relaxation phenomena in linear polymer chains, and it correspondsto an extension of the homogeneous models recently studied[2]. The solution of the model is obtained exactly forarbitrary n by reducing the problem to a set of n coupled equations which is solved numerically. The dynamic criticalexponent z and the dynamic susceptibility are determined and the universality of dynamics is discussed.We also discussthe effects of those new ingredients on the Nagel scaling. [1] M. Lopez de Haro, J. Taguena-Martinez, B. Espinosa,and L.L. Goncalves, J Phys. A 26, 6697(1993); 29(E), 7353 (1996). [2] M. Lopez de Haro, J. Taguena-Martinez, L.L.Goncalves and A. P. Vieira, J. Non-Cryst. Solids 329, 82 (2003) [3] P. K.Dixon, L. Wu, S. R. Nagel, B. D. Williamsand J. P. Carini, Phys. Rev. Lett. 72, 1108 (1990). Work partially financed by the Brazilian agencies CNPq, Finepand Fapesp.



5.3.33

Study of stochastic energetics in Brownian motors

Raishma Krishnan1 and A. M. Jayannavar2

1,2 Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India

Using the method of stochastic energetics we study the nature of currents, input energy, entropy production andefficiency in different types of Brownian motors or ratchets. Our focus here is on various classes of adiabatically rockedratchet systems. The current exhibits a peak as a function of noise strength. The behaviour of input energy or energyloss in the medium indicates that there is no underlying resonance or synchronization phenomena associated with thesecurrent peaks. Also, the maxima seen in current and entropy production is found not to be correlated. Our studyof the efficiency of noise induced energy transduction in a temporally asymmetric rocked ratchet show the system tobe highly efficient. Time asymmetry in the rocking ratchet profile is found to favour current in one direction whilesuppressing that in the other direction. This ensures a large efficiency of ∼ 50% as compared to the subpercentageefficiency obtained in various other earlier ratchet models due to the intrinsic irreversibility associated in the mode oftheir operation.


5.3.34 Poster 5.3.34 not being presented.5.3.35

Equations of electrodynamics of continuous media taking into accountnonequilibrium correlations

Alexander Sokolovsky1 and Anton Stupka2

1,2 Department of Quantum Macrophysics, Dnepropetrovsk National University, 13, Nauchnaya St., Dnepropetrovsk,49050, Ukraine

In the framework of the Bogolyubov reduced description method (RDM) a system consisting of electromagnetic fieldand fluid from charged particles has been studied. The consideration was based of the quasi-relativistic quantumelectrodynamics taken in the Coulomb gauge. As the reduced description parameters (RDP) average magnetic andtransversal electric fields, their binary fluctuations (correlations) and usual hydrodynamic variables for the fluid werechosen. In the correspondence with the RDM the presented theory is based on the functional hypothesis and aboundary condition of the complete correlation weakening. A perturbation theory over field-particle interaction andsmall gradients of variables describing the system was built. It was implied also that magnetic, electric fields andgradient of vector potential have the same order. A spatial dispersion of some values of the fluid was discussed. Aclosed system of time equations for description of the electromagnetic field in the fluid with accounting of fluctuationsof the field has been obtained. One can consider the equations for fluctuations as a system of kinetic equations for theWigner distribution functions of photons. The developed theory was applied to a description of interaction of soundin the fluid and electromagnetic field. This work was supported by INTAS under project 00-577.



5.3.36

To kinetics of non-Hamilton systems

Isaac Goldhirsch1, Alexander Peletminskii2, Sergey Peletminskii3 and Alexander Sokolovsky4

1 Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, 69978, Israel2 Electro-Physical Scientific and Technical Centre, P.O.Box 8812, 28,Chernyshevsky St., Kharkov, 61002, Ukraine

3 Institute for Theoretical Physics, National Science Center ”Kharkov Institute of Physics and Technology”, 1,Akademicheskaya St., Kharkov, 61108, Ukraine

4 Department of Quantum Macrophysics, Dnepropetrovsk National University, 13 Nauchnaya St., Dnepropetrovsk,49050, Ukraine

System of particles in the presence of dissipative interparticle forces has been studied. The investigation is based onthe Hamilton equations with a dissipative function. Generalized Liouville equation and generalized BBGKY hierarchyfor reduced distribution functions were derived. On this base a generalized Landau kinetic equation (the case of weakinteraction of particles) and a generalized Boltzmann equation (the case of low density of particles) were obtained inthe framework of the Bogolyubov reduced description method. This approach is based on the functional hypothesisand a boundary condition of complete correlation weakening. It was shown that this boundary condition givesequations, which can be easy generalized to take into account long-range nonequilibrium correlations in the system.The received Boltzmann equation was written in the usual form in the terms of limiting coordinates and momenta ofthe corresponding two-particle problem. Dynamics of two particles interacting with potential and dissipative forces wasstudied in detail. In the framework of the dynamics a perturbation theory in small dissipative forces was constructed.A comparison of the obtained kinetic equations with equations proposed by other authors for investigation of granularmatter was performed. This work was supported by INTAS under project 00-577.



5.3.37

Reduced description of nonequilibrium processes taking into accountnonequilibrium correlations

Sergey Peletminskii1,Yuriy Slyusarenko2 and Alexander Sokolovsky3

1,2Institute for Theoretical Physics, National Science Center ”Kharkov Institute of Physics and Technology”, 1,Akademicheskaya St., Kharkov, 61108, Ukraine

3Department of Quantum Macrophysics, 13, Nauchnaya St., Dnepropetrovsk, 49050, Ukraine

The reduced description of nonequilibrium states with accounting of nonequilibrium fluctuations (correlations) as newindependent variables, which describe state of system, has been discussed. The Bogolyubov reduced descriptionmethod (RDM) was placed in the base of the consideration. Fluctuations smoothed on a microscopic scale lengthwere studied. It was given a general proof that averaging of the RDM equations without fluctuations over initialrandom states of the system leads to the RDM equations taking into account the smoothed fluctuations. In theend time equations for the reduced description parameters in the presence of nonequilibrium fluctuations were builtin the terms of functions introduced by Bogolyubov in his theory without fluctuations. The reduced descriptionhas been studied also in the presence of an external random field. It was shown that averaging over the externalrandom field leads to equations of the RDM taking into account fluctuations with additional terms, which describecorrelations of the field. On the base of the developed theory nonequilibrium entropy of the system taking into accountnonequilibrium fluctuations was built and the H-theorem was proved. As an application a possibility to obtain theKolmogorov-Obukhov turbulent spectra was discussed. This work was supported by INTAS under project 00-577.



5.3.38

Kinetic equations for electron in crystal with taking into accountelectron-phonon and phonon-phonon long-range correlations

Alexander Sokolovsky1, Sergey Sokolovsky2 and Ivan Chernenko3

1 Department of Quantum Macrophysics, Dnepropetrovsk National University, 13 Nauchnaya St., Dnepropetrovsk,49050, Ukraine

2,3 Department of Radioeletronics, Dnepropetrovsk National University, 13 Nauchnaya St., Dnepropetrovsk, 49050,Ukraine

In the framework of the Froehlich model kinetics of an electron in a polar crystal has been considered. The influenceof binary electron-phonon and phonon-phonon correlations on dynamics of an electron has been considered. Theinvestigation began from coupled system of kinetic equation for electron and hydrodynamic equations for a phonon gasin the crystal. The necessary kinetic equation for electron was derived with the Bogolyubov reduced description method(RDM). Nonequilibrium correlations have been taken into account with a method of averaging of equations for reduceddescription parameters (RDP) over initial random state of the system. It is known that the last procedure reproducesresults of the RDM theory of nonequilibrium processes in a system with accounting of fluctuations (correlations) asadditional RDP. The investigation was restricted by spatially uniform and isotropic states of the phonon gas. Inthis case hydrodynamic RDP of the phonons do not depend on coordinates and time and correlations are rotationallyinvariant and uniform in the space. On the base of the obtained coupled system of equations for the Wigner distributionfunction of electron and the mentioned correlation functions an analysis of kinetics of the system was performed. Thiswork was supported by INTAS under project 00-577.



5.3.39

Stochastic derivation of kinetic equation for excitons in system ofemitters of electromagnetic field

Sergey Lyagushin1, Yuriy Salyuk2 and Alexander Sokolovsky3

1,2,3 Department of Quantum Macrophysics, Dnepropetrovsk National University, 13, Nauchnaya St.,Dnepropetrovsk, 49050, Ukraine

A system of two level emitters of electromagnetic field has been investigated in the quasispin Dicke model. Theconsideration is based on a kinetic equation for statistical operator of the emitters received with the Bogolyubov reduceddescription method (RDM). With this kinetic equation dynamics of emitters weak interacting with an equilibriumphoton bath has been reduced to dynamics of a spin system. Reduced description of the system with average quasispindensities has been built in a generating functional approach developed for spin systems. On this base the reduceddescription of the system with average quasispin densities and its smoothed correlation functions has been developed.This gives a more complete description of the system because the correlation functions define the Wigner distributionfunction for excitons in the system. It is known that the RDM theory with the smoothed correlations can be reproducedwith an averaging of the corresponding equations without correlations over initial states. By this way a time equationfor small correlations, which is a kinetic equation for excitons in a low density approximation, has been obtained. Theresults were compared with equations received in the framework of generating functional approach. This work wassupported by INTAS under project 00-577.


5.3.40

Separation of Mixtures : Blow Torch and Levitation Effect

A.V. Anil Kumar1, S. Yashonath2 and G. Ananthakrishna3

1,2 SSCU, IISc, Bangalore3 MRC, IISc, Bangalore

A new conceptual basis for the separation of multicomponent molecular mixtures is proposed. A separation methodwhere different components of the mixtures are driven in opposite directions is realised by a judicious combinationof two effects viz., levitation and blow torch effects. Monte Carlo simulations of two Lennard-Jones binary mixtureswith different sized components are shown to be separated well if at least one of the components lies in the anomalousregime and the others lie in the linear regime. Separation factor of 108 are obtained on nano length scales may becompared to 103 obtainable through conventional methods of separation.



5.3.41

Approach to equilibrium in spin systems

Tapas Kumar Sinha1

1ComputerCentre, Bijni Complex, North Eastern Hill University, Shillong 793 003, India

Ising spins have been extensively studied and still continue to be the subject of active research. One area which hasnot received much attention is the approach to equilibrium. The approach to equilibrium is an essential signatureof statistical systems both near and far from equilibrium. Spin half systems can be mapped to the random walker.A method for treating both biased and unbiased random walks has been developed by Kac [1]. We extend [1] tointeracting two state quantum systems. Next we study the approach to equilibrium of both classical and quantumspin systems in presence and absence of magnetic fields.

References :[1] Kac, M. Random walk and the theory of Brownian motion, American Mathematical Monthly 54 (1947), 369-391.

[email protected]

5.3.42

Clustered bottlenecks in mRNA translation and protein synthesis

Tom Chou1 and Greg Lakatos2

1 Dept. of Biomathematics UCLA2 Dept. of Physics UBC

We construct an algorithm that generates large, band-diagonal transition matrices for a totally asymmetric exclusionprocess (TASEP) with local hopping rate inhomogeneities. The matrices are diagonalized numerically to find steady-state currents of TASEPs with local variations in hopping rate. The results are then used to investigate clusteringof slow codons along mRNA. Ribosome density profiles near neighboring clusters of slow codons interact, enhancingsuppression of ribosome throughput when such bottlenecks are closely spaced. Increasing the slow codon cluster size,beyond ∼ 3 − 4, does not significantly reduce ribosome current. Our results are verified by extensive Monte-Carlosimulations and provide a biologically-motivated explanation for the experimentally-observed clustering of low-usagecodons.



5.3.43

Condensation in a two species zero-range process

Tom Hanney1 and Martin Evans2

1,2 School of Physics, University of Edinburgh, Edinburgh, UK

Condensation phenomena and phase separation are observed in a variety of physical systems. A generic mechanism forunderstanding these phenomena is provided by condensation transitions in the zero-range process — a model of manyinteracting particles which move on a lattice. In the condensate phase, a finite fraction of particles accumulate at asingle site. We consider a generalisation of the zero-range process to include two species of particles, and investigatehow the interaction of the two species of particles can lead to new mechanisms of condensate formation. The steadystate of the model is exactly soluble and we exploit this to derive the phase diagram for a quite general choice ofdynamics. In particular, we find a novel phase in which a condensate of one of the particle species is sustained by a‘weak’ condensate of particles of the other species.


5.3.44

Light scattering and sound propagation in polyatomic gases withclassical degrees of freedom

Wilson Marques Junior1

1 Departamento de Fisica, Universidade Federal do Parana, Caixa Postal 19044, 81531-990, Curitiba, Brazil

In this work we analyze time-dependent problems like sound propagation and light scattering in dilute polyatomic gasesby using a kinetic model of the Boltzmann equation that replaces the collision operator with a single relaxation-timeterm. The model equation contains several position and time dependent coefficients that are determined by preservingsome of the main physical properties of the Navier-Stokes-Fourier description. Comparison of the theoretical resultswith avaliable experimental data shows that the model equation can be used to describe the acoustic properties andthe light scattering spectrum of polyatomic gases as long as the external oscillation frequency is smaller than thefrequency required for the translational and the internal degrees of freedom to come to thermal equilibrium.

1 [email protected]


5.3.45

Dynamics of Sliding Particles on Fluctuating Interfaces

Sakuntala Chatterjee1 and Mustansir Barma2

1,2Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005,India

We wish to study how temporal fluctuations of a surface affect the dynamics of hard-core particles, which are slidinglocally downwards on the surface, under gravity. This is an example of a passive scalar problem where the driving fieldis the surface fluctuation and the passive field is the particle density. We first study the dynamics of hills and valleys,i.e. those portions of the interface, respectively above and below a reference level. To this end we define a coarsegrained variable σ(x, t) = sgn [h(x, t)− 〈h(t)〉] and study the auto-correlation function A(t) = 1

L

∫ L

0dx〈σ(x, t)σ(x, 0)〉.

For t & 1, our numerical simulations of 1-d interface suggest the scaling form A(t) ∼ 1 − b(

tLz

)β , where z is thedynamical exponent and β describes the temporal growth of height correlation. The unusual point is that the systemsize L enters strongly in the decay of A(t) even at small times (t & 1), in contrast to the height-height correlationfunction. Using the Gaussian character of the Edwards-Wilkinson interface, we calculate A(t) analytically. We verifythat the scaling form for A(t) is valid with β = 1

4 , z = 2. For the Kardar-Parisi-Zhang interface we have carriedout numerical simulations and find that the scaling form holds with β = 1

3 , z = 32 . To study the dynamics of the

sliding particles, we have carried out numerical simulations. Our results show that the density-density auto-correlationfunction has the form C(t) = C0(t) + Cs( t

Lz ), with a non-scaling, short-time part C0 and a scaling part Cs. For small

values of the scaling argument t/Lz, we find Cs decays with a cusp, Cs ∼ Cs(0)[1 − b′( t

Lz )β′], showing that the

movement of the particles is strongly governed by the dynamics of the underlying interface. However, the value of thecusp exponent β

′is different from β.

[email protected]@theory.tifr.res.in




Mound formation and coarsening in surface growth

Buddhapriya Chakrabarti1 and Chandan Dasgupta 2

1 Department of Physics, University of Massachusetts, Amherst, MA 01003. USA2 Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012.

INDIA

A conserved growth equation, modeling the nonequilibrium kinetics of MBE thin-film growth, is studied in onedimension using numerical integration. The model exhibits competing linear (Ehrlich-Schwoebel type) and non-linearinstabilities that are controlled by higher order gradient nonlinearities. The steady states of this model are found tobe “mounded” with or without slope selection. In the absence of noise, the nature of the steady state depends onwhich instability is active at early times. When noise is present, the model exhibits a nonequilibrium phase transitionbetween mounded phases with and without slope selection as a function of a control parameter. The coarseningexponent is different in the two phases.


5.4.3

Spatial Patterns Arising from Non-local Competition Interactions

M. A. Fuentes1 and V. M. Kenkre2

1,2 Consortium of Americas for Interdisciplinary Sciences and Department of Physics and Astronomy, University ofNew Mexico, Albuquerque, New Mexico 87131, USA

Analytic considerations are applied to recently discovered patterns (Phys. Rev. Lett. 91, 158104, 2003) arisingfrom a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-localcompetition interactions among individuals. We show how stability arguments yield a condition for pattern formationinvolving the ratio of the pattern wavelength and an effective diffusion length of the individuals.



5.4.4

Multi-point Fluctuations of the 1D Polynuclear Growth Model andRandom Matrix Theory

Tomohiro Sasamoto1 and Takashi Imamura2

1 Department of Physics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan2 Department of Physics, Graduate School of Science,University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033,

Japan

Recently, the understanding of the fluctuation properties of the 1+1 dimensional KPZ universality class have greatlyadvanced. The results obtained so far are mainly for the height fluctuation at one point. In this presentation, we reportseveral results on the multi-point equal time height fluctuations of the one-dimensional polynuclear growth (PNG)model, which belongs to the KPZ universality class. The results are presented for two cases; (i) the model in half-spaceand (ii) the model with external sources. For both cases, the multi-layer version of the model is reduced to a processwith a determinantal weight, for which the asymptotics can be analyzed. For the model in half-space, the fluctuationsnear the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal/symplectic to unitarytransition ensemble at soft edge in random matrix theory. For the model with external sources, the relationshipbetween the fluctuations of the PNG model and those of the random matrices are also clarified.


5.4.5

Phase separation of a binary fluid in the inertia dominated regime.

Anirban Sain1 and Martin Grant2

1 Physics Dept., Indian Institute of Technology Bombay, Powai, Mumbai-400076, India.2 Physics Dept., McGill University, Rutherford Building, 3600 rue University, Montreal, QC, Canada H3A 2T8.

The phase separation kinetics of a binary fluid is studied analytically through an effective one-fluid model with a noisespectrum which is determined self-consistently. We obtain the velocity correlation spectra, and find that scaling isassociated with a velocity length scale Lv ∼ t1/2. Our results can be quantitatively tested by numerical or experimentalstudies.



5.4.6

Contact line dynamics in peeling of an adhesive tape.

Rumi De1 and G. Ananthakrishna2

1 Materials Research Centre, Indian Institute of Science, Bangalore, India.2 Materials Research Centre, Indian Institute of Science, Bangalore, India. Centre for Condensed Matter Theory,

IISc, India

We investigate the spatio-temporal dynamics of peeling of an adhesive tape. Detailed experimental studies haveshown that the peeling of an adhesive tape is jerky within a window of pull velocities and is accompanied by acousticemission (AE). There is no theoretical model that explains the ”contact line” dynamics or the nature of AE duringthe peeling process. Earlier works ignored the width of the tape, and thus deal only with ”contact point” dynamics.Further the derived equations of motion are known to pose numerical difficulties in solving the equations as they fallin the category of differential algebraic equations. To understand the peeling dynamics fully, we have modeled it byconsidering the width of the tape and also by including the kinetic energy arising from stretched part of the adhesivetape. The inclusion of this additional time scale makes the equations of motion to fall into the normal category ofordinary differential equations, thus circumventing the need to use special methods. Further, we include an additionaldissipative energy term that mimics the burst of acoustic signal. Our analysis shows that the contact line profile isrugged for certain values of the parameter space, namely, inertia of the roller, mass and elastic constant of the tape.We also find soliton wave like propagative solutions in other regimes.


5.4.7

Stress distributions in gravity-driven dense granular flows

Shubha Tewari1, Allison Ferguson2 and Bulbul Chakraborty3

1 Department of Physics, Mount Holyoke College, South Hadley, MA 01075, USA2,3 Department of Physics, Brandeis University, Waltham, MA 02454, USA

We study in simulation a dense granular flow under gravity. We have previously reported[1] the presence of clusters offrequently colliding particles that persist for a timescale longer than the typical time between inter-particle collisions.We evaluate here the importance of these transient inhomogeneities to coarse-grained stress propagation in theflow. We calculate the stress distribution as well as spatial and temporal correlations of the stress. We find thatthere is a positive correlation between particles undergoing frequent collisions and those experiencing the largest forces.

References :[1] A. Ferguson, B. Fisher and B. Chakraborty, to appear in Europhysics Letters.



5.4.8

Cluster dynamics and physical properties of magneto rheologicalsuspensions under perturbation

J.L. Carrillo1,E. de la Calleja2,F. Donado3 and M.E. Mendoza4

1,2,4Instituto de Fisica, Universidad Autonoma de Puebla, Puebla, Mexico3Centro de Investigacion Avanzada en Ingenieria, Universidad Autonoma del Estado de Hidalgo, Pachuca, Mexico

Magnetorheological fluids are composed by micrometric soft magnetic particles dispersed in an inert fluid. Underthe application of a static magnetic field, these fluids change drastically their physical properties. This is due to thecomplex structure formed by the particles. It has been shown that this structure has multifractal characteristics whichcan be associated to different stages of aggregation processes [1]. In this work, we report the results of our analysisof the process of reconstruction which occurs when this structure is perturbed by external fields. The rearrangementof the particles can be followed by measuring, at different stages, the mass fractal dimension and the mass radialdistribution. We analyse theoretically the change in the physical properties of the suspension along the reconstructionprocess. [1] J.L. Carrillo, F. Donado and M.E. Mendoza, Phys. Rev. E 68, 061509 (2003).

[email protected]@[email protected]@sirio.ifuap.buap.mx

5.4.9

Patterns of aggregation in the coprecipitation of iron oxalates

M.E. Mendoza1, J.L. Carrillo2, M.A. Perez3 and R. Silva4

1,2,4 Instituto de Fisica, Universidad Autonoma de Puebla, Puebla, Mexico3 Facultad de Quimica, Universidad Autonoma de Puebla, Puebla, Mexico

Prismatic microcrystals of iron oxalates were prepared by coprecipitation of aqueous solutions of iron salts at differentpH and at room temperature. We analyze the effect of the application of a static magnetic field on the coprecipitationprocess. The kinetics of the process was followed by optical microscopy and digitally recorded. We found that thepresence of a magnetic field strongly influence the aggregation of microcrystals, producing prismatic smooth surfacecrystals. In order to characterize these patterns of aggregation, we measure the mass fractal dimension of the aggregatesand found that there appears several stages in the aggregation process, clearly distinguished by their scaling behavior.



5.4.10

Delamination Patterns of Laterally Compressed Elastic Films

Nariya Uchida1

1 Department of Physics, Tohoku University, Sendai 980-8578, JAPAN

Thin solid films deposited on substrates show complex delamination patterns upon cooling. Mismatch between thethermal expansion coefficients of the film and the substrate causes lateral compressive stress in the film, which bucklesand delaminates above a threshold stress. Previous theoretical studies mostly concentrated on undulation and branch-ing of a straight nucleus. Here I numerically study the delamination patterns (”blisters”) using a minimal continuummodel, focusing on a crossover from nucleation growth to spinodal-like instability. The film is modeled as an elasticmembrane bound to the substrate by Hookean springs, which irreversibly break at a critical extension. The delami-nation process following an initial compression is simulated by solving an overdamped dynamic equation. For strongcompression, we found that the bending energy as a function of time behaves as t−0.45 after an initial exponentialgrowth. The power law is consistent with previous results for the forced buckling of a suspended membrane. Forweak compression, the blisters form a network after a long incubation time, in good agreement with experimentalobservation. In the late stage, the bending energy approaches the same power law as above. I will present the patternsand a phase diagram at the conference.

1 [email protected]

5.4.11

Lane Formation in Driven Colloids

Jaydeb Chakrabarti1

1 SNBNCBS, Calcutta, India

Recently it has been shown that a strongly interacting colloidal mixture consisting of oppositely driven particles,undergoes a nonequilibrium transition towards lane formation provided that the driving strength exceeds a thresholdvalue. We show that there is a reentrance effect in lane formation: for fixed high driving force and increasing particlesdensities, there is a transition towards lane formation which is followed by another transition back to a state withno lanes. Our results are obtained by both Brownian dynamics computer simulations and by a phenomenologicalgeneralization of the density functional theory to include the effects of both the strong correlation in the system andthe drive. Our phenomenological theory brings out the following simple intuitive picture of the reentrant behaviour:For very small densities the particles are almost noninteracting, hence the drive will not induce any instability so thatthe system will stay mixed for entropy reasons. For intermediate densities, there is an interaction and the strong drivewill put the particles into lanes. For very high densities, on the other hand, the interaction is very strong exceedingthe external drive so that the latter will not again induce lane formation.

1 [email protected]


5.4.12

Spatiotemporal behaviour of the Gierer- Meinhardt model.

Swati Bhattacharya1 and Jayanta Kumar Bhattacharjee2

1 S.N.Bose National Centre for Basic Sciences, Sector III, JD Block, Salt Lake, Kolkata 700098, India2 Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India

One of the well known models for pattern formation in a reaction diffusion system is the Gierer-Meinhardt model.The model has two species. The slowly diffusing one is autocatalytic, while the fast diffusing one is antagonistic tothe former. The phase boundary of the model is well known. The steady homogeneous phase can make a transitionto a steady patterned phase or an oscillatory homogeneous phase. We have determined the nature of the transitionacross the boundaries by using an amplitude equation as well as by setting up a Galerkin model. The role of thecodimension-2 point and the tricritical point in understanding the spatiotemporal behaviour of the GM model hasbeen studied.


5.4.13

The Creation Process of Faults in Dry Granular Systems

So Kitsunezaki1

1 Department of Physics, Nara Women

We study quasi-static deformation of cohesionless granular systems. In numerical simulations of mono-disperse systemsof particles with regular arrangements, we found that the heterogeneities appear through a fingering-like instabilityand develop into several microscopic shear zones. By limiting our consideration to the infinitesimal deformationprocesses, we regard the arrangement of particles as a lattice and assume that linear elastic forces act on the particles.In our model we introduce new variables indicating the slip distance at each contact to consider the Coulomb friction.The equations of our model can be reduced to simpler equations in the limit of small tangential interactions amongparticles using a perturbative analysis. We qualitatively discuss the instability of critical stress states and the growthof microscopic shear zones based on the long-wave approximation of the reduced equations.

1 [email protected]


5.4.14

A fully consistent diffuse interface approach to brittle fracture

Veronica I. Marconi1 and Eduardo A. Jagla2

1,2 The Abdus Salam International Centre for Theoretical Physics, Condensed Matter Group, Strada Costiera 11,(34014) Trieste, Italy

We present a continuum model for the propagation of cracks and fractures in brittle materials where the full set ofvariables are the components of the strain tensor ε. The evolution equations are based on a free energy that reducesto that of linear elasticity for small ε, and accounts for cracks through energy saturation at large values of ε. Weregularize the model including terms dependent on gradients of ε in the free energy. No additional fields are introduced,and then the whole dynamics is perfectly defined. We show the broad spectrum of possibilities of this new techniquepresenting a couple of non trivial applications for quasistatic crack propagation in 2D. One example is the growingof parallel cracks, which is important for materials scientists, engineers and geoscientists. In addition the model canalso be used to study different problems in dynamic fracture mechanics such as crack instabilities and bifurcation,sound emission, and can also be extended to study 3D problems. Therefore this new approach appears as a properphenomenological way to describe the very important applied problem of predicting crack propagation in both, thequasi-static and dynamic case, which still posses many non elucidated aspects.


5.4.15

Front propagation in the restricted bosonic lattice model

Niraj Kumar1 and Goutam Tripathy2

1,2 Institute of Physics,Sachivalaya Marg,Bhubaneswar -751005,India

We study front propagation in the reaction-diffusion process A+AA on the one dimensional lattice, where maximumof N particles can occupy per lattice site.We observe that velocity and diffusion-coefficient of the front differ drasticallyfrom the mean-field behavior,which is given by Fisher equation.This reflects,how the internal fluctuations play animportant role in the case of lower values of N.We also discuss some exact results as well as the results based on someapproximations for N=2.



5.4.16

Fluctuation of the top position in the dynamics of sandpile

Chiyori Urabe1

1 Graduate School of Human and Environmental Studies ,Kyoto University,Kyoto,606-8501,Japan.

The top position of a sandpile fluctuates rapidly by additions of particles and avalanches on the process of its formation.We investigate the time development of the top position on various conditions by 2-dimensional numerical simulationsin the discrete element method. In order to make a sandpile, we drop particles periodically one by one from a fixedhight to the center of a floor with a finite length. The results of simulations show that the power spectrum of timeseries of the top position is Lorentzian like in the cases that we drop particles from a low height at a long interval.In contrast, the power spectrum indicates a 1/f decay approximately in the opposite cases. Because the exponent ofdecay correlates with the kinetic energy of the system, we conjecture that statistic characters of the time series of thetop position depend significantly on the magnitude of avalanches. We would like to discuss the dynamics of avalanchesand the top position.

1 [email protected]

5.4.17

Pattern Formation in a 2-d Array of Oscillators with Phase-ShiftedCoupling

Pan-Jun Kim1, Tae-Wook Ko2, Hawoong Jeong3 and Hie-Tae Moon4

1,2,3,4 Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, Korea

We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator isallowed to interact with its neighbors within a finite radius. We find various patterns including squarelike pinwheels,(anti)spirals with phase-randomized core, and antiferro pattern embedded in (anti)spirals. We consider symmetryproperties of phase oscillators to explain the observed behavior, and estimate the wave lengths of patterns by linearanalysis. Finally, we point out the implications of our work for the biological neural networks.



5.4.18

Thermal convection in mono-disperse and bi-disperse granular gases: Asimulation study

Daniela Paolotti1, Alain Barrat2, Umberto Marini Bettolo Marconi3 and Andrea Puglisi4

1,3 Dipartimento di Fisica, Universita di Camerino and Istituto Nazionale di Fisica della Materia, via Madonna delleCarceri, 62032 Camerino, Italy

2 Laboratoire de Physique Theorique, Unite Mixte de Recherche UMR 8627, Batiment 210, Universite de Paris-Sud,91405 Orsay Cedex, France

4 Laboratoire de Physique Theorique Batiment 210, Universite de Paris-Sud, 91405 Orsay Cedex, France

We present results of a simulation study of inelastic hard-disks vibrated in a vertical container. An Event-DrivenMolecular Dynamics method is developed for studying the onset of convection. Varying the relevant parameters(inelasticity, number of layers at rest, intensity of the gravity) we are able to obtain a qualitative agreement of ourresults with recent hydrodynamical predictions. Increasing the inelasticity, a first continuous transition from theabsence of convection to one convective roll is observed, followed by a discontinuous transition to two convective rolls,with hysteretic behavior. At fixed inelasticity and increasing gravity, a transition from no convection to one roll can beevidenced. If the gravity is further increased, the roll is eventually suppressed. Increasing the number of monolayersthe system eventually localizes mostly at the bottom of the box: in this case multiple convective rolls as well as surfacewaves appear. We analyze the density and temperature fields and study the existence of symmetry breaking in thesefields in the direction perpendicular to the injection of energy. We also study a binary mixture of grains with differentproperties (inelasticity or diameters). The effect of changing the properties of one of the components is analyzed,together with density, temperature and temperature ratio fields. Finally, the presence of a low-fraction of quasi-elasticimpurities is shown to determine a sharp transition between convective and non-convective steady states.



5.4.19

Instabilities in mixing layers

Maalika Priyadarshini Manoharan1,Rama Govindarajan2, and R Narasimha3

1Mechanical Engineering Department, Indian Institute of Technology, Chennai, India.2,3Engineering Mechanics Unit, Jawaharlal Nehru centre for Advanced Scientific Reasearch ,Jakkur,Bangalore

560064,India

The ultimate aim of this work is to try and understand some aspects of turbulent flow from stability arguments. Forthis purpose, the simplest flow to consider would be one without walls. We study here a two-dimensional mixinglayer, created when two parallel streams of velocity U and λU come onto contact with each other. The mixing layeris spatially developing: it grows in its lateral extent downstream. A similarity solution for the laminar mean flowis obtained. A non-parallel stability equation, containing all effects upto R−1 in the Reynolds number R (based onthe local thickness of the mixing layer) is formulated. This partial differential equation is treated as a parametrico.d.e., describing an “extended” eigenvalue problem, and is solved by spectral collocation. The results we obtainare qualitatively different from earlier work where the flow was assumed to be locally parallel: we show that at aReynolds number R = 0, the flow is stable, contrary to accepted wisdom. The dominant instability modes, and theirresemblance, if any, to the coherent structures seen in turbulent mixing layers, will be discussed at the conference.

1m−[email protected]@[email protected]

5.4.20

Energy Spectrum in Two-Dimensional Granular Turbulence

Masaharu Isobe1

1 Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555, Japan

We have showed the macroscopic statistical properties on the freely evolving quasielastic hard disk (granular) sys-tem by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically andfound it to be remarkably analogous to an enstrophy cascade process in the decaying two-dimensional fluid turbu-lence(PRE,68,040301,(2003)). In this paper, we especially focus on the spatial correlations, such as energy spectrumand energy dissipation scale, in a wide parameter space. The comparison between the expectation of Kraichnan-Batchelor theory in fluid turbulence and our granular model is discussed.

1 [email protected]


5.4.21

Polynuclear growth model and universality in the random matrix with adeterministic source

Takashi Imamura1 and Tomohiro Sasamoto2

1 Department of Phsics, University of Tokyo, Japan2 Department of Physics, Tokyo Institute of Technology, Japan

Recently the deep relation between the random growth process and the random matrix theory has been revealed. Thepolynuclear growth (PNG) model is one of the models which provide us the understanding of this relation. When theappropriate boundary condition is applied in the PNG model, we find that the distributions of the height at somepoint is described by the largest eigenvalue distribution of the two independent GOE random matrix called GOE2. Inthis session we present another interpretation of the distribution as that in the random matrix with a deterministicsource proposed by Brezin-Hikami. We also discuss the relation between the stochastic process which express theheight fluctuations for some region in the above model and the largest eigenvalue process in the multi-matrix modelwith a deterministic source.


5.4.22

Spatio-temporal oscillations and rheochaos in a simple model of shearbanding

Suzanne M Fielding1 and Peter D Olmsted2

1,2 Polymer IRC, School of Physics and Astronomy, University of Leeds, Woodhouse Lane, Leeds. LS2 9JT. UK.

Complex fluids commonly undergo flow instabilities and flow induced phase transitions that result in spatially hetero-geneous shear banded states. In many cases, these banded states show oscillations or erratic fluctuations suggestingrheological chaos. However most existing theories predict only steady, time-independent bands. We therefore introducea simple model of shear banding in which the flow induced phase is rendered unstable by coupling between flow andmicrostructure (eg mean chain length in a wormlike micellar surfactant). By varying the strength of the instabilityand the applied shear rate, we find a rich variety of oscillatory and rheochaotic shear banded flows.



5.4.23

Lateral Instability in Viscous Fingers

Eugenia Corvera Poire1 and Aurora Hernandez-Machado2

1Edif. B. Facultad de Quimica, Ciudad Universitaria. Mexico, D.F. 04510. Mexico2Departament ECM. Facultat de Fisica, Universitat de Barcelona. Diagonal 647, E-08028, Barcelona Spain

We study a lateral instability of the Saffman-Taylor finger by means of a phase field model. We observe such aninstability in three situations in which small perturbations are overimposed to a constant pressure drop. We firststudy the case in which the perturbation consist of a dynamic signal with a single oscillatory mode. Then with adynamic signal consisting of random noise and finally we study the finger evolution under a constant pressure dropin a cell with static disorder. We discuss why this lateral instability has not been observed in most experimentalsituations.

[email protected]@ecm.ub.es

5.4.24

Scaling and Glassy Behavior in Lamellar Ordering

Giuseppe Gonnella1, Antonio Lamura2 and Aiguo Xu3

1,3 Dipartimento di Fisica, University of Bari, Italy2 Institute for Applied Calculus, CNR, Bari, Italy

Kinetics of lamellar ordering is relevant for many systems in condensed matter. Competition between attractive andrepulsive forces often produces lamellar structures. Examples are di-block copolymer solutions, ternary mixtures,supercooled liquids, fluids in Raleigh-Benard experiments above the convective threshold. Growth properties of thesesystems are not always well understood. The purpose of our work was to analyse the effects of hydrodynamics inthis process [1]. Our model, based on Navier-Stokes and convection-diffusion equations, is particularly appropriatefor describing copolymer systems. Lattice Boltzmann Methods coupled with finite difference schemes are used; thesizes of the lattices considered are large enough in order to minimize finite size effects. We show that, while athigh viscosity the system evolves into frozen configurations, at low viscosities order is reached on large scales anddynamical scaling is verified [2]. The structure factor behaves like C(~k, t) ∼ L(t)αf [(k − kM )L(t)] where kM is theequilibrium wave number of lamellae, L(t) is a characteristic length calculated by the structure factor, and α = 1.25.L(t) first grows as a power law with exponent z = 0.3 while, at later times, its behavior changes over to a slowerlogarithmic growth. This scaling, expected for glassy systems, is a new results for systems without quenched disorder[3]. The motion of grain boundary defects between lamellae differently oriented can explain the evolution of L(t).We have also considered the effects of shear flow. Our results show that in this case lamellar ordering occurs withpower-law behavior at all times.

References :[1] G. Gonnella, E. Orlandini, and J.M. Yeomans, Phys. Rev. Lett. v. 78 p. 1695 (1997)[2] Aiguo Xu, G. Gonnella and A. Lamura, preprint in preparation.[3] M. Rao and A. Chakrabarti, Phys. Rev. Lett. v. 71 p. 3501 (1993).



5.4.25

Effect of Stress - Jump Boundary Condition : Viscous Flow Past aSpherical Void in Porous Media

G. P. Raja Sekhar1 and M. K. Partha2

1 Assistant Professor, Department of Mathematics, I I T Kharagpur, Kharagpur 721302.2 Research Scholar, Department of Mathematics, I I T Kharagpur, Kharagpur 721302.

The effect of the spherical void of a characteristic size for different permeabilities in porous media in an un disturbeduniform flow is investigated analytically. The flow inside the void is governed by Stokes equations and the flow in theporous region is governed by Brinkmans equation. The flow field is computed by matching the boundary conditionsat the porous fluid interface. At the porous - liquid interface continuity of velocity components, continuity of normalstress and the stress jump boundary condition for the tangential stresses have been used. Ochao Tapia has proposedthis stress jump boundary condition by statistical averaging technique and it involves a parameter, which is called thestress jump coefficient. Here, we have found that the effect of the void increases with the decrease of permeability andalso the effect of stress jump coefficient is observed very much. Even at high values of permeability there is a changein the flow field, velocity profiles etc. which is not seen if we ignore the stress jump condition. Also the velocity at thecenter of the void is influenced by the parameter.

1 [email protected]

5.4.26

Pattern Selection in a Model of Directional Solidification

R.N. da Costa Filho1, E. Granato2 and J.M. Kosterlitz3

1 Departamento de Fisica, Universidade Federal do Ceara, Caixa Postal 6030, Campus do Pici, 60451-970 Fortaleza,Ceara, Brasil

2 Laboratorio Associado de Sensores e Materiais, INPE, Sao Jose dos Campos, SP Brasil3 Department of Physics, Brown University, Providence RI 02912, USA

A symmetric phase field model is used to study wavelength selection in two dimensions. Simulations show that, abovea velocity threshold and for almost all initial conditions except for periodic states inside the Eckhaus stable band,additive stochastic noise selects a solid/fluid interface with a definite wavelength. This is the most probable state atlate times.



5.4.27

Dynamical obstruction in a constrained system and its realization inlattices of superconducting devices

Pierre Pujol1, Claudio Castelnovo2 and Claudio Chamon3

1 ENS-Lyon, France.2,3 Boston University, USA.

We study a variant of Baxter’s 3-color model in which local interactions and defects are included, and discuss itsconnection to triangular arrays of Josephson junctions of superconductors with broken time-reversal symmetry andkagome networks of superconducting wires. The model is equivalent to an Ising model in a hexagonal lattice with andadditional constraint. Defects in the superconducting models correspond to violations of this constraint. In the absenceof defects, and for ferromagnetic interactions, we find that the system is critical for a range of temperatures (criticalline) that terminates when it undergoes an exotic first order phase transition with a jump from a zero magnetizationstate into the fully magnetized state at finite temperature. Dynamically, however, we find that the system becomesfrozen into domains. Domain growth appears frozen within the time scales studied with Monte Carlo simulations, withthe system trapped into a “polycrystalline” phase. This dynamical obstruction has its origin in the topology of theallowed reconfigurations in phase space. Eventually, only the proliferation of defects may overcome this obstruction,at much longer time scales. Also as a consequence of the dynamical obstruction, there exists an effective temperature,lower than the static critical temperature, at which the system is seen to jump from a “supercooled liquid” to the“polycrystalline” phase within our Monte Carlo time scale. In contrast, for antiferromagnetic interactions, we arguethat the system orders for infinitesimal coupling because of the constraint, and we observe no interesting dynamicaleffects.



5.4.28

A kinetics driven commensurate - incommensurate transition

Abhishek Chaudhuri 1, P. A. Sreeram 2 and Surajit Sengupta3

1,2,3 Satyendra Nath Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake Calcutta - 700098

The steady state structure of an interface in an Ising system on a square lattice placed in a non-uniform external field,shows a commensurate - incommensurate transition driven by the velocity of the interface. The non-uniform field hasa profile with a fixed shape which is designed to stabilize a flat interface, and is translated with velocity ve. For smallvelocities the interface is stuck to the profile and is rippled with a periodicity which may be either commensurate orincommensurate with the lattice parameter of the square lattice. For a general orientations of the profile, the localslope of the interface locks in to one of infinitely many rational directions producing a devil’s staircase structure.These “lock-in” or commensurate structures dissappear as ve increases through a kinetics driven commensurate -incommensurate transition. For large ve the interface becomes detached from the field profile and coarsens withKardar-Parisi-Zang exponents. The complete phase -diagram and the multifractal spectrum corresponding to thesestructures have been obtained numerically together with several analytic results concerning the dynamics of the rippledphases. Our work has technological implications in crystal growth and the production of surfaces with various desiredsurface morphologies. Preliminary results of this work have appeared in, Abhishek Chaudhuri, P. A. Sreeram andSurajit Sengupta, Phys. Rev. Lett. 89, 176101, (2002).


5.4.29

Experimental study of the fractal nature of a diffusion front

Akihiko Okazaki1, Kaneyasu Maruyama2 and Sasuke Miyazima3

1 Dept. of Computer Science, Chubu Univ., Kasugai, Japan2,3Dept of Biological Chemistry, Chubu Univ., Kasugai, Japan

We present an experimental study for the fractal nature of a diffusion front by the use of a great number of smallsteel balls. The experimental apparatus is made up of a diffusion vessel, a personal computer, a stepping motor, anda digital video camera. The diffusion vessel is a shallow rectangular box, and about 40,000 pieces of steel balls whosediameter are 1mm are put into one side of the vessel. Shaking the vessel with the stepping motor under computercontrol, balls diffuse. Motion of steel balls is recorded on a video tape, and hull and external perimeter are extractedwith a image processing program. A diffusion phenomenon of steel balls is confirmed by investigating the relationbetween the average distance of diffusion front and the time. The fractal dimensions of hull and external perimeterare analyzed by means of the box-counting method and the scale-transformation method respectively. We can confirmexperimentally that the diffusion front is the fractal nature, and that the fractal dimensions of hull and externalperimeter are 1.73 - 1.83 and 1.45 - 1.54 respectively.



5.4.30

Pattern formation in presence of external force field

Deb Shankar Ray1

1 Indian Association for the Cultivation of Science, Kolkata, India

Mass transport in an ionic reaction-diffusion system gets affected by the presence of external force field. We show thatsymmetry breaking instability leading to formation of spatial structures may result in when a constant electric fieldcauses a diffusion driven stable state to become unstable. We analyse different situations for experimentally viablemodel chemical systems and different orientations of the field.

1 [email protected]

5.4.31

Stable multi-armed spiral formation driven by defects

Inmaculada Rodriguez-Ponce1 and Franz Schwabl 2

1,2 Physik-Department, Technische Universitaet Muenchen, James-Franck strasse, 85747 Garching bei Muenchen,Germany

We study the dynamic properties and interaction of stable multi-armed spiral structures in excitable media. Themodel is based on the equations that describe the early stage of development in the self-organization of Dictyosteliumdiscoideum cells. We discuss the stability of the different patterns, focusing on the interplay between the maximumnumber of arms in a multiarmed spiral and the presence of local heterogeneities (defects), as well as, between excitabilityproperties. The interaction between structures is analyzed in terms of core drifts and frequency changes.


5.4.32

Long time simulations of granular hydrodynamics

Srikant Marakani1 and Gene F. Mazenko2

1,2 James Franck Institute, 5640, S. Ellis Ave, Chicago, IL 60637, USA

Using a granular hydrodyamic model of granular flows, we present very long time simulations of a granular fluid in twodimensions without gravity and with periodic boundary conditions in a square domain. We performed the simulationsfor several values of the viscosity, dissipation coefficient and thermal conductivity. We briefly present the results foundfrom the simulations. We find that the long time state of the system is either a shear band or a vortex state. Ourresults are in general agreement with molecular dynamics simulations. The clustering state is found to be metastable.



5.4.33

Self-similar solution and fractal structure in one-dimensionalself-gravitating system with power-law expansion

Takayuki Tatekawa1 and Kei-ichi Maeda2

1,2 Dept. of Phys., Waseda Univ., 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, JAPAN

In self-gravitating system, scale-free or fractal structure forms spontaneously during evolution. For example, spatialtwo-point correlation function of galaxy obeys power law of separated distance. For elucidation of the origin of scale-free structure, we analyze one-dimensional sheet model with cosmic expansion. In our previous study, the fractalstructure forms spontaneously and the dimension seems stable. On the other hand, in one-dimensional sheet modelwithout cosmic expansion, scale-free correlation function appears during evolution. Is the cosmic expansion importantfor the formation of scale-free structure? In this study, we analyze one-dimensional sheet model which expansion rateis given by power-law of time. We derived self-similar solution for arbitrary expansion rate, and calculated long-timeevolution. From numerical analysis, we show that the fractal dimension of structure converges and found simplerelation between the dimension and expansion rate.


5.4.34

On the deterministic growth of the dendrites’ side branches

Yves Couder1 and Jean Maurer2

1,2Laboratoire de Phyique Statistique, 24 rue Lhomond 75231 Paris cedex 05, France

The dynamics of growth of the side branches of dendrites from near the tip to very far from it, is investigatedexperimentally during the crystallization of ammonium bromide in a quasi two-dimensional cell. Two regimes areobserved. At small Peclet numbers a self-affine fractal forms. In this regime it is known that the mean lateral frontgrows as t0.5). Here the length of each individual branch is shown to grow (before being screened off) with a power-law behavior ta. The value of the exponent a(0.5 < a < 1) is determined from the origin: the larger the initialdisturbance, the larger the value of a). Coarsening takes place when the branches of small a are screened-off by theirneighbors. The corresponding decay of the growth of a weak branch is exponential and defined by its geometricalposition relative to its dominant neighbors. These results show that the branch structure results from a deterministicgrowth of initially random disturbances. At large values of the Peclet number the faster of the side branches escapeand become independent dendrites. The global structure is then dense in the 2D space. The crossover between thetwo regimes and the spacing of these independent branches is characterized.

[email protected]



5.5.1

Local and Nonlocal Shell-to-Shell Energy Transfers inMagnetohydrodynamic Turbulence

Mahendra K. Verma1

1Dept. of Physics, I. I. T., Kanpur 208016, India

In this paper we present an analytic calculation to compute the shell-to-shell energy transfer in magnetohydrodynamicturbulence. The calculation is based on first-order perturbative field theory. We find that energy transfers fromvelocity-shell to velocity-shell, and magnetic-shell to magnetic-shell is local and forward. The energy transfers fromkinetic to magnetic shells however depends on Alfven ratio (ratio of kinetic to magnetic energy). In magneticallydominated plasma, more energy flows from magnetic to kinetic shells; the flow is reversed in kinetic-energy dominatedplasma. Magnetic helicity induces backward energy transfer.

1 [email protected]

5.5.2

Localized Structure in the Lyapunov Vectors for Many-Particle Systems

Tooru Taniguchi1 and Gary P. Morriss2

1,2 School of Physics, University of New South Wales, UNSW Sydney NSW 2052, Australia

We discuss a localized structure of Lyapunov vectors in quasi-one-dimensional systems consisting of many hard disks.For quantitative discussions we introduce a definition of a ”localization width” whose logarithm is given by the entropyof the distribution of particle component amplitudes in the Lyapunov vector. Using the localization width we show thatthere are two kinds of dependence of the localization width on the Lyapunov exponent index for the larger exponents:one is exponential, and the other is linear. Differences, due to these kinds of localizations also appear in the shapes ofthe localized peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the spatial and momentumparts of the Lyapunov vectors. We show that the Krylov relation predicting a logarithmic dependence of the largestLyapunov exponent with respect to the density is satisfied in the same density region as the linear dependence of thelocalization widths is observed.



5.5.3

Experimental observation of Homoclinic bifurcations in Chua’s Circuit

Syamal Kumar Dana1,Satyabrata Chakraborty2, and Garani Ananthakrishna3

1,2Instrument Division, Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032, India3Material Recearch Centre and Centre for Condensed Matter Phyisics, Indian Institute of Science, Bangalore, India

We report our experimental observations on homoclinic bifurcations in Chua’s circuit, namley, homoclinic chaos nearbifurcation point, and gluing bifurcation in asymmetric system. We observed homoclinicity to a saddle focus in aChua’s oscillator when a second Chua’s oscillator in stable equilibrium is coupled in the weaker limit. Homoclinicchaos may also be observed with lower dimension of the coupled system a stable node. When the first oscillator is nearthe periodic adding regime of alternate period-doubling and saddle node bifurcation with a single parameter variation,the first Chua’s circuit shows homoclinic chaos of Shil’nikov type as induced by the stable node of the second oscillatorfor a selected coupling strength of weaker limit. The coupling strength acts as the bifurcation parameter. A countablyinfinite number of unstable periodic orbits are found near the bifurcation point, which reveals the stretching andfolding of global dynamics near saddle focus. For coupling strength a little away from the homoclinc point, burstingare observed, which has strong relevance to the studies on the mechanism of bursting neurons. Moreover, gluingbifurcation near homoclinicity to a saddle focus of a modified Chua’s oscillator, where some additional asymmetryis introduced in the circuit. Two asymmetric homoclinic orbits glued to a single symmetric orbit for two-parameterbifurcation of codimension two. Several alternate periodic and chaotic states are observed for paramter variation.More complicated situations are also discussed.

[email protected] [email protected]@mrc.iisc.ernet.in


5.5.4

Effect of dichotomous non-stationarity and parametric noise on theproperties of intermittency in dynamical systems

Jan Jacek Zebrowski1 and Rafal Baranowski2

1 Faculty of Physics, Warsaw University of Technology, ul.Koszykowa 75, 00-662 Warszawa, Poland2 National Institute of Cardiology, ul.Alpejska 42, Warszawa-Anin, Poland

Regular intermittencies of the Pomeau and Manneville classification are very common in different physical systems andhave also been found in various bio-medical studies such as on neuron discharge or on the properties of blood vessels.The effect of additive noise on the statistical properties of type I intermittency is well known (Hirsch 1983). However,especially in biomedical applications, parametric noise and non-stationarity of the system parameters should be takeninto account. By means of simple models based on the logistic map we demonstrate that parametric noise actingon type I intermittency results in a modification of the distribution of laminar phase lengths: a long tail extendingtowards large laminar phases with the characteristic U-shaped main part of the distribution remianing intact. Onthe other hand, dichotomous changes of the control parameter of the logistic map within the intermittency range -for some combinations of the parameters of such a change - may result in the appearance of additional peaks in thelaminar phase distribution. This research is motivated by observations of human heart rate variability in which - forcertain types of pathology - type I intermittency may be obtained. We show that the simple models described aboveexplain the distinct shapes of the laminar phase distribution measured in human heart rate variability. The possibilityof the occurrence of other kinds of intermittency in heart rate variability will also be discussed.


5.5.5

Decay of Magnetohydrodynamic Turbulence from Power-Law InitialConditions

Chirag Kalelkar1 and Rahul Pandit2

1,2 Department of Physics, Indian Institute of Science, Bangalore - 560 012, India.

We derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales inunforced, incompressible, homogeneous and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulencewith power-law initial energy spectra. We also derive bounds for the decay of the cross- and magnetic helicities. Wethen present results from systematic numerical studies of such decay both within the context of an MHD shell modeland direct numerical simulations (DNS) of 3DMHD. We show explicitly that our results about the power-law decay ofthe energies hold for times t < t∗, where t∗ is the time at which the integral scales become comparable to the systemsize. For t < t∗, our numerical results are consistent with those predicted by the principle of ‘permanence of largeeddies’.



5.5.6

Relative entropy of chaotic dynamical systems

Balamurali Krishna Mayya K. 1 and Ravindra E. Amritkar2

1,2 SRF, Theoretical Physics and Complex Systems Division, Physical Research Laboratory, Navarangpura,AHMEDABAD-380009, India.

We apply an algorithm, based on Lempel- Ziv compression technique to calculate relative entropy, to try and distinguishdata generated by chaotic dynamical systems. The chaotic data is generated for different well known chaotic dynamicalsystems (both discrete and continuous) and each data set is suitably discretized. The algorithm to calculate relativeentropy successfully picks out the dynamics of the given unknown data from those of the known ones in most cases.The algorithm fails for data generated with parameter values lying in the intermittency regions close to the criticalparameter value. A symbolic dynamics representation is a good characterization of chaotic dynamical systems andcan be used for the above algorithm. However, for a given time series it is not easy to construct such a symbolicdynamics. In the work described above the algorithm to calculate relative entropy, when applied to the suitablydiscretized data sets, successfully picks out the dynamics of the unknown data. Therefore the results indicate that asuitable discretization is representative of the dynamics inherent in the chaotic time series.


5.5.7

Bifurcations in a non-abelian logistic equation

Debabrata Dutta1, J. K. Bhattacharjee2, Amitabha Nandi3 and R Ramaswamy 4

1 S N Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 7000982 Theoretical Physics Department,Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032

3,4 School of Physical Sciences,Jawaharlal Nehru University, New Delhi 110 067

We consider a variant on the usual logistic map. This variation modifies the value of the control parameter r in amemory dependent manner. The new map is xn+1 = [r0 + α sgn(xn−1 − xn)]xn(1 − xn). We consider r0 + α ≤ 4and for a given r0 explore the bifurcation structure by varying α. In this paper, we focus on the usual intermittencyestablished by this map. Intermittent dynamics is observed with new (nonstandard) exponents.



5.5.8

Stochastically forced nonlinear oscillators: bifurcation and transition tochaos

Irina Bashkirtseva1 and Lev Ryashko2

1,2 Dept. of Math., Ural State University, Lenina 51, 620083, Ekaterinburg, Russia

Stochastic fluctuations of periodic processes play an important role for understanding of the corresponding phenomenafor lasers, celestial mechanics, chemical and biological systems. The various transitions (”bifurcations”) throughperiodic to more complicated regimes are a central problem in modern nonlinear dynamic theory. We suggest anew techniques [1] for investigation of the local stochastic dynamics near limit cycles. This techniques is based onnonequilibrium quasipotential. An approximation of quasipotential is expressed by some function. This function(sensitivity function) is introduced as a base tool of a quantitative description for a system response on the externaldisturbances. An effective numerical technique of sensitivity function construction for 2D and 3D-cycles is presented.The new cycle numerical characteristics (sensitivity factor, parameter of stiffness) are suggested. The possibilities ofsensitivity function to predict some peculiarities of dynamics for stochastically and periodically forced oscillators areshown. From sensitivity analysis, the critical (chaotic) values of Brusselator parameter are found [2]. The detailedinvestigation of multiscroll cycles of the Lorenz model is given. The thin effects observed in stochastic Lorenz modelnear chaos in a period-doubling bifurcations zone is presented. Application of sensitivity analysis technique forlaminar-to-turbulent subcritical transition is demonstrated [3].

References :[1] Bashkirtseva I.A., Isakova M.G., Ryashko L.B. Quasipotential in stochastic stability analysis of the nonlinearoscillator orbits. J. Neural, Parallel & Scientific Computations, V.7, N3, pp.299-310, 1999.[2] Bashkirtseva I.A., Ryashko L.B. Sensitivity analysis of the stochastically and periodically forced Brusselator.Physica A, 2000, V.278, pp.126-239.[3] Fedotov S., Bashkirtseva I., Ryashko L. Stochastic analysis of a non-normal dynamical system mimicking alaminar-to-turbulent subcritical transition. Phys. Rev. E, V.66, 2002.


5.5.9

Synchronization of Coupled Dynamical Elements on Networks

Sarika Jalan1 and R. E. Amritkar2

1,2 Physical Research Laboratory, Ahmedabad - 380 009, India

Coupled dynamical elements on complex networks from beautiful synchronized clusters. We identify two differentways of cluster formation in these coupled networks, (i) self-organized synchronization and (ii) driven synchronization.We study the synchronized dynamics on some simple networks using linear stability analysis and Lyapunov functionanalysis. Lyapunov function analysis gives a hint for origin of the two different ways of cluster formation.



5.5.10

Stochastic stability of the forced invariant manifolds

Lev Ryashko1

1 Dept. of Math., Ural State University, Lenina 51, 620083, Ekaterinburg, Russia

Many phenomena of statistical physics, mechanics and biological systems are due to the interaction of coupled oscilla-tors. The invariant manifolds (cycles, tori) are an essence of this interaction. The stability analysis of th ese manifoldsis important link of an investigation of the bifurcation chain from order to chaos. The problem of an invariant man-ifold stability of nonlinear system with respect to stochastic disturbances is considered [1,2]. The stability analysison the basis of Lyapunov function is used [3]. The local approximation (near stable deterministic manifold) of thequadratic toroidal Lyapunov function is investigated. The stochastically forced toroidal manifolds are considered indetail. For the 2-torus case, the simple approximation is constructed. A parametric stochastic stability criterion isgiven. Application of this approach to control of probabilistic properties for manifolds is discussed. 1. BashkirtsevaI.A., Ryashko L.B. Sensitivity analysis of the stochastically and periodically forced Brusselator. Physica A, 2000, 278,pp.126-239. 2. Ryashko L.B. Lyapunov functions in stability analysis and stabilization of 2-torus. J Appl. NonlinearDynamics, 2001, 4,5, pp.140-153. 3. Ryashko L.B., Schnol E.E. On exponential attracting invariant manifolds ofODEs. Nonlinearity, 2003, v.16, pp.147-160.

1 [email protected]

5.5.11

Universality in Transition to Synchronization in Coupled Circle Maps

Prashant M. Gade1,D. V. Senthilkumar2 and Sudeshna Sinha3

1Center for Modelling and Simulation, Dept. of Physics, Univ. of Pune, Pune, 4110072Centre for Nonlinear Dynamics, Dept. of Physics, Bharatidasan University, Tiruchirapalli.

3Institute of Mathematical Sciences, Taramani, Chennai, 600113.

We study persistance property in the transition to synchronous fixed point in coupled circle maps. This problem hasbeen previously investigated by Menon, Sinha and Ray. We have tried to analyze effects of sign of coupling (negativeor positive) and nature of coupling (linear or nonlinear) in these systems. We observe that the universality class isaffected by these changes and transition is not necessarily in the universality class of directed percolation.



5.5.12

Controlling the Ultimate State of Projective Synchronization in Chaos:Application to Chaotic Encryption

Bing-Hong Wang1 and Shouliang Bu2

1,2 Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China

The ultimate state of projective synchronization is usually considered to be hardly controllable due to its close de-pendence on the initial conditions of both drive and response systems. In this report, we show that the scaling factorof projective synchronization can be controlled to be proportional to a given scalar function with respect to timeeven without the knowledge of the initial conditions of response system. Further, we apply it to the chaotic encryp-tion. Comparing with some existing implementations, it is found that the present scheme owns several remarkableadvantages. To our knowledge, it is for the first time that the projective synchronization is applied to chaos-basedencryption.

1 [email protected]

5.5.13

Chaotic Synchronization of Symbolic Information in Arrays ofBose-Einstein Condensates.

Carlos1, Leopoldo2 and Pando3

1 Instituto de Fisica2 Universidad Autonoma de Puebla

3 Puebla

We have studied a ring of weakly coupled Bose-Einstein condensates with on-site defects. This system is modelled withthe discrete nonlinear Schrodinger equation (DNLSE). There is a range of parameters, which model the defect, wheresuitable chaotic signals extracted from the system show evidence of symbolic synchronization. We explain the originof this behaviour. As is well known, all kinds of chaotic synchronization are characteristic of dissipative systems. TheHamiltonian nature of our model , however, does not inhibits our system from showing synchronization of symbolicinformation. We also consider the statistical properties of a time series determined by the Poincare section of thismultidimensional Hamiltonian system. For a reference see C.L. Pando L., PHYS LETT A 309 (1-2): 68-74 MAR 172003, C.L. Pando L and E. Doedel, Phys. Rev E (to appear MAR 2004) and C.L. Pando L., oai:arXiv.org:nlin/0305011, (2003).

1 [email protected]



5.5.15

Effect of dichotomous non-stationarity and parametric noise on theproperties of intermittency in dynamical systems

Jan Jacek Zebrowski1 and Rafal Baranowski2

1 Faculty of Physics, Warsaw University of Technology, ul.Koszykowa 75, 00-662 Warszawa, Poland2 National Institute of Cardiology, ul.Alpejska 42, Warszawa-Anin, Poland

Regular intermittencies of the Pomeau and Manneville classification are very common in different physical systems andhave also been found in various bio-medical studies such as on neuron discharge or on the properties of blood vessels.The effect of additive noise on the statistical properties of type I intermittency is well known (Hirsch 1983). However,especially in biomedical applications, parametric noise and non-stationarity of the system parameters should be takeninto account. By means of simple models based on the logistic map we demonstrate that parametric noise actingon type I intermittency results in a modification of the distribution of laminar phase lengths: a long tail extendingtowards large laminar phases with the characteristic U-shaped main part of the distribution remianing intact. Onthe other hand, dichotomous changes of the control parameter of the logistic map within the intermittency range -for some combinations of the parameters of such a change - may result in the appearance of additional peaks in thelaminar phase distribution. This research is motivated by observations of human heart rate variability in which - forcertain types of pathology - type I intermittency may be obtained. We show that the simple models described aboveexplain the distinct shapes of the laminar phase distribution measured in human heart rate variability. The possibilityof the occurrence of other kinds of intermittency in heart rate variability will also be discussed.


5.5.16

Log-Poisson Statistics and Extended Self-Similarity in DrivenDissipative Systems

Kan Chen1 and Ciriyam Jayaprakash2

1Department of Computational Science, Faculty of Science, National University of Singapore, Singapore 1175432Department of Physics, Ohio State University, 174 W 18th Avenue, Columbus, OH 43210, USA

The Bak-Chen-Tang forest fire model was proposed as a toy model of turbulent systems, where energy (in the form oftrees) is injected uniformly and globally, but is dissipated (burns) locally. We present our new results on the statisticsof the higher-order moments for the spatial distribution of fires. We show numerically that the spatial distribution ofdissipation can be described by Log-Poisson statistics which leads to extended self-similarity (ESS). Similar behavioris also found in models based on directed percolation; this suggests that the concept of Log-Poisson statistics of(appropriately normalized) variables can be used to describe scaling not only in turbulence but also in a wide rangeof driven dissipative systems.

[email protected]@mps.ohio-state.edu


5.5.17

Classical Stochasticity and Quantum Decoherence from Discretizationof Time

M. C. Valsakumar1 and P. Rameshan2

1 Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India2 Department of Physics, University of Calicut, Tenhipalam 673 635, India

A formulation of classical and quantum mechanics with time as a discrete parameter is discussed. The aim is toexplore the genuine consequences of discrete time evolution rather than to develop numerical methods that accuratelyapproximate continuous time evolution. Derivation of a discrete time Liouville equation that preserves the nonnegativecharacter of the phase space density of a classical Hamiltonian system is discussed first. It is shown that irrespectiveof the number of degrees of freedom, one function of the phase space variables becomes stochastic. This variablehas a unique probability density, viz., the Γ-density. The motion of even free particles become correlated. The sameformalism enables quantum mechanical treatment through density matrices (equivalently via the Wigner distributionfunctions). The diagonal terms of the density matrix are time invariant, whereas the off-diagonal terms connectingnondegenerate states decay exponentially. Thus discretization of time leads to stochasticity at the classical level anddecoherence in quantum mechanics.


5.5.18

Multifractal Analysis of PDF’s with Fat Tail — Application toTurbulence

Toshihico Arimitsu1 and Naoko Arimitsu2

1 Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan2 Faculty of EIS, Yokohama National University, Hodogaya-ku, Yokohama 240-8501, Japan

It is shown that a harmonious representation of the probability density functions (PDF’s) by means of two distinctTsallis-type distribution functions provides us with a unified description for experimentally or simulationally observedPDF’s in the highest accuracy compared with other multifractal models such as the log-normal model and the pmodel. In order to perform a transparent comparison, the framework of the multifractal analysis is rephrased in itsmost sophisticated fashion in which the tail part (the fat tail part) of PDF, giving the probabilities of events largerthan its standard deviation, is written down once the multifractal spectrum for the spatial distribution of singularitiesis specified, whereas the center part, giving the probabilities of events smaller than its standard deviation, is assumedto be analyzed by the Tsallis-type PDF for the variable itself. The various PDF’s (of velocity fluctuations, of velocityderivatives and of fluid particle accelerations) extracted out from the direct numerical simulation conducted by Gotohet al. and the PDF of fluid particle accelerations observed by Bodenschatz et al. in their Lagrangian measurement ofparticle accelerations are analyzed with the help of the multifractal spectrums for the log-normal, the p model andthe harmonious representation.



5.5.19

Renormalization Group Analysis of the Velocity-Dependent RandomForce Model

Jeong-Man Park1

1 Dept. of Physics, The Catholic University of Korea, Puchon, Korea

Statistical mechanics models of isotropic turbulence and fluid flow through random media are introduced. The effectsof turbulent stresses and the effects of randomness in the media are renormalized into a velocity-gradient-depedentrandom force and a velocity-dependent random force, respectively, in the Navier-Stokes equations. The asymptoticproperties of the long-wavelength fluctuations are deduced by using the dynamic renormalization group method. Unlikethe Foster, Nelson, and Stephen’s random force model where the convection term is marginal, the convection term inour models is renormalized to vanish so that the model is well-defined within the context of the epsilon expansion. AKolmogorov 5/3-energy spectrum is obtained when the force correlation is tuned for the Richardson separation law.Also nontrivial intermittency correction to the single-time structure functions are calculated.

1 [email protected]

5.5.20

Coexistence of chaotic and non-chaotic states in the 2DGauss-Navier-Stokes dynamics

Lamberto Rondoni1, Claudio Giberti2 and Cecilia Vernia3

1 Politecnico di Torino - Italy2 Univ. della Insubria - Italy

3 Universita‘ di Modena - Italy

Recently, Gallavotti proposed an equivalence conjecture in hydrodynamics, which states that forced-damped fluids canbe equally well represented by means of the Navier-Stokes equations (NS) and by means of time reversible modificationsof NS called Gauss-Navier-Stokes equations (GNS). This Equivalence Conjecture received numerical support in severalrecent papers concerning two-dimensional fluid mechanics. The corresponding results rely on the fact that the NSand GNS systems only have one attracting set. Performing similar two dimensional simulations, we find that thereare conditions to be met by the GNS system for this to be the case. In particular, increasing the Reynolds number,while keeping fixed the number of Fourier modes, leads to the coexistence of different attractors. This makes difficulta test of the Equivalence Conjecture, but constitutes a spurious effect due to the insufficient spectral resolution. Withsufficiently fine spectral resolution, the steady states are unique and the Equivalence Conjecture can be convenientlyestabilished.

1 [email protected]


5.5.21

Homology structure of ergodic measures related with nonautonomousHamiltonian flows

Anatoliy Prykarpatsky1

1 Department of Applied Mathematics at AMM University of Sciences and Technology, Krakow 30059 Poland

Abstract. There is developed an approach to studying ergodic properties of time-dependent periodic Hamiltonianflows on symplectic metric manifolds having applications in mechanics and mathematical physics. Based both onJ. Mather’s results about homology of probability invariant measures minimizing some Lagrangian functionals andon the symplectic field theory devised by A. Floer and other for investigating symplectic actions and Lagrangiansubmanifold intersections, an analog of Mather’s -function is constructed subject to a Hamiltonian flow reducedinvariantly upon some compact neighborhood of a Lagrangian submanifold. Some results on stable and unstablemanifolds to hyperbolic periodic orbits having applications in the theory of adiabatic invariants of slowly perturbedintegrable Hamiltonian systems are stated within the Gromov-Salamon-Zehnder elliptic techniques in symplecticgeometry.Key words: Ergodic measures, Holonomy groups, Dynamical systems, Quasi-complex structures, Symplectic fieldtheoryAMS Subject Classification: 37A05, 37B35, 37C40, 37C60, 37J10, 37J40, 37J45

References :[1] Abraham R., Marsden J. Foundations of Mechanics. Cummings, NY, 1978.[2] Arnold V.I. Mathematical methods of classical mechanics. Springer, 1978.[3] Salamon D., Zehnder E. Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm.Pure Appl. Math. 1992,45, 1303-1360[4] Floer A. A relative Morse index for the symplectic action. Comm. Pure Appl. Math. 1988, 41, 393-407[5] Aebischer B., Borer M. and other. Symplectic geometry: Introductory course. Birkhause Verlag, Basel, 1992,79-165[6] Floer A. Morse theory for Lagrangian intersections. J. Diff. Geom. 1988, 28, 513-547[7] Hofer H. Lusternik-Schnirelman-theory for Lagrangian intersections. Ann. Ins. H. Poincare. 1988, 5,N5, 465-499[8] Eliashberg Y., Givental A., Hofer H. Introduction to symplectic field theory. //arXive: math.SG/0010059 6 Oct2000, 1-102[9] Mather J. N. Action minimizing invariant measures for positive definite Lagrangian systems. Math. Zeitschr.1991, 2017, 169-207[10] Mane R. On the minimizing measures of Lagrangian dynamical systems. Nonlinearity. 1992, 5, 623-638[11] Prykarpatsky A.K. On invariant measure structure of a class of ergodic discrete dynamical systems. Nonlin.Oscillations, 2000, 3, N1, 78-83[12] McDuff D. Elliptic methods in symplectic geometry. Bull. AMS, 1990, 23, 311-358[13] Edwards R.E. Functional analysis. Holt, Rinehart and Winston Publ., New York, 1965[14] Kryloff N.M., Bogoliubov N.N. La theorie generale de la mesure et son application a l’etude des systemesdynamiques de la mechanique nonlineaire. Ann. Math. II, 1937, 38, 65-113[15] Niemycki V.V., Stepanov V.V. Qualitive theory of differential equations. Princeton, Univ. Press, 1960

[email protected]



5.6.1

Dynamical Correlations in Water

Anirban Mudi1 and Charusita Chakravarty2

1,2 Department of Chemistry, IIT Delhi, Hauzkhas, New Delhi, India

Water displays several anomalous thermodynamic and kinetic features that are connected with the presence of a three-dimensional network of hydrogen bonds. In this work, we probe the dynamics of the hydrogen-bonded network usingpower spectral analysis of tagged particle quantities that are sensitive to the local molecular environment. In particular,we focus on the behaviour of 1/fα or flicker noise which is a generic feature of systems with multiple time scales and, inthe case of water, originates from hydrogen bond network relaxations. Using molecular dynamics simulations of bulkSPC/E water, we show that power spectral analysis provides a simple and direct way of summarising information onhydrogen bond network dynamics. For example, the variations in mobility associated with the diffusional anomaly aremirrored in the exponent of the 1/fα region of the spectrum and the frequency of crossover from 1/fα to white noisebehaviour is shown to provide a good index of the time and length scales over which correlations in the network vanish.

References :[1] M. Sasai , I. Ohmine, and R. Ramaswamy , J. Chem. Phys. 96, 3045 (1992).[2] A. Mudi, R. Ramaswamy, and C. Chakravarty , Chem. Phys. Lett. 376, 683 (2003).[3] A. Mudi and C. Chakravarty, Mol. Phys. (to be published).[4] A. Mudi , R. Ramaswamy, and C. Chakravarty (submitted).

1 anir [email protected] [email protected]

5.6.2

Density functional theory of fluids in the isothermal-isobaric ensemble

A. Gonzalez1, J.A. White2, F.L. Roman3 and S. Velasco4

1,2,3,4 Dept. Fisica Aplicada, Univ. Salamanca, E-37008 Salamanca, Spain

We present a density functional theory for inhomogeneous fluids at constant external pressure. The theory is formulatedfor a volume-dependent density, n(r, V ), defined as the conjugate variable of a generalized external potential, ν(r, V ),that conveys the information on the pressure. An exact expression for the isothermal-isobaric free-energy densityfunctional is obtained in terms of the corresponding canonical ensemble functional. As an application we considera hard-sphere system in a spherical pore with fluctuating radius. In general we obtain very good agreement withsimulation. However, in some situations a peak develops in the center of the cavity and the agreement between theoryand simulation becomes worse. This happens for systems where the number of particles is close to the magic numbersN = 13, 55, and 147.



5.6.3

Anisotropic interactions and infrared spectral profiles in liquids

A. Medina1, J.M.M. Roco2, A. Calvo Hernndez3 and S. Velasco4

1,2,3,4 Departamento de Fsica Aplicada, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain

Molecular dynamics (MD) simulations are capable to reproduce the prototypical lineshapes of the infrared spectraof diatoms in non-polar liquid solvents. At these densities, the spectral profiles lack of isolated absorption lines andsemiclassical simulation of the rotational and vibrational contributions satisfactorily reproduce experiments. Line-shapes present three different structures: [a] two well isolated branches (P and R) with a deep valley between them,[b] a unique branch resulting from the collapse of P and R branches and the most interesting case, [c] two separatedbranches and a third peak centered approximately at the vibration frequency of the isolated diatomic . This peak,so-called Q-branch, has been matter of several studies from its discovery, around 1960. Its physical origin was farto be well understood for a long time. In our study MD simulations allow a direct translation of the peculiarities ofspectral lineshapes in terms of the rotation of the diatomic. We proof that quasifree rotation and rotational diffusionare directly related to [a] and [b] spectral profiles and a peculiar hindered rotation due to the existence of solute-solventrotational pseudocomplexes explains three maxima lineshapes.


5.6.4

Structural, thermodynamic and dynamical properties of a forced solid -liquid interface in the hard disk system.

Abhishek Chaudhuri1 and Surajit Sengupta2

1,2 Satyendra Nath Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake Calcutta - 700098

A solid- liquid interface can be forced by using a non- uniform external chemical potential (µ) field with a hyperbolictangent profile, µ = µ0 tanh(z− z0− vet), where z is the direction perpendicular to the interface and z0 is the positionof the interface at time, t = 0. The resultant densities are thereby arranged to have values slightly higher and slightlylower than the equilibrium bulk freezing density on either side of the step. We implement this idea in the hard disksystem which is simulated using a dynamic Metropolis Monte Carlo algorithm in the constant NVT ensemble. Westudy thermodynamic properties of the system eg. the density, the solid order parameter (density profile) and thestress tensor as a function of z for ve = 0 and for small non-zero values of ve. At zero and small ve the interfaceis in local equilibrium and variation of all thermodynamic properties are as expected. As ve increases we observedeviations. We connect our work to experiments on crystal growth from the melt and the dynamics of the freezingtransition.



5.6.5

Melting and Potential Energy Landscapes of Atomic Liquids

Somendra Nath Cahkraborty1 and Charusita Chakravarty2

1,2Department of Chemistry,IIT Delhi,Hauz Khas,New Delhi,India

The melting transition in atomic solids is known to become stronger as the range and softness of the interparticle inter-actions decreases. For example, the volume change on melting varies from 2-3% for alkali metals to approximately 16%for the rare gases near the triple point. These changes in melting behaviour are associated with changes in the rangeof liquid phase stability and the behaviour on supercooling. In this work, we use isothermal-isobaric ensemble MonteCarlo simulations of Morse liquids to establish that the variable range Morse systems are convenient for modelling themelting behaviour of a range of atomic solids, including metals and van der Waals solids. We then study the potentialenergy landscapes of the liquids in the neighbourhood of the melting transition as a function of the range param-eter of the Morse potentials, focusing in particular on the statistical properties of inherent structures and quasi-saddles.

References :[1] L.Angelani,R.DiLeonardo,G.Ruocco,A.Scala and F.Sciortino,Phys.Rev.Lett.85,5356(2000).[2] K.Broderix,K.K.Bhattacharya,A.Cavagna,A.Zippelius and I.Giardina,Phys.Rev.Lett.85,5360(2000).[3] P.Shah and C.Chakravarty, J. Chem. Phys., 115, 8784(2001).[4] P.Shah and C.Chakravarty, J. Chem. Phys., 116, 10825(2002).[5] P.Shah and C.Chakravarty, Phys. Rev. Lett., 88, 255501-1(2002).[6] P.Shah and C.Chakravarty, J. Chem. Phys., 118, 2342(2003).[7] P.Shah, S.Roy and C.Chakravarty, J. Chem. Phys., 118, 10671(2003).[8] S.N.Chakraborty, N.Ghosh, P.Shah and C.Chakravarty, Mol. Phys. (submitted).

[email protected]@chemistry.iitd.ernet.in

5.6.6

Measuring motion regimes in weakly excited granular matter

Jorge Fiscina1, Manuel Caceres2 and Frank Muecklich3

1,3 Saarland University. Department of Materials Science. Geb. 22 , 7. Etage. 66123 Saarbruecken, Germany2 Instituto Balseiro, 8400 S.C. de Bariloche, Argrentina

A laser facility based on a coupled charge device permits us the to investigate the dissipation dynamics of a vibratedgranular matter bed under gravity. A spot of 70 microns reveals the vertical movement of individual particles at thesurface of a weakly excited granular matter bed. The realisations z(t) are measured from the top of the container,and the kinetic energy is estimated from their corresponding velocity registers. In addition, we observed the differentcooperative motion behaviour through the FFT power spectra. After Hayawaka and Hong, we discuss our results inthe picture of the volune exclusion principle that such realisations corresponds to Fermi particles from the near theFermi level. We analyse the power spectra measurements by asociation to the motion of a non-Markovian particle,we fit the measured motion regimes with the SDE solutions for a generalized Langevin particle.



5.6.7

The molecular dynamics simulation of thermodynamic fluctuations insmall liquid systems

George Vladimirovich Kharlamov1

1 Department of Theoretical Mechanics, Novosibirsk State University of Architecture and Civil Engineering, 630008,Novosibirsk, Leningradskaya, 113, Russia

In the submitted work the equilibrium distribution functions of fluctuations of momentum, energy, number of particles,temperatures and pressure in gases and liquids are simulated by molecular dynamic method. The theory of thesefluctuations is constructed by methods of statistical mechanics and statistical thermodynamics. Good agreement ofthe analytical formulas and the results of numerical experiment is revealed. At increase in volume (an average numberof particles in the system) the received expressions transform into distribution functions of small fluctuations in thecomplete agreement with A.Einstein’s small fluctuation theory. For small subsystems of gases and liquids placed in abig thermodynamic system (thermostat), essential correlations of fluctuations of momentum and number of particles,of momentum and energy, of number of particles and temperatures, etc. are observed. The relaxation of fluctuationsof number of particles, momentum and energy in gases and liquids has been investigated by the molecular dynamicsmethod. Two regions of dependence of fluctuations autocorrelation function on time have been established. The firstregion is characterized by fast initial decay on times about two-three times of free pass of molecules of a liquid or gas.The second region has the character of ”a long-time tail . For autocorrelation function of momentum fluctuations thetime dependence of the second region is exponential both for gases, and for liquids.

1 [email protected]

5.6.8

Analytic solutions for Baxter’s model of sticky hard sphere fluids withinclosures different from the Percus-Yevick approximation

Domenico Gazzillo1 and Achille Giacometti 2

1,2 Dipartimento di Chimica Fisica, Universita

We discuss structural and thermodynamical properties of Baxter’s adhesive hard sphere model within a class of closureswhich includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlationfunction vanishing beyond a certain range, each closure being identified by a different approximation within theoriginal square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, withthe cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported.Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures,which may yield less accurate predictions but are easily extensible to multi-component fluids, and more sophisticateclosures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidaland protein solutions, however, it is found that the perturbative closures, even when limited to first-order, producesatisfactory results.



5.6.9

Interaction of proteins in solutions: a numerical study of differentscreening regimes

Achille Giacometti1, Domenico Gazzillo2, Giorgio Pastore3 and Tushar Kanti Das4

1,2 Dipartimento di Chimica Fisica, Universita3 Dipartimento di Fisica Teorica, Strada Costiera 11, Miramare I-34100 Trieste, Italy

4 Dept. of Physics, Shahjalal University of Science and Technology, Sylhet-3100 Bangladesh

We assess the limit of validity of a simple approximation for the radial distribution functions, recently proposed toinvestigate interaction of proteins in solution, by using Monte Carlo and Integral Equation techniques. This approxi-mation was recently proposed to account for the protein-protein interaction in the experimental Small-Angle-Scatteringstudy, in the limit of small concentration and strong coupling. Within this framework, protein macroparticles interactvia a screened Yukawa potential, in the form of a binary system (monomers and dimers). An Ewald construction iscarried out to account for possible drawbacks in the calculation of the weakly screened case. Our results indicate thatthe perturbative approximation is valid in this system even at strong coupling provided that the screening is not toosmall. A comparison with integral equation calculations, shows that only the hypernetted-chain (HNC) closure has asatisfactory behavior under these conditions, whereas other classical closures fail to describe the MC results even inthose cases where the first-order approximation provides a satisfactory description.


5.6.10

Testing replica theories for equal-time correlations in liquids withquenched disorder

Ankush Sengupta1, Surajit Sengupta2 and Gautam I Menon3

1,2 S. N. Bose National Centre for Basic Sciences, Kolkata, India3 Institute for Mathematical Sciences, Chennai, India

We test approximate replica-based theories (Phys. Rev. Lett. 73, 1023, (1994)) of equilibrium liquid state structurein the presence of random quenched disorder against detailed Monte Carlo simulations of the inverse twelfth powersoft-disk system in two dimensions. The disorder is modelled by a Gaussian distributed quenched random potentialwith short ranged spatial correlations. A variety of liquid state approximate closure schemes, the mean-spherical(MSA), Percus-Yevick (PY) and hypernetted chain (HNC) approximations, are used to obtain both diagonal andoff-diagonal replicated correlations which are compared with the simulation results. We find that within the replicasymmetric phase, the contribution of the disorder potential to the diagonal correlations is relatively weak and theoverall magnitude of the off-diagonal component small. Both MSA and PY approximations represent the replicatedcorrelation functions with reasonable accuracy, though the HNC approximation underestimates the structure at highdensities. Our results are potentially applicable to a wide range of two-dimensional problems involving disorder, suchas rare gases adsorbed on disordered substrates at sub-mono-layer coverage, colloidal particles on a rough surface,magnetic bubble domains, flux lattices in dirty superconductors etc.



5.6.11

Statistical mechanics of segregation in a model for granular binarymixtures

Marco Tarzia1, Annalisa Fierro2, Mario Nicoldemi3 and Antonio Coniglio4

1,2,3,4 Universita di Napoli and INFM, Naples, Italy

In the framework of a statistical mechanics approach a la Edwards to granular materials [1], we discuss the sizesegregation phenomena observed in a simple lattice model for hard sphere binary mixtures under gravity [2].The system phase diagram is calculated in the Bethe-Peierls approximation both for the 2d and the 3d case. In2d where gravity plays no role, we find fluid and crystal phases, and when crystallization is avoided, a secondorder critical point and a fluid-fluid (rich respectively in small and large grains) coexistence curve. These resultsare in agreement with those previously obtained in binary mixtures without gravity [3], and with experimentalfindings in bidimensional granular mixtures under shaking, where the formation of stripes rich respectively insmall and large grains are observed [4]. A similar phase diagram is also found in 3d in the case where smalland large grains have densities almost equal. Different densities in presence of gravity instead induce verticalsegregation phenomena (Brazil nut effect and reverse Brazil nut effect), and no coexistence curve between differentphases are observed. Finally, we compare these results with ones obtained in Ref. [5] for a “fluidized” granular system.

References :[1] A. Coniglio and M. Nicodemi, Physica A 296, 451 (2001); A. Fierro, M. Nicodemi and A. Coniglio, Europhys.Lett. 59, 642 (2002); Phys. Rev. E 66, 061301 (2002).[2] A. Fierro, M. Nicodemi, and A. Coniglio, Jour. Phys.: Cond. Matt. 15, S1095 (2003); M. Nicodemi et al, toappear in “Unifying Concepts in Granular Media and Glasses”, edt.s A. Coniglio, A. Fierro, H. J. Herrmann and M.Nicodemi; A. Coniglio et al, Physica A in press.[3] M. Dijkstra, R. van Roij, and R. Evans, Phys. Rev. E 59, 5744 (1999).[4] P. M. Reis and T. Mullin, Phys. Rev. Lett. 89, 244301 (2002); P.M. Reis, G. Ehrhardt, A. Stephenson and T.Mullin cond-mat/0312331.[5] J. A. Both and D. C. Hong, Phys. Rev. Lett. 88, 124301 (2002).



5.6.12

Granular Dynamics in Compaction and Stress Relaxation

Ping Wang1,J. Brujic2,O. Sindt3,D. L. Johnson4 and Hernan A. Makse5

1,5Levich Institute and Department of Physics, City College of New York, New York, NY 10031, USA2,3,4Schlumbeger-Doll Research, Ridgefield, CT 08677, USA

The nonlinear elastic and viscoelastic properties of cohesionless granular assemblies are studied both experimentallyand numerically. As a prelude to granular dynamics measurements, we investigate the system’s exploration of all possi-ble static configurations through a novel compaction procedure at varying confining pressures. Once the system is fullycompactified we assume no further changes in volume and study the stress relaxation dynamics after the applicationof uniaxial strain. The stress relaxation is characterized by a fast exponential decay followed by a slow, logarithmicdecay. Numerical simulations indicate that the slow stress relaxation is associated to the collective relaxation due tograin rearrangements through sliding and rolling in the bulk.

[email protected]@levdec.engr.ccny.cuny.edu

5.6.13

A theoretical study of collective dynamics in liquid binary mixtures

Taras Bryk1

1Institute for Condensed Matter Physics, Nat. Acad. Sci. of Ukraine, 1 Svientsitskii Str., Lviv 79011, Ukraine

We present a theoretical study of collective dynamics in a liquid metallic alloy Li4Pb, well-known as a ”fast sound”compound, and Lennard-Jones binary liquids. A combination of analytical multivariable approach and moleculardynamics simulations is used for analysis of six time correlation functions of primary interest describing partialdensity, energy-density and energy-energy correlations. We discuss a possibility to treat the high-frequency branch inlong-wavelength region as optic-like phonon excitations [1-3]. A key for understanding the branch behaviour in Li4Pbis an analysis of changes in spectra of collective excitations obtained for a model Lennard-Jones liquid mixture withidentical numerical density but different mass ratio of components.

References :[1] T.Bryk, I.Mryglod. J.Phys.:Cond.Matt. v.14, L445 (2002) [2] T.Bryk, I.Mryglod. J.Phys.:Cond.Matt. v.12, 3543(2000) [3] T.Bryk, I.Mryglod. Phys.Rev.E. v.61, 2088 (2000)

[email protected]


5.6.14

Multifractal Analysis of PDF’s with Fat Tail — Application toGranulence

Toshihico Arimitsu1 and Naoko Arimitsu2

1 Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan2 Faculty of EIS, Yokohama National University, Hodogaya-ku, Yokohama 240-8501, Japan

The multifractal analysis (MFA) of fluid turbulence is applied to granular turbulence (granulence) in order to see howfar MFA works for the study of the data extracted by Radjai and Roux (Phys. Rev. Lett., 89 (2002) 064302) in theirtwo-dimensional simulation of a slow granular flow subject to homogeneous quasi-static shearing. They reported thatthere is an evident analogy between the scaling features of turbulence and of granulence in spite of the fundamentallydifferent origins of fluctuations in these systems. With the help of MFA, it is shown that the system of granulence andof turbulence have indeed common scaling characteristics. MFA is a unified self-consistent approach for the systemswith large deviations, which has been constructed based on two distinct Tsallis-type distribution functions providesus with a unified description for experimentally or simulationally observed PDF’s in the highest accuracy comparedwith other multifractal models such as the log-normal model and the p model proposed originally in the analysis ofturbulence.


5.6.15

Phase Behavior and Transport Properties of Binary Mixtures:Computer Simulation Studies

Subir K. Das1,Jurgen Horbach2,Kurt Binder3

1,2,3Institut f”ur Physik, Staudinger Weg 7, Johannes Gutenberg–Universit”at, D–55099 Mainz, Germany

We investigate the phase behavior and transport properties of a dense symmetrical (A,B) Lennard-Jones mixture.A Monte Carlo simulation in the semi grandcanonical ensemble (SGMC) yields the phase diagram. The equlibratedconfigurations from the SGMC are used as the initial configurations for molecular dynamics (MD) simulations tostudy the static (isothermal compressibility κT and concentration susceptibility χ) and transport properties (shearviscosity ηS and bulk viscosity ηB). These quantities are computed as a function of temperature as one approachesthe coexistence curve starting from the one-phase region at high temperature. There is a substantial increase of χand ηB near the coexistence line signalling the vicinity of the critical point. On the other hand κT and ηS shows onlya weak temperature dependence near the coexistence curve. We calculate the location of the spinodal temperaturefrom χ and ηB . As a second example, we also present results for the structure and dynamics of amorphous Al-Nimixtures. MC simulation at constant pressure is used to calculate the density at several compositions. The equilibratedconfigurations from the MC simulations are used as the initial configurations for the MD simulations to study thestatic and dynamical properties. We use an embedded atom potential, proposed by Mishin et al., [Phys. Rev B 65,224114 (2002)], to describe the atomic interactions. We elucidate the appearance of the prepeak in the experimentalneutron scattering structure factor in Al-rich compositions (Maret et al., [Phys. Rev. B 42, 1598 (1990)], Meyer et al.,private communication). We compute the diffusion constant as a function of composition and temperature and findgood agreement with the experiment.

[email protected]



Hydrodynamics of Nanometric Scale Molecules

Fabrice Thalmann1 and Carlos Marques2

1,2LDFC, CNRS and Universite L.Pasteur, Institut de Physique 3, rue de l

We investigate the importance of hydrodynamic effects on the brownian motion of colloidal size particles and nano-metric size molecules. Our purpose is to determine the lower range of applicability of the classical, macroscopic Stokeshydrodynamics. In particular, we address the problem of the efficiency of a very small size propeller. Using the Oseentensor for hydrodynamic interactions, we make predictions for the translational and rotational diffusion coefficientsand the rotation/translation coupling of some simple chiral molecules. These predictions are then compared withmolecular dynamics simulations of these molecules embedded in an explicit solvent.

[email protected]@fresnel.u-strasbg.fr


5.7.1

Mutual attraction of charged nanoparticles at interfaces

Martin Oettel1, Alvaro Dominguez Alvarez2 and Siegfried Dietrich3

1,2,3 Max-Planck-Institute for Metals Research, Heisenbergstr. 3, 70569 Stuttgart, Germany

The experimentally observed long–range attraction between like–charged colloids trapped at fluid interfaces (asreported, e.g., in [1]) can be explained by charge–induced capillary interactions. The short–ranged electrostaticstresses exerted by the colloidal particles on the interface lead to long–ranged capillary forces for which the capillarylength or the finite system size are of crucial importance. This fact has been overlooked in previous treatments [2,3].For realistic values of the characteristic parameters, the interface deformation induced by the charges is small enoughto allow for a perturbative description leading to explicit expressions for the capillary interaction.

References :[1] M. G. Nikolaides et al., Nature 420 (2002) 299.[2] M. Megens and J. Aizenberg, Nature 424 (2003) 1014.[3] L. Foret and A. Wurger, cond-mat/0310657.



5.7.2

Anchoring of nematics - a Monte Carlo study

N. Satyavathi1, K. Venu2, V. S. S. Sastry3 and K. P. N. Murthy4

1 Department of Physics, Osmania University, Hyderabad 560 007 Andhra Pradesh, India2,3 School of Physics, University of Hyderabad, hyderabad 560 034, Andhra Pradesh, India

4 Materials Science Division, Indira Gandhi Centre for Atomic Research, kalpakkam 603 102, Tamilnadu, India

We study anchoring of the director orientation in spherical droplets of liquid crystal formed by dispersion in polymernetworks (PDLC). We consider a lattice model of PDLC and study wetting and anchoring as a function of substrate- bulk interaction and temperature. Free wheeling liquid crystal molecules are placed on the vertices of a cubiclattice. We consider pair-wise additive nearest neighbour interaction modelled by the Lebwohl-Lasher potential. Weconsider a spherical droplet in the cubic lattice; the lattice sites inside the spherical droplet constitute the bulk. Thoseoutside constitute the substrate; a liquid crystal molecule placed on the substrate lattice site has its long axis directedtoward the centre of the spherical droplet. At high temperatures, the liquid crystals in the bulk are oriented in adisorderly fashion; entropy wins over energy; the system is in an isotropic phase. When the temperature is lowered,the competition from the disordering entropy decreases and the ordering effect of the interaction becomes relativelymore important; below a transition temperature the system develops a spontaneous orientational order; it transformsto a nematic phase and is characterized by a nematic director; however there is no particular direction that thenematic director can choose in the absence of an external mechanism that helps it make a choice; in other words thenematic director simply fluctuates throughout the space. Anchoring is a mechanism that pins the nematic director toa particular orientation. However the substrate we consider in this work anchors the director radially. There emergesa competition between radial anchoring induced by the substrate and axial ordering arising from energy competingand winning over entropy. We carry out Monte Carlo simulations at various temperatures above and below the N-Itransition point and for different relative strengths of bulk-substrate interaction as compared to bulk-bulk interaction.We investigate the relation between the less understood anchoring and better understood wetting. We address theseand related issues by interpreting the Monte Carlo results in terms of orientational anchoring and orientational wetting.



5.7.3

Wang-Landau Monte Carlo simulation of isotropic - nematic transitionunder confinement

D. Jayasri1,V. S. S. Sastry2 and K. P. N. Murthy3

1,2School of Physics, University of Hyderabad,Hyderabad 560 034, Andhra Pradhesh, India.3Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamilnadu, India

Liquid crystals exhibit a weakly first order transition from a disordered isotropic phase at high temperatures toan ordered nematic phase at low temperatures. What happens to the nature and content of the phase and of thephase transition when the liquid crystal is confined ? The importance of this question to a technologist involved inmaking display and switching devices with confined liquid crystals, needs no emphasis; for a scientist involved inbasic studies also, this question is important since a confined system exhibits interesting phenomena: for example,upon confinement, the isotropic-nematic phase transition temperature is lowered[1]; also confinement softens thetransition[2, 3] . Monte Carlo simulation of lattice models has emerged as a useful tool for investigating theseand related issues; but simulation of small confined systems is beset with problems arising due to large statisticalfluctuations that tend to completely hide any Monte Carlo signal that would otherwise capture the interestingphenomena. Hence attempts were made to model the effect of confinement in terms of quenched orientational disorderin the bulk; the advantage of such a scheme is that we can them simulate reasonably large systems. Indeed liquidcrystals confined to a porous matrix can be simulated by incorporating quenched disorder at randomm locations in thebulk; periodic boundaries would reduce the finite size effects in the simulation; we can also employ finite size scaling tofurther take care of finite size effects. Recently Venu, Sastri and Murthy[4] reported a phenomenological relation thatexpresses the strength of quenched disorder in terms of the Monte Carlo system size, the average size of a pore in theporous medium and the size of a liquid crystal molecule; a preliminary study showed the usefulness of the empiricalrelation; it predicted correctly the experimental results on the suppression of transition temperature, the enthalpyof the transition and softening of the transition from the first to the second. Metropolis sampling was employed inthe Monte Carlo simulations. Metropolis sampling is not very efficient for simulating large systems especially if weare interested in studying first order phase transition; the low probable microstates describing the phase coexistencenever appear in a statistically significant number in a finite Metropolis sample; non-Boltzmann sampling techniqueare required. To this end we simulated the system with entropic/multicanonical Monte Carlo techniques; in fact weemployed the recent Wang-Landau algorithm[5, 6] in the simulation. Wang-Landau algorithm has been found to beefficient for simulating systems with discrete energy like Ising and Potts models; however there are problems when wesimulate systems with a continuous energy. Hence in our study we discretized the Lebwohl-Lasher (LL)[7] potential;we first checked the performance of the discrete model by simulating the bulk transition. We found that the discretemodel correctly predicts the nature of the transition and the transition temperature. The discrete LL model wasthen used in conjunction with the Wang-Landau algorithm and a series of simulations were carried out with differentsystem sizes and different strengths of disorder. We find that the transition temperature is lowered when the disorderstrength increases; also we find definitive signatures of softening of transition upon increase of disorder.

References :[1] L. Wu, B. Zhou, C. W. Garland, T. Bellini and D. W. Schaffer, Phys. Rev. E 51 2157 (1995).[2] A. Golemme, S. Zumer, D. W. Allender and J. W. Doane, Phys. Rev. Lett. 61 2937 (1988);[3] G. S. Iannachione, G. P. Crawford, S. Zumer, J. W. Doane and D. Finotello, Phys. Rev. Lett., 71 2595 (1993).[4] K. Venu, V. S. Sastri and K. P. N. Murthy, Europhys. Lett. 58, 646 (2002).[5] F. Wang, and D. P. Landau, Phys. Rev. Lett. 86 2050 (2001);[6] F. Wang and D. P. Landau, Phys. Rev. E 64 056101 (2001).[7] P. A. Lebwohl and G. Lasher, Phys. Rev. A 6, 426 (1972) .



5.7.4

Thin film of liquid crystals on the surface of a colloidal particle - aMonte Carlo study

T. Sairam1,V. S. S. Sastry2 and K. P. N. Murthy3

1,2School of Physics, University of Hyderabad, Hyderabad 560 034, Andhra Pradesh, INDIA3Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamilnadu, INDIA

Study of the influence of boundary on the macroscopic characteristics of liquid crystals is of importance from applica-tions and basic research point of view. For, in display devices and switches we have liquid crystals in suitably confinedgeometries and hence the effect of the bounding substrates on the performance characteristics of these devices needscareful considerations. Upon cooling, the isotropic liquid crystal spontaneously orders into a nematic, at temperatureT ≤ TIN . The nematic director however fluctuates from one macroscopic local region to the other. It is preciselyin this context the influence of the bounding substrate comes into picture; it helps the nematic director choose asymmetry direction upon phase transition. For example a homeotropic boundary helps the nematic director orientperpendicular to the tanget plane. All is well if there is no conflict between the anchoring influence (at all T ) of thesubstrate and the ordering influence (manifest at T ≤ TIN ) of the mutual interaction energy of the liquid crystalmolecules of the bulk. The substrate tries to order the liquid crystal molecules closest to it; this order propagates tothe interior as T → TIN from the above; for T ≤ TIN , the entire system of liquid crystal molecules spontaneouslyorders with the nematic director oriented in a symmetry direction chosen by the substrate. What happens when theanchoring influence of the substrate is in conflict with the ordering influence of the mutual interaction? Considera molecularly thin film of liquid crystals deposited on the surface of a small spherical colloidal particle of radiusR << 1. The colloidal particle imposes homeotropic boundary condition on the inner surface of the curved thin film;the outer surface of the film is free. This problem can be modeled on a three dimensional cubic lattice: Consider asphere embedded in a cubic lattice; the lattice sites interior to the sphere form the substrate core representing thecolloidal particle; a few layers of the lattice sites outside the sphere constitute the thin film; each lattice site holds afree- wheeling liquid crystal molecule; all the liquid crystal molecules inside the sphere have frozen orientations eachdirected toward the centre of the sphere. Each liquid crystal molecules in the thin film interacts with its six nearestneighbours; the interaction is modelled by the Lebwohl-Lasher potential. The liquid crystal molecules on the innerlayer of the film interact with the radially frozen nearest neighbour liquid crystal molecules of the substrate, with thesame L-L potential; but the strength of interaction is tuned by a parameter 0 ≤ ε ≤ 1. The substrate tries imposeradial order in the film; the mutual interaction of liquid crystal molecules in the film tends to order them axially whenT ≤ TIN . These two ordering mechanisms are in conflict with each other for small R; the conflict however vanisheswhen R →∞. The response of the thin film to these conflicting and competing influences will crucially depend on R,T and ε. We take R = 32 lattice spacings and investigate the behaviour of the thin film of n layers, as a function oftemperature. When n is greater than five or so, the thin film behaves exactly like bulk; the substrate does not haveinfluence in the ordering. Hence in the studies we take n = 3 − 5. We study the behaviour for different values of ε,employing Markov Chain Monte Carlo with Metropolis sampling. For ε ≈ 1, we find the thin film orders radially; theradial order increases monotonically with decrease of T ; for ε ≈ 0, the substrate has no influence on the thin film andno radial order emerges; the order that emerges below TIN is axial. However when ε . εc ≈ 0.64 we find the followinginteresting phenomenon. As T decreases, radial order builds up initially; when T = TC < TIN , the the growth ofradial order gets arrested; indeed upon further cooling the radial order starts falling, giving way to axial order; thisfall continues until the radial order stabilizes at a small value at very low temperatures. The peak value of the radialorder at T = TC < TIN , decreases with decrease of ε and eventually vanishes when ε → 0. For ε > εc, the spontaneousemergence and growth of radial order is accompanied by increase of fluctuations both in energy and order parametrer.The specific heat and orientational susceptibility both show a peak at T = TIN . For ε . εc, the phenomenon of thearrest of growth of radial order and its subsequent fall upon decrease of temperature is also accompanied by increasesof fluctuations in energy and order. There appears a second peak in the specific heat and susceptibility curves atT = TC < TIN . We conjecture that this second peak owes its origin to the freezing of disorder generated by theconflict between radial and axial orders.



5.7.5

Characteristic Properties of Nano-Structured Non-Equilibrium Systems

Yoshitake Yamazaki1, Zhong-can Ou-Yang2, Kunquan Lu3, Dianhong Shen4, Herbert Gleiter5, andXing Xhu6

1 Institute of Physics, CAS, Beijing, China, ITP, Phys.Peking Univ. Beijing, China2 Institute of Theoretical Physics, CAS, Beijing, China

3,4Institute of Physics,CAS,Beijing, China5 Institute of Nanotechnology, FZK, Karlsruhe, Germany

6 Physics, Peking University, Beijing, China

It may be supposed that non-equilibrium systems e.g. like nano-structured materials, consist of a lot of nano-metersized sub-systems of local equilibrium states. Characteristic properties of each sub-system are discussed: Mesoscopicphase transitions to solid-like, liquid-like and gas-like phases together with glass-like phases are derived, and theirmesoscopic critical behaviors are discussed by mean field and renormalization theories.


5.7.6

Force-extension relation for semiflexible polymers from a transfermatrix approach

P. Ranjith1,P. B. Sunil Kumar2 and Gautam I. Menon3

1,2Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.3The Institute of Mathematical Sciences, Chennai 600113, India.

We present calculations of the force-extension relation and the distribution of the end-to-end vector for semiflexiblepolymers using transfer matrices. We investigate the entire range of persistence lengths, showing that the force-extension relation differs depending on whether one works in the fixed force or the fixed extension ensemble, for finitechains. We study the parameter regime where the end to end vector distribution has been reported to have a doublehump, by directly computing the internal energy and entropy contributions to the free energy. We find that evensmall heterogeneities alter experimentally measurable quantities from the pure case. However, upon averaging overdisorder, physical quantities of interest can still be expressed simply in terms of an effective persistence length. Wedescribe the relevance of our results to experimental measurements on real biological polymers, such as actin.



5.7.7

Power laws in the orientational relaxation of model nematogens nearisotropic to nematic phase transition

Prasanth P Jose1 and Biman Bagchi2

1,2 Solid State and Structural chemistry Unit, Indian Institute of Science, Bangalore - 560012, India.

Recent ultrafast Kerr relaxation experiments by Gottke et al. [J. Chem. Phys. 116, 360 (2002) and 116,6339 (2002)]have revealed the existence of an interesting pronounced temporal power law decay in the orientational relaxation nearisotropic-nematic phase transition (INPT). We have carried out very long ( 50 ns) molecular dynamics simulations ofmodel(Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The modelchosen is known to undergo an isotropic to nematic phase transition at a reduced density ρ∗ ' 0.315 at temperatureT ∗=1.0 for aspect ratio(κ=3). In the vicinity of INPT, both the single particle and collective second rank orientationaltime correlation function (OTCF) suddenly undergo dramatic change from exponential-like to power law decay. Atlong times, the decay of collective OTCF is again exponential-like, as predicted by Landau-de Gennes mean fieldtheory. Dynamics of pseudo-nematic domains inside the isotropic phase has been further studied by computing thedynamic orientational pair correlation function (DOPCF), obtained from the coefficients of expansion of the distinctpart of molecular van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits powerlaw relaxation when the pair separation length is below certain critical length. These results have been interpreted interms of the mode coupling theory of orientational dynamics near the INPT.



5.7.8

Clusters, slow dynamics and structural arrest in colloidal gelation

Emanuela Del Gado1,Annalisa Fierro2,Nicolas Sator3,Lucilla de Arcangelis4 and Antonio Coniglio5

1Laboratoire des Verres, Universite2,5Dipartimento di Scienze Fisiche, Universita

3LPTL, Universite4Dipartimento di Scienze dell

In polymer gelation the transition from a viscous liquid into an elastic disordered solid is well understood in terms of aspanning structure formation, which makes the system able to bear stresses. The dramatic change in the viscoelasticproperties, resulting in the divergence of the viscosity and the onset of an elastic modulus, can be well described interms of percolation theories where the bonds between monomers are considered permanent. In colloidal systems atlow temperature particles are linked due to presence of the attractive interaction but the bonds are not permanent asin chemical gelation. In any case one expects that at very low temperature the lifetime of the bonds is extremely highand the onset of a spanning network should produce a phenomenon closely related to standard irreversible gelation.We have studied slow dynamics and structural arrest in gelation phenomena by means of a lattice model and bymolecular dynamics simulations of interacting colloidal particles [1, 2, 3]. Our results corroborate this scenario andsuggest the presence of two lines in colloidal systems: An interrupted gel which occurs close to the percolation lineand, at higher volume fraction, a second line corresponding to structural arrest. At high temperatures the first linebecomes less and less observable, as the clusters are not living enough and are not detectable, while the second linetends, as the temperature increases, to the hard sphere glass. At very low temperature, the interrupted gel line andthe structural arrest line will come close to each other, until they merge and become indistinguishable. In this regionstructural arrest is expected therefore to combine many features of gelation and glass transition.

References :[1]E. Del Gado, A. Fierro, L. de Arcangelis and A. Coniglio, to appear in Physical Review E (2004), cond-mat/0310776;Europhysics Letters 63, 1 (2003)[2] N. Sator, A. Fierro, E. Del Gado and A. Coniglio, cond-mat/0312591[3] E. Del Gado and W. Kob, in preparation



5.7.9

Nonlinear bead spring chain models for dilute polymer solutions:Rescaled intra-molecular interactions and successive fine graining

P Sunthar1 and J Ravi Prakash2

1,2 Department of Chemical Engineering, Monash University, Melbourne, VIC 3800, Australia

The equilibrium behaviour of a dilute polymer solution, with the polymer molecules modelled as flexible bead-springchains with non-linear springs, is examined in the limit of long chains. It is shown that it is essential to suitably rescaleboth the excluded volume and hydrodynamic interaction parameters by the characteristic length of a single spring inorder to obtain universal predictions. A novel successive fine graining procedure in which a polymer of fixed contourlength is modelled by a hierarchy of discrete bead-spring chains with increasing numbers of beads is introduced. Thedevelopment of this methodology is shown to eliminate the need for system specific parameter estimation proceduresthat are currently adopted. It also provides a means of systematically investigating the effect of finite chain extensibilityon the rheological behaviour of dilute polymer solutions. The classic experiments of Smith and Chu (Science 281,1335) on the behaviour of DNA molecules in elongational flow are used to validate the predictions of the proposedprocedure.


5.7.10

Nematic liquid crystal confined between periodically patternedsubstrates

L. Harnau1,S. Kondrat2 and A. Poniewierski3

1Max-Planck-Institut fuer Metallforschung, Heisenbergstr. 3, D-70569 Stuttgart, Germany, and Institut fuerTheoretische und Angewandte Physik, Universitaet Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

2,3Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

Alignment of nematic liquid crystals induced by surfaces is interesting both from practical and fundamental pointof view. Recently it has been shown that patterned surfaces with a fundamental wavelength in a micrometer rangeare also of great interest because of the expected applications in liquid crystal display devices. Here we study anematic liquid crystal confined between two different substrates, possessing alternating stripe patterns of planar andhomeotropic anchoring. The nematic liquid crystal is described within the Frank-Oseen theory, whereby the anchoringenergy function is given by the Rapini-Papoular expression. By numerical minimization of the free energy we determinephase transitions between uniform and distorted nematic textures [1]. The calculations exhibit that phase transitionscan be triggered by changing the shift of the stripe patterns with respect to each other. Rich phase behavior ispredicted for the case of a generalized expression for the surface free energy. Additional weak surface roughness leadsto a destabilization of uniform textures. [1] Orientational phase transition and the solvation force in a nematic liquidcrystal confined between inhomogeneous substrates, S. Kondrat, A. Poniewierski and L. Harnau, Eur. Phys. J. E 10,163, (2003).



5.7.11

Molecular modeling of PAMAM dendrimers

Prabal K. Maiti1,Tahir Cagin2,Shiang-Tai Lin3,Guofeng Wang4 and William A. Goddard III5

1 Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125 and Departmentof Physics, Indian Institute of Science, Bangalore, 560012, India

2,3,4,5Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125

The structure and dynamics of poly amido amide (PAMAM) dendrimers have been at the center of many discussions,but controversy remains concerning the distributions of atoms, channels, and strain inside these molecules. In thispaper, we report the results of systematic investigations of the atomistic structure of ethylene diamine (EDA) coredPAMAM dendrimer up to the 11th generation (294,852 atoms), at which point the strain energy rises to the point that itlimits uniform growth of additional layers. Using Molecular dynamics simulation we have calculated various structuralproperties such as: radius of gyration, shape tensor, asphericity, fractal dimension, monomer density distribution,solvent accessible surface area, molecular volume, end-group distribution functions. We find that the radius of gyrationscales as Rg N1/3 over the entire range of generations. Contrary to common expectation we find that the outer subgenerations penetrate substantially into the interior of the dendrimer, even for G11. Consequently, the terminal aminegroups are distributed throughout the interior, not just on the periphery of the dendrimer. However for G6 throughG11 there is a large region of uniform density, supporting the uniform scattering model often used in interpreting theSANS (small angle neutron scattering) and SAXS (small angle X-ray scattering) data, which lead to sizes in excellentagreement with the calculations. To study the effect of solvent and varying pH condition we also report variousstructural and conformational properties of generations 4, 5 and 6 PAMAM at various protonation levels in explicitsolvent. The presence of solvent leads to swelling of the dendrimer (e.g. by 33the solution pH from high pH ( 10,no protonation) to intermediate (only primary amines protonated), to low pH ( 5, tertiary amines also protonated)changes the radius of gyration of G5 from 21 to 22 to 25 , respectively. We find significant water penetration insidethe dendrimer, with 3 H2O/tertiary amine for high pH and 6 water for low pH (all for G5). This indicates that theinterior of the dendrimer is quite open with internal cavities available for accommodating guest molecules suggestingusing PAMAM dendrimer for guest-host applications. This estimate of internal waters suggests that sufficient wateris available to facilitate metal ion binding.

1 [email protected]@wag.caltech.edu3 [email protected]@[email protected]


5.7.12

Atomic level simulation of Seeman DNA nanostructures

Prabal K. Maiti1,Tod A. Pascal2,Nagarajan Vaidehi3,Jiyoung Heo4 and William A. Goddard III5

1 Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125 and Departmentof Physics, Indian Institute of Science, Bangalore, 560012, India

2,3,4,5 Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125

The paranemic crossover (PX) DNA molecules and their JXM topoisomers (M denotes the number of missing crossoverpoints), recently synthesized by the Seeman group at NYU, are important components for novel nanomechanicaldevices and for constructing periodic arrays that could be useful in other nanoscale applications. The enhancedrigidity compared to an ordinary double helix of DNA arising from the crossovers makes them useful in structuralDNA nanotechnology. However, there is little data on the effect of crossovers on the structure and stability of crossovermolecules. We use molecular dynamics (MD) simulations to obtain a comprehensive understanding of relationshipbetween structure, topology, and stability of various Paranemic crossover (PX/JX) molecules. These studies includedall atoms of the PX/JX structures plus an explicit description of solvent and ions. This is the first MD simulation ofsuch complex DNA motifs. The average dynamics structures over the last 1 ns of 3 ns long simulation preserve theWatson-Crick hydrogen bonding as well as helical structure. The root-mean-square deviation in coordinates (CRMSD)from the initial canonical structure remains within 3-4 for PX65 over the dynamics, but it goes up to 7-8 for PX55,PX75, PX85 and PX95. The CRMSD with respect to the dynamics averaged structure converged to 2-3 for PX55,PX65 and PX85 but for PX75 and PX95 it exhibits large fluctuations. We have also computed the strain energy forthe formation of PX molecules with reference to B-DNA molecules of the same length and sequence. PX55 and PX65have similar strain energy in the range of 20 kcal/mol/bp, but it increases dramatically for PX75, PX85 and PX95.Various helicoidal parameters indicate that PX65 has the values for helical twist and other helical parameters thatare close to the values expected for normal B-DNA of similar length and sequence. All these findings indicate thatPX65 is structurally more stable compared to other PX motifs in accordance with the experimental findings. We alsofind that PX65, with 6 crossover points, is the most stable, and that the stability, decreases monotonically with thenumber of crossover points PX65¿JX1¿JX2¿JX3¿JX4, with 6, 5, 4, 3 and 2 crossover points respectively. Thus forPX65/JX1 the strain energy is 3 kcal/mol/bp, while it is 13 kcal/mol/bp for JX2, JX3, and JX4. Another measureof the stability is the change in the structure from the minimum energy structure to the equilibrium structure at300K, denoted as CRMSD. We find that CRMSD is 3.5 for PX65, increases to 6 for JX1, and increases to 10 forJX2/JX3/JX4. As the number of crossover points decreases, the distance between the two double helical domains ofthe PX/JX molecules increase from 20 for PX65 to 23 for JX4. This indicates that JX2/JX3/JX4 are less likely toform, at least in with Na (+). However, in all cases the two double helical domains have average helicoidal parameterssimilar to a typical B-DNA of similar length and base sequence. Such studies should aid the design of optimized DNAstructures for use in nanoscale components and devices.



5.7.13

Acoustic spectra of nematic liquid crystals subject to variation of theshape of molecules

Anatoly Petrovich Ivashin1,Valentina Tadeuscevna Matskevich2,Michail Yurievich Kovalevsky3 andLyubov Viktorovna Logvinova4

1,2Akademicheskaya str.,1. National Science Centre ”Kharkov Institute of Physics and Technology”, kharkov,Ukraine, 61108

3,4Pobedy str.,85, Belgorod State University, Belgorod, Russia, 308007

In the submitted report, within the framework of the Hamilton approach, the nonlinear hydrodynamics equations foruniaxial and biaxial nematics taking into account the variation of the molecule shape are obtained. The additionalhydrodynamic parameters connected with broken symmetry are introduced in terms of distortion tensor. They consistof both the anisotropy axes characterizing the orientation of molecule and parameters considering the form andconformational slackness of molecules [1]. The densities of additive integrals of motion and their flux densities arerepresented in terms of a thermodynamic potential. The spectra of collective excitations for nematic with disc - androd-shape molecules are obtained. The character of an anisotropy of wave front propagation is established. It isshown that the introduction of conformation degrees of freedom reduces to a possibility of second and third soundspropagation in such nematic. Dynamic equations for uniaxial nematic in the presence of an external varying field areobtained. The hydrodynamic asymptotic of two- time Green functions for arbitrary physical quantities are found inthe case with one conformation degree of freedom. 1. Ivashin A.P., Kovalevsky M.Yu., Logvinova L.V., MatskevichV.T. // Ukrainian Journal of Physics, Vol.49, N1, 2004.

[email protected]@ic.kharkov.ua


5.7.14

Kinetics of Order-Order Transition in Triblock Copolymer Solution:HEX cylinder to BCC spheres.

Rama Bansil1,Huifen Nie2,Karl Ludwig3 and Milos Steinhart4

1,2,3Physics Dept., Boston Unibersity, Boston, MA, USA4institute of Macromolecular Chemistry, Czech Academy of Sciences, Prague, Czech Republic

We have used synchrotron based time resolved small angle x-ray scattering (SAXS), to study the kinetics of an order-order transition (OOT) in a 0.45%(w/v) solution of Kraton G1650, a polystyrene-block-poly (ethylene-co-butylene)-block-polystyrene (SEBS) triblock copolymer in mineral oil, a selective solvent for the middle EB block. Hexagonallyarranged (HEX) cylindrical micelles, formed by the insoluble S block, transform into spheres which pack onto body-centered-cubic(BCC) lattice upon heating around 127C. Upon temperature quenching, the decrease in the BCC Braggpeak intensities is accompanied by simultaneous development of a HEX primary peak and then the two phases coexistthroughout the experimental observation. In contrast, the reverse transition is characterized by the quick disappearanceof the HEX Bragg peaks in about 100 seconds, followed by the growth of the pure BCC Bragg peaks. However, theBCC phase seems to be meta-stable, as indicated by the decrease in the BCC peak intensity after approximately onehour. The development of peaks at a lower wave number than the position of the primary BCC peak is related togrowth of grains. Detailed analysis and interpretation in terms of a model of the pearling instability will be presented.Supported by: NSF-DMR.

[email protected]@[email protected]@imc.cas.cz


5.7.15

Evolution of local dynamics in an aging colloidal glass formed bycharged nanoscopic disks

Ranjini Bandyopadhyay1, Dennis Liang2, M. A. Borthwick3, S. G. J. Mochrie4, J. L. Harden5, andR. L. Leheny6

1,2,6 Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles St., Baltimore MD 21218,USA

3 Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02139, USA4 Physics Department, Yale University, 217 Prospect St., New Haven CT 06520, USA

5 Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 N. Charles St., BaltimoreMD 21218, USA

We employ multispeckle X-ray photon correlation spectroscopy to determine the dynamic structure factor f(q,t) ofa colloidal glass formed by nanometer-sized, highly charged disks at scattering wave vectors q corresponding tointerparticle length scales. The slow dynamics of the glass is characterized by a structure factor f(q,t) ∼ exp[-(t/T)b],where b ∼ 1.6. The characteristic relaxation time T increases with the sample age tW as T ∼ tW

a, where a isapproximately equal to 2, and decreases with q as T ∼ q−x, where x ∼ 1. Such a compressed exponential form of thedynamic structure factor with a characteristic relaxation time which varies inversely with q is consistent with a recentmodel by Bouchaud and Pitard that describes relaxation in an elastic medium in terms of strain from random, localstructural rearrangements. The apparent contrast measured from f(q,t) further implies caged motion of the particlesat short times, with an average excursion distance that decreases significantly with sample age.



5.7.16

Inhomogeneous Ordered and Disordered Phases of Highly ChargedColloids

P.S.Mohanty1, B.V.R. Tata2, J.Yamanaka3 and T. Sawada4

1,2 Materials Science Division, Indira Gandhi C,entre for Atomic Research, Kalpakkam -603 102, Tamil Nadu, India3 Faculty of Pharmaceutical Sciences, Nagoya City University, 1-3 Tanabe-dori, Mizuho, Nagoya 467 - 8603, Japan

4 National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan

Monte Carlo simulations have been performed for deionised aqueous charged colloidal suspensions as a function ofeffective charge density, σe on the particles. We vary σe in our simulations over a range where a reentrant order-disorder transition in suspensions of silica and polymer latex particles has been reported (Yamanaka et al Phys. Rev.Lett., 80, 5806 (1998); Toyotama et al Langmuir, 19, 3236 (2003)). Our simulations show a homogenous liquid-likeordered phase freezing into a homogenous crystalline structure upon increasing σe. Further increase in σe resulted inan inhomogeneous ordered state up to a certain value of σe and an inhomogeneous disordered state beyond this value ofσe. In conformity with experiments our simulations also show the occurrence of reentrant order-disorder transition asa function of σe. However, our simulations predict an inhomogeneous ordered state over a narrow range of σe, whichhas not been investigated experimentally. Hence we carried out static light scattering and confocal laser scanningmicroscope (CLSM) studies on latex suspensions over a charge density range 0.2 - 0.5 µC/cm2. Iridescence is observedin samples with σe = 0.41 µC/cm2 and samples of higher σe did not exhibit iridescence. Volume fraction of the solidphase estimated from the light scattering data is found to be higher than that measured independently. CLSM studieson these samples confirm their inhomogeneous nature by revealing the coexistence of voids with ordered regions insamples of low σe and voids with disordered regions in samples of high σe. These results provide unambiguous evidencefor the occurrence of gas-solid transition in highly charged colloids.



5.7.17

”Micro-pottery” - Spontaneous Assembly of Soap Fibres at Air-SolutionInterface

Janhavi S. Raut1, Pradeep Bhattad2, Aditi Kulkarni3 and Vijay M. Naik4

1,2,3,41 Hindustan Lever Research Centre and Unilever Research India, 64, Main Road, Whitefield, Bangalore - 560066, INDIA

Crystal growth is a coupled process involving phase transformation, heat and mass transfer, and fluid flow. It isknown that even in absence of externally imposed flow, local temperature and/or concentration gradients in theneighbourhood of growing crystals can induce flows under the influence of body force fields, or due to surface tensionimbalances generated at free surfaces. Flow fields in turn drag and align the crystallites along streamlines as wellas influence energy and mass transport at growing crystal faces. We report studies carried out on a crystallisingsoap system, wherein the transient coupling between the growing soap fibres and the induced flow fields acts likean assembly of creative potters to generate intriguing arrays of nearly axisymmetric fibre superstructures at the air-solution interface. Although the exact origin and nature of the phenomena is not yet clear, controlled experimentsshow that the superstructure formation is purely a surface phenomena. The superstructures can be generated at flatas well as curved surfaces independent of their orientation with respect to gravity. These facts indicate that surfacetension, rather than density gradients are likely to play the decisive role in this phenomena. Leaving aside its shearaesthetic charm, an ability to control the size and shape of these structures can open up avenues for application innano-fabrication, purification and controlled release.


5.7.18

The Writhe Distribution Of Tense Semiflexible Polymers

Supurna Sinha1

1 Theoretical Physics Group, Raman Research Institute, Bangalore- 560080, India

In recent years there have been experiments on single DNA molecules which are stretched and twisted. Motivatedby these experiments we consider a perturbative approach around very high forces, where we calculate the writhedistribution in a simple, analytically tractable model. Our results are in qualitative agreement with recent simulationsand experiments.

1 [email protected]


5.7.19

Phase behaviour of polydisperse colloid-polymer mixtures

Peter Sollich1 and Moreno Fasolo2

1,2 Dept of Maths, KCL, UK

We study theoretically, for the first time, the equilibrium phase behaviour of mixtures of polydisperse hard spherecolloids and polymers, taking full account of the conservation of the size distribution for both species. Our treatmentis based on the Asakura-Oosawa model [1], which treats the polymers as spherical particles interacting only withthe colloid. Within the van-der-Waals approximation of Lekkerkerker et al [2], we need as input only suitable freeenergy expressions for the colloidal fluid and crystal. We compute complete phase diagrams using the moment freeenergy method [3]. The intricate features of phase separation in pure polydisperse colloids, including fractionationinto several solids, combine with the appearance of polymer-induced gas-liquid coexistence to give a variety of phasediagram topologies. The threshold value of the polymer radius above which gas-liquid separation appears is found todecrease with increasing colloid polydispersity. Marked polymer partitioning is present between coexisting phases;e.g. the gas phase is extremely rich in polymers and can act as a ”polymer reservoir”.

References :[1] S Asakura and F Oosawa, J. Chem. Phys. 22:1255, 1954.[2] H N W Lekkerkerker et al., Europhys. Lett. 20:559, 1992.[3] P Sollich et al., Adv. Chem. Phys., 116:265, 2001.


5.7.20

Folding of the alpha-helix and beta-sheet structures of proteins by usinga minimal off-lattice model

Chung-I Chou1,Rong-Sheng Han2,Hsu-Sheng Huang3,Yi-Wen Wu4 and Ting-Kuo Lee5

1Department of Physics, Chinese Culture University, Taipei 111, Taiwan2,3,4,5Institute of Physics, Academia Sinica, Nankang, Taipei 115, Taiwan

We develop an off-lattice minimal energy model of proteins. The model is composed of a polypeptide chain, andhas the Ramachandran angles as its degrees of freedom. The force field of this model is based on hydrogen bondsand the anisotropic hydrophobicity forces. The energy form of the anisotropic hydrophobicity forces is designed byanalyzing the protein data banks. By using this model, we can fold several different secondary structures of proteinsin simulations, including the alpha-helix, beta-sheet and the alpha / beta structures. We will show the comparisonswith our results and the real protein structures.

[email protected]


5.7.21

Opening of a weak link in a Semiflexible ring polymer

K. P. Santo1 and K. L. Sebastain2

1,2 Department of Inorganic and Physical chemistry, Indian Institute of Science, Bangalore

The dynamics of opening of contact formation between different parts of a long chain molecule is of considerableinterest in biology. The related processes of opening of a loop or closing to form a loop also is of considerable interestand has attracted the attention of experimentalists/theorists. Theoretical results are available in the completely exiblelimit. However, this limit is not realized in many cases. Recently, there have been investigations for the semi- flexiblecase too. We present results for the opening of a weak link in a semi-flexible ring polymer, which takes the semi-flexibility rigorously into account.


5.7.22

Aspects of the dynamics of active membranes

David, LACOSTE1 and Andy, LAU2

1 ESPCI, 10 rue Vauquelin, 75005 PARIS, FRANCE2 Department of Physics, University of Pennsylvania, Philadelphia, PA 19104-6396, USA

We discuss some theoretical aspects of the time dependence of the fluctuations of an active membrane (such as a fluidmembrane containing pumps or ion channels), using the framework developed by S. Ramaswamy, J. Toner and J.Prost. This study could apply to experiments in which the brownian motion of a tagged particle attached to an activemembrane would be recorded. We discuss how to relate theoretically the time dependence of the fluctuations of themembrane to the dynamics the pumps.



5.7.23

Diffusion of Polymer and Effect of Flow in Hyaluronan Solution – aBrownian Dynamics Simulation

Masako Takasu1 and Jungo Tomita2

1,2 Dept. Computational Science, Kanazawa University, Kakuma Kanazawa 920-1192 Japan

The diffusion properties in extracellular matrix such as hyaluronan are important for the transport of macromoleculesin our body. The experiments of diffusion in hyaluronan solution have been done by Masuda et al. We have performedBrownian dynamics simulation to investigate the diffusion of polymer in hyaluronan solution. The temperaturedependence of diffusion constant shows non-monotonic behavior. The effect of flow is also investigated.

1 [email protected]

5.7.24

Crossing barriers in one and three dimensions by long chain

Alok K. R Paul1,Ananya Debnath2 and K. L. Sebastian3

1,2,3Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore, 560012, India

We consider a generalization of Kramers problem to a long chain polymer trapped in a biased double well potential.Initially, the polymer is in the less stable well and it can escape from this to the other well by the motion of its N beadsacross the barrier to attain the configuration having lower free energy. We use the continuum version of the RouseModel. In one dimension we study the problem numerically and find that the results are in agreement with the kinkmechanism suggested earlier. In three dimensions, it has not been possible to get analytical results for an arbitrarypotential. Therefore, we assume the form of the solution of the non-linear equation as kink solution, and find a doublewell potential in three dimensions. To verify the kink mechanism, simulations of the dynamics of a discrete Rousepolymer model in a double well, in three dimensions were done. We find that the time of crossing is proportional tothe chain length in agreement with the kink mechanism. The shape of the kink solution is also in agreement with theanalytical solution.



5.7.25

The Sol-Gel Transition Temperature of Gelatin Solution

Namiko Cho1, Masanori Cho2, Hirofumi Sakashita3 and Yoshinori Miura4

1 College of Pharmaceutical Sciences, Daiichi University, Hukuoka, Japan 815-8511@2 Faculty of Engineering, Sojo University, Kumamoto, Japan@860-0082

‘3,4 Center for Advanced Instrumental Analysis, Kyushu University, Kasuga, Japan 816-8580

Gelatin gel is a typical thermoreversible gel. The sol-gel transition temperature (Tg) of gelatin solution dependson the concentration of gelatin. The Tg was measured in the concentration range from 1 percent to 30 percent.The experimental result is represented as follows. Tg=281.1+30.57(d-0.009)0.20, where d is the density of gelatin.We explain the concentration dependence of Tg on the basis of the site-bond percolation model described by twoprobabilities of the site occupation and the bond formation.

1 [email protected]@@2 [email protected] [email protected] [email protected]

5.7.26

Structural crossover in binary hard-sphere mixtures

C. Grodon1, M. Dijkstra2, R. Evans3 and R. Roth4

1,4 MPI fuer Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany2 Debye Institute, Utrecht University, Princetonpln 5, 3584 CC Utrecht, The Netherlands

3 H.H. Wills Physics Laboratory, University of Bristol, BS8 1TL Bristol, UK

The asymptotic behavior of pair correlation functions in pure hard-sphere fluids exhibits damped oscillatory decaywith a wavelength that corresponds roughly to the particle size. In binary hard-sphere mixtures, however, we facetwo distinct length scales, namely the two different particle sizes. Still the asymptotic decay for all pair correlationfunctions has to be the same for both components. We study such asymptotic decay by calculating leading-order polesof the Fourier transforms of the pair correlation functions. We obtain the required pair direct correlation functionswithin the framework of DFT using two versions of the fundamental measure theory. For moderate size ratios we findcrossover lines in the phase diagram at which the wavelength of oscillation changes discontinuously. Moreover, wefind that the crossover in the asymptotic behavior can be observed at small separations and we verify our results bynumerically computing density profiles around a big hard sphere by DFT calculations and Monte Carlo simulations.Using an effective one-component description we confirm the occurrence of the crossover line. In this approachfor highly asymmetric mixtures we find regions in the phase diagram with monotonic exponential decay which areseparated from those with oscillatory decay by a Fisher-Widom line. Furthermore, we find the crossover behavior inother, inhomogeneous, situations like in the density profiles of each component at a wall and in the solvation force inbinary hard-sphere mixtures confined between two parallel walls.



5.7.27

Dynamic Light Scattering Study of the Gelatin Solution by UsingPolystyrene Latex Spheres as probes

Masanori Cho1, Namiko Cho2, Hirofumi Sakashita3 and Yoshinori Miura4

1 Faculty of Engineering, Sojo University, Kumamoto, Japan@860-00822 College of Pharmaceutical Sciences, Daiichi University, Hukuoka, Japan 815-8511

3,4 Center for Advanced Instrumental Analysis, Kyushu University, Kasuga, Japan@816-8580

We measure the viscosity of the gelatin solution in order to study the sol-gel transition. We use the dynamic lightscattering from polystyrene latex spheres dispersed in gelatin solution. From the autocorrelation function of theintensity scattered light, we obtain the temperature dependence of the viscosity of the gelatin solution. We examinefour samples of which the gelatin concentrations are 1.4 percent, 2.5 percent, 4.8 percent and 10.2 percent. We findthat the temperature dependence of the viscosity of every sample obeys the Vogel-Fulcher law.

1 [email protected] [email protected]@@3 [email protected] [email protected]

5.7.28

Properties of ensembles of directed polymers in 3D, entanglement androughening

Viljo Petaja1,Matti Sarjala2,Mikko Alava3 and Heiko Rieger4

1,2,3Helsinki University of Techn., Lab. of Physics, P.O.Box 1100, FIN-02015 HUT, Espoo, Finland4Theoretiche Physik, Universitat des Saarlandes, 66041 Saarbrucken, Germany

Magnetic flux line ensembles in dirty type II superconductors are intensively studied representatives of elasticmanifolds in a disordered environment. Interactions with different types of disorder and among the flux linesthemselves lead to interesting phenomenological properties such as changes of critical current jc. A lot of effort hasbeen devoted to characterize the resulting complex phase diagram[1, 2]. We investigate properties of flux lines ordirected polymers in disordered media (DPRM) with an exact numerical method[3]. The algorithm finds a jointground state for N lines in three dimensions. From the ground state we calculate spatial and energy fluctuations ofthe lines. We find that spatial fluctuations of lines lead to formation of line bundles. We consider both pure pointdisorder and correlated disorder[4, 5].

References :[1] T. Nattermann, S. Scheidl, Adv. Phys. 49 (2000) 607[2] G. Blatter et al, Rev. Mod. Phys. 66 (1994) 1125[3] H. Rieger, Phys. Rev. Lett. 81 (1998) 4488[4] T. Hwa et al, Phys. Rev. Lett. 71 (1993) 3545[5] J. Lidmar, D.R. Nelson, D.A. Gorokhov, Phys. Rev. B 64 (2001) 144512

[email protected]@[email protected]@mx.uni-saarland.de


5.7.29

Simulation Study of Transport Phenomena in (Charged) ColloidalSystems: A New Hybrid MD-LB Method with Hydrodynamic

Interactions

Apratim Chatterji1 and Juergen Horbach2

1,2 Institut fur Physik WA 331 Johannes Gutenberg-Universitat D-55099 Mainz Germany

We present a hybrid computational scheme in which we couple Molecular Dynamics (MD) and Lattice Boltzmann(LB) simulation techniques in order to study the dynamics of (charged) colloidal dispersions. We consider explicitly asystem of spherical macroions, counterions and coions in the framework of the primitive model. In the LB techniqueused, a simple kinetic equation is solved on a lattice such that the linearised Navier Stokes equations are recovered.In our new simulation scheme, we couple the colloidal particles to the LB fluid in order to describe the hydrodynamicinteractions, i.e., long-range interactions between the colloids that stem from momentum transport by the fluid. Thecoupling of the LB fluid with the ionic particles is achieved by exchanging momentum by local viscous forces betweenthe points on the surface of the colloidal particles and the nearest lattice nodes of the LB fluid, keeping the momentumconserved. This is similar to the method used by P. Ahlrichs and B. Dnweg for study of polymeric systems [JCP,111, 8225, (1999)]. The phase space coordinates of the ionic particles are updated by MD where the forces from thefluid are taken into account. We reproduce the long time tails for the velocity ~v and angular velocity ~Ω relaxationof a colloidal particle in the fluid, ~v and ~Ω relax as t−3/2 and t−5/2, respectively. We calculate the effective frictioncoefficient ξeff of a colloidal particle moving with a constant velocity in a fluid, account for finite size effects, and seethat the value of ξeff is consistent with the stick boundary conditions. Thermal fluctuations applied in our model arein accordance with the fluctuation dissipation theorem. Using this scheme, we measure the translational and rotationaldiffusion constants as a function of the colloid packing fraction for neutral and charged colloidal systems. We alsopresent results of the investigation of electrokinetic effects by studying the motion of a single macroion, surroundedby counterions and coions, in a flow field.

[email protected]@uni-mainz.de


5.7.30

Competition between Short-Ranged Attraction and Short RangedRepulsion in Crowded Configurational Space; A Lattice Model

Description

D. Cellai1, H. Cuevas2, A. Lawlor3 and G. D. McCullagh4

1,2,3,4 Irish Centre for Colloids and Biomaterials, Dept. of Chemistry, University College Dublin, Belfield, Dublin 4

There has been considerable interest recently in the phase-structure, dynamical arrest, and kinetics of particledispersions (colloidal, nano-, and bio-) where the system has short ranged attractions [1,2,3]. These issues have beenraised, in part, because of an interest in understanding how proteins crystallize [4]. Whilst progress is possible withtheory, and with simulation, these methods are limited by either the long time-scales involved, or by the nature ofthe approximation. Here we introduce a remarkably simple nearest-neighbor Ising model that for some ranges ofparameters exhibits classical ’gas, liquid, crystal and glass transition’, and in others, exhibits the behavior that isnow becoming recognized as being due to the short-ranged nature of the interactions [5,6]. The model excludes cr

nearest neighbors, and permits attraction towards ca neighbors. We believe [6] that variation of cr and ca alone issufficient to recover much of the existing behavior of such systems are the range of attraction is varied, including thenovel dynamical arrest. Preliminary data are offered to confirm this belief.

References :[1] K. A. Dawson, Curr. Opin. Colloid Interface Sci., 7, 218 (2002).[2] J. Bergenholtz and M. Fuchs, Phys. Rev. E, 59, 5706 (1999).[3] K. Dawson, G. Foffi, M. Fuchs, W. Goetze, F. Sciortino, M. Sperl, P. Tartaglia, Th. Voigtmann, and E. Zaccarelli,Phys. Rev. E 63, 011401 (2001).[4] M. G. Noro, N. Kern, and D. Frenkel, Europhys. Lett., 48, 332 (1999).[5] K. A. Dawson, A. Lawlor, P. De Gregorio, G. D. McCullagh, E. Zaccarelli, G. Foffi, and P. Tartaglia, FaradayDiscussions, 123/2 (2002).[6] D. Cellai, H. Cuevas, A. Lawlor, G. D. McCullagh, and K. A. Dawson, ’Competition between Short-RangedAttraction and Short Ranged Repulsion in Crowded Configurational Space; A Lattice Model Description’, unpublished.



5.7.31

Dynamics of asymmetric colloid-polymer mixtures

Emanuela Zaccarelli1, Francesco Sciortino 2 and Piero Tartaglia3

1,2,3 Dip. di Fisica, Universita

We study colloidal systems with short-ranged attractive depletion interactions, caused by the addition of small polymersin solutions, by means of extensive numerical simulations and compare our results with existing theory and experiments.In particular, working in the effective one-component picture, we observe at high volume fraction a reentrant liquid inbetween two distinct glasses with anomalous dynamics. We also study the dynamics at low volume fractions, whereexperimentally gel phases are observed. However, within this picture a gel transition is only found via phase separation.We finally compare these results with those for the full binary mixture, where also polymers are explicitly taken intoaccount. Despite the fact that thermodynamics is the same within the two pictures, when the size of polymers issufficiently small with respect to that of the colloids, we show that a dynamical criterion must be satisfied in order tohave also the same dynamical properties.


5.7.32

Investigations on biaxial liquid crystal phase of rectangular moleculesby numerical simulation

Ikuo ONO1 and Katsumi KASONO2

1Dept. of Mathematical and Physical Science, Facult. of Science, Japan Womens University, 2-8-1Mejirodai,Bunkyou-ku,Tokyo 112-8681,JAPAN

2School of Medicine, Jikei University,Kokuryo-chou, Choufu,Tokyo,JAPAN

Monte Carlo simulations have been performed on the assemblies of rectangular molecules, to investigate liquid crystalphase transition. Our rectangular molecules are assumed to be represented by tightly connected 5× 2 or 5× 3 ... rigidspheres. The phase transitions for these systems are known to depend on the concentration of molecule, but not on thetemperature. The successive phase transitions are expected to appear isotropic, nematic, smectic A, biaxial smecticphase and crystal, in accordance with the increase of concentration. In the biaxial phase possibility of occurrence offerro- and antiferro-electric phases will be discussed, when molecules have intrinsic dipole moment.

[email protected]@mx8.ttcn.ne.jp


5.7.33

One Component Description of Very Asymmetric Mixtures: IntegralEquation Strategies and Molecular Dynamic Simulations

Juan A. Anta1,Fernando Bresme2,Maria Cortada3 and Santiago Lago4

1,3,4Departamento de Ciencias Ambientales, Universidad Pablo de Olavide, Seville, Spain2Department of Chemistry, Imperial College of Science, Technology and Medicine, London, UK

Asymmetric mixtures, such as colloidal dispersions are of major importance in physics, chemistry and biology. Thesesystems are characterised by large asymmetries in the size of the constituents, and their dynamics involve verydifferent time scales. Statistical mechanics tools such as ”integral equations” provide a route to tackle the study ofthe structure and phase behaviour of these systems. In this work we present a description of very asymmetric systemsin the context of the Ornstein-Zernike integral equation theory. In most cases of relevance in physics, chemistry andbiology, one is interested in the study of the effective interactions and correlations between the larger components ofthe mixture. Here we apply a coarse-graining method to define the one component system (OCS) of larger particles.In our approach, the OCS is defined by a pairwise additive effective potential which is obtained self-consistently fromthe correlations between large-small and small-small particles. Taking advantage of the asymmetry in size betweenthe ”large” and the ”small” components, we consider different levels of approximation for all correlations involvedin the problem; Correlations between small particles are treated using the simplest Random Phase Approximation,and correlations between large and small particles are approximated through the Hypernetted-Chain Closure (HNC).The use of more sophisticated closures (reference HNC, bridge diagrams, etc) is restricted to the description of theOCS only. In this way we achieve a very accurate description of correlations between large particles in a wide rangeof systems; liquid metals (1), charged colloidal suspensions (2,3) and hard-core Yukawa mixtures, both repulsiveand attractive. Furthermore, the present method is computationally more simple and has a larger solution regionthan more sophisticated multicomponent integral equation approaches (3). This makes it possible to extend theapplicability of the theory to charged colloidal systems with added salt. We also use molecular dynamics simulationsof a system consisting of one large charged particle and its counterions to obtain the correlations between large andsmall particles. This information coupled with the integral equation theory is used to study colloidal suspensionswith very large size and charge asymmetry.

References :[1] J. A. Anta and A.A. Louis, Physical Review B, 61, 11400 (2000)[2] J. A. Anta and S. Lago, Journal of Chemical Physics, 116, 10522 (2002)[3] J. A. Anta, F. Bresme and S. Lago, Journal of Physics: Condensed Matter, 15, S3491 (2003)

[email protected]@[email protected]@dex.upo.es


5.7.34

Structure, dynamic properties and critical behavior of ternary mixturesof polymers and solvents

Petr STEPANEK1, Zdenek TUZAR2, Peter CERNOCH3, Frederic NALLET4, and LaurenceNOIREZ5

1,2,3 Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic4 Centre de recherches Paul-Pascal, CNRS, Pessac, France

5 Laboratoire Leon Brillouin, CEA, Saclay, France

We investigate ternary systems where a diblock copolymer A-B is dissolved in an immiscible mixture of two othercomponents a and b, where a is compatible with block A and b is compatible with block B. Components a and b areeither polymers or solvents selective for the respective blocks. Formation of regular nanostructures is observed withcharacteristic distance typically 100 nm consisting of domains of a and b, stabilized by the block copolymer A-B. Wehave investigated these systems using small angle neutron scattering, dynamic light scattering, static birefringenceand pulsed-field gradient NMR. Depending on the composition of the mixed solvent the ordered phases formed belowthe coexistence curve of the neat solvents had a hexagonal or cubic structure, or the structure of a bicontinuousmicroemulsion. Analysis of the scattered intensity at large wave vectors q shows that the chains at the interface ofthe two solvents are not stretched. The dynamics of the ordered systems can be followed over 10 orders of magnitudeand include these processes: polymer and solvent diffusion, internal relaxations, cooperative diffusion, and viscoelasticrelaxation. Critical slowing down has been observed near the phase transitions between the ordered and disorderedphases. We acknowledge support of the Grant Agency of the Czech Republic (No. 203/02/1262) and by the EuropeanCommission through the Improving Human Potential Programme.



5.7.35

Chaotic orientational and rheological behavior of tumbling liquidcrystals

Siegfried HESS1 and Martin Kroger2

1 Inst.f.Theor.Physik, TU Berlin, Hardenbergstr.36, D-10623 Berlin, Germany2 Polymer Physics, Materials Science, ETH Zentrum, ML H18,CH-8092 Zurich, Switzerland

The rheological properties of nematic liquid crystals, in particular stiff main chain polymers and worm-like micelles arestrongly affected by the dynamic behavior of the molecular alignment. Starting from a closed nonlinear inhomogeneousrelaxation equation for the five components of the alignment tensor it has been demonstrated ( G. Rienacker, M. Kroger,and S. Hess, Phys.Rev.E 66, 040702(R) (2002); Physica A 315, 537 (2002)) that the rather complex orientation behaviorof tumbling nematics can be chaotic in a certain range of the relevant control variables, viz. the shear rate and tumblingparameter. Even spatial chaos was found in spatially inhomogeneous systems (B. Chakrabarti, M. Das, C. Dasgupta,S. Ramaswamy, and A.K. Sood, preprint: arXiv:cond-mat/0311101 v1., Phys. Rev. Lett. (2004)). Here the underlyingtheoretical foundation of the relevant equations is briefly discussed and the rheological consequences, i.e. the shearstress and the normal stress differences, as well as dynamics of the alignment tensor are presented. For selected statepoints, long-time averages are evaluated both for imposed constant shear rate and constant shear stress. Orientationaland rheological properties are displayed as functions of the shear rate. The transitions between different dynamicstates are detected and discussed. Representative examples of alignment orbits and rheological phase portraits giveinsight into the regular and the chaotic dynamic behavior.

1 [email protected]

5.7.36

Characteristic Properties of Nano-Structured Non-Equilibrium Systems

Yoshitake Yamazaki1, Zhong-can Ou-Yang2, Kunquan Lu3, Dianhong Shen4, Herbert Gleiter5, andXing Xhu6

1 Institute of Physics, CAS, Beijing, China, ITP, Phys.Peking Univ. Beijing, China2 Institute of Theoretical Physics, CAS, Beijing, China

3,4Institute of Physics ,CAS,Beijing,China5 Institute of Nanotechnology, FZK, Karlsruhe, Germany

6 Physics, Peking University, Beijing, China

It may be supposed that non-equilibrium systems e.g. like nano-structured materials, consist of a lot of nano-metersized sub-systems of local equilibrium states. Characteristic properties of each sub-system are discussed: Mesoscopicphase transitions to solid-like, liquid-like and gas-like phases together with glass-like phases are derived, and theirmesoscopic critical behaviors are discussed by mean field and renormalization theories.



5.7.37

Mixtures of Colloids and Liquid Crystals

D. Vollmer1,G. Hinze2,B. Ullrich3 and A. B. Schofield4

1,3 MPI for Polymer Research, Mainz, Germany2Inst. of Physical Chemistry, Mainz, Germany

4School of Physics, The University of Edinburgh, Edinburgh EH9 3JZ, UK

We studied three-dimensional particle networks that form upon cooling of suspensions of polyacrylmethacrylate col-loids in liquid crystal through the isotropic-nematic transition. Rheological data suggest that network formationdepends only weakly on particle size within the range of 100-800nm. NMR and calorimetry indicate the presenceof isotropic material down to 10K below the bulk transition temperature and ”smearing” of the specific heat curve,strongly reminiscent of the effect of alcanes on phase transition kinetics. We suggest that alcane impurities mayalter the temperature and time range of phase transition and, due to coexisting isotropic and nematic regions andwetting of the particles with isotropic material, promote rearrangement of the colloids in networks. During subsequentcooling/heating cycle, networks were only partially reversible and exhibited consiberable memory effects even withperiods of several hours above transition temperature. Repeated cooling led to compactification and further increaseof storage and loss moduli.


5.7.38

Depletion force between two large spheres suspended in a bath of smallspheres: Onset of the Derjaguin limit

Martin Oettel1

1 Max-Planck-Institute for Metals Research, Heisenbergstr. 3, 70569 Stuttgart, Germany

We analyze the depletion interaction between two hard colloids in a hard–sphere solvent and pay special attentionto the limit of large size ratio between colloids and solvent particles which is governed by the well–known Derjaguinapproximation. For separations between the colloids of less than the diameter of the solvent particles (defining thedepletion region), the solvent structure between the colloids can be analyzed in terms of an effective two–dimensionalgas. Thereby we find that the Derjaguin limit is approached more slowly than previously thought [1]. This analysisis in good agreement with simulation data which are available for a moderate size ratio of 10. Small discrepancies toresults from density functional theory (DFT) at this size ratio become amplified for larger size ratios. Therefore wehave improved upon previous DFT techniques by imposing test particle consistency. However, the improved resultsshow no convergence towards the Derjaguin limit and thus we conclude that this implementation of DFT togetherwith previous ones which rely on test particle insertion become unreliable in predicting the force in the depletionregion for size ratios larger than 10.

References :[1] M. Oettel, cond-mat/0310523, accepted in PRE

1 [email protected]


5.7.39

Does the compactivity of jammed granular matter have a truethermodynamic meaning? Experiments have the answer

Chaoming Song1, Ping Wang2 and Hernan Makse3

1,2,3 Levich Institute of City College of New York, NY, USA

A densely packed granular system, in which all the grains are in contact with their neighbors, is an example of jammedmatter. Since there is no thermal energy of consequence within the system, the exploration of the available jammedconfigurations of the constituent particles for a given system volume must be facilitated by an external energy input,such as tapping or slow shear. Provided that all the jammed configurations are equally probable and bear no memoryof their creation, we arrive at the ergodic hypothesis, implying that a statistical mechanics approach is justified. Thisforms the basic tenet of the thermodynamic formulation for jammed matter, which characterizes the state of thepacking by the ‘compactivity’ or ’effective temperature’ and the entropy. The existence of jammed reversible stateshas been suggested by several experiments employing tapping, oscillatory compression or sound propagation as theexternal mechanical perturbation. On the other hand, macroscopic variables, such as the effective temperature, havenot been previously measured in the laboratory. Until present, the only evidence of their significance in describing thesystem has emerged from computer simulations of glassy systems and sheared granular matter as well as theoreticalmean field models of spin glasses. This line of research has led to the design of a decisive experiment which we are aboutto present. The measurement of the granular effective temperature is realized in the laboratory by slowly shearing ajammed ensemble of spherical beads in a couette geometry confined by an external pressure. The particle trajectoriesyield the diffusivity and the mobility from which the effective temperature is deduced using a FDT relation. All theparticles, independent of their properties, equilibrate at the same compactivity, thus satisfying the condition of a truethermodynamic temperature. This result provides a proof that the problem of jammed matter is a generalization ofthe statistical mechanics introduced by Boltzmann.



5.7.40

Entropic sampling of lattice and continuous polymer models withinWang-Landau algorithm

Pavel Nikolaevich Vorontsov-Velyaminov 1, Nikolay Aleksandrovich Volkov2 and Anton AlekseevichYurchenko3

1,2,3 Faculty of Physics, Department of Molecular Biophysics, 198504, Stariy Peterhoff, Ulianovskaya st. 1,Saint-Petersburg, RUSSIA

Entropic sampling [1992 Phys.Rev.Lett. 6¯8 9; 1993 Phys.Rev.Lett. 7

¯1 211] technique proposed recently by Wang and

Landau (WL) [ 2001 Phys. Rev. Lett. 8¯6 2050] is extended here to simulation of free [2004 J.Phys.A 3

¯7 1573] and ring

polymer chains in three-dimensional continuous and lattice space. Combination of homogeneous and WL entropicsampling provides reliable data for events with very low probabilities down to 10−40. Scaling relations for SAWsare well reproduced; distributions over the number of contacts are obtained and equilibrium canonical averages, i.e.internal energy, heat capacity, excess canonical entropy, mean square end-to-end distance, are calculated as a result ina wide temperature range. The athermal case for continuous free chains is studied by sorting conformations of a freelyjoined phantom chain over a stochastic variable the minimum distance between nonbonded beads. This distributionprovides us with excess specific entropy in the whole range of diameters. WL-sorting of conformations over a setof energy intervals makes it possible finally to calculate canonical averages in a wide temperature range includingcoil-globule transition. Analogous procedure is implemented to ring continuous and lattice models (polygons).


5.7.41

DNA collapsing transiton in the presence of multivalent cation; Whycondensed phase is preferred at higher temperature?

Takuya Saito1, Takashi Iwaki2 and Kenichi Yoshikawa3

1,2,3 Department of Physics, Graduate School of Science, Kyoto University, Kyoto, Japan

By the addition of multivalent cations, long DNA chains exhibit collapsing transition. Recently the observation of singleDNA chains with a fluorescence microscopy clarified that the DNA collapsing transition is largely discrete at the levelof single molecules. To clarify the mechasm of the DNA collapsing transition, we performed single-chain observationof long DNAs in the presence of tetravalent cations (spermine), by changing the temperature and monovalent saltconcentration. It was found that the compact state is more stable at higher temperature. The apparent change inentropy from coil to compact state was found to be ∆Stotal ' +30kB . We consider the free energy of single DNAchain as the summation of the terms; electrostatic energy, elastic entropy, mixing entropy and translational entropy.The experimental results on the temperature dependence indicate that the change in translational entropy shouldbe positive and should overcome the other three terms. We propose the mechanism of the collapsing transition thatthe positive change in the entorpy for the collapsing transition is originated from the exchange between tetravalentand monovalent cations. The apparent entropy change deduced from the measurement at different temperatures iscompared with that from the salt effect.



5.7.42

Statistical model for dissociation in the order-disorder transition of lipidchains

Vera Bohomoletz Henriques1 and Camilla Ratto Barbetta2

1,2 Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, S. Paulo, Brasil, cep 05315970

Vesicles present in aqueous lipid dispersions serve as experimental models for membranes. These systems present aphase transition with latent heat at ambient temperature, usually associated with an order-disorder transition of thehydrocarbonic chains. The properties of non-dissociating lipids in solution, such as DPPC, have been extensivelystudied, both from the experimental, as well as from the theoretical point of view. However, different experimentaltechniques, such as light scattering, calorimetry, conductivity and others, have shown that dissociation, as for DMPG,might lead to a double or multiple transition. We propose a minimal model for the order-disorder transition in thepresence of dissociation, in which adsorption of particles (mimic counter-ions) from the solution favor ordered chains.Chain are described by a two-state model. Three phases are present: two gel phases, one with, the other withoutdissociation, and a fluid dissociated phase. We suggest comparison with the experimental phase diagram.



5.7.43

Statistics of voids in a computer model of the lipid membrane

Vladimir P.Voloshin1,Marina G.Alinchenko2,Aleksey V.Anikeenko3,Nikolai N.Medvedev4 and PalJedlovszky5

1,2,3,4Institute of Chemical Kinetics and Combustion, Novosibirsk, Russia5University of Budapest, Hungary

We present a statistical analysis of intermolecular voids in computer model of a lipid bilayer in water. The voidsare determined as regions of space between molecules accessible for a probe (test particle) of a given size. Characterof the voids depends essentially on the size of a probe: rare separate pores have a place in the case of rather bigprobe, for a very small probe almost entire empty space between molecules is one complex void. Main attention inour work is given to large voids playing a basic role in the process of passive diffusion of small non-charged moleculesin lipid membranes, and to the percolation analysis, to study situations in which a probe be able to pass through themodel. The Voronoi-Delaunay method, generalized to work with molecular systems (ensembles of spheres of differentsize with partial overlapping), is applied for delimitation of voids. The basic geometrical construction of the methodis the Voronoi S-tessellation, where the Voronoi cells are defined as regions of space the nearest to the surface ofa given object in the system. (In the case of spheres it is the known additively weighted Voronoi diagram). Thistessellation defines also a dual construction consisting of the Delaunay S-simplexes, which define elementary cavitiesbetween atoms. Connectivity between them is determined with help of the Voronoi S-network. The analysis of voidsis discussed as a percolation problem on the Voronoi S-network. A site of the Voronoi S-network is colored if radiusof a probe does not exceed the value of radius of the interstitial sphere centered on the given site. This empty sphereis inscribed between atoms of the corresponding Delaunay S-simplex. The bond between neighboring sites is coloringif the radius of a probe does not exceed the value of bottle-neck radius between the sites. Any cluster of colored sitesand bonds corresponds to a void accessible for a used probe. The volume of a void is the sum of empty volumes of theDelaunay S-simplexes which consist in the cluster. Morphology of the cluster defines a shape of the corresponding void.Volumes, lengths, radii and measure of sphericity were calculated for the obtained voids. Orientation of voids was alsodetermined and average cosine of the angle between axis void and normal to the bilayer was calculated. As the lipidbilayer is essentially inhomogeneous along the perpendicular to its plane, the profiles of the average characteristics ofvoids were calculated. Significant difference of percolation thresholds across and along bilayer was shown. Criticalradii of probe for percolation in these directions were obtained.



5.7.44

Effective Charge of Polyelectrolyses Close to Precipitation

D. Vollmer1,R. Deen2,N. Volk3 and M. Schmidt4

1Max Planck Institute for Polymer Research, Mainz, Germany2,3,4Inst. of Phys. Chemistry, Univ. of Mainz, Germany

The behaviour of polyelectrolytes close to precipitation is investigated by conductivity, light scattering and calorimetry.Especially, the effective charge f of a polyelectrolyte close to precipitation is determined. As expected on theoreticalgrounds (Manning condensation) the effective charge depends on temperature and salt. Surprisingly however, wefound that f strongly decreases with increasing salt concentration, and can be up to a factor of five below the valueaccording to Manning condensation. By mixing two solvents we could show that f also shows a pronounced dependenceon solvent quality.

[email protected]

5.7.45

Mesoscopic Behaviors of Nano-Structured Membranes

Yoshitake Yamazaki1, Zhong-can Ou-Yang2, Kunquan Lu3, Dianhong Shen4, Xing Xhu5, andHerbert Gleiter6

1 Institute of Physics, CAS, Beijing, China, ITP, Phys.Peking Univ., Beijing, China2,3,4 Institute of Theoretical Physics, CAS, Beijing, China

5 Physics, Peking University, Beijing, China6 Institute of Nanotechnology, FZK, Karlsruhe, Germany

Nano-structured membranes are supposed to be a non-equilibrium system, consisting of a lot of nano-sized sub-membranes of local equilibrium states. Characteristic properties of each sub-membrane are discussed: Mesoscopicphase transitions to flat-like, crumpled-like and tubule-like phases together with glass-like phases are derived, andtheir mesoscopic critical behaviors are discussed by mean field and renormalization theories.



5.7.46

Overcharging in Colloids with Multivalent Ions

Salete Pianegonda1,Yan Levin2 and Marcia C. Barbosa3

1,2,3Instituto de Fsica, Universidade Federal do Rio Grande do Sul,Caixa Postal 15051, 91501-970, Porto Alegre, RS,Brazil

We study the effect of charge renormalization and electrolyte association in a dilute solution of charged colloids andmonovalent and trivalent salt. We take into account the association between the mono and multivalent salt particlesin order to find the resulting distribution of free ions. These free ions might associate to the colloid renormalizingits charge. We find the number of mono and trivalent electrolytes that are actually associated to the colloid. Thisnumber is lower than the one expected when the association between the mono and trivalent electrolytes is not takeninto account


5.7.47

Wetting properties of a hard-spherocylinder fluid on a model substrate

Daniel de las Heras1,Luis Mederos2 and Enrique Velasco3

1,3 Departamento de Fısica Teorica de la Materia Condensada. Universidad Autonoma de Madrid. E-28049 Madrid.Espana

2 Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Cientıficas. E-28049 Madrid. Espana

A density-functional theory is used to analyze the wetting properties of a hard spherocylinder fluid on a modelsubstrate. The substrate imposes an exclusion boundary condition over the molecular center of mass, while at thesame time favoring a molecular orientation, either parallel or perpendicular to the wall, in a region next to thesubstrate. We have found an extremely rich phenomenology: as the strength with which the substrate orients themolecules is increased, wetting by nematic phase is followed by partial wetting which then leads to reentrant wettingby nematic. Also , in the region of partial wetting, an anchoring transition and a metastable wetting by isotropicphase is also obtained.



5.7.48

Bulk inhomogeneous phases of anisotropic particles: A fundamentalmeasure functional study of the restricted orientations model

Yuri Martınez-Raton1

1 Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matematicas, Universidad Carlos III deMadrid, Avenida de la Universidad 30, E-28911, Leganes, Madrid, Spain

The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) iscalculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studiedthrough minimization of the fundamental measure functional (FMF) of hard parallelepipeds. As a result a rich phasebehavior is obtained which include, apart from the usual liquid crystal phases, a very peculiar phase (called discoticsmectic) which was already found in the only existing simulation of the model, and which turns out to be stablebecause of the restrictions imposed on the orientations. The phase diagram is compared at a qualitative level withsimulation results of other anisotropic particle systems.

[email protected]



5.8.1

Structure, Dynamics and Energetics of Water in Aqueous MicellarSolutions

Subrata Pal1, Sundaram Balasubramanian2 and Biman Bagchi3

1,3 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore - 5600122 Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre of Advanced Scientific Research, Bangalore -

560064

Water, inevitably present at the surface of biological macromolecules and self-organized assemblies, plays a critical rolein the structure, stability and function of these systems. The unique features of a macromolecule and water as a solventmake the issue of solvation unconventional, with question about the static versus dynamic nature of hydration andthe physics of orientational and the translational diffusion at the boundary. The structure, energetics, and dynamicsof the interfacial water molecules in the aqueous micelle and protein have been investigated using large-scale very longatomistic molecular dynamics simulation. The simulation shows that the water molecules at the interface fall into twobroad categories, bound (by hydrogen bond) and free. The environment around interfacial water molecules is moreordered than that in bulk and exhibit markedly slower dynamics. The life time of the hydrogen bond between a polarhead group and water molecule is found to be much longer than that between two water molecules. A significant blueshift in the librational band of the interfacial water molecules is also observed. The study of solvation dynamics of anatural probe in the hydration layer is found to undergo a remarkable slow down in agreement with the experimentalobservation. The above study have been extended to explore protein hydration dynamics.




Influence of Hydrogen Bonding Interactions on Interfacial Properties

SJ Suresh1 and VM Naik2

1,2 Unilever Research, Hindustan Lever Research Centre, 64 Main Rd., Whitefield, Bangalore 560066, India

Only a few examples are needed to illustrate the broad application of the principles of hydrogen bonding. Theyare principally responsible for the determination of structures of many organic and inorganic crystals, stabilizationof structures of proteins, self-assembly of amphiphilic molecules in water, and, in-fact, all physical and chemicalproperties of water that make it possible for life itself to evolve and exist. As Pimental pointed out, it is hardly anexaggeration to say that in the chemistry of living systems, the H-bond is as important as the carbon-carbon bond.Owing to this importance, hundreds of papers have appeared in the past on various aspects of H-bonding, suchas H-bonding in solids, theory of H-bonding, reaction kinetics in H-bonded solvent systems, application of variousspectroscopic techniques to H-bonded systems and ab initio quantum calculations on H-bonded systems. Of particularinterest to this presentation is one of the rather poorly understood subjects, namely the role of hydrogen bonding oninterfacial properties, an understanding of which could be extremely useful in dealing with several industrial processessuch as mineral floatation and oil recovery, and while developing products of practical value, such as detergents andpaints. The presentation will comprise of two parts: a) A brief overview of our theoretical contributions to this areaover the past few years (Refs. 1-9), b) Progress we have made in more recent times on the modelling of dielectricbehavior of hydrogen bonding liquids in the interfacial region.

References :[1] SJ Suresh and VM Naik, Langmuir, 12, 6151 (1996)[2] SJ Suresh and VM Naik, Langmuir, 13, 4785 (1997)[3] SJ Suresh and VM Naik, J. Chem. Phys., 109, 6021 (1998)[4] SJ Suresh, CP Patni and M Mishra, J. Coll. Int. Sci., 210, 225 (1999)[5] SJ Suresh and VM Naik, J. Chem. Phys., 111, 10389 (1999)[6] SJ Suresh and VM Naik, J. Chem. Phys., 113, 9727 (2000)[7] SJ Suresh, Encyclopedia of Surface and Colloid Science, Pub: Marcel Dekker, New York (2002)[8] SJ Suresh and VM Naik, J. Chem. Phys., 116, 4212 (2002)[9] SJ Suresh, J. Phys. Chem. B, 108, 715 (2004).



5.8.4

Chaotic and Regular Motion of Sorbates in Carbon Nanotubes : SizeDependence

Bhide S.Y.1, S. Yashonath2 and G. Ananthakrishna3

1,2 SSCU,IISc,Bangalore3 MRC, IISc, Bangalore

Transport properties of spherical sorbate molecules of various sizes in carbon nanotubes are investigated using molec-ular dynamics simulations. Our studies show a diffusive behavior at small sizes crossing over to ballistic nature as thesize becomes comparable to the diameter of the nanotubes. In order to understand this, we have carried out Hamil-tonian dynamics of single sorbate molecules as well. Interestingly, we find that Hamiltonian dynamics contributessignificantly to the transport properties at all sizes. At small sizes the motion is chaotic which is supported by theexistence of a positive Lyapunov exponent while at large sizes the motion is ballistic.


5.8.5

Pressure of a fluid confined in a random porous medium

W. Dong1, X. S. Chen2 and W. M. Zheng3

1 Laboratoire de Chimie, Ecole Normale Superieure de Lyon, 46, Allee d Italie, 69364 Lyon Cedex 07, France2,3 Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China

The derivation of the statistical-mechanics expression for the pressure of a fluid confined in a random porous mediumhas not been a straightforward task. The virial expression first derived by Madden [1] has been shown to be erroneoussince it does not give the correct result for an ideal gas in a hard sphere matrix [2]. From the mechanical definition(force balance equation), Dong derived an expression for mechanical pressure [3]. From the thermodynamic definition(partial derivative of free energy with respect to volume), Kierlik et al derived an expression for thermodynamicpressure and found it is not identical to the mechanical pressure [4]. The expression obtained by Kierlik et al is such acomplex one that it does not even allow one to use it in simulations for calculating the thermodynamic pressure. Theorigin of this difficulty is that Kierlik et al derived in fact an partial differential equation which should be satisfiedby the thermodynamic pressure rather than a virial euqation of the pressure. We present here a bona fide virialequation for the thermodynamic pressure which can be easily used in simulations and discuss in details its relation tothe expression derived by Kierlik et al and some open questions. [1] W.G. Madden, J. Chem. Phys. 96, 5422, (1992).[2] M.L. Rosinberg, G. Tarjus and G. Stell, J. Chem. Phys. 100, 5172, (1994). [3] W. Dong, J. Chem. Phys. 102,6570, (1995). [4] E. Kierlik, M.L. Rosinberg, G. Tarjus and P. Monson, J. Chem. Phys. 103, 4256, (1995).

1 [email protected]


5.8.6

Adsorption Isotherms Arising from Levy Distributions

F.Brouers1 and O.Sotolongo-Costa2

1 Institut de Physique B5, University of Liege, 4000, Belgium2 Department of theoretical Physics, University of Havana, Cuba

Although it has been used for more than 80 years, the physical interpretation of the power-law adsorption empiricalformula attributed to Freundlich:

θ = Ka

is still far to be understood. In heterogeneous and porous materials, one would like to relate the factor K and theexponent a to the geometric and energetic characteristics of the adsorbing materials. In this communication we showthat using the properties of the one-sided Levy stable distributions, the exponent a can be simply related to thewidth of the adsorption energy distribution and using the principle of maximum entropy applied to the non-expensivegeneralization of the Shannon-Boltzmann entropy, can be naturally related to the Tsallis q non-extensive parameter:a=(2-q)/(q-1).

1 [email protected]

5.8.7

Finite Size Scaling of Depinning Transition in quenched randompotentials

Jin Min Kim1,Changhan Lee2 and Yup Kim3

1,2Dept. of Physics, Soongsil Univ., Dongjak-gu, Seoul 156-743, Korea3Dept. of Physics, Kyunghee Univ., Seoul Korea

We study the pinning-depinning transition of a driven interface specially for the quenched Kardar-Parisi-Zhang (QKPZ)equation. We consider the average velocity of the interface growth as an order parameter and detrmine the values ofvarious critical exponents using a finite size scaling at or near the critical point. The results for both the quenchedEdwards-Wilkinson equation and the quenched Mullin’s equation are also discussed.



5.8.8

Boundary induced crystal-smectic transition in a hard disk system

Debasish Chaudhuri1 and Surajit Sengupta 2

1,2 Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Calcutta - 700098

Studies of small assemblages of molecules with one or more dimensions comparable to a few atomic spacings aresignificant in the context of nano-technology. Here we show that small size and hard constraints can produce essen-tially new phenomena without a counterpart in the bulk system. We report results of computer simulations of thesimplest possible, nontrivial, molecular system, namely, two-dimensional hard disk “atoms” confined within a quasione-dimensional channel. Bulk hard disks in two dimensions are known to melt from a high density triangular latticeto an isotropic liquid with a narrow intervening hexatic phase. In contrast, for channel widths of a few atomic spacings,we find evidence for a smectic phase which nucleates as well-defined bands within the solid demarcated by equilibriumsolid-smectic interfaces. The smectic phase arises when the size of the system in the direction parallel to the fixed wallsis increased. A crystal to smectic transition, though predicted for anisotropic molecules is extremely unusual for harddisks – the anisotropy in this case arising purely from the confined geometry. Our results may be directly verified inexperiments on sterically stabilized “hard sphere” colloids confined in glass channels and for similarly confined atomicsystems.


5.8.9

Wetting at curved substrates: Non-analytic behavior of interfacialproperties

M. Thomas1, R. Roth2 and R. Evans3

1,3 H.H. Wills Physics Laboratory, University of Bristol, BS8 1TL Bristol, UK2 MPI fuer Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany

Interfacial properties of fluids adsorbed on substrates are studied with increasing effort both experimentally andtheoretically. From these studies it is evident that the geometry of the substrate has a profound influence on thenature of fluid adsorption, in particular whenever wetting phenomena are considered. We present an extensive studyof interfacial properties of a fluid adsorbed on hard curved substrates where complete wetting by the gas (drying)occurs. To this end we consider both short-ranged and long-ranged (Van der Waals) fluid-fluid interactions. In bothcases we argue, using an effective binding potential picture, that the wall-fluid surface tension and the density ofthe fluid at contact acquire contributions non-analytic in 1/R, where R is the radius of curvature. The nature ofthe non-analyticities is very different for the two types of interactions. Our predictions are in excellent agreementwith numerical results from fully microscopic density functional theory calculations. Our results have importantrepercussions for the solvation of big solvophobic solute particles.



5.8.10

Properties of the Liquid-Vapor Interface

Jose Gpe. Segovia1 and Victor Romero-Rochin2

1fisica teorica, Division Academica de Ciencias Basicas, Universidad Juarez Autonoma de Tabasco, CunduacanTabasco, Mexico

2Sistemas Complejos, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico D. F. , Mexico

We use the density funtional theory, for the route of stress tensor,to study the surface properties of the curvedliquid-vapor interface.We obtain the microscopic expresisions for the surface tension, thespontaneous curvature, andthe rigidity constants of bending, and of Gaussian curvature. Additionally is found a expression of the location ofthe Gibbs dividing surface. The rigidity constants of bending, and the rigidity constant of Gaussian Curvature, arenegatives

[email protected]@fisica.unam.mx

5.8.11

Bifurcation of Coverage in the Condensation-Evaporation Problem withRepelling Particles

Sujata Tarafdar1,Nikolai I. Lebovka2, and Tapati Dutta3

1Condensed Matter Physics Research Centre, Physics Department, Jadavpur University,Kolkata 700032, India.2F. D. Ovcharenko Biocolloid Chemistry Institute 42, Vernadsky Av., Kyiv, Ukraine

3Physics Department, St. Xavier’s College Kolkata 700016, India

This work reports a simplified algorithm for study of condensation and evaporation of particles which repel each other.Two cases are considered (1) with a mobile two-dimensional adsorbed layer and (2) with an immobile layer. Case (1)is studied analytically as well as by computer simulation and (2) only by computer simulation. Different results areobtained for the mobile and the immobile surface layers. However, the coverage for the steady state shows a bifurcaionleading to a two point limit cycle for high temperature and low pressure in both cases. Here the coverage oscillatesbetween a high and a low value without ever reaching a steady state. The results for the immobile case depend inaddition on the initial coverage.



5.8.12

Unbending transition and substrate-shape for critical wettingtransitions.

Carlos Rascon1 and Andrew O. Parry2

1 Dept of Mathematics, Universidad Carlos III de Madrid, Spain2 Dept of Mathematics, Imperial College London, United Kingdom

Adsorption of fluids in geometrically structured substrates gives rise to new phenomena which are absent on planarsubstrates (of identical chemical composition). This occurs for corrugated walls that are periodic in one directionand translationally invariant along the other. The adsorption properties of these substrates depart progressivelyfrom those of the planar case as the amplitude of the corrugation increases and can result in completely differentphenomena. For a periodic substrate with a sinusoidal shape, for example, sufficientely large amplitudes produce afirst-order surface phase transition, known as ”unbending”, corresponding to surface condensation-like discontinuitiesin adsorption isotherms. Intriguingly, unbending is absent if the periodic corrugation is linear (a periodic array oflinear wedges). Here, we show that the presence of unbending for periodic corrugated substrates is related to theadsorption properties of single infinite wedges. For these, the linear wedge is a marginal case that separates wedgesthat are asymptotically flat (for which unbending is absent) from those asymptotically divergent (for which unbendingoccurs). We include numerical results and model calculations that illustrate that the range of the intermolecular forcesplays no role in this discussion.


5.8.13

Model macroions solution confined by a semipermeable chargedmembrane

Marcelo Lozada-Cassou1 and Felipe Jimenez-Angeles2

1,2 Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo. Lazaro Cardenas No. 152, C.P. 07730,Mexico D.F., Mexico

We study a model for macroions in an electrolyte solution, confined by a semipermeable membrane. The membranefinite thickness is considered and both membrane surfaces are uniformly charged. The model explicitly includeselectrostatic and size particles correlations. Our study is focused on the adsorption of macroions on the membranesurface and on the osmotic pressure. Concerning the adsorption phenomena we exhibit a new class of overcharging,which refers to the adsorption of an effective charge onto a like charged wall. In addition, macroions produce surfacecharge reversal, charge inversion and layering. It is argued that electrostatic and the steric repulsive interactions giverise to depletion forces which produce macroions adsorption, even if the wall or the macroparticle are uncharged or ifthe wall and macroions are like-charged. Across this talk it is discussed the agreement of our results with computersimulations and with experimental results. The theoretical prediction for the osmotic pressure shows a good agreementwith experimental results.



5.8.14

Study of layering structures at free liquid surfaces with DensityFunctional theories

Ramiro Checa1, Enrique Chacon2 and Pedro Tarazona3

1,3 Dep. Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, E-28049 Madrid, Spain2 Instituto de Ciencias de Materiales de Madrid, CSIC, E-28049 Madrid, Spain

We analyze using Density Functional theories the liquid-vapor interface of several simple fluids with a pairwise in-teraction that reproduce similar values for ratio Tt/Tc same as the experimental values of metals like Hg or Ga. Wefind that the principal factor to get layering structures could be a low melting temperature as in previous results ofMC simulations. We explore two generic questions about layering in the density profiles of our models: the relevanceof Fisher-Widom line and the role of capillary waves on the nature of interface that we obtain with two differentsdensity functional approximations (WDA and FMT).We conclude that it is necessary to interpret the density profilesas intrinsic density profiles.


5.9 Topic 9 : Quantum-mechanical problems (quantum phase tran-sitions; strongly correlated fermions; Bose-Einstein condensation;mesoscopic quantum phenomena, etc.)

5.9.1

Localization of quantum walks on a square lattice

Norio Inui1, Norio Konno2 and Yoshinao Konishi3

1,3 2167, Shosha, Himeji, Hyogo, 671-2201, Japan2 79-5 Tokiwadai, Yokohama, 240-8501, Japan

The two-dimensional quantum walks are closely related to the search algorithm on a quantum computer and thedistribution of the walker has been studied. The Grovers walk is one of the typical discrete time quantum walks,however, the distribution is striking different from other types of quantum walks. The Grover walk starting from afixed point is localized near the starting point. In the present talk, the distribution of the Grover walk is analyticallygiven and the reason why the walker who moves according to the degree-four Grover’s operator can remain at thestarting point with a high probability is explained. The key factor for the localization is due to the degenerationof eigenvalues of the time evolution operator, and the global time evolution of the quantum walk on a large latticeis mainly determined by the degree of degeneration. The dependence of the localization on the initial state is alsoconsidered.



5.9.2

Thermodynamic properties and thermal correlation lengths of aHubbard model with bond-charge interaction

Andreas Schadschneider1 and Andreas Kemper2

1,2 Institut fur Theoretische Physik, Universitat zu Koln, 50937 Koln, Germany

We investigate the thermodynamics of a one-dimensional Hubbard model with bond-charge interaction X usingthe transfer matrix renormalization group method (TMRG). Numerical results for various quantities like spin andcharge susceptibilities, particle densities, specific heat and thermal correlation lengths are presented and discussed.We compare our data also to results for the exactly solvable case X/t = 1 as well as to bosonisation results forweak coupling X/t ¿ 1, which shows excellent agreement. We confirm the existence of a Tomonaga-Luttinger anda Luther-Emery liquid phase, in agreement with previous studies at zero temperature. Thermal singlet-pair corre-lation lengths are shown to dominate density and spin correlations for finite temperatures in certain parameter regimes.

Reference : [1] A. Kemper, A. Schadschneider: Phys. Rev. B68, 235102 (2003)


5.9.3

Effect of disorder on interacting Bosons and Femions in optical lattices

Dariush Heidarian1 and Nandini Trivedi2

1,2 Dept. of Theoretical Physics, Tata Institute of Fundamental Research, Colaba, Mumbai 400 005, India

We find that a Bose-Einstein condensate in an optical lattice and a confining harmonic potential shows a layered struc-ture of alternating superfluid and Mott regions. An impurity at the center of the trap generates oscillatory behaviorin the order parameter as a function of the impurity strength. Attractive and repulsive impurities show distinctivelydifferent behavior. Interacting fermions in an optical lattice at half filling have a Mott gap and antiferromagneticlong range order AFLRO. A strong impurity closes the gap but the AFLRO persists. In the presence of intermediaterandom on-site disorder we further find a novel inhomogeneous metallic phase.



5.9.4

Magnetic properties of a helical spin chain with alternating isotropicand anisotropic spins: magnetization plateaus and finite entropy

V. Ravi Chandra1, S. Ramasesha2 and Diptiman Sen3

1,3 Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560012, India2 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India

We study a model which could explain some of the unusual magnetic properties observed for the one-dimensionalhelical spin system Co(hfac)2NITPhOMe. One of the properties observed is that the magnetization shows plateausnear zero and near one-third of the saturation value if a magnetic field is applied along the helical axis, but not ifthe field is applied in the plane perpendicular to that axis. The system consists of a spin-1/2 chain in which cobaltions (which are highly anisotropic with an easy axis ei) and organic radicals (which are isotropic) alternate with eachother. The easy axis of the cobalts ei lie at an angle θi with respect to the helical axis, while the projection of ei+1−ei

on the plane perpendicular to the helical axis is given by 2π/3. For temperatures and magnetic fields which are muchsmaller than the coupling between the nearest-neighbor cobalts and radicals, one can integrate out the radicals toobtain an Ising model for the cobalts; this enables one to compute the thermodynamic properties of the system usingthe transfer matrix approach. We consider a model in which the tilt angles θi are allowed to vary with i with periodthree; we find that for certain patterns of θi, the system shows the magnetization plateaus mentioned above. At theends of the plateaus, the entropy is finite even at very low temperatures while the magnetic susceptibility and specificheat also show some interesting features.


5.9.5

Study of orbital ordering in undoped manganites using Jahn-Tellerinteraction

Sudhakar Yarlagadda1 and Manidipa Mitra2

1 Saha Institute of Nuclear Physics, Calcutta, India2 S. N. Bose National Center for Basic Sciences, Calcutta, India

To understand the orbital ordering of LaMnO3 in the ground state, we study it in the A-type spin antiferromagneticstate. We calculate the two-dimensional response functions associated with the Jahn-Teller Q2 and Q3 distortions andfind that they diverge at the wavevector (π,π). Furthermore, the Q2 response function diverges faster which indicatesthat perhaps the ordering of the orbitals at low temperatures is dominated by the Q2 distortion. We calculate theground state energy for the cases when only one of the Q2 and Q3 modes is excited cooperatively and find that theQ2 excited state yields lower energy.



5.9.6

Persistent current in mesoscopic Hubbard rings of ordered binary alloys

Santanu Kumar Maiti1, Jayeeta Chowdhury2 and Sachindra Nath Karmakar3

1,2,3 Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700 064, India

We present exact calculation of persistent currents in small ordered binary metal rings threaded by magnetic flux φ.In the absence of any electron-electron correlation, the persistent current in normal metal rings exhibit a saw-toothbehavior with φ0 flux periodicity, φ0 = ch/e being the elementary flux quantum. The electron-electron interactiondrastically changes this saw-tooth shape, and produces interesting kink-like structures in the persistent current. Quitesurprisingly we observe that in some cases, the current inside the kinks become independent of the Hubbard correlation.In ordered binary alloy rings above quarter filling, we observe an initial increase in current for low values of interaction,and, then get back the usual decrease of current with the increase of interaction. On the other hand, these systemsalways exhibit a decrease in current with interaction at quarter filling and also below quarter filling. Another importantobservation is that the singular behavior of persistent current disappears due to interaction in the half-filled systemswith even number of electrons. For the half-filled systems, the mobility of electrons drops to zero with interaction,and it converges to a constant value in the non-half-filled case.


5.9.7

Global quantum entanglement in the transverse Ising model

Tzu-Chieh Wei1, Dyutiman Das2, Swagatam Mukhopadhyay3, Smitha Vishveshwara4, and Paul M.Goldbart5

1,2,3,4,5 Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, U.S.A.

Entanglement measures have recently been applied to spin models that exhibit quantum phase transitions at zerotemperature. However, the measures invoked in these discussions are essentially bipartite: they quantify the entan-glement either between pairs of spins or between a subsystem and the remainder of the system. Here, we invokea recently-developed global measure, capable of quantifying entanglement of states as a whole, and apply it to theground-state of the transverse Ising model. Along the way, we explore the relationship between quantum correlations,which become pronounced close to the transition, and global entanglement.



5.9.8

Quantum phase transition in quantum Hall system

B. Karmakar1, M. R. Gokhale2, A. P. Shah3, B. M. Arora4, L. A. Ponomarenko5, D. T. N. deLang6, A. de Visser7 and A. M. M. Pruisken8

1,2,3,4 Tata Institute of Fundamental Research, Mumbai 400005, India.5,6,7 Van der Waals-Zeeman Institute, University of Amsterdam, The Netherlands.

8 Institute of Theoretical Physics, University of Amsterdam, The Netherlands.

There is currently considerable interest in accurately determining the nature of plateau-plateau (PP) and plateau-insulator (PI) phase transition in quantum Hall system. Each of these transitions occurs as the corresponding Landaulevel crosses the Fermi energy with the increase of magnetic field. Width of the Landau level ν0 scales algebraicallywith temperature as T k, where k is the critical exponent. At a PP transition, width of longitudinal resistance ∆B andinverse of maximum slope of Hall resistance (dρxy/dB)−1

max vary with temperature as T k at the lowest temperature.In the PI transition the longitudinal resistance ρxx varies exponentially as exp[−(ν − νc)/ν0(T )], where ν is fillingfraction and νc is the critical filling of the spin split lowest Landau level. The universality of the quantum criticalityproposed by Pruisken[1] predicts that the critical exponent k is same for all PP and PI transitions. The value of kwas first measured 0.42 from PP transitions by Wei et al.[2] from InGaAs/InP hetrostructure. However, there is aconsiderable debate about the universality of k arising mainly from the experimental investigations on the differentmaterial systems[3]. There is a realization that sample inhomogeneities complicate the study of quantum criticality,much more so for the PP transition compared to the PI transition[4]. Recent experiment on PI transition suggests[5]k = 0.57. We have carried out measurements on a modulation doped near ideal InP/InGaAs/InP quantum wellsample. The values of exponents (i) k for 2 → 1 PP transition is obtained 0.58 and (ii) that for PI transition 0.68.Details of the investigation will be reported in the poster.

References :[1] A. M. M. Pruisken, Phys. Rev. Lett. 61, 1297 (1988).[2] H. P. Wei et al. Phys. Rev. Lett. 61, 1294 (1988).[3] S. Koch. et al. Phys. Rev. B 43, 6828 (1991); D. Shahar et al. Solid State Commun. 107, 19 (1998).[4] B. Karmakar et al. Comd-mat/0309694.[5] D. T. N. de Lang et al. Physica E 12, 666 (2002).



5.9.9

Rb clusters in anisotropic traps: ground and finite temperatureproperties

Sumita Datta1

1 S. N. Bose National Centre for Basic Sciences, Block JD Sector III, Salt Lake, Kolkata 700 098, West Bengal

We study the ground and finite temperature properties of Rb clusters in a tight harmonic trap in connection with BoseEinstein Condensation. They behave as new quantum fluids (a gas in the dilute limit and a liquid in the dense limit)and we study their many body physics within the realistic potential model (LJ or Morse type), by diffusion MonteCarlo method namely Generalized Feynman Kac path integration. Our goal is to explain the temperature dependenceof frequencies and damping rate.

1 [email protected]

5.9.10

The Casimir Effect in Carbon Nanotubes

Pier Giuseppe Gabrielli1 and Simone Gabrielli2

1 Unit Materiali Centro Ricerche Casaccia ENEA2 Physics Department Universit di Roma LaSapienza

When separations between objects are small enough, certain quantum effects become manifestly significant: theCasimir effect, for example, is the force between two solid objects that arises from quantum fluctuations in the groundstate energy of the electromagnetic field. Fixing the ends of a slightly stretched carbon nanotube on a microdevice inproximity of and parallel to a rigid flat plate, due to Casimir forces, nanotube deflects, deflection strongly dependingon the separation of nanotube and surface and on the geometry. Since single-wall carbon nanotubes (SWNT) arepredicted to be metallic or semiconducting depending on their diameter and the helicity, Casimir effect could changediameter and/or the helicity and would be possible to modulate their electronic properties . The strength of Casimirforces and the changes of some properties of SWNT are discussed.


5.9.11

BCS-BEC crossover at T = 0: A Dynamical Mean Field TheoryApproach

Arti Garg1, H.R.Krishnamurthy2 and Mohit Randeria3

1,3 Dept. of Theoretical Physics, T.I.F.R, Colaba, Mumbai-400 005, India2 Dept. of Physics, I.I.Sc., Banglore, India

The crossover from BCS pairing to Bose-Einstein condensation is a problem of great interest in diverse contexts,ranging from short coherence length superconductors to pairing in trapped Fermi gases. It has generally been thoughtthat a Hartree-Fock-Bogoliubov mean field theory (MFT) is adequate to describe this crossover in the broken symmetryphase. In order to examine the validity of simple MFT and explore physics beyond it, we study the effects of quantumfluctuations at T = 0 using the Dynamical MFT approach using iterated perturbation theory as the impurity solver.We find that, for the attractive Hubbard model in the intermediate coupling regime, quantum fluctuations lead tolarge quantitative effects resulting in a reduction of both the superconducting order parameter and energy gap. Aqualitative change is found in the single-electron spectral function which shows incoherent spectral weight for energieslarger than three times the gap, in addition to the usual Bogoliubov quasiparticles.


5.9.12

Dielectric Critical Behaviour at Metal-Insulator transition underLattice Compression

S. K. Shukla1, N. N. Shukla2, R. Prasad3 and D. Kumar4

1,2,3 Department of Physics, Indian Institute of Technology, Kanpur-208016, India4 School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India

We present a scaling theory of metal-insulator transition which is based on the critical behaviour of dielectric constantand conductivity. The theory is applied to study the continuous metal-insulator transition in crystalline CesiumIodide under change of lattice parameter. The ab-initio calculations of band structure and various quantities relatedto dielectric response in the transition regime are performed. Specifically, we have calculated the conductivity andscreening length on the metallic side, and frequency-dependent dielectric constant and the band gap on the insulatingside. These calculations allow us to establish the power-law singularities of various quantities on two sides of thetransition. The critical behaviour is analysed by applying the scaling principle to the wavevector and frequencydependent dielectric function.



5.9.13

New Statistical Theory of Superconductivity and Superfluidity

Manuel de Llano1

1 Instituto de Investigaciones en Materiales - UNAM - Mexico City, Mexico

By recognizing the vital importance of two-hole Cooper pairs in a many-electron (or a many-fermion system in general)the concept of pairing is re-examined in a Bethe-Salpeter equation approach with striking conclusions. Ideal-Fermi-gas-based pairs are unstable but become finite-lifetime resonances when based on the BCS ground-state Fermi sea.Moreover, they possess a linear (as opposed to quadratic) dispersion relation. This enables Bose-Einstein condensation(BEC) to occur in precisely all dimensionalities d where superconductors have been found, namely, for d greater thanunity. A general statistical theory is then discussed for superconductors (and for neutral-fermion superfluids, suchas trapped ultra-cold Fermi atoms), which boils down to a BEC theory. This new theory, complete in that it doesnot ignore two-hole pairs, reduces to all the old known continuum statistical theories, such as the BCS theory. Onthe practical side, the complete theory provides substantially higher transition temperatures, with no adjustableparameters, than BCS theory itself under the same inter-fermionic interactions. It also suggests an explanation of themysterious role played by holes in all superconductors. Collaborators: J. Batle, M. Casas, M. Fortes, F.J. Sevilla andV.V. Tolmachev.

1 [email protected]

5.9.14

Electron delocalization in disordered films induced by temperature,magnetic field and film thickness

R. K. Brojen Singh1 and Deepak Kumar2

1 Institut fur Physik, Technische Universitat, D-09107 Chemnitz, Germany2 School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India

We have studied the delocalization transition of non-interacting electrons in disordered thin films induced by tem-perature, magnetic field and film thickness. We also report results for two-dimensional systems. We have used forthis purpose (i) a numerical technique based on transfer matrix method for quasi one-dimensional systems; (ii) self-consistent theory of localization for weak fields generalized to situations lacking time-reversal invariance. Numericalresults provide strong evidence for a zero-temperature insulator to metal transition (MIT) with both field and filmthickness. In self-consistent theory we discuss two procedures which give different results on MIT induced by field,temperature and thickness. The role of temperature is considered through the phase decoherence length.



5.9.15

Semiclassical Asymptotics for the Dirac-Maxwell System

Peter Alexander Markowich1 and Christof Sparber2

1,2 Department of Mathematics, University of Vienna, Austria

We study the coupled Maxwell-Dirac system from a semiclassical point of view.A rigorous WKB-analysis, locally intime, is performed for small solutions (of the order of magnitude sqrt(eps), where the semiclassical parameter eps is themicroscopic/macroscopic scale ratio. The main technique is an adaptation of weakly nonlinear dispersive geometricaloptics, a main difficulty lies in dealing with the well-known zitterbewegung,


5.9.16

Chaotic scattering of waves and particles in the cosine billiard. Theoryvs. Experiment

German A. Luna-Acosta1, U. Kuhl2, J.A. Mendez-Bermudez3 and H.-J. Stockmann4

1 Instituto de Fisica, U.A.P., Puebla, Apdo. postal J-48, Puebla, Pue. 72570, Mexico2,4 Fachbereich Physik der Philipps Universitat,Renthof 5, D-35032 Marburg, Germany3 Max Planck Institute fur Stromungsforschung, Bunsenstrasse 10, D-37073, Gottingen

We study theoretically and experimentally dynamical and transport properties of waves scattering within the cosinebilliard. We use the classical counterparts of the scattering probability matrix and wave functions, as well as Husimidistribution to study theoretically the quantum-classical correspondence for the cases of full and mixed chaotic mo-tion.[1] The billiard is realized experimentally as a 2D microwave billiard, where the electro-magnetic field is governedby the Helmholtz equation, mathematically equivalent to the Schrdinger equation. The experiments show evidence ofthe main features predicted by theory, e.g., scattering scars, and quasi bound states trapped in resonance islands inphase space. However, the experiment shows that the theoretical model must be refined to include emission of circularwaves and finite leads in order to have closer agreement.[1] G.A. Luna-Acosta, J.A. Mendez-Bermudez, and P. Seba, Phys. Rev. E, Vol.66 (2002) 046207.



5.9.17

Simple and universal semiclassical approximation of quantum fidelity

Jiri Vanicek1

1 Pitzer Center for Theoretical Chemistry, U. of California, Berkeley, USA

Many phenomena in physics can be expressed in terms of so-called fidelity: an overlap at time t between initiallyidentical states propagated with slightly different Hamiltonians. We present a numerically feasible simple and universalsemiclassical method to evaluate quantum fidelity (Loschmidt echo) in classically chaotic, quasiintegrable, and evenmixed systems. It was thought that such evaluation would be intractable, but instead we show that a uniformsemiclassical expression not only is tractable but it gives remarkably accurate numerical results. Besided containingthe Fermi-golden-rule and Lyapunov regimes of fidelity decay in chaotic systems and the gaussian and algebraic regimesin quasiintegrable systems, it follows the detailed features of fidelity. Remarkably, our approach explicitly contains the“building blocks” of analytical theories of recent literature, and thus permits a direct test of the approximations madeby other authors in these regimes, rather than an a posteriori comparison with numerical results. Our semiclassicalmethod works for pure states as well as mixed. Using a simple dephasing picture, the four qualitatively differentregimes follow immediately from the statistics of classical action which we demonstrate numerically. Interestingly, thepresent approximation provides a bridge between the semiclassical Van Vleck and quantum Feynman propagator.

1 [email protected]

5.9.18

Limit temperature for entanglement in generalized statistics

Norma Canosa1 and Raul Rossignoli2

1,2 Departamento de Fisica, Universidad Nacional de La Plata CC 67 (1900) La Plata, Argentina

We examine the main properties of generalized thermal states derived from general non-additive entropic forms andtheir application to quantum entanglement. It is shown that all these states become more mixed as the temperatureincreases, approaching the full random state for T → ∞. The formalism is then applied to investigate the limittemperature for entanglement in a two-qubit XXZ Heisenberg chain, which is independent of the applied magneticfield in the conventional von Neumann based statistics. In contrast, this temperature is shown to be field dependentin a generalized statistics, even for small deviations from the standard form. Results for the Tsallis-based statisticsare analyzed in detail.



5.9.19

Quantum Walk and Dissipation in a Ring

Takashi Oka1, Norio Konno2, Ryotaro Arita3 and Hideo Aoki4

1,3,4 Department of Physics, University of Tokyo, Hongo, Tokyo, Japan2 Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya-ku,

Yokohama, Japan

The quantum origin of dissipation has been of a long-standing interest. Specifically, nonlinear electron transportproperties driven by external electric fields in a ring geometry have been a testing ground for many novel ideas[1-3].The dissipation has been discussed in terms of successive Landau-Zener quantum tunneling processes caused by thedisorder due to impurities[1-2] or the electron-electron interaction[3]. Here, we study a model for a mesoscopic ringwhere we can assign a Landau-Zener transition matrix to each energy gap in the adiabatic spectrum. We have solvedthe problem by mapping it to a problem of a one-dimensional quantum walk with a reflecting boundary, where the en-ergy levels play the role of qubit. By employing the PQRS method[4], we have obtained the generating function for thetransition amplitudes. Transport properties as well as the time evolution of the energy expectation value are discussed.

References :[1] D. Lenstra and W. van Haeringen, Phys. Rev. Lett. 57, 1623 (1986).[2] Y. Gefen and D. J. Thouless, Phys. Rev. Lett. 59, 1752 (1987).[3] T. Oka, R. Arita, and H. Aoki, Phys. Rev. Lett. 91, 66406 (2003).[4] N. Konno, T. Namiki, T. Soshi, and A. Sudbury, J. Phys. A 36, 241 (2003).



5.9.20

Nature of insulating state in NaV2O5 above charge-ordering transition:A LDA+DMFT study

Tanusri Saha-Dasgupta1, I. Dasgupta2, A. I. Lichtenstein3 and V.I.Anisimov4

1 S.N.Bose Natl Centre, Kolkata, India2 IIT Mumbai, Mumbai, India

3 University of Nijmegen, Nijmegen, The Netherlands4 Institute of Metal Physics, Ekaterinburg, Russia

A current route to describing the physical properties of real materials with strongly correlated electrons, is to derive alow-energy Hubbard Hamiltonian using Wannier-functions obtained by a density-functional calculation, and to solveit using many-body techniques like the Dynamical Mean-field Approximation (DMFT). As an example, in the presentstudy, we consider the case of low-dimensional quantum spin system, NaV2O5. The nature of the insulating state inthe quarter-filled ladder compound NaV2O5 is investigated within a cluster dynamical mean-field approach coupledwith LDA. We show that the realistic description of the material is crucial for understanding properties.


5.9.21

Macroscopic Oscillation of Bose Einstein Condensates in harmonic traps

Tapas Kumar Sinha1,Sailesh Mishra2,Pawan Kumar Rawat3

1Computer Centre, Bijni Complex, North Eastern Hill University, Shillong 793 0032Physics Department, St. Edmunds College, North Eastern Hill University,Shillong 793 003 India

3Mathematics Department,St. Edmund

The recent discovery of Bose-Einstein condensates in ultra cold vapors of Li atoms [1] has opened a new field in thestudy of macroscopic quantum phenomena. Macroscopic non linear oscillations have been observed in the condensates.However the exact mechanism still escapes us. We suggest in this paper that excited Li atoms couple energeticallywith the unexcited Li atoms. The excited Li atoms de-excite by giving energy to the un-excited Li atoms. Thisphysical picture is supported by the numerical simulation results of Huepe et. al.[2] Fig. 2. Based on this concept ofenergy interchange between the Li atoms, we have derived coupled NLS equations of motion for the substrate. Thisshould be compared with NLS equation used in [3].We find Soliton solutions by using Hirota’s bilinear method.

References :[1] M.N. Anderson et. al., Science 269,198 (1995);C.C Bradley et. al., Phys. Rev. Lett., 75, 1687 (1995); K. B. Davieet. al., Phys Rev. Lett., 75, 3969 (1995); D. G. Fried et. al., Phys. Rev. Lett., 81, 3811 (1998)[2] C. Huepe et. al., PRA 68, 023609 (2003)[3] Yu. S. Kivshar,T. J. Alexander, and S. K. Turitsyn, Phys. Lett. A 278, 225-230 (2001).[4] R. Hirota, Solitons edited by R.K. Bullough and P. J. Caudrey (Springer, Berlin 1980); Porsezian, Journal ofNonlinear Mathematical Physics V.5, N 2, 126, (1998); M. N. Vinoj and V. C. Kuriakose, Pramana, 57, 987, (2001).

[email protected]



5.10.1 Poster 5.10.1 moved to the Oral Section.5.10.2 Poster 5.10.2 moved to the Oral Section.5.10.3

The time-of-flight signal in a gaussian disordered chain

J. A. Freire1 and M. G. E. da Luz2

1,2 Departamento de Fisica, UFPR, Curitiba, Brazil

We consider a one-dimensional master equation model [1] for the time-of-flight (TOF) experiment performed onan organic disordered material where the charge transport occurs via thermally activated hops between localizedelectronic states. From the model we obtain an expression for the average transit time in terms of the site energies andof the forward hopping rates [2]. In the particular case of a blocking cathode we are able to perform the (gaussian)average over the site energies and to obtain an exact expression for the transit time as a function of the applied fieldand of the variance of the energy distribution. We also obtain numerically the TOF signal I(t) and show that itexhibits two power-law regimes whose exponents do not sum up to 2, as in the time-dependent-random-walk model byScher and Montroll. We investigate the dependence of the exponents with the field and with the amount of disorder.Finally, we show how the field dependence of the exact average transit time can be inferred from tR, the time of thetransition between the two power-law regimes.

References :[1] J. A. Freire, M. G. E. da Luz, D. Ma, and I. A. Hummelgen, Appl. Phys. Lett. 77, 693 (2000).[2] J. A. Freire and M. G. E. da Luz, J. Chem. Phys. 119, 2348 (2003).



5.10.4

Temperature and frequency dependence of heat capacity near the glasstransition within a kinetic model

Dwaipayan Chakrabarti1 and Biman Bagchi2

1,2 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India

We consider a kinetic model of glassy dynamics that introduces cooperativity through the constrain of β organizedα process within the landscape paradigm. In this model, the β process is assumed to be thermally activated anddescribed by a two-level system. The α process is described as a β relaxation mediated cooperative transition ina double well. The model derives its motivation in recent computer simulation findings that hopping is a highlycooperative phenomenon promoted by certain coherence in many body fluctuations. The heat capacity behavior ofa supercooled liquid subjected to a temperature cycle through its glass transition is qualitatively reproduced withinthe model. In particular, the overshoot of the heat capacity during the heating scan is well reproduced and is shownto be directly related to delayed energy relaxation. In addition, the calculated scan rate dependencies of the glasstransition temperature Tg and the limiting fictive temperature TL

f show qualitative agreement with the known results.Heterogeneity is found to significantly reduce the overshoot of heat capacity. Furthermore, the frequency dependentheat capacity has been calculated within the present framework and found to be rather similar to the experimentallyobserved behavior of supercooled liquids.


5.10.5

Critical elasticity of two-dimensional random diluted central forcenetworks under tension

Zicong Zhou1, Bela Joos2 and Pik-Yin Lai3

1 Department of Physics and Institute of Life Sciences, Tamkang University, 151 Ying-chuan, Tamsui, Taiwan251371, Republic of China

2 Ottawa Carleton Institute of Physics, University of Ottawa Campus, Ottawa, Ontario, Canada, K1N-6N53 Department of Physics and Center for Complex Systems, National Central University, Chung-li, Taiwan 3203,

Republic of China

We study the rigidity of two dimensional site-diluted central force triangular networks under tension. We calculatethe shear modulus µ directly and fit it with a power law of the form, µ ∼ (p − p∗)f , where p is the concentration ofsites, p∗ its critical value, and f the critical exponent. We find that a small tension leads to a fairly large drop of p∗

and f , followed by a slow decrease down to the values of the diluted Gaussian spring network with increasing tension.Moreover, the stress itself has a different critical behavior than the shear modulus. We also find that the range of thecritical regime, i.e. the regime where the power law is valid, is also sensitive to tension. The tension-free system isvery special and has a narrower critical regime with the power law failing for p > 0.8. In contrast, a small tension issufficient to extend the power law to near p = 1. These behaviors can be explained in terms of the existence of thesimple meandering paths, defined as paths on which every node connects to others with only two nonparallel bonds.



5.10.6

Weak disorder expansion for localization lengths

Rudolf A Roemer1 and Hermann Schulz-Baldes2

1 Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV4 9BU, UK2 Institut fuer Mathematik, Technische Universitaet Berlin, 10623 Berlin, Germany

We present a perturbative formula for the largest localization length of an Anderson model on a strip. It is expressedin terms of a new energy dependent doubly stochastic matrix, the size of which is proportional to the strip width.This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Thedependence on energy, strip width and disorder strength is thoroughly compared with the results obtained by thestandard transfer-matrix method. Good agreement is found for all energies in the band of the free operator and thiseven for quite large values of the disorder strength.


5.10.7

Lengthscale-dependent out-of-equilibrium fluctuation-dissipationrelations for coarsening and glassy systems: exact results

Peter Mayer1 and Peter Sollich2

1,2 Dept Maths, KCL, UK

Violations of FDT out of equilibrium are well understood for mean field models, and can be used to define aneffective temperature Teff . Under what conditions an analogous Teff exists in non-mean field systems is unclear;minimally, it should be independent of the observable whose correlator and response are being considered. Weanalyse the observable-dependence of FDT violations in the coarsening dynamics of the Glauber-Ising chain at lowtemperature, obtaining new exact results for domain wall observables and higher order spin products as well as theirnonlocal analogues. We find that long-wavelength observables give the simplest FDT plots: straight lines with anon-equilibrium slope 1/Teff . Shorter wavelength observables give different, curved FDT plots, but with the sameasymptotic slope because the latter is dominated by the long-wavelength contributions. A meaningful definition ofan effective temperature is thus possible for large, non-equilibrated length scales. Recent simulations on 2d-Isingmodels at criticality suggest that this conclusion is rather generic. We extend our results to a simple glass model, theFredrickson-Andersen model, which maps to diffusion-coagulation at low temperatures. We again find consistency inthe asymptotic FDT slopes for local and non-local observables, though now with a negative Teff .



5.10.8

Performance Limitations of Flat-Histogram Methods

Prakash Dayal1, Simon Trebst2, Stefan Wessel3, Diethelm Wuertz4, Matthias Troyer5, SanjibSabhapandit6 and Susan Coppersmith7

1,2,3,4,5 Department of Theoretical Physics, ETH, Zurich, Switzerland6,7 Deapartment of Physics, University of Wisconsin-Madison

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed tosample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased randomwalk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the±J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Frechet extremal valuedistribution that obeys exponential scaling. The shape parameter of these distributions furthermore indicate thatstatistical sample means become ill-defined already for moderate system sizes within these complex energy landscapes.

1 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

5.10.9

Ground-State Energy Size Effects of the Sherrington-Kirkpatrick Modeland Related Models

Sigismund Kobe1

1 Technische Universitat Dresden, Institut fur Theoretische Physik, D-01062 Dresden, Germany

Exact ground states of the Sherrington-Kirkpatrick (SK) spin-glass model are calculated using the branch-and-boundalgorithm. The interactions Jij between N Ising spins (with N up to 90) are chosen from a Gaussian distribution Gij .Assuming that the N dependence of the mean ground-state energy per spin follows 〈e(N)

0 〉 = e∞0 + bN−ω with ω = 23 ,

the ground-state energy per spin results in e∞0 = −0.7637(4), which is close to the analytical result. Furthermore,related models can be introduced by replacing the interactions of the SK model according

P (Jij) = xδ(Jij + |Gij |) + (1− x)δ(Jij − |Gij |). (5.8)

For x = 1 all ferromagnetic interactions of the SK model are replaced by antiferromagnetic ones. An estimation of theground-state energy of this model is based on exact calculations up to N = 59 spins and results in e∞0,afm = −0.474.The scaling exponents for the ground-state energies and for their standard deviations are given. There are indicationsfor a transition from a ferromagnetic state to a spin-glass state with varying x near x = 0.5.

1 [email protected]


5.10.10

Spatiotemporal heterogeneities in the relaxation of simple glassy modelsystems and in experiments

Estelle Pitard1

1 Laboratoire des Verres, Universite Montpellier 2, 34095 Montpellier, France

New experiments on soft glassy materials show that their relaxation is heterogeneous in time and space. We inves-tigate this issue by studying numerically a simple kinetically constrained glassy model (Kob-Andersen model) wherecooperativity lengths can be identified. Models regarding the intermittent relaxation of gels will also be presented.

1 [email protected]

5.10.11

The Anderson Model of Localization with Scale-Free Disorder

Macleans L. Ndawana1, Rudolf A. Roemer2 and Michael Schreiber3

1,2 Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, UnitedKingdom

3 Chemnitz University of Technology, 09107 Chemnitz, Germany

We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in thepresence of scale-free diagonal disorder characterized by a disorder correlation function g(r) decaying asymptotically asr−α. We study the dependence of the localization-length exponent ν on the correlation-strength exponent α. For fixeddisorder W , there is a critical αc, such that for α < αc, ν = 2/α and for α > αc, ν remains that of the uncorrelatedsystem in accordance with the extended Harris criterion. At the band center, ν is independent of α but equal to thatof the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.



5.10.12

Magnetic Phase Diagram of Borocarbide Superconductors LuNi2B2Cand YNi2B2C

Deepshikha Jaiswal Nagar1, Dilip pal2, A.D. Thakur3, S.M Yusuf4, H. Takeya5, M.R. Eskildson6,P.C. Canfield7, S. Ramkrishnan8 and A.K. Grover9

1,2,3,8,9 Department of Condensed Matter Physics and Material Science, Tata Institute of Fundamental Research,Mumbai 400 005

4 Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai5 National Institute for Material Science, Tsukuba, Ibaraki 305, Japan

6 Nieuland Science Hall, University of Notre Dame, USA7 Ames Laboratory, Iowa State University, Ames, USA

High purity single crystals of borocarbide superconductors, LuNi2B2C ( Tc 14.5 K ) and YNi2B2C ( Tc 15 K ),display a variety of interesting physical phenomenon in magnetization measurements. These include the change in localsymmetry of the flux line lattice at low temperatures and low fields from rhombohedral to square, the observation ofsecond magnetization peak distinct from the quintessential peak effect, the presence of dHVA oscillations deep insidethe vortex state and across the region of the peak effect even at temperatures as high as about 10 K etc. However,measurement of magnetization values per se are not adequate to unambiguously demarcate the phase boundaries ordelineate the regions within which different vortex states have specific characteristics. We have, therefore, combinedthe results of the measurement of quadrupole moments of a sample alongwith those of the dipole moment of thesample usig a vibrating sample magnetometer, to construct the magnetic phase diagram in weakly pinned crystals ofLuNi2B2C and YNi2B2C for H // c over the entire ( H , T ) range. The phase boundaries, across which supercoolingand superheating can persist resulting in phase coexistence, can be conveniently ascertained.



5.10.13

Power-law behavior in the sensitivity to initial conditions for a classicalmap analog of the Anderson model

Hugo Hernandez-Saldana1, Felix M. Izrailev2 and Alberto Robledo3

1,3 Instituto de Fisica, Universidad Nacional Autonoma de Mexico. Apdo. Postal 20-364 Mexico DF 01000 Mexico2 Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, Puebla, Pue. 72570, Mexico

The metal-insulator transition in the Anderson model for disordered materials with long range correlations has beenassociated to bounded and unbounded chaotic behavior in a classical map version of the corresponding discreteSchrodinger equation [1]. In a simplified version of the classical map we explore the transition states at which theLyapunov exponent vanishes. Power-law decay in sensitivity to initial conditions is found for classical trajectories insuch transition states, characterized by a tangent bifurcation. Both the trajectories and the sensitivity follow exactly aq-exponential form[2]. Implications of this behavior in other versions of the classical map and in their metal-insulatortransition counterpart are also analyzed and discussed. [1] A.A. Krokhin and F.M. Izrailev. Phys. Rev. Lett. 82(1999) 4062; Ann. Phys. (Leipzig) 8 (1999) 153. [2] C. Tsallis. et al,Nonextensive Statistical Mechanics and itsapplications. S.Abe and Y. Okamoto Ed. (Springer Verlag, Heidelberg, 2001).


5.10.14

Force fluctuations in the jammed state of hard disks

Tamas Unger1, Janos Kertesz2 and Dietrich E. Wolf3

1 Institute of Physics, Budapest University of Technology, Hungary and Institute of Physics, UniversityDuisburg-Essen, Germany

2 Institute of Physics, Budapest University of Technology, Hungary3 Institute of Physics, University Duisburg-Essen, Germany

The force fluctuations in static, two-dimensional granular packings are investigated by means of contact dynamicswhich is an appropriate technique to explore the convex set of allowed solutions in the space of contact forces.Configurations are generated for given values of the friction coefficient and then an ensemble of solutions is foundfor fixed arrangements of contacts. At zero friction there are no fluctuations in accordance with the isostaticity ofthe packing. With appropriate boundary conditions the magnitude of the fluctuations at undetermined contacts asa function of the friction is non-monotonous. The increase for small friction can be attributed to the opening of theangle of the Coulomb cone, while the decrease is due to the reduction of the number of contacts as friction increases.The latter leads even to spacial localization of undetermined contacts.



5.10.15

Duality of the random model and the multicritical point

Koujin Takeda1 and Hidetoshi Nishimori2

1,2 Department of Physics, Tokyo Institute of Technology, 2-12-1, Oh-okayama, Meguro, Tokyo 152-8581, Japan

We studied the dual structure of the random model with bimodal randomness. By recent work, the exact location ofthe multicritical point of the two-dimensional random bond Ising model is expected from the conjecture derived fromthe self-dual structure of the system. We analyzed the four-dimensional Z2 random-plaquette lattice gauge model, andusing self-duality of the model in conjunction with the replica method, we showed that this model has exactly the sameself-dual structure as that of the two-dimensional random-bond Ising model. This observation enables us to derive aconjecture on the exact location of the multicritical point of the model. We also studied the two-dimensional randombond Ising model on hexagonal and triangular lattices, which can be mapped to each other by duality. We obtainedthe conjectured relation between two multicritical points of the dual systems. Duality between the random-bond Isingmodel and the random-plaquette lattice gauge model on three-dimensional lattice was also studied.



5.10.16

1/f Noise in the Steady States of Multi-Species Resistor Networks

Cecilia Pennetta1 and Eleonora Alfinito2

1,2 INFM-NNL, Dip. Ingegneria Innovazione, Univ. di Lecce, Via Arnesano, 73100 Lecce, Italy

We study a network made by different species of resistors. The network is in contact with a thermal bath at thetemperature T0 and the resistances of the elementary resistors depend linearly on temperature. A thermally activatedbreaking probability is attributed to each resistor. Recovery of the resistors is also allowed with a similar probability.Each resistor species is then characterized by the values of the activation energies of the breaking and recoveryprocesses, ED,i and ER,i, by the reference value of the resistance at the thermal bath temperature, r0,i, and by atemperature coefficient, αi, where i = 1, ...Nspec and Nspec is the number of species. An external electrical bias isapplied to the network. Consequently, the temperature of each resistor is determined by Joule heating effects andthermal exchanges among neighbour resistors and with the thermal bath[1]. The competition between the processesof breaking and recovery determines the evolution of the network, which is studied by Monte Carlo simulations. Inparticular, we focus on the steady states of the network and on the properties of the resistance fluctuations whichare studied under different external conditions. Therefore, this model extends a previous model[2, 3, 4], based on anetwork made by a single species of resistors subjected to breaking and recovery. The previous model describes verywell many features associated with the stability of the electrical properties and with electrical breakdown phenomenaof composites materials [3, 5] and granular metals[6]. However, it is limited to systems whose resistance fluctuationsare characterized by a single characteristic time, i.e. systems exhibiting Lorentzian noise. For contrast, the powerspectral density of resistance fluctuations of the multi-species network scales as the inverse of the frequency in thegeneral case, while it may become Lorentzian when the external conditions lead to a selection of only few species inthe steady state of the network.

References :[1] C. Pennetta, L. Reggiani and G. Trefan, Phys. Rev. Lett., 84, 5006 (2000).[2] C. Pennetta, G. Trefan and L. Reggiani, Phys. Rev. Lett., 85, 5238 (2000).[3] C. Pennetta, L. Reggiani, G. Trefan, E. Alfinito, Phys. Rev. E, 65, 066119 (2002).[4] C. Pennetta, E. Alfinito, L. Reggiani, S. Ruffo, Cond-mat/0401352. Phys. Rev. Lett. 83, 1215 (1999) and C. D.Mukherjee,[5] K. K. Bardhan, Phys. Rev. Lett. 91, 025702 (2003).[6] I. DeMunari, A. Scorzoni, Cond-mat/0402557.

[email protected]@unile.it


5.10.17

Mean-field theory of the Potts-glass model in a field

Terufumi Yokota1

1 Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan

Mean-field Potts-glass model in a field is investigated by the replica method. Change in the freezing temperaturefor the transverse degrees of freedom is shown to be proportional to the field strength for small fields. This is incontrast with the Gabay-Toulouse line for the vector spin-glass model, where the change in the freesing temperatureis quadratic of the field strength.

1 [email protected]

5.10.18

Non equilibrium relaxation of the Coulomb glass model

Alejandro B. Kolton1, Daniel Grempel2 and Daniel Domınguez3

1 DPMC, Universite de Geneve, 24 quai Ernest-Ansermet, CH - 1211 Geneve 4, Switzerland2 CEA-Saclay/DRECAMS/SPCSI, 91191 Gif-sur-Yvette CEDEX, France3 Centro Atomico Bariloche, 8400 S.C de Bariloche, Rio Negro, Argentina

We study numerically the nonequilibrium relaxation of the Coulomb glass model as a function of temperature. At lowtemperatures we find aging in the two time autocorrelation functions with a temperature-dependent aging exponent.Diffusion in this aging regime is found to be anomalous and highly heterogenous, with a fraction of diffusive electronsclearly separated from a fraction of electrons with confined motion. We show that aging behaviour is related to avery slow interchange of electrons between these two dynamical modes. We discuss the consequences for the transportproperties.



5.10.19

Light transport in complex photonic systems

Diederik Wiersma1, Sushil Mujumdar2 and Riccardo Sapienza3

1,2,3 European Laboratory for Non-linear Spectroscopy and INFM, via Nello Carrara 1, 50019 Sesto Fiorentino(Florence), Italy

We will give an overview on the latest developments on light transport in complex photonic systems. In particular wewill discuss the transport of optical waves in a range of materials going from fully ordered, like photonic crystals, topartially disordered systems like quasi-crystals, and liquid crystals, and to completely disordered structures. We willgo in detail into the latter case in which optical waves exhibit localization effects [see e.g. Riccardo Sapienza, SushilMujumdar, Cecil Cheung, A.G. Yodh, Diederik Wiersma, Anisotropic Weak Localization of Light, Phys. Rev. Lett.,92, 033903 (2004)] and in which one can obtain random laser emission [see e.g. Diederik Wiersma, Stefano Cavalieri,A temperature-tunable random laser, Nature 414, 708 (2001); and Sushil Mujumdar, Marilena Ricci, Renato Torre,Diederik Wiersma, amplified photon noise in random lasers, submitted].


5.10.20

Levy Statistics for Random Single–Molecule Line Shapes in a Glass

Eli Barkai 1, Yu. G. Vainer2, A. V. Naumov 3 and L. Kador4

1 251 Nieuwland Science Hall, University of Notre DameNotre Dame, IN 46556-5670 USA2,3 Institute of Spectroscopy, Russian Academy of Sciences, Moscow Reg., Troisk 142190, Russia

4 Institute of Physics and BIMF, University of Bayreuth, D-95440 Bayreuth, Germany

Experimental advances have made it possible to measure the spectral line shape of a single dye molecule embedded indifferent types of glassy materials. Because each individual molecule is in a unique static and dynamic environment,the line shapes of chemically identical single molecules varies from molecule to molecule. Thus single moleculesserve as local probes for dynamics and statics of the glassy system. We examine the statistical properties of lineshapes of single molecules (tetra-tert-butylterrylene) in a low temperature (T = 2K) glass (polyisobutylene ). Forlow-temperature glasses the fundamental question is: Is the standard tunneling model (STM) valid for glasses?Experimental data shows that most single molecules are coupled to two level systems (TLS) as expected from theSTM, a few single molecules (10%) show non standard behaviors (e.g. single moleculecoupled to three level system).A detailed theoretical and experimental analysis shows that statistical properties of the random line shapes aredescribed by L’evy statistics. This behavior is a manifestation of long range interactions between the TLSs and thesingle molecule. A universal amplitude ratio is investigated which shows that the STM assumptions are compatiblewith the experimental data.

References :[1] E. Barkai, A. V. Naumov, Yu. G. Vainer, M. Bauer, L. Kador Phys. Rev. Lett. 91 075502 (2003).



5.10.21

Replica bounds for diluted non-Poissonian spin systems

Silvio Franz1, Michele Leone2 and Fabio Lucio Toninelli3

1 The Abdus Salam International Center for Theoretical Physics, Condensed Matter Group, Strada Costiera 11, P.O.Box 586, I-34100 Trieste, Italy

2 Institute for Scientific Interchange, viale Settimio Severo 65, Torino, Italy3 Institut fuer Mathematik, Universitaet Zuerich, Winterthurerstrasse 190, CH-8057 Zuerich, Switzerland

I will present an extension of replica bounds and free energy subadditivity arguments to diluted spin-glass modelson graphs with arbitrary, non-Poissonian degree distribution. These are relevant in applications to combinatorialoptimization problems and error correcting codes. The new difficulties specific of this case are overcome introducingan interpolation procedure that stresses the relation between interpolation methods and the cavity method. As abyproduct we obtain self-averaging identities that generalize the Ghirlanda-Guerra ones to the multi-overlap case.


5.10.22

The phase diagram of spin glasses at zero temperature

Florent Krzakala1

1 Universita di Roma La Sapienza, Dip. di Fisica, P. A. Moro 2, Roma I-00185, Italy

The spin glass phase diagram, since the initial solution of the Sherrington-Kirkpatrick model, has always been a verydiscussed and puzzling problem, either analytically or numerically. We will concentrate here on the zero temperaturecase of finite connectivity spin glasses, with or without magnetic field and/or ferromagnetic bias. We will first considermean field spin glasses, which allows analytical studies of the phase diagram (and of the zero-temperature equivalentof the ”de Almeida-Thouless line”). Then, we will consider the three-dimensional Edwards-Anderson spin glass, usinghowever numerical computation of groundstates. We will discuss differences and similarities in the two problems.

1 [email protected]


5.10.23

Statistical Mechanics of Interacting Growth Walks

K. P. N. Murthy1 and S. L. Narasimhan2

1 MSD, IGCAR, Kalpakkam,603 102 Tamilnadu, INDIA2 SSPD, BARC, Trombay, Mumbai 400 085, Maharashtra, INDIA

We investigate the statistical mechanics of Interacting Growth Walk (IGW) on a lattice. An IGW is a self avoidingwalk that grows as per local energetics present at the time of each growth step. The local growth is tuned by theso-called growth temperature TG = 1/(kBβG). We show that IGW belongs to the same universality class as InteractingSelf Avoiding Walks (ISAW). IGW predicts correctly the phase transition from an extended phase at high TG to a col-lapsed phase at low TG. At the transition point we have the equivalence of a theta polymer. The correlation exponent,the entropic exponent and the crossover exponent in these three phases are predicted correctly. For a given TG wecalculate employing Monte Carlo simulation, the distribution of bath temperature. we find the distribution is sharplypeaked; we calculate the typical bath temperature to which the IGW ensemble corresponds to. Centering around thecalculated typical bath temperature we carry out multicanonical reweighting and extract equilibrium properties fromthe nonequilibrium IGW ensemble. We interpret the spread in ρ(T ) for a given TG as arising due to energy disorder;we then calculate the specific heat which shows a sharp peak at the collapse transition and a broad hump representingperhaps the presence of dynamically generated frozen disorder, like in glasses. We can say that different portions of anIGW have equilibrated at different bath temperatures. This paper is essentially based on the following publications[1-3]

References[1] S. L. Narasimhan, P. S. R. Krishna, K. P. N. Murthy and M. Ramanadham, Physical Review E (Rapid Commu-nications) 65, 010801 (2002).[2] S. L. Narasimhan, V. Sridhar and K. P. N. Murthy, Physica A 320, 51 (2003).[3] S. L. Narasimhan, P. S. R. Krishna, A. K. Rajarajan and K. P. N. Murthy, Physical Review E 67 011802 (2003)


5.10.24

Unusual metallic phase in a disordered Mott insulator in 2D

Nandini Trivedi1 and Dariush Heidarian2

1,2 Department of Theoretical Physics; Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai400005

We show that, with increasing randomness, the spectral gap in a 2D Mott-Hubbard insulator is destroyed first at adisorder Vc1 while antiferromagnetism persists up to a higher Vc2. Most unexpectedly, between Vc1 and Vc2 thesystem is *metallic* and is sandwiched between the Mott insulator below Vc1 and the Anderson insulator aboveVc2. The formation of the metal starts with the spectral gap getting destroyed locally in regions where the disorderpotential is high enough to overcome the inter-electron repulsion thereby generating puddles where charge fluctuationsare enhanced. With increasing disorder, these puddles percolate and concomitantly the states at the Fermi energy getextended resulting in a spatially inhomogeneous metallic phase that coexists with antiferromagnetic order. We willdiscuss the implications of our results for experiments.



5.10.25

Low-Temperature Excitations in Spin Glasses in dimensions d = 3 tod = 7.

Stefan Boettcher1

1 Physics Dept; Emory University; Atlanta, GA30307; USA

Pairing the Extremal Optimization heuristic[1] with an exact reduction algorithm for tracing out most spins, bond-diluted lattice spin glasses with up to 106 variables become tractable. Using this approach, more accurate or entirelynew results for the stiffness exponents yd – fundamental for low-temperature excitations – are computed for lattices indimensions d = 3 to d = 7, where the connection with mean-field predictions can be studied (see cond-mat/0310698).For instance, we find y3 = 0.24(1) and yd increasing with d, although less than predicted by replica theory.For more details, see http://www.physics.emory.edu/faculty/boettcher/.

Reference :[1] PRL86,5211(2001)

1 [email protected]

5.10.26

Instantaneous Normal Modes from Euclidean Random Matrix theory

Stefano Ciliberti1, Tomas S. Grigera2, Victor Martin Mayor3, Giorgio Parisi4, and Paolo Verrocchio5

1,3,5 Departamento de Fisica Teorica I, Universidad Complutense de Madrid, 28040 Madrid (Spain)2 Insitituo de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA, CONICET-UNLP) 1900 La Plata

(Argentina)4 Dipartimento di Fisica, Universita

Euclidean Random Matrices (ERM) have been shown to be very useful in the study of topological disordered systems,ranging from glasses to spin glasses and disordered magnetic semiconductors. In this talk I will discuss a general methodfor studying spectra and localization properties of ERM in low density systems. I will show how the formalism canbe applied to address the problem of Instantaneous Normal Modes in liquids and glasses.




5.10.28

Percolation transition in two-dimensional system of Ni granularferromagnets

Yakov M. Strelniker 1, Richard Berkovits 2, Aviad Frydman3 and Shlomo Havlin4

1,2,3,4 Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Recent magnetoresistance measurements performed on quenched condensed granular Ni thin films which are on theverge of electric continuity seem to indicate that in these systems the electric conductivity is governed by the resistanceof a small number of grains [A. Cohen et all, Solid State Comm. 129, 291 (2004)]. We model this system by arandom 2D resistor network and perform Monte Carlo simulations of magneto-transport features. In our model thehopping conductivity between two neighboring ferromagnetic grains depends on both the distance between the grains[σ ∝ exp(−κRij), where κ is coefficient of the exponential decay and Rij is the distance] and the mutual orientationof the magnetic moments of these grains. The dependences of the simulated magnetoresistance versus the appliedmagnetic field are in good agreement with the experimental measurements and indicate that few resistors govern thetotal conductivity. We analyze the effect of the width, κ, of the disorder on the total conductivity along with theeffect of the “cutting” the bond where the local current is maximal, in order to test the condition where a single bonddominates the system. The effect is stronger when the system is smaller or the distribution is broader. To quantifythis effect, we study the ratio between the total resistivity after the “cutting” and the total resistivity before, ρcut/ρ.We find that the transition between the case when ρcut/ρ ∼ 1 (no effect of single bond—weak disorder) to the casewhen ρcut/ρ À 1 (strong effect of a single bond—strong disorder) scales as κ/L1/1.3, where L is the size of the system.


5.10.29

Dynamical Gauge Theory for Gauge Glass Models

Yukiyasu Ozeki1

1 Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguroku, Tokyo 152-8551, JAPAN

The gauge glass model H = −J cos(φi − φj − Aij) is investigated from dynamical points of view. Using the methodof gauge transformation, we show the gauge invariance of dynamical systems in any dimensions for both stochasticand deterministic dynamics. This provides some exact relations for dynamical quantities, We discuss the absence ofre-entrant transition in low temperature regime, a restriction for the mixed phase regime in the phase diagram, themulti-critical dynamics, and the equivalence of two ageing processes in the SG phase. Next we propose a quantumversion of the model (the quantum gauge glass). Showing the gauge invariance, we derive some exact relations forstatic quantities. Although the relations is not so useful as in the classical case, some restrictions on the phase diagramscan be investigated. It can be applied to the ground state and the system with an external field.

1 [email protected]


5.10.30

Universal behaviour of the coefficients of the continuous equation incompetitive growth models

Diego Muraca1, Lidia A. Braunstein2 and Ruben C. Buceta3

1,2,3 Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata,Funes 3350, Mar del Plata, Argentina

The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one withprobability p and the other with probability 1 − p. The p−dependance produce crossovers between two differentregimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, arequadratic in p (or 1-p). We show that the origin of such dependance is the existence of two different average timerates. Thus, the quadratic p-dependance is an universal behavior of all the competitive growth models. We deriveanalytically the continuous equations for two competitive growth models, in 1+1 dimensions, from the microscopicrules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in eachregime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derivedanalytical equations. The results are in excellent agreement with those of the microscopic competitive growth modelspresented here and with the proposed scalings.


5.10.31

Quasi-1D Photonic arrays in microwave experiments. Effects ofrandomnes and impurities.

Germn A. Luna-Acosta1, U. Kuhl2, H.Schanze3 and H.-J. Stockmann4

1Instituto de Fisica, Universidad Autonoma de Puebla, Mexico2,3,4Fachbereich Physik der Philipps Universitat, Renthof 5, D-35032, Marburg, Germany

We experimentally study the transport properties of quasi- 1D periodic and randomly disordered arrays, as well asthe effect of impurities in periodic arrays. The set up consists of a microwave guide supporting a single transversalmode with teflon inserts of length d’ alternating with air spacings of constant or varying length d(i), where i is aninteger labeling the site position. Structural random disorder is realized by forming an array with randomly generatedair spacings. We consider the cases of weak, medium, and strong disorder. The impurity consists of a teflon piece ofdifferent length in an otherwise periodic array. We observe clean transmission bands in the case of periodic arraysand a number of small oscillations in the transmission bands indicating the position of the impurity in the array, aspredicted by simple transfer matrix calculations. The cases of weak, medium, and strong random disorder show thatlocalization due to randomness is strongly inhibited in the neighborhood of the teflon resonances. We discuss theseresults in connection with theories of correlated and uncorrelated disorder

[email protected]@[email protected]@physik.uni-marburg.de


5.10.32

Kovacs effect in facilitated spin models

Jeferson J. Arenzon1 and Mauro Sellitto2

1 Instituto de Fsica - UFRGS, Porto Alegre - RS, Brazil2 Abdus Salam ICTP, Trieste, Italy

We investigate the Kovacs (or crossover) effect in facilitated spin models on the Bethe lattice, i.e. random graph withfixed connectivity, and compare with those obtained in finite dimension where the glass transition is known to beabsent but the low temperature relaxation is very slow. We consider quenching temperatures T1 and T2 both aboveand below the dynamical glass transition Tg, and the mixed case T1 < Tg < T2 as well. Although the Kovacs humpshows a two-step behavior qualitatively similar for all cases we have examined, we find that the T2 dependence of theKovacs peak time allows to distinguish among different mechanisms (e.g., defect vs. cooperative diffusion) responsiblefor the slow relaxation. The inherent structure dynamics show features resembling those obtained recently in a realisticmodel of molecular liquid.


5.10.33

Duality of the random model and the quantum toric code

Koujin Takeda1 and Hidetoshi Nishimori2

1,2Department of Physics, Tokyo Institute of Technology, 2-12-1, Oh-okayama, Meguro, Tokyo 152-8581, Japan

We study the Z2 random-plaquette lattice gauge theory as a model of toric code, which is one of the topologicalquantum memory, using the dual structure of the system. In this model, the critical point on the Nishimori linebetween ordered (Higgs) phase and disordered (confinement) phase can be regarded as the accuracy threshold of theerror correction of quantum memory. For four-dimensional random plaquette gauge model, we can show that the modelhas exactly the same self-dual structure as that of the two-dimensional random-bond Ising model. This observationenables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model.For three dimensional random plaquette gauge model, we can expect the location of the critical point on Nishimoriline from the one of the three-dimensional random bond Ising model using duality between these models.

[email protected]@phys.titech.ac.jp


5.10.34

Stochastic description of the dynamics of a random-exchangeHeisenberg chain

Mendeli H. Vainstein1, Rafael Morgado2, Fernando A. de Oliveira3, Francisco A. B. F. de Moura4,and Mauricio D. Coutinho-Filho5

1,2,3 Institute of Physics and International Center of Condensed Matter Physics, Universidade de Brasilia, Brasilia,Brazil

4 Department of Physics, Universidade Federal de Alagoas, Maceio, Brazil5 Department of Physics, Universidade Federal de Pernanbuco, Recife, Brazil

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, characterized by a powerspectrum in the momentum space behaving as k−β [1], using a stochastic description[2]. We establish a directconnection between the fluctuations in the spin-wave density of states and the noise density of states. For continuousranges of the exponent β, we find super-diffusive and ballistic spin-wave motions. Both diffusion exponents predictedby the stochastic procedure agree with the ones calculated using the Hamiltonian dynamics[3].

References :[1] F. A. B. F. de Moura, M. D. Coutinho-Filho, E. P. Raposo, and M. L. Lyra, Phys. Rev. B 66, 014418 (2002).[2] R. Morgado, F. A. Oliveira, G. G. Batrouni and A. Hansen, Phys. Rev. Lett. 89, 100601 (2002).[3] M. H. Vainstein, R. Morgado, F. A. Oliveira, F. A. B. F. de Moura and M. D. Coutinho-Filho, submitted to Phys.Rev. E



5.10.35

Rejuvenation and Memory Effects in the Binary EA Model for SpinGlasses in 3 and 4 dimensions.

Sergio Jimenez1, Victor Martin-Mayor2 and Sergio Perez-Gaviro3

1 Departamento de Fisica Teorica, Facultad de Ciencias Universidad de Zaragoza, 50009 Zaragoza, SPAIN2 Departamento de Fisica Teorica, Universidad Complutense, Avenida Complutense, 28040 Madrid, SPAIN

3 Instituto de Biocomputacion y Fisica de Sistemas Complejos (BIFI). Universidad de Zaragoza, 50009 Zaragoza,SPAIN

The spectacular rejuvenation and memory effects found in experimental Spin Glasses[2] and not observed innumerical simulations[3] have made people doubt about the validity of the Edwards Anderson Model to describethe nature of the Spin Glass Phase. We present a detailed study of the rejuvenation and memory effects for theEdwards-Anderson Model in 3 and 4 dimension with binary couplings. In order to do that we have considereddifferent temperature-change protocols. We find that rejuvenation effects are much stronger in the binary modelthan in the Gaussian one. We find similar behavior both in 4 and 3 dimensions, contrary to previous works donewith Gaussian Couplings[1]. We have considered the Off Equilibrium Fluctuation-Dissipation relations to relate thecorrelation measured in simulations to the susceptibility, finding not negligible effects. We have observed also veryclear memory effects for all the temperature-change protocols performed. This simulations have been done usingSUE, a special purpose machine to simulate the 3D EA model, built and designed at the University of Zaragoza andRTN3 a PC cluster running under Linux.

References :[1] Ludovic Berthier, Jean-Philippe Bouchaud. Phys. Rev. B 66, 054404 (2002)[2] K. Jonason, E. Vincent, J. Hammann, J.P. Bouchaud, P. Nordblad,Phys. Rev. Lett. 81, 3243 (1998)[3] M. Picco, F. Ricci-Tersenghi, F. Ritort,Phys. Rev. B 63, 174412 (2001)


5.10.36

Applications of cluster Monte Carlo algorithms in diluted spin glasses

Thomas Jorg1

1 Dipartimento di Fisica and INFM, Universita di Roma ”La Sapienza”, 00185 Roma, Italy

Recently a cluster Monte Carlo algorithm has been used very successfully in the 2 dimensional Edwards-Anderson(EA) model. We show that this algorithm and variants thereof can also be used successfully in systems with a non-zerospin glass transition temperature. The application of such algorithms to the low-connectivity Viana-Bray model andto the site-diluted EA model in 3 dimensions is discussed and their efficiency is compared to parallel tempering. Thespin glass transition is studied in the 3d site-diluted EA model with Gaussian couplings for two different values of thedilution. Finally, we commment on the possibility that the site-diluted EA model has the same critical behaviour asthe undiluted EA model.

1 [email protected]


5.10.37

Monte Carlo Simulations of 3D Bond-Diluted Potts Models

Pierre-Emmanuel Berche1, Christophe Chatelain2, Bertrand Berche3 and Wolfhard Janke4

1Groupe de Physique des Materiaux (UMR CNRS No 6634), Universite de Rouen, F-76801 Saint Etienne duRouvray Cedex, France

2,3Laboratoire de Physique des Materiaux (UMR CNRS No 7556), Universite Henri Poincare, Nancy 1, F-54506Vandoeuvre les Nancy Cedex, France

4Institut fur Theoretische Physik, Universitat Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany

Large-scale Monte Carlo simulations of the bond-diluted three-dimensional Ising and 4-state Potts model are presented.The phase diagram and the physical properties at the phase transition are studied using finite-size scaling techniques.In the Potts case, evidences are given for the existence of a tricritical point dividing a regime where the transitionremains of first order and a second regime where the transition is softened to a continuous one by the influence ofdisorder. In the former regime, the nature of the transition is essentially clarified through an analysis of the energyprobability distribution. In the latter regime critical exponents are estimated. Rare and typical events are identifiedand their role is qualitatively discussed in both regimes.

[email protected]@[email protected]@itp.uni-leipzig.de

5.10.38

The glass transition and liquid-gas spinodal boundaries of metastableliquids

Ashwin S.S1, Gautam I. Menon2 and Srikanth Sastry3

1,3JNCASR, Jakkur, Bangalore2IMSc, C.I.T Campus, Taramani, Chennai

The stability of a liquid is bounded by the liquid-gas spinodal and the glass transition. It was shown recently insimulation that these two limiting boundaries intersect at finite a temperature. We investigate this from an analyticalpoint of view. We calculate these stability boundaries in the framework of one step replica symmetry breaking andthe Zerah-Hansen scheme for a model liquid.




5.11.1

Protein folding simulations with Interacting Growth Walk model

S. L. Narasimhan1, K. P. N. Murthy2 and M. Ramanadham3

1,3 Solid State Physics Division, BARC, Mumbai 400 085, INDIA2 Materials Science Division, IGCAR, Kalpakkam 603 102, Tamilnadu, INDIA

Proteins are non-branching heteropolymers obtained from twenty commonly occuring amino acids. Their specificbiological functions are intimately related to their native conformational structures. Amino acids can be classifiedbroadly into hydrophobic (H) or polar (P) types; we can then treat a protein as a copolymer made up of two types ofamino acids with non-bonded nearest neighbour contact interactions. In this paper we consider the problem of findingthe native conformational structure of a given sequence of H and P type amono aids and contact interactions. Ourmethod is based on a self avoiding walk model proposed recently; it is called the Interacting growth walk (IGW). In theIGW model the growth is dictated by local growth rules dependent on local energy changes. Employing this growthalgorithm we study several benchmark sequences and find conformations that yields minium energy. We compare theperformance of the porposed IGW algorithm with other Monte Carlo search techniques. For several of the sequenceswe find that out method leads to energy lower than the ones obtained by other methods.


5.11.2

Nonlinear Elasticity of α helical domains

Buddhapriya Chakrabarti1 and Alex J. Levine2

1,2 Department of Physics, University of Massachusetts, Amherst, MA 01003, USA

We propose a minimal model of an α-helical polypeptide that incorporates both conformational degrees of freedomand secondary structure. Using this model we obtain the force-extension and torque-angle relations of an isolatedα-helical domain. We calculate these force extension curves using a perturbative expansion in both the low forceand the high force limit and develop a diagrammatic scheme to extend this perturbation scheme to arbitrary order.Further we calculate the equilibrium torque-angle curves for torques applied to ends of the domain. Finally, with endsfree, and in the absence of external forces and torques model is amenable to a nonperturbative solution; we evaluatethe scattering function in this limit.



5.11.3

Performance of networks of artificial neurons: the role of clustering

Beom Jun Kim1

1 Dept. of Molecular Science and Technology, Ajou Univ., Suwon, South Korea

The performance of the Hopfield neural network model is numerically studied on various complex networks, such asthe Watts-Strogatz network, the Barabasi-Albert network, and the neuronal network of the C. elegans. Through theuse of a systematic way of controlling the clustering coefficient, with the degree of each neuron kept unchanged, wefind that the networks with the lower clustering exhibit much better performance. The results are discussed in thepractical viewpoint of application, and the biological implications are also suggested.

1 [email protected]

5.11.4

A simple Hopfield-like cellular network model of plant intelligence

Jun-ichi Inoue1 and Bikas K. Chakrabarti2

1 Complex Systems Engineering,Graduate School of Engineering, N13-W8, Kita-ku, Sapporo 060-8628, Japan2 Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700064,India

We introduce a simple cellular-network model to explain the capacity of the plants as memory devices. Followingearlier observations (Bose [1] and others [2-4]), we regard the plant as a network in which each of the elements (plantcells) are connected via negative (inhibitory) interactions. To investigate the performance of the network, we constructa model following that of Hopfield, whose energy function possesses both Hebbian spin glass and anti-ferromagneticterms. With the assistance of the replica method, we find that the memory state of the network decreases enormouslydue to the effect of the anti-ferromagnetic order induced by the inhibitory connections. We conclude that the abilityof the plant as a memory device is rather weak.

References :[1] J. C. Bose, The Nervous Mchanism of Plants, Longmans, London (1923).[2] A. Trewavas, Nature vol. 415, p. 841 (2002).[3] B. K. Chakrabarti and O. Dutta, cond-mat/0210538, Ind. J. Phys. A Vol. 77, pp. 549-551 (2003).[4] I. Bose and R. Karmakar, Physica Scripta Vol T106, pp. 9-12 (2003).



5.11.5

New approach towards protein adsorption and exchange

Imre Derenyi1, Gergely Szollosi2, Martin Halter3 and Janos Voros4

1,2 Department of Biological Physics, Eotvos University, Pazmany P. stny. 1A, H-1117 Budapest, Hungary3,4 Laboratory for Surface Science and Technology, ETH Zurich, Wagistr. 2, CH-8952 Schlieren, Switzerland

Protein adsorption and exchange play an important role in many technological applications, such as biomaterials(e.g., implants, contact lenses), biosensors or food packaging. Still, the process is not fully understood and manycontroversial theories about the reversibility of protein adsorption and other puzzles and paradoxes exist. With asingle channel grating coupler instrument we are able to measure the adsorption and exchange of proteins on varioussurfaces (that differ, e.g., in their hydrophobicity). These measurements have led us to the development of a newmodel, which is based on the assumption that each protein has several different conformations in the adsorbed statewith different footprint sizes and binding energies, separated by energy barriers. Proteins can adsorb to or desorbfrom the surface and make transitions between the conformations. Numerical simulations of large numbers of proteins- supplemented by analytical calculations - allow us to reproduce the experimental data, identify the conformations ofproteins, and understand the mechanism of protein adsorption and exchange in more details.

1 [email protected]

5.11.6

Electronic transport in DNA

Daphne Klotsa1, Rudolf A Roemer2 and Matthew S Turner3

1,2 Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, UK3 Department of Physics, University of Warwick, Coventry CV4 7AL, UK

Based on a theoretical model proposed by Cuniberti et al. [1] we are focusing on electron localisation along theDeoxyribose Nucleic Acid (DNA) double helix, using a tight-binding Hamiltonian. The possibility that this organicsuper molecule might facilitate electron transfer, along the overlapping π-orbitals [2], as a means of signalling otherbiomolecules, has led us to perform calculations varying the DNA sequences. We have performed simulations onrandom sequence, λ- and telomeric DNA. For the first two the resulting localisation lengths as functions of energyand disorder show similar behaviour whereas the latter - specific sequence DNA - gives significantly larger localisationlengths. In all cases an energy bandgap, indicating semiconducting behaviour, has been observed. Counter intuitively,for random absorption of Sodium (Na) atoms onto the backbone, preliminary results have shown localisation lengthsto increase with increasing disorder. A ‘moving window’ technique will be used in order to assess whether particularshorter fragments of a sequence behave differently, whose contribution would inevitably be smoothed out when thewhole sequence is considered. Finally, we are looking at another theoretical way of modelling DNA’s complex structureand properties, the ‘ladder model’ - an extension of the aforementioned model. [1] G. Cuniberti, et al., Phys. Rev. B65, 241314 (2002). [2] P. J. de Pablo, et al., Phys. Rev. Lett. 85, 4992 (2000).



5.11.7

Statistical properties of DNA coding sequences revisited: The role ofthe inverse bilateral symmetry in bacterial chromosomes

Hugo Hernandez-Saldana1, Rafael Mendez-Sanchez2, Juan R. Bobadilla3, Tzipe Govezensky4, andMarco V. Jose5

1 Instituto de Fisica, Universidad Nacional Autonoma de Mexico. Apdo postal 20-364. Mexico DF 01000 Mexico2 Centro de Ciencias Fisicas, Universidad Nacional Autonama de Mexico. Cuernavaca, Mor. Mexico.

3,4,5 Instituto de Investigaciones Biomedicas, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria,Mexico D.F., C.P. 04510, Mexico

A central issues of the statistical properties of DNA sequences are long-range correlations in intergenic regions (Penget al. 1992), but not in intronless genes. The hypothesis that the Inverse Bilateral Symmetry (IBS) observed inwhole bacterial chromosomes constitutes an organizing principle for understanding DNA sequences is put forward.A renormalization group (RG) approach shows that the relative dispersion of distance series of single bases alongeach half of the intact chromosome exhibits a random behaviour but modulated by a log-periodic variation. Incontrast, the distance series of most triplets for each half of the intact bacterial chromosome or from intronless codingregions,follow long-range inverse power-law correlations. When the whole chromosome or exclusively protein-codingregions are considered, multiscale series arise. It is concluded that the scaling properties of distance series of singlebases are different from those of triplets. Contrary to the classical result that the DNA coding regions of bacterialgenomes are purely uncorrelated random sequences, we found that DNA random fluctuations are modulated by log-periodic variations. We also examined and discussed if the distance series could represent a system operating far fromequilibrium in the context of q-exponential distributions



5.11.8

Thermal stability of a helical conformation in bee venom melittin

Yoshinori Miura1 and Hirofumi Sakashita2

1,2 Center for Advanced Instrumental Analysis, Kyushu University, Kasuga, Japan

Melittin, a protein of 26 amino acid residues, is monomeric and helical in methanol[1]. We have studied thermal sta-bility of a helical conformation in melittin by using 500MHz proton nuclear magnetic resonance (NMR) spectroscopy.In order to observe the NMR signals of the labile protons, melittin was dissolved in methanol ”CD3OH”. We foundthat between 20C and 50C most of backbone amide proton signals are sharp doublets as a result of slow hydrogenexchange with the solvent, but between 50C and 60C some of them turn to broad and weak peaks owing to fasthydrogen exchange. In contrast, even at 60C some other signals remain doublets. The slow exchange is caused bya strong hydrogen bond between a backbone amide proton and a backbone oxygen. On the other hand, weakening(or breaking) the hydrogen bonds induces the fast exchange. The result of this experiment indicates that melittinundergoes local melting below the temperature at which melittin transforms into a fully disordered conformation.We discuss the following questions : (1) Is the helix-coil transition of melittin first order or not? (2) To what extentdo hydrophobic interaction and van der Waals force affect the thermal stability of a helical structure in melittin?,(3) Does the helical structure of melittin collapse by decreasing temperature? (i.e., does cold denaturation exist inmelittin?)

References :[1] R. Bazzo, et al.,Eur. J. Biochem., 173,139-146,(1988).



5.11.9

Water Dynamics Near a Protein Surface

Sarika Maitra Bhattacharyya1, Zhen-Gang Wang2 and Ahmed H. Zewail3

1 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, 560012, India2,3 Laboratory of Molecular Sciences and Division of Chemistry and Chemical Engineering, California Institute of

Technology, Pasadena, California-91125

Water plays a crucial role in determining the structure, dynamics and functionality of proteins and biological macro-molecules. On the other hand, the dynamics of water, near the macromolecule surface (hydration layer) is known tobe quite different from that of the bulk. I will discuss a model which represents the dynamics of water near a proteinsurface and compare it with experimental results. The model consists of a layer of bound and free water moleculesat the surface of the protein in dynamic equilibrium with each other and coupled with the bulk water away fromthe protein surface. The dynamics of the hydration layer is found to have two timescales where the fast one is bulklike and the slow one is not only dependent on the bound to free transition rate, k2 (as was predicted by a previousmodel) but it also depends on the free to bound transition rate, the diffusion of free water and the thickness of thehydration layer. This effect, identified as the feedback mechanism is found to further slow down the slow dynamics.The weight of the contribution of the slow component to the overall relaxation dynamics is found to be inverselyproportional to the slow decay time. For a heterogeneous surface with spatially varying k2, the water dynamics ina probe region covering several sites is described by the cumulated effects from these water molecules, with the slowdynamics given by the sum of the exponentials, with contributions inversely proportional to their respective decaytime. To a very good degree, this slow dynamics can be fitted to a single exponential; however the apparent time scaledoes not represent any particular site. The study also provides important insight to the observed dynamical behaviorand can be extended to study the effect of water on protein functionality and protein-glass transition.



5.11.10

In silico studies on cell motility

S.V.M. Satyanarayana1 and A. Baumgaertner2

1 RSD, IGCAR, Kalpakkam - 603 1022 IFF, Forschungszentrum Juelich, Germany

Cell motility is a cyclic process of spatially segregated and temporally regulated subprocesses. The subprocessesinclude cell polarization, protrusion, adhesion, cell body translocation and tail retraction with each process beingtightly regulated by complicated signaling cascades. The cell motility has been reconstituted in vitro by using minimumnumber of purified proteins. We model the cell and its motile machinery on a two dimensional square lattice: membraneis modeled interms of flexible ring polymer and the actin monomers are beads diffusing inside the cell. The modelis quantitative since we fix the lattice spacing and simulation time by using experimentally known size of actin andreaction rates of actin polymerization respectively. The reaction diffusion process involved in treadmilling of actinnetwork is simulated using Monte Carlo method. We implement the Arp2/3 induced branchig in our model. Thevelocities of the cell computed are comparable to the experimentally measured speeds of keratocyte. Our studiesunderline the importance of membrane flexibility for polymerization and therby protrusion. We also show that thepresence of treadmilling actin filaments on both directions lead to persistent random walk of the model cell. Weshow that long lived, stable network is efficient in pushing the membrane and hence gives rise to larger cell speeds.These arguments will be rationalised based on the analysis of computed F-actin fraction, network remodeling time,membrane relaxation time and cell velocities as a function of the membrane contour length and protein concentration.



5.11.11

A Complex Network Approach to the Electrical Properties of G ProteinCoupled Receptors

Cecilia Pennetta1,Eleonora Alfinito2,Vladimir Akimov3,Lino Reggiani4 and Gabriel Gomila5

1,2,4INFM, NNL and Dip. Ingegneria Innovazione, Univ. di Lecce, Via Arnesano, 73100 Lecce, Italy3INFM, NNL, Via Arnesano, 73100 Lecce, Italy

5Lab. NanoBioEngineering, Univ. Barcelona, C/ Josep Samitier 1-5, Science Park, 08028 Barcelona, Spain

We present a complex network approach [1] to the study of the electrical properties of a G protein coupled receptor(GPCR) [2]. This family of proteins is an important class of trans-membrane receptors. Their importance arises fromthe fact that they are involved in cell recognition and communication processes, moreover, they mediate our senses ofvision, smell and taste. As a consequence, the study of the electrical properties of GPCRs is of relevant interest in viewof the potential realization of single-protein nanodevices devoted to many technological applications. We note thatall GPCRs share the seven helices trans-membrane structure [2]. Unfortunately, the detailed information about theiratomic structure is available only for rhodopsin (photonic receptor). Therefore, by taking advantage of the commontopology of the peptidic chain of rhodopsin and of the other GPCRs, we have developed the following ”coarse grain”description of their electrical properties. The receptor is modeled as a complex network of elementary impedances.The positions of the alpha-carbon atoms, Cα, of each amino acid [3] are taken as the reference positions of the networknodes. The amino acids are assumed to interact electrically among them. Charge transfers between neighbouringamino acids [4] and/or changes of their electronic polarization [5] are taken to affect the state of these interactions.Therefore, a link is drawn between any pair of nodes neighbouring in space within a given distance and an elementaryimpedance is associated with each link. The expression of the elementary impedance can be related to the physicaland chemical properties of the amino acid pair [5] and to their relative distance. Accordingly, the conformationalchanges of the receptor induced by the photons or, in general, by the capture of a ligand [6], are translated into avariation of its electrical properties. The impedance spectrum of the network and its fluctuations are then studiedand analyzed for different values of the parameters introduced in the model. [1] R. Albert and A. L. Barabasi, Rev.Mod. Phys., 74, 47 (2002).[2] J. Lameh et al., Pharmaceutical Research, 7, 1213 (1990).[3] Res. Collab. Struct. Bioinformatics, Protein Data Bank, State Univ. of New Jersey, http://www.rcsb.org/pdb.[4] Q. Xie et al., Chem. Phys. Lett., 312, 237 (1999).[5] X. Song et al., J. Chem. Phys., 116, 9359 (2002).[6] H. Yang et al., Science, 302, 362 (2003).



5.11.12

A Unified Model of Evolutionary Ecology

Ambarish Kunwar1, Dietrich Stauffer 2 and Debashish Chowdhury3

1,3 Physics Department, Indian Institute of Technology, Kanpur-2080162 Institute for Theoratical Physics, Cologne University, D-50923, Cologne, Germany

Many models developed in the last decade to explain the evolution and the statistics of extinction of species usingthe concepts and techniques of STATISTICAL PHYSICS claim that the statistical distributions of several quantitiesassociated with the extinction of species follow POWER LAWS. However, almost all of these models focus only onthe ”macro” evolution. We have developed a UNIFIED MODEL that describes both ”micro” and ”macro” evolutionswithin a single theoretical framework [1]. The ecosystem is described as a dynamic network. The ”micro” evolutionover ecological time scales is described by the population dynamics within each node. while the appearance ofnew nodes, slow changes of the links and disappearance of existing nodes accounts for the ”macro” evolution overgeological time scales. In contrast to several earlier claims in the literature, we have observed strong deviations frompower law in the regime of long lifetime. After incorporating the generic hierarchical architecture of foodweb into ourUNIFIED MODEL distribution of lifetimes of species follows power laws only over a limited regime [2,3,4]. Becauseof the various known limitations of the available fossil data it is questionable whether real extinctions follow power law.

References :[1] D. Chowdhury, D. Stauffer and A. Kunwar, Phys. Rev. Lett. 90, 068101 (2003).[2] D.Chowdhury and D. Stauffer,PRE,68, 041901-1 (2003).[3] D. Stauffer and D.Chowdhury,PHYSICA A,336, 102 (2004).[4] D.Chowdhury and D. Stauffer,PHYSICA A (in press)



5.11.13

Membrane statistical physics: A general theory of non-equilibriumdynamics of multi-component fluid membranes

MICHAEL L. LOMHOLT1, LING MIAO2 and PER LYNGS HANSEN3

1,2,3 MEMPHYS-CENTER FOR BIOMEMBRANE PHYSICS, DEPT. OF PHYSICS, UNIVERSITY OFSOUTHERN DENMARK, CAMPUSVEJ 55, DK-5230 ODENSE M, DENMARK

Membranes are the most essential structural elementand an important functional element in biological cells. Eachmembrane is composed of a core, bimolecular layer of amphipilic lipids, into which transmembrane proteins areembedded and to which peripheral proteins are attached. In its functional state, the membrane is fluid and its two-dimensional geometry deforms easily. From the point of view of statistical physics, the motion of the constituentmolecules and the dynamics of the geometrical deformation are two essential aspects of membrane dynamics. Wepresent a general and systematc theory of non-equilibrium dynamics of multi-component fluid membranes, whichwas experimentally motivated. We have derived the core elements of the theory – the equations of dynamics andboundary conditions – from a minimal number of principles of statistical physics: the basic laws of thermodynamics,the assumption of local thermodynamic equilibrium in a non-equilibrium system and the dynamic formulation of lawsof conservation of mass, momentum and energy. The derivation and the equations of dynamics contain features thatare not present in the traditional treatment of surface and interface dynamics, reflecting some essential differencesbetween a membrane and a conventional interface between two immiscible fluids.


5.11.14

Role of wiring cost and pattern retrieval performance in the evolutionof C. elegans neural network

Yong-Yeol Ahn1 and Hawoong Jeong2

1,2 Physics dept. KAIST, Daejeon, South Korea

Recently, it was found that the pattern retrieval performance of the nematode C. elegans’s neural network is not goodas simple network with low clustering coefficient. In this paper, we construct a complete map of neural network usingthe geometrical location of each neurons on C. elegans. And we optimize a randomized neural network using a fitnessfunction which is defined by pattern retrieval performance and wiring cost, and we compare the optimized networkwith original neural network.



5.11.15

Stochastic simulation of transcription initiation regulation

Sandeep Krishna 1 and G.V.Shivashankar2

1 National Center for Biological Sciences, TIFR-Bangalore2 National Center for Biological Sciences, TIFR-Bangalore and Raman Research Institute

We study the impact of fluctuations in transcription initiation regulatory modules in the expression of a single gene. Wehave set up a stochastic simulation using the Gillespie algorithm for modeling the expression of the gene. Models havebeen created for different transcription initiation processes; we have studied circuits in which the gene is unregulated,autoregulated and regulated by enhancer looping. The simulation scheme includes various sources of noise, suchas thermal noise, partitioning of molecules during cell division, fluctuations in cell division time and fluctuations inplasmid copy number. The simulation reproduces features of the protein distribution that are observed in experiments– a long tailed protein distribution is observed in the unregulated case, and a bimodal distribution in the autoregulatedcase. The simulation allows us to investigate the dependence of these features on the various different sources of noiseand, especially, the transcription initiation process.


5.11.16

Electrostatic interactions in macro-biomolecules

Navin Chandra1, Soma Samaddar2 and Siddhartha Roy2

1 SNBNCBS, JD Block, Sector-III, Salt Lake, Kolkata-98, West Bengal India2 Biophysics Department, Bose Institute, Centenary Campus P 1/12, C.I.T Road, Scheme - VIIM, Kolkata -

700054, West Bengal, India

Protein (read enzyme)-DNA interaction is very important in living beings as it forms the basis of important phenomenaof gene expression, DNA replication etc. Electrostatics also has contribution in such interactions. DNA is negativelycharged molecule. Proteins also have charges on its atoms. The environment (solvent) in which they (the protein-DNA) lie can also have charged ions. This way electrostatics does have some role to play in protein-DNA binding. Wetry to find out its (electrostatics’) contribution in such interactions. We use a software (named Delphi) to calculatethe electrostatic energy of the protein-DNA complex and also the electrostatic contribution to the binding energy ofsuch complex. We have done calculations for two such systems, (1) Glutaminyl tRNA synthetase complexed withtRNA and (2) lambda repressor-operator complex.



5.11.17

Hierarchical Self-Organizing Map Clustering for Protein FoldingAlphabets

Mookyung Cheon1 and Iksoo Chang2

1,2 National Research Laboratory for Computational Proteomics and Biophysics, Department of Physics, PusanNational University, Pusan 609-735, Korea

The 20 kinds of amino acids are building blocks for proteins. The classification of amino acids’ characters helps toreduce the complexity of protein properties. Here we present the classification of 20 amino acids by the hierarchicalself-organizing map clustering using the Miyazawa-Jernigan pairwise-contact and perceptron-learned one-body energyparameters. It gives the biological interpretations for each group, whose clusterings are in agreement with the previousworks, but provides more detailed and characteristic features of amino acids clustering. Hydrophobic, medium, loop-favoring, and polar amino acids are grouped and each representative amino acid is identified. Hierarchical self-organizing map clustering is proved to be a good clustering tool in biophysics and protein science.


5.11.18

Short time kinetics of folding and unfolding CI2 protein : Monte Carlosimulation using Munoz-Eaton energy function

Kwanghoon Chung1, Mookyung Cheon2 and Iksoo Chang3

1,2,3 National Research Laboratory for Computational Proteomics and Biophysics, Department of Physics, PusanNational University, Pusan 609-735, Korea

Folding and unfolding behavior of CI2(Chymotrypsin Inhibitor 2) protein is studied by Munoz-Eaton energy function.After transforming the conformational ensembles of a protein to the configurations of spin variable in Ising model, weperformed Monte Carlo simulation for a short time kinetics to keep track a time evolution Pk(t) of the on set of kth

pairwise-contact in CI2 protein. Folding and unfolding events of CI2 protein is described by Pk(t) and is explained bythe concept of the local contact order of pairwise-contact along the sequence of amino acids. The orders in folding andunfolding events are also explained in terms of the entropic barrier which is evident from the topology of a protein.



5.11.19

Simple model for the kinetics of packaging of DNA into a capsid againstan external force

K. P. Santo1 and K. L. Sebastian2

1,2 Department of Inorganic and physical Chemistry, Indian Institute of Science, Bangalore, India

We propose a simple model for the kinetics of packaging of viral DNA into a capsid against an external force trying toprevent it. The model leads to a Butler-Volmer-type dependence of the rate of packaging on the pulling force F andfits the experimental data well.


5.11.20

Correlation between hydrophobic attraction and the free energy ofhydrophobic hydration

Prabhakar Bhimalapuram*1, Kenichiro Koga2 and Benjamin Widom3

1 SSCU, IISc, India2 Deptartment of Chemistry, Okayama University, Japan

3 Department of Chemistry and Chemical Biology, Cornell University, USA

The poster presents a calculation on a particular lattice model incorporating the hydrophobic effect at a microscopiclevel, for which parameters are chosen to represent methane as solute in water. We correlate the free energy ofhydration of a (nonpolar) solute at infinite dilution and the strength of the solvent-mediated attraction at contactbetween two such solvated solutes, and find a linear correlation between them (both expressed in units of kT ) overthe relevant range of temperatures [1]. This has been recently verified using computer simulation of realistic modelsof water [2]. [1] B. Widom, P. Bhimalapuram, Kenichiro Koga, Phys. Chem. Chem. Phys (2003) 5, 3085. [2]. D.Paschek, arXiv:cond-mat/0312252.



5.11.21

A model for the evolution of the Influenza A virus

Francesca Tria1, Luca Peliti2 and Michael Lassig3

1 Abdus Salam International Center of Theoretical Physics (ICTP), Trieste, Italy2 Dipartimento di Scienze Fisiche, Universita “Federico II

3 Institut for Theoretical Physics, University of Cologne, Germany

Influenza is peculiar among viral diseases in that it may infect repeatedly the same individual in spite of the immunityconferred by each infection. This is due to the high mutation rate of the influenza virus, which allows it to escapethe immune response of the host population. We have introduced and analyzed a model describing the evolutionarydynamics of the influenza virus determined by the interaction with the immune response of the host population, takinginto account cross-immunization, i.e., the fact that an individual immune to a given strain will not be susceptible toinfection to different, but closely related, strains. In a certain range of parameters one observes successive epidemicsdue to newly arising viral strains.


5.11.22

Size Selectivity in Ion Channels

R. Roth1 and D. Gillespie2

1 MPI fuer Metallforschung, Heisenbergstrasse 3, 70569 Stuttgart, Germany2 Department of Molecular Biophysics and Physiology, Rush Medical College, Chicago, IL 60612, USA

Ion channels have a very important role in biological cells: they regulate the flux of ions through the membrane andhence control the concentration of ions inside and outside of the cell. The precise control of the concentration of ionsis of vital importance to the cell. A key part of an ion channel is the so-called selectivity filter which e.g. in the caseof a Na channel selects Na over K, which have the same charge but a different size. But how does this selectivityfilter work? We present a simple model of a selectivity filter that allows to study the physics of size selectivity with aminimal number of parameters. To this end we consider a mixture of water and ions, all modeled as uncharged hardspheres of different radii and concentrations, inside a corrugated cylindrical pore formed by the protein. We take themain features of real ion channels, like the L-type Calcium channel and CLC Chloride channel, in an effective way intoaccount: in the selectivity filter of the L-type Calcium channel charged residues result into an attraction of positivecharged ions, like Li, Na, or K into the filter which results into small ion selectivity. The hydrophobic repulsion ofwater from the protein in the selectivity filter of the CLC Chloride channel results in large ion selectivity. Our model,which predicts trend that are observed in experimental studies of ion channels, allows us to understand the mechanismof size selectivity in simple terms, which are in good agreement with DFT calculations.

1 [email protected] dirk [email protected]


5.11.23

Thermal Melting of Triple Helices and Crystal Melting in CollagenModel Peptides (Pro-Pro-Gly)10 and (Pro-Hyp-Gly)10

H. Sakas1, Y. Miura2, M. Watanabe3, S. Shibata4, M. Cho5, and N. Cho6

1,2,3,4 Center for Advanced Instrumental Analysis, Kyushu University, Kasuga, Japan5 Faculty of Engineering, Sojyo University, Kumamoto, Japan

6 Faculty of Engineering, Kyushu Kyoritu University, Kitakyushu, Japan

Normal collagen, found in connective tissues such as bone and tendon, is composed of three polypeptide chains witha length of 300nm, and undergoes thermal melting of triple helices to three coils in an aqueous solution at about38C: this transition is irreversible and collagen becomes gelatin (the entangled chains(coils) shows a reversible sol-geltransition at about 30C). In contrast to normal collagen, the synthesized collagen-model-peptides, such as (Pro-Pro-Gly)10 and (Pro-Hyp-Gly)10 with a length of 10nm, reveal a peculiar transition feature in an aqueous solution: (1)both peptides undergo a reversible triple-helices to (three)coils transition below 60C, and do not become gelatin whenboiled even at 100C; (2) they crystallize (as an assemble of triple-helices, not of statistical coils) at room temperatureand show a crystal-melting transition with increasing temperature—- in particular in (Pro-Pro-Gly)10 this transitiontemperature depends strongly on the concentration of the peptide in water; (3) only in the peptide (Pro-Hyp-Gly)10a new phase transition appears at 90-105C—- a slight difference in the chemical structure (only one of three CH2atoms of side chain in Proline(Pro) amino acid residue are replaced by H and OH in Hydroxyproline(Hyp) results ina new phase; (4) triple-helices are mainly stabilized by the hydrogen bonding between intra-chains (in triple-helices)and the new phase is probably caused by the inter-chain hydrogen bonding associated to side chain OH, on the otherhand, hydrophobic and van der Waals interactions may also take part in as crystal forming force. We have investigatedthese transitions of two components (peptide and water) and finite size systems by using 500MHz 1H nuclear magneticresonance (NMR) spectroscopy and high-sensitive differential scanning calorimetry (DSC) to clarify the behaviour ofthe hydrogen bonding and a latent heat around the melting transitions and a possible structure of the new phase.



5.11.24

Impact of lipid rafts on cellular signaling via enhanced rebinding ofligands

Manoj Gopalakrishnan1, Kimberly Forsten-Williams2 and Uwe C. Tauber3

1,3 Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435, USA.2 Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA

24061-0211, USA.

We study how lipid raft-induced clustering of receptor proteins on the cell surface leads to longer association of ligands,thereby enhancing the chemical signal. As the first part of this study, we use mean-field calculations and numericalsimulations to study the rebinding of dissociated ligands. Within certain limits, we derive the complete mathematicalform of the dissociation curve for a homogeneous distribution of receptors, and find that it is non-exponential at alltimes. We compare our result with recent experiments, and very good agreement is found. Clustering of bindingsites (as occurs via trapping of receptor proteins by lipid rafts) is found to increase the effects of rebinding, therebyslowing down the dissociation even further. We discuss two models of rafts in this context, and outline the results ofnumerical simulations. Relevant experimental results in the context of basic Fibroblast Growth factor (FGF-2) andits co-receptor Heparan Sulfate Proteoglycans (HSPG) are also discussed.


5.11.25

A stochastic model of all-or-none gene expression

Rajesh Karmakar1 and Indrani Bose2

1,2 Department of Physics, Bose Institute, 93/1, A. P. C. Road, Kolkata-700009, India

Abstract. There is now considerable experimental evidence that, in single cells, gene expression occurs in abrupt,stochastic bursts. Some prokaryotic and eukaryotic systems further exhibit the phenomenon of all-or-none geneexpression (GE) in which the amount of proteins synthesized has a bimodal distribution. In the steady state, afraction of cells is in the high state, i.e., the level of proteins synthesized is high. In another fraction of cells, theprotein level is low. The fraction of cells in which protein production occurs at intermediate levels is very small,i.e., in most of the cells, the level of proteins is either high or low. In some systems, the binary character of GEhas been attributed to autocatalytic and positive feedback mechanisms involved in GE. There are, however, otherexperimental systems which exhibit the all-or-none phenomenon in the absence of feedback processes. We propose asimple, stochastic model of GE without feedback in which a gene makes random transitions between the inactive andactive states. Protein synthesis occurs only when the gene is in the active state. Transcription factors bind/unbindat the appropriate regions of the gene and regulate the transitions between the two states of the gene. The MasterEquation, describing the stochastic GE processes, can be solved analytically. The parameter regimes corresponding tounimodal and bimodal distributions in protein levels have been identified. The results obtained are in good agreementwith the experimental results of Zlokarnik et al [1]. [1] Zlokarnik et al, Science 279, 84 (1998).



5.11.26

Associative memory on a small-world neural network

Luis G. Morelli1, Guillermo Abramson2 and Marcelo N. Kuperman3

1Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34100 Trieste, Italy2,3Centro Atomico Bariloche, CONICET and Instituto Balseiro, 8400 S. C. de Bariloche, Argentina

We study a model of associative memory based on a neural network with small-world structure. The efficacy of thenetwork to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder parameter.The more ordered networks are unable to recover the patterns, and are always attracted to non-symmetric mixturestates. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value ofthe disorder. We also give a statistical characterization of the spurious attractors for all values of the disorder of thenetwork.


5.11.27

Population dynamics and survival in a two-dimensionalcellular-automaton replicator

Luis G. Morelli1 and Damian H. Zanette2

1 Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34100 Trieste, Italy2 Centro Atomico Bariloche and Instituto Balseiro, 8400 Bariloche, Rio Negro, Argentina

We propose a model for interacting species on a two dimensional lattice. The model is a cellular automaton, withreplicator-like local interactions. Individuals in a local neighborhood compete to occupy an empty site. The probabilityto do so is given by the fitness of the corresponding species, determined by the interactions among the species presentin the neighborhood. In the case of two species, we characterize the different interaction schemes and study thedynamical and equilibrium properties, like the density of each species, the fraction of individuals in border regions,and spatial patterns. We find a phase transition as the attitudes between the two species change from altruistic toselfish. For a large number of species, we give a characterization of the dynamics for different regimes of interaction.Altruistic, selfish, and mixed populations are considered. The survival probability of a given species is characterizedin terms of its own attitude to the rest of the population and the attitude of the population towards the species. Thestructure of interactions in the surviving community is also investigated.



5.11.28

Storage capacity in recurrent networks of spiking neurons storingsparsely coded random memories

Gianluigi Mongillo1, Emanuele Curti2, Giancarlo La Camera3 and Daniel Amit4

1 Dip. di Fisiologia Umana, Universita2,4 INFM, Dip di Fisica, Universita

3 Institute of Physiology, University of Bern

A recently developed MF theory allows a reliable description of asynchronous steady (attractor) states of activity ofrecurrent networks of spiking neurons, storing sparsely coded random memories. Plastic synapses have two stablestates, potentiated and depressed. Memories are embedded within the synaptic matrix according to a stochasticHebbian learning rule: the probability that a synapse is potentiated depends on the number of potentiating anddepressing patterns of activity experienced upon presentation of the memories to be stored. MF-equations admit twotypes of solution: 1. Symmetric (ergodic) - corresponding to a state in which all neurons emit at the same, low, meanrate; 2. Retrieval (broken symmetry) - corresponding to a state in which neurons coding for a given memory emitat enhanced rates with respect to the rest. Storage capacity is the maximal number pc of memories, for which theMF equations admit both solutions. Storage capacity is studied as a function of 1. Ratio of the high-to-low synapticefficacy; 2. Efficacy of inhibitory to excitatory synapses; 3. Relative strength of potentiating/depressing pattern; 4.Coding level. The results obtained in MF-theory are compared with simulations of large (10000 cells) microscopicnetworks of spiking neurons. The dependence of the storage capacity on finite-size effects is also studied by simulations.


5.11.29

Nonlinear Rheology of active particle suspension

Sudipto Muhuri1 and Madan Rao 2

1,2 Raman Research Institute , Bangalore-560080, India

We study the interplay of activity, order and flow through a set of coarse-grained equations governing the hydrodynamicvelocity, concentration and stress fields in a suspension of active, energy dissipating particles. There are two aspects ofthis problem that we investigate — (1) the stability of the ordered phase under an imposed shear flow and (2) its linearand nonlinear rheological response subject to a constant shear stress or strain rate. Our predictions for the nonlinearrheology of such systems may be tested on bacterial suspensions and cell extracts with motors and filaments.



5.11.30

Active Fission-Fusion: Morphology of Vesicles and Phase Segregation

Kripa.G1, K.C.Lakshmi2, P.B.Sunil Kumar3 and Madan Rao4

1 Raman Research Institute, C.V.Raman Avenue, Bangalore 560 080, INDIA2,3 Dept of Physics, Indian Institute of Technology Madras, Chennai 600 036, INDIA

4 Raman Research Insitute, Bangalore 560 080 and National Centre for Biological Sciences, UAS-GKVK, Bangalore560 065, INDIA

Intracellular compartments are subjected to a constant flux of membrane bound cargo. This gives rise to the peculiarmorphology and composition of these organelles. In this study, we investigate the influence of active fission-fusion ona closed vesicle and the resulting steady states and shape instabilities. We also discuss a novel activity induced phasesegregation on a multi-component membrane subject to fission-fusion.


5.11.31

Active fission-fusion on Lipid Vesicles: a Monte Carlo study

K. C. Lakshmi1, Kripa.G2, P. B. Sunil Kumar3 and Madan Rao4

1,3 Department Of Physics, IIT Madras, Chennai2 Raman Research Institute, Bangalore

4 Raman Research Institute and National Centre for Biological Sciences, Bangalore

The membranes of intracellular organelles such as ER, Golgi and endosomes are subject to random fission and fusion ofmembrane bound cargo. It is believed that the complex morphologies of these organelles are maintained dynamicallyby this active trafficking. We present results from Monte Carlo simulations of active fission and fusion dynamics onclosed vesicles in two and three dimensions. We study the steady states and the scaling behaviour of shape measuressuch as the radius of gyration and fold size as a function of the vesicle size and fission-fusion rates.



5.11.32

Modeling the Blood Cycle of Malaria

Rita Maria Zorzenon dos Santos1

1Departamento de Fısica -Universidade Federal de Pernambuco- Cidade Universitaria- 50670-901-Recife-PE-Brazil

Human malaria is caused by four different species of the Plasmodium protozoa, and among them the harmful one isthe Plasmodium falciparum, which is responsible for 90% of malaria morbidity and mortality in the world. The lifecycle of this parasite is very complex and is divided into many stages, according to its alternated interaction withthe human host and the mosquito vector. In humans there are two main stages, one in which the parasite targetare the liver cells, and the second one, in which their target are the red blood cells (erytrocytes) and the spleenplays an important role. In this late stage, each infected erythrocyte releases dozens of parasites that will infect newerytrocytes, establishing a feedback mechanism that will sustain the parasitemia during periods of time that vary frompatient to patient. In the case of re-infection, which is very common in the endemic areas, it has been observed thatthe primary infection does not bring immunization against the parasite: after few re-infections the patient may die.In this talk we introduce a cellular automata model [1] that describes the spread of the infection in the spleen andthe development of the parasitemia, taking into account the role of the immune system. The results obtained, whenvarying some of the parameters, show a good qualitative agreement with and exhibit the same diversity of behavior ofthe data collected from a study with hundreds of patients. Under multiple re-infections, our model also reproduces thefact that the parasitemia does not die out as observed among the patients. We also discuss the mechanisms underlyingthe different behaviors observed. [1] R.M. Zorzenon dos Santos, S.T.Rubim de Pinho, L. Silva, T. B. Gurgel, preprint

(2004).

[email protected]


5.11.33

A phase ordering model of directional sensing in the eucaryotes

Andrea Gamba1, Antonio de Candia2, Stefano Di Talia3, Antonio Coniglio4, and Guido Serini5

1 Dipartimento di Matematica, Politecnico di Torino2,4 Dipartimento di Scienze Fisiche, Universita di Napoli

3 Laboratory of Mathematical Physics, The Rockefeller University5 Institute for Cancer Research and Treatment, Universita di Torino

The ability of eucaryotic cells to sense spatial gradients of soluble chemoattractant factors and to move towards theirincreasing concentrations is central in the development of complex organisms. Cells exposed to shallow gradientsin chemoattractant concentration respond with strongly asymmetric accumulation of signalling molecules. This earlyamplifying stage then triggers effector pathways leading to cell movement. Although many factors implied in directionalsensing are known, the mechanism itself is still rather misterious. We have considered the possibility that the mainfeatures of directional sensing observed in the experiments are the consequence of a phase ordering process takingplace on the plasma membrane, driven by the distribution of the external signal. We have developed a theoreticalmodel based on this principle, which is able to reproduce several experimental facts, like the large amplification ofshallow chemical gradients, the selective localization of chemical factors, the macroscopic response timescales, andspontaneous cell polarization.



5.11.34

Method of invariant grids for studying chromatin dynamics.

Alexander Gorban1, Arndt Benecke2 and Andrei Zinovyev3

1 Eidgenssische Technische Hochschule Zrich - Swiss2,3 I.H.E.S. - Bures-sur-Yvette - France

Chemical kinetics equations serve as predictive tool in analysis of many biological systems. One of the main difficultiesin the approach is poor knowledge of rate constants and complexity of the equations describing real-life processes.In this respect methods of description reduction of chemical kinetics equations are very important in analysis ofsuch systems in biology. One well-known mathematical fact is that the most interesting dynamics of the systems inmultidimensional space happens mainly along so-called inertia manifolds. In the case of the closed systems, thesemanifolds are positively invariant (if a trajectory starts on the manifolds, it will not leave it until the equilibrium).We propose a method of construction of low-dimensional manifolds of reduced description for equations of chemicalkinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of thecondition of invariance as an equation, and its solution by Newton iterations. A grid-based version of MIM is developed.Generalizations to open systems are suggested. The set of methods covered makes it possible to effectively reducedescription in chemical kinetics. The most essential new element is the systematic consideration of a discrete analogueof the slow (stable) positively invariant manifolds for dissipative systems, invariant grids. We develop the Newtonmethod and the relaxation method for the invariant grids construction. The problem of the grid correction is fullydecomposed into the problems of the grid’s nodes correction. The edges between the nodes appear only in thecalculation of the tangent spaces. This fact determines high computational efficiency of the invariant grids method.The method was tested on simple chemical reactions like two-dimensional catalytic reaction and four-dimensionaloxidation reaction. Having a model of chromatin dynamics, we apply the method to the qualitative and quantitativestudy of complex dynamics of chromatin. Using two-dimensional invariant grid constructed, we will demonstrate howthe picture of the chromatin dynamics can be visualized. We believe that the methods we developed will serve asuseful tools for model reduction in complex biological systems, as well as in other applications of chemical kineticsapproach.



5.11.35

Darwins theory of evolution from the point of view of statistical physics

Alexey Veniaminovich Melkikh1

1 Physics-technical department, Ural State Technical University, Ekaterinburg, Russia

Now the problem of biological evolution rates and mechanisms remains actual. In particular, it is earlier shown by theauthor [1], that random Darwins evolution can not explain characteristic times of species origin. It is offered determin-istic model of evolution of the organisms, including control and decision making on genes transformation in conditionsof uncertainty. Conformational degrees of freedom of proteins (not coded in DNA) are the additional informationresource, providing work of molecular control systems. The mechanism of controlled genome transformation is thereverse transcription. As the basic equation of evolution Fokker-Plank-Kolmogorov equation is written. The deter-ministic term in it is consequence of control molecular systems work and diffusive term is caused by random propertiesof an environment (but not mutations, as against the traditional darwinian theory). Constructed model has allowedto remove the contradiction on characteristic times of new species origin and as to explain a known phenomenon ofadaptive mutations. References 1. Melkikh A.V. Quantum demon and the problem of the biological evolution rate// Quantum limits to the second law: First International Conference on Quantum Limits to the Second Law. AIPConference Proceedings, 2002. Volume 643, Issue 1, pp. 476-481.

1 [email protected]

5.11.36

Percolation on disordered trees and the impossibility of a mitochondrialEve

Armando G. M. Neves1

1 Depto. de Matematica, UFMG, Belo Horizonte, Brazil

Consider bond percolation in a disordered tree model as follows. Trees have an origin (zeroth generation) and everyvertex following it is linked to a random number of descendents in the next generation. Descendent numbers areindependent and identically distributed and the probability of having i descendents is qi, i = 0, 1, 2, . . . ,

∑∞i=0 qi = 1.

Each bond is open with probability p and closed with probability 1−p. We exactly calculate the percolation thresholdpc for such model. We relate percolation in this model with the question of existence of a mitochondrial Eve inthe following manner. The origin represents an ancestral woman. Vertices linked to another vertex in the precedinggeneration are children of that vertex. Bonds linking a parent to a daughter are considered to be open and the others,closed. Percolation means survival of the mtDNA lineage of the woman at the origin. Our result for pc implies thatwhenever the average number of children per parent is larger than 1/p, a finite fraction of the ancestral mtDNAlineages will survive, contradicting thus existence of only one surviving lineage (Eve hypothesis). In particular, whenp = 1/2, there can be no Eve if population grows with time.

1 [email protected]


5.11.37

Protein Folding Dynamics of HP-36 and Beta amyloid

Arnab Mukherjee1 and Biman Bagchi2

1,2 Solid state and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India

In order to understand complex dynamics of protein folding, a new and generalized minimalistic model has beendeveloped and used to explore the correlation between energy landscape, topology and dynamics of folding. Thebackbone atoms are replaced by spheres of same size, whereas individual amaino acids are connected to backboneatoms with varying sized spheres, taken from Levitt [J. Mol. Bio. (1976).].Effective water mediated interactionsamong amino acids are mapped from standard hydropathy scale. Absence of peptide bonds in the model proteins iscompensated by the incorporation of a new ”helix potential” with different helix propensities for each amino acids.This model has been applied to study HP-36 and beta amyloid. The study shows several interesting structural anddynamical features. The best folded structure of HP-36 has an RMSD of 4.5 Awith the real NMR structure. Model betaamyloid produces the beta bend at the appropriate position. Subsequent to quenching, the folding shows multistagedynamics, which an intermediate long plateau [J. Chem. Phys. 118, 4733 (2003); 120, 1602 (2004)], characterizingthe slow rate determining step – similar to the observation of Sali et al. [Nature 369, 248,(1994)].


5.11.38

Secondary network emerging from simple perturbation

Seung-Woo Son1, Dong-Hee Kim2, Yong-Yeol Ahn3 and Hawoong Jeong4

1,2,3,4 Dept. of Physics, Korea Advanced Institute of Science and Technology, Daejon, 305-701, Korea

In complex networks, attack on a single node can drastically change the communication pattern between other nodes.To investigate this effect, we measure the change of the betweenness centrality (BC) under the removal of a single node.Based on this response, the secondary networks are constructed through two different methods: minimum spanningtree and from the formation of the giant component with the same size as the original network via percolation approach.We find that the change of BC is proportional to the BC of the removed node and the constructed secondary networksbased on this perturbation are again scale-free in both cases.



5.11.39

Scaling in Synthetic Gene Networks Constructed from Gene ExpressionData

Himanshu Agrawal1

1 School of Information Technology, Jawaharlal Nehru University, New Delhi, India

We study gene networks synthesized from gene expression data obtained from many types of cancers. The networksare synthesized using several different algorithms with each algorithm having a single tunable parameter Q. For eachnetwork we calculate “homogeneity.” For each algorithm, in the range of Q corresponding to minimum homogeneity,the degree distribution of the networks shows scaling. We discuss implications of these findings in several contexts.

1 [email protected], [email protected]

5.11.40

Random Energy Model for the T Cell Immune Response

Jeong-Man Park1 and Michael W. Deem2

1 Dept. of Physics, The Catholic University of Korea, Puchon, Korea2 Dept. of Bioengineering and Physics, Rice University, Houston, Texas, USA

The vertebrate immune system is a wonder of modern evolution. Occasionally, however, the memory within theadaptive immune system leads to inappropriate recruitment of preexisting T cells against novel viral diseases. Wepresent a physical theory of the naive and memory T cell responses and show how the sequence-level dynamics ofthe T cell repertoire is related to the immune response against mutated viral antigens. Correlations in the immuneresponse to mutated antigens and how original antigenic sin arises from competition between naive and memory Tcells are discussed. Applications of our approach include development of design rules for multicomponent vaccinationto rapidly mutating or multiple-subtype viruses and modeling the immune response to tumor cell evolution.



5.11.41

Evolution towards criticality: A paradigm for accidental pathogens

Nico Stollenwerk1

1 University of London, Royal Holloway School of Biological Sciences Egham, Surrey TW20 0EX, UK

In a model for bacterial infections with various mutants we find the epidemiological system evolving towards criticalitywithout outer tuning of a control parameter. This is an indication for self-organized criticality. The epidemic modelis a susceptible-infected-recovered hosts system (SIR) for the harmless agent infecting hosts I, acting as a backgroundto a mutant strain Y which occasionally creates severely affected hosts X, hence a model for accidental pathogens.The full system of SIRYX is described in the master equation framework, confirming limiting assumptions about areduced YX-system with the SIR-system in stationarity. In this limiting case we can analytically show convergence topower law scaling typical of critical states [1]. Furthermore, in this approximation we can show analytically that thecontrol parameter, the pathogenicity in this model, evolves to be predominantly in its critical value zero [2]. Thesefindings are then confirmed by simulations of the full SIRYX-system. A good empirical example for this mechanism isprovided by meningococcal disease (meningitis and septicaemia), for which we apply our model to data, gojng beyondthe above mentioned publications. Hence meningitis data sets from England and Wales, and Norway, are analyzed.The SIRYX stochastic system close to criticality is adjusted to the 7 years long weekly England and Wales data tocapture the fast seasonal response to seasonal forcing in the contact rate. On this level it cannot be distinguishedfrom a simpler SIRX system, suggested before. Surprisingly, in simulations hugh epidemic outbreaks are found lastingover decades as they are observed in the 40 years long yearly Norwegian data. Just the parameter set obtained fromthe short England and Wales data was used and no information on longer fluctuation included initially. Consideringthese long term fluctuations, the SIRYX discribes the data variance much better than the simpler SIRX system. Thesimple SIRX system can be rejected on the basis of showing effectively Poisson like behaviour, variance over meanbeing close to unity, which is clearly contradicting the data.

References :[1] Stollenwerk, N., & Jansen, V.A.A. (2003, a) Meningitis, pathogenicity near criticality: the epidemiology ofmeningococcal disease as a model for accidental pathogens. Journal of Theoretical Biology 222, 347–359.[2] Stollenwerk, N., & Jansen, V.A.A. (2003, b) Evolution towards criticality in an epidemiological model formeningococcal disease. Physics Letters A 317, 87–96.

1 [email protected]


5.11.42

Synchronous Firing and Growth of Cortical Neuronal Networks

L. C. Jia1, M. Sano2, Pik-Yin Lai3, and C. K. Chan4

1Inst. of Medical Image, YuanPei Uni. of Sci. and Tech., Hsinchu, Taiwan 3002Dept. of Phys., Uni. of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

3Dept. of Phys. and Center for Complex Systems, National Central Uni., Chung-Li, Taiwan 3204Institute of Physics, Academica Sinica, Nankang, Taipei, Taiwan 115

Network correlation connectivities (k) of cortical neural cultures are studied experimentally by synchronized firing (SF)and determined from measured correlations between fluorescence intensities of firing neurons. The bursting frequency(f) during SF of the networks is found to be an increasing function of k. With f taken to be proportional to k, asimple random model with diffusive growth and a k dependent connection probability p(k) has been constructed toexplain our experimental findings successfully. In particular, the special form of p(k) ∼ e−

kko gives the experimental

observed result that f is characterized by a critical age (tc) and a critical frequency (fc) as: f = fc + f0log( ttc

). fc isalso observed to scale with the cell density as fc ∝ 1/

√ρ which can be explained by our model. The implications of

the results on the mechanism of network growth are also discussed in terms of theoretical models.

1 [email protected]


5.11.43

Divergence based clustering methodology for Gene classification

Rajeev Azad1, Pedro Bernaola Galvan2, Wentian Li3 and Ramakrishna Ramaswamy4

1 Department of Biological Sciences, University of Pittsburgh, Pittsburgh PA 15260, USA2 Departamento de Fisisca Aplicada, Universidad de Malaga, Malaga E29071, Spain

3 Center for Genomics and Human Genetics, North Shore-LIJ Research Institute, Manhasset, NY 110304 School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, INDIA

To unravel the mosaic organization of genomes and to identify putative alien genes in a genome, statistical methodsof pattern recognition as well as methods to detect phylogenetic incongruencies are required. The present availabilityof over one hundred completely sequenced prokaryotic genomes has made possible comparative genome analysis whichestablish horizontal gene tranfer as a dominant force driving microbial genome evolution. We suggest a clusteringmethod based on an entropic measure, Jensen-Shannon divergence, for identifying alien (or atypical) genes in a genome.Applications to several genomes have been made using both 4-symbol as well as 12-symbol alphabets, and we findthat genes within a genome cluster in a large set of typical genes and several small clusters of atypical genes. Ourmethod takes the relative length of genes into consideration and has the potential to classify genes even if the datasetis small.


5.11.44 Poster 5.11.44 moved to Oral Section.


5.11.45

Physical mechanisms of specific promoter recognition

Aprotim Mazumder 1 and G.V.Shivashankar2


DNA is wrapped around histone proteins and further condensed into a compact chromosome structure within eukary-otic cells. The mechanisms of how specific sequences are accessed in such compact chromosomes are poorly understood.We have started to address this issue by using simple biological model systems (single He-La cells) and taking advantageof recent developments in state of the art live cell single molecule tracking methods. We plan on using Histone-GFPcell-lines and novel fluorescent probes (such as quantum dots) conjugated with specific transcription factors for thesestudies. Such methods allow one to probe quantitatively the mechanisms of diffusion within confined geometry ofa cell nucleus to recognize the specific sequences, and directly monitor, in real time, the resulting changes in thelocalized histone-DNA interactions using fluorescence anisotropy time-series analysis. In addition, we also plan todevelop non-invasive approaches to physically manipulate localized chromosome structure that may provide a physicalframework to understand how information is accessed and processed at the single gene level.


5.11.46

Tracking fluctuations in transcription initiation

Bidisha Banerjee 1 and G.V.Shivashankar2


Noise in gene expression, caused by various intrinsic and extrinsic factors, is either exploited or suppressed in cellsas survival strategies or during development. Since transcription initiation is the most dominant mechanism of generegulation, we study the effect of noise in this regulatory module ((a) operator state (b) enhancer looping and nucle-osome stability) using single cell biophysical measurements. As a first step to probe transcription noise and its timeevolution, we report the results of operator state fluctuations for the entire bacterial growth cycle, using single cellanalysis and synthetic gene circuits. In the unregulated circuit, during the cell cycle, we observe a crossover from lognormal-to-normal distribution of expressed proteins and an unusual linear dependence of their standard deviation onthe mean gene expression levels. With negative feedback circuits we find the existence of bimodality as the cell-cycleprogresses. We suggest that such long tail and bimodal distributions may be used as selection mechanisms in develop-mental switches and for assigning cell identity. We are beginning experiments to understand the role of noise in othertranscription initiation modules.



5.11.47

Partition function zeros of the two-dimensional HP model

Chi-Ning Chen1

1 Department of Physics, National Dong-Hwa University, Hualien, Taiwan 974

We study the two-dimensional lattice HP model of protein folding by partition function zeros, which are obtainedby exact enumeration and Monte Carlo simulations. We find the loci of partition function zeros relate to the foldingproperties of different HP sequences.

1 [email protected]

5.11.48

Folding of the alpha-helix and beta-sheet structures of proteins by usinga minimal off-lattice model

Chung-I Chou1, Rong-Sheng Han2, Hsu-Sheng Huang3, Yi-Wen Wu4, and Ting-Kuo Lee5

1 Department of Physics, Chinese Culture University, Taipei 111, Taiwan2,3,4,5 Institute of Physics, Academia Sinica, Nankang, Taipei 115, Taiwan

We develop an off-lattice minimal energy model of proteins. The model is composed of a polypeptide chain, andhas the Ramachandran angles as its degrees of freedom. The force field of this model is based on hydrogen bondsand the anisotropic hydrophobicity forces. The energy form of the anisotropic hydrophobicity forces is designed byanalyzing the protein data banks. By using this model, we can fold several different secondary structures of proteinsin simulations, including the alpha-helix, beta-sheet and the alpha / beta structures. We will show the comparisonswith our results and the real protein structures.

1 [email protected]


5.11.49

Single molecule analysis of translation regulation

Deepak Sinha 1 and G.V.Shivashankar2

1 National Center for Biological Sciences, TIFR-Bangalore2National Center for Biological Sciences, TIFR-Bangalore and Raman Research Institute

The temporal kinetic barriers in transcription and translation play an important role in gene regulation. Thoughfor most genes, transcription seems to be the principal regulator of gene expression, many examples are found whereexpression of a gene is regulated at the translation level. In translation, the temporal mRNA structures control themovement of the ribosome - a molecular machine. Translating the mRNA into a protein requires overcoming thesetemporal topological barriers. Although mRNA structure is presumed to be a critical determinant of translational con-trol of gene expression, to date little direct experimental evidence has addressed the significance of structure. We havedeveloped single molecule fluorescence detection methods to directly capture mRNA polymerization, secondary struc-ture formation, its conformation fluctuations and the dynamics of ribosome motors. We have also recently measuredthe ribosome forces to be of the order of 26 piconewtons during translation by monitoring the kinetics of gene expres-sion. Reference: Kinetic measurement of ribosome stalling force, Deepak Sinha, U.S.Bhalla and G.V.Shivashankar(preprint)


5.11.50

Single molecule analysis of nucleosome dynamics

Dipanjan Bhattacharya1 and G.V.Shivashankar2

1,2 National Center for Biological Sciences, TIFR-Bangalore and Raman Research Institute

In biological cells, non-specific Histone - DNA interactions, mediated by charge, are essential in the condensation ofDNA polymer into a compact chromosome. During transcription, the nucleosome-DNA complex has to be remodeledto access sequence information and the mechanisms of such remodeling are poorly understood. We have developed acombination of force and fluorescence based methods to address aspects of nucleosome stability. As a model system,we use the polytene chromosome derived from the salivary glands of drosophila larvae, in which the histone protein(H2-B) is labeled with EGFP. The fluorescence anisotropy of H2B-EGFP, which is a direct measure of the nucleosomefluidity, is measured. We find evidence that the nuclesome stability is sensitive to different regions on the chromosomeand the mechanical tuning of the chromatin structure. Our results may have implications in understanding thebiophysics of nucleosome stability in gene regulation. Reference: Development of single molecule tracking confocalmicroscope combined with force spectroscopy for gene expression analysis, Deepak Sinha, Dipanjan Bhattacharya,Bidisha Banerjee, Feroz Meeran and G.V.Shivashankar (preprint)



5.11.51

Force-induced desorption transition of a linear polymer chain adsorbedon an attractive surface

Pramod Kumar Mishra1,Sanjay Kumar2 and Yashwant Singh3

1,2,3Department of Physics, Banaras Hindu University, Varanasi, 221 005, India

We consider a model of self-avoiding walk on a lattice with on-site repulsion and an attraction for every vertex ofthe walk visited on the surface to study force-induced desorption of a linear polymer chain adsorbed on an attractivesurface and use the exact enumeration technique for analysing how the critical force for desorption fc(T) dependenceon the temperature. The curve fc(T) gives the boundary separating the adsorbed phase from the desorbed phase.Our results show that in two-dimensions where surface is a line the force fc(T) increases monotonicaly as temperatureis lowered and becomes almost constant at very low temperature. In case of three-dimensions we, however, find re-entrance, i.e. fc(T) goes through a maximum as temperature is lowered. The existence of this re-entrance is explainedon the basis that while the entropic contribution is extensive in case of adsorbed part but not in the desorbed part asthe desorbed part is in a shape of a rod perpendicular to the surface. The re-entrance in phase diagram has also beenfound in a directed walks model.


5.11.52

Mean-field theory for a network of spiking neurons storing sparselycoded random memories

Emanuele Curti1, Gianluigi Mongillo2, Giancarlo La Camera3 and Daniel Amit4

1,2 Dip. di Fisiologia Umana, Universita3 Institute of Physiology, University of Bern

4 INFM, Dip. di Fisica, Universita

A mean-field (MF) theory has been developed to provide quantitative description in terms of mean emission rates ofthe asynchronous steady states of activity of realistic recurrent networks of excitatory and inhibitory spiking neuronsstoring sparsely coded random memories. Plastic synapses have two states, potentiated and depressed. Memories areembedded within the synaptic matrix according to a stochastic Hebbian learning rule: the probability a synapse beingpotentiated depends on the number of potentiating and depressing patterns of activity experienced upon presentationof the p memories to be stored. No symmetry is assumed on the synaptic matrix: no detailed balance. The neuralpopulations subtending MF analysis are composed by neurons with the same multiplicity, i.e. the number of memoriesin which they are active. Steady emission rates are obtained self-consistently, by solving a system of 2p + 1 non-linearcoupled equations and compare well with simulations of the microscopic model. For sparse coding (f ¿ 1, f codinglevel), the number of MF-equations reduces to order (pf)

12 , because the number of memories in which a neuron is

active falls off quite sharply as the multiplicity deviates from its mean value fp. The theory allows to study theexistence of retrieval states as a function of network parameters.



5.11.53

Fluctuation force spectroscopy of biological interactions

G.V.Soni1 and G.V.Shivashankar2


We study the potential energy interaction landscape and its modulation between biomolecules in a Brownian world.Such landscape plays an important role in the interaction between RNA polymerase (a molecular motor) and theDNA promoter sequence to initiate gene transcription. Fluctuations of a spring, tethered with RNA polymeraseand interacting with a single DNA molecule provide a powerful method to analyze the interaction energy landscape.As a first step to realizing this, we have developed single particle tracking of an optically trapped bead wherethe Langevin forces of 32 femto-newtons on a 3 mm trapped bead is measured. Using this method, we haverecently studied the onset of correlations in bacterial dynamics, where we find that the motile bacterium exertsa mean force of 76 femto-newtons on the trapped bead. Such correlated dynamics lead interesting regimes ofdynamic viscosity. We are currently refining the methodology, by using force cantilever and fluctuation analysis, tocapture the interaction between a RNA polymerase and the DNA molecule - which forms the basis for gene expression.

References :[1] Single particle tracking of correlated bacterial dynamics, G.V.Soni, B.M. Jaffar Ali, Y.Hatwalne andG.V.Shivashankar, Biophysical Journal (2003), 84, 2634-2637.[2] Development of an optical tweezer combined with micromanipulation for DNA and Protein nanobioscience,G.V.Soni, Feroz Meeran, T.Roopa and G.V.Shivashankar, Current Science (2002), 83, 1464-1470.[3] Single particle nanorheology of self-propelled active particles, G.V.Soni, G.Ananthakrishna and G.V.Shivashankar(2003) preprint.


5.11.54

Gene networks using pairwise BLAST score for identifying“homologous” genes in Mycoplasma pneumoniae

Anchal Vishnoi1, Vivek2, Himanshu Agrawal3 and Ramakrishna Ramaswamy4

1,2,3 School of Information Technology, Jawaharlal Nehru University, New Delhi, India.4 School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India.

Genomic evolution mechanisms — fusion, fission, and translocation of segments of DNA — result in duplication andfragmentation of genes. We study sequence similarity in genes of Mycoplasma pneumoniae to understand evolution ofits genome. We use normalized pairwise BLAST score to construct gene network with links connecting “homologous.”The network is constructed using a thresholding procedure. Threshold is selected by minimizing the homogeneity ofresulting networks. Analysis of the networks shows that genes sharing the same functional group classify together.



5.11.55

Gene networks using positional nucleotide frequency for classifyinggenes by evolutionary path in Escherichia coli

Vivek1, Anchal Vishnoi2, Himanshu Agrawal3 and Ramakrishna Ramaswamy4

1,2,3 School of Information Technology,Jawaharlal Nehru University, New Delhi, India4 School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India

Genome evolution involves both vertical inheritance and horizontal transfer of genetic material. Several methods havebeen devised to classify genes into vertically inherited and horizontally transferred groups. We investigate the use ofpositional nucleotide frequency to classify genes into these categories for Escherichia coli. Every gene is representedas a 12-dimensional vector, each dimension corresponding to fractional content of a base in codon positions 1, 2, or3. We construct networks from the data, with links representing similarity in evolutionary origin of genes, using analgorithm having one parameter Q. We consider the range of Q for which the networks are maximally inhomogeneous.Analysis of these networks reveals that many horizontally transferred genes classify together.


5.11.56

Finite size scaling of structural transition in a model four helix bundleprotein

Prem P. Chapagain1 and Bernard S. Gerstman2

1,2 Department of Phyiscs, Florida International University, University Park, Miami, FL 33199, USA

Using lattice Monte Carlo simulations, we investigate the characteristics of unfolding transitions of a model four-helixbundle, which contains elements of protein secondary and tertiary structure. The unfolding occurs cooperatively witha sharp peak in the heat capacity curve. By varying the helical turns as identical units, we calculated the criticalexponents for different strengths of hydrophobic interactions under the framework of finite size scaling theory. We findthat the critical exponents and hence the nature of the transition depend on the strength of hydrophobic interaction.



5.11.57

Design and extraction of energy parameters for protein fold recognition

Muyoung Heo1, Suhkmann Kim2, Mookyung Cheon3, Eun-Joung Moon4, Kwanghoon Chung5, andIksoo Chang6

1,2,3,4,5,6 National Research Laboratory for Computational Proteomics and Biophysics, Department of Physics, PusanNational University, Pusan 609-735, Korea

Using the protein threading and perceptron learning, we designed the various forms of energy parameters for therecognition of native state of proteins. We proposed several forms of one and two body energy functions among aminoacids in the physical and biological parameter spaces. We benchmarked our energy parameters to identify the nativefold for a new set of proteins, and report a remarkably high (> 95%) success ratio for identifying the native fold. Wealso discuss the implication of various parameters, and extend the possible application of these parameters.


5.11.58

Chaotic itineracy in the oscillator neural network without Lyapunovfunctions

Satoki Uchiyama1, and Hirokazu Fujisaka2

1Department of Artificial Complex Systems Engineering,2Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Chaotic itineracy (CI), which is defined as an incessant spontaneous switching phenomenon among multi-quasiattractors in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case ofan oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S.Uchiyamaand H.Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neuro-dynamics. It is fount that CI in neural nets can be understood as the intermittent dynamics of weakly-destabilizedchaotic retrieval solutions.

1 [email protected]@acs.i.kyoto-u.ac.jp


5.11.59

Retarded Error Catastrophe in a Two-dimensional Growing System

Shoichi Toyabe1 and Masaki Sano2

1,2 Department of Physics,the University of Tokyo,Tokyo 113-0033,Japan

Although evolution often entails physical space, interactions between the space and the evolution remain incompletelyunderstood. Spatial structure will impose restraint conditions on selection of elements and the selected elements willform spatial structure. On this occasion, selection of a higher order, which exceeds Darwinian principle of the survivalof the fittest, may emerge even if there is no explicit interaction between elements. We investigated error catastrophetheory in a growing pattern by cellular automata. Its known that in a open system critical error threshold Pc forcatastrophe decreases monotonically as diffusion constant D decreases, and Pc goes to 0 as D goes to 0 . However,we found that in a growing pattern error threshold Pc is always higher than in a open system and remains a finitevalue as D goes to 0 because wild types grow more rapidly than mutants and prevent the growth of mutants spatially.Additionally, although diversity of species becomes large when D is small, information for the wild types survive longtime. This situation resembles disparity theory of evolution proposed by Furusawa et al. We conclude that formationof a growing pattern may be an advantageous strategy for evolution.


5.11.60

Biological two-species systems described by cellular automata

Tania Tome1 and Kelly Carvalho2

1,2Institute of Physics, University of Sao Paulo, Sao Paulo, Sao Paulo, Brazil

We consider two probabilistic cellular automata to analyse the sthocastic dynamics of a biological two-species system.We focus our attention on the dynamic patterns exhibited by both models. Performing Monte Carlo simulations weobserve a time oscillating behavior that occurs at a local level. We also study the phase diagram of the models. Theseare very rich and exihibit nonequilibrium phase transitions from an absorbing state to an active state.

[email protected]@if.usp.br


5.11.61

Solitons in a DNA Lattice and the Principle of Genomic instability

Tapas Kumar Sinha1

1 Computer Centre, Bijni Complex, North Eastern Hill University, Shillong, 793 003 India

ABSTRACT In a recent paper (1) Liang et. al. have reported ESR observation of both a slow, large amplitudecollective mode and a faster internal oscillation mode in DNA of varying sizes tethered by spin labels . We suggestin this paper that the large amplitude mode corresponds to a tanh soliton and the faster mode corresponds to thekink soliton. Expressions for the Tanh soliton as well as the kink soliton are derived (2). ESR profiles based onthese solutions exhibit reasonable agreement with corresponding experimental profiles. We further suggest that DNArepair proteins (which can bind only onto single strands) bind to looped out single stranded region of the Tanh Solitonthereby initiating DNA repair. The presence of the Tanh Solitons is a thus a necessity for the survival of the DNA. Onthe other hand, if one affects the looped out region in any way (i.e. shape, velocity of the Tanh Soliton, for instanceby either binding a ligand, damaging the base) so that DNA repair proteins do not bind, then DNA repair will nottake place leading to improper functioning of the DNA even its extinction. This is the principle of genomic instability.References: 1) Liang et. al., J. Phys. Chem., B 2000, 104, 5372-5381 2) A Model for DNA and DNA Repair System ByT. K. Sinha and R. N. Sharan, Trends in Radiation and Cancer Biology edited By R. N. Sharan, ForschungszentrumJulich GmbH, 1998

1 [email protected]


5.11.62

Coherent States in a DNA Lattice

Tapas Kumar Sinha1

1 Computer Centre, Bijni Complex, North Eastern Hill University, Shillong 793 003

The recent discovery of coherence in chaotic oscillators [1]-[4] has spurred researchers working with chaos or close tochaos to look for coherence in their systems. One such system is the DNA. The interactions of the DNA are nonlinear[5]. Systems with non linear interactions are known to exhibit chaos. In this paper we ask whether the nonlinear interactions in the DNA can induce coherence in the DNA Lattice. We show in this paper that Solitons in aDNA Lattice can induce a spatio-temporal coherence in the DNA Lattice. This result is verified by the observationof coherent emissions (or Biophotons) from the DNA of living cells [6].

References :[1] Zonghua Liu and Ying-Cheng Lai, PRL, 21, 4737 (2001).[2] A. S. Pikovsky and J. Kurths, PRL, 78, 775 (1997).[3] A. Neiman, P. L. Saparin and L. Stone, PRE 56, 270 (1997); S. G. Lee, A. Neiman and S. Kim, PRE 57, 3292(1998); T. Ohira and Y. Sato, PRL 82, 2811 (1999); A. Neiman et. al., PRL, 83, 4896 (1999); B.Linder and L.Schimansky-Gier, Phys. Rev E 60, 7270 (1999); 61, 6103 (2000);Y. Yang et. al., PRE 61,740 (2000); B. Hu and C.Zhou, PRE, R1001 740 (2000); M. C. Eguia and G. B. Mindlin, PRE 61, 6490 (2000); Y. Jiang and H. Xin, PRE 62,1846 (2000).[4] D. E. Postonov et. al., PRE 59, R3791 (1999); S. K. Han et. al., PRL 83, 1771 (1999); G. giacomelli et. al., PRL84, 3298 (2000).[5] A Model for DNA and DNA Repair System By T. K. Sinha and R. N. Sharan, Trends in Radiation and CancerBiology edited By R. N. Sharan, Forschungszentrum Julich GmbH, 1998.[6] F. A. Popp et. al., Physical aspects of Biophotons, Experientia, 44, 576 (1988); F. A. Popp et. al., Emission ofvisible and ultraviolet radiation by active biological systems, Coll. Phenomena, 3, 187 (1981);D. H. J. Schamart andR. Van Wijk, Photon emission and the degree of differentiation in Biological Systems(B. Jezowska-Trzebiatowska et.al., eds.) 137 (1987).

1 [email protected]


5.11.63

Physical Basis of coherent emissions from the DNA of living cells

Tapas Kumar Sinha1

1 Computer Centre, Bijni Complex, North Eastern Hill University, Shillong 793 003

Weak Coherent emissions from living cells have been observed [1]. However the origin of these emissions is still notclear. One clue about the mechanism comes from the fact the intensity distribution is Poissonian.We have earliersuggested that large amplitude collective modes exist in the DNA lattice [2]. These solitons induce spatio-temporalcoherence. The solitons interact with the base pairing protons. Coherent de-excitations of the base pairing protonsresults in in the observed coherent emissions. We also find that the intensity distributio profile has a Poissoniandistribution as observed experimentally.

References :[1] F. A. Popp et. al., Physical aspects of Biophotons, Experientia, 44, 576 (1988); F. A. Popp et. al., Emission ofvisible and ultraviolet radiation by active biological systems, Coll. Phenomena, 3, 187 (1981);D. H. J. Schamart andR. Van Wijk, Photon emission and the degree of differentiation in Biological Systems(B. Jezowska-Trzebiatowska et.al., eds.) 137 (1987).[2] A Model for DNA and DNA Repair System By T. K. Sinha and R. N. Sharan, Trends in Radiation and CancerBiology edited By R. N. Sharan, Forschungszentrum Julich GmbH, 1998.

1 [email protected]

5.11.64

An exact theory of histone-DNA adsorption and wrapping

Tom Chou1

1 Dept. of Biomathematics, UCLA

We find exact solutions to a one-dimensional (1D) interacting particle theory and apply the results to the adsorptionand wrapping of polymers (such as DNA) around protein particles (such as histones). Each adsorbed protein isrepresented by a Tonks gas particle. The length of each particle is a degree of freedom that represents the degreeof DNA wrapping around each histone. Thermodynamic quantities are computed as functions of wrapping energy,adsorbed histone density, and bulk histone concentration (or chemical potential); their experimental signatures arealso discussed. Histone density is found to undergo a two-stage adsorption process as a function of chemical potential,while the mean coverage by high affinity proteins exhibits a maximum as a function of the chemical potential. However,fluctuations in the coverage are concurrently maximal. Histone-histone correlation functions are also computed andexhibit rich two length scale behavior.

1 [email protected]


5.11.65

First passage distributions of pulling-assisted DNA unzipping

Greg Lakatos1, Birger Bergersen2 and Tom Chou3

1,2 Dept. of Physics, UBC3 Dept. of Biomathematics, UCLA

We investigate the voltage-driven transport of hybridized DNA through membrane channels. As membrane channelsare typically too narrow to accommodate hybridized DNA, the de-hybridization of the DNA is the critical rate limitingstep in the transport process. Using a two-dimensional stochastic model as well as a Fokker-Plank approach, we showthat the de-hybridization process proceeds by two distinct mechanisms; thermal denaturation in the limit of lowdriving voltage, and direct stripping in the high to moderate voltage regime. Additionally, we investigate the effectsof introducing defects into the DNA strand.


5.11.66

Forcing self-assembled biomolecular structures using optical tweezer

T.Roopa1 and G.V.Shivashankar2

1,2 National Center for Biological Sciences, TIFR-Bangalore and Raman Research Institute

Application of localized point like forces perpendicular to the membrane layer leads to membrane nanotubulation.We report a novel regime of tubule formation in multi-lamellar membrane vesicles using an optically trapped bead toapply a localized sub-pN force on a cationic vesicle. The force extension curves reveal a saturation phase, with thetubule length extending up-to tens of microns, beyond a threshold force of 0.6 pN ± 0.2 pN. Such tubulation processshows no evidence of hysterisis, suggesting a new flow phase in multi-lamellar membrane vesicle tubulation. Furtheran oscillatory force exerted during tubulation leads to an interesting observation of resonance at a characteristicfrequency, presumably matching the time scales of the flow phase. We then use the tubule as a sensor for monitoringthe dynamics of charge induced DNA integration on cationic membrane vesicles. We are currently exploring theseapproaches to the study of long-range correlations within chromatin assembly.

References :[1] Nanomechanics of membrane tubulation and DNA assembly, T.Roopa and G.V.Shivashankar Applied PhysicsLetters (2003), 82, 1631-1633.[2] Dynamics of membrane tubulation and DNA assembly, T.Roopa, N.Kumar, S.Bhattacharya and G.V.Shivashankar(2003) preprint.



5.11.67

Multicanonical Chain Growth Method for Folding Lattice Proteins

Michael Bachmann1 and Wolfhard Janke2

1,2 Institut fur Theoretische Physik, Universitat Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany

We present a temperature-independent Monte Carlo method for the determination of the density of states of latticeproteins that combines the fast ground-state search strategy of nPERM chain growth algorithms with multicanonicalreweighting ideas for sampling the full energy space. Since the density of states contains all energetic information of astatistical system, we can directly calculate the mean energy, specific heat, Helmholtz free energy, and entropy for alltemperatures. We demonstrate the efficiency of this method in applications to lattice proteins described by the effectivehydrophobic-polar HP model. For a selected sample of HP sequences we first discuss ground-state properties, and thenidentify and characterize the transitions between native, globule, and random coil states for increasing temperature.For short sequences with up to 19 monomers we validate our numerical results by comparison with exact enumerationdata.


5.11.68

Analysing (gene expression) data by a map to permutations

T.M.A. Fink1,F.C.S. Brown2 and K. Willbrand3

1Institut Curie, CNRS UMR 144, 75248 Paris Cedex 05, France2Dartement de Mathematiques, Ecole Normale Supieure, 75231 Paris Cedex 05, France

3Laboratoire de Physique Statistique, Ecole Normale Supieure 75231 Paris Cedex 05, France

We introduce a new approach for analyzing data. Application is focused on gene expression data. It is distinct fromthe common clustering method. We compare the gene expression results to properties of random data: we assume thatbiologically interesting results are rare events for the random model. An essential point of the choosen model is itsindependence from the type of noise in the data. This is achieved by mapping the space of sequences of N real valuesto the space of permutations of size N. Calculations are then done for the distribution of the sequence’s signature. Theidea of working on permutations can also be used to create a new gene-gene distance measure, able to be included inclustering algorithms.



5.11.69

On the growth and structure of the leaf venation networks

Yves Couder1,Ludovic Pauchard2 and Steffen Bohn3

1Laboratoire de Physique Statistique, 24 Rue Lhomond, 75231 Paris cedex 05, France2Laboratoire FAST, Campus Universitaire, 91405, Orsay, Cedex, France3Rockefeller Univerity, 1230 York Avenue, New York, NY10021, USA

The venation patterns of plant leaves exhibit a large variety of morphologies. One of the usual hypothesis for theformation of the veins patterns is that they result from growth in a diffusive concentration field, i.e. in a scalar field.But the observed morphologies, in particular the anastomosis of different veins, are difficult to understand in thisframework. In contrast it is argued here that these morphologies correspond to what would be expected if the growthoccurred in a tensorial field. In order to support this hypothesis, analogic experiments on the growth and morphologiesof cracks in a dessicating gel are done. By choosing adequate boundary conditions it is possible to obtain patternshaving the same geometry as venation patterns of both dicotyledons and monocotyledons. The analogy of cracks andveins suggests two hypotheses: i) A mechanical stress field is generated inside the leaf during the parallel growth oftwo different types of tissues: the mesoderm and the epidermis. ii) Strands of cells of the mesoderm differentiate intoprocambial cells as they are submitted to a mechanical stress larger than a threshold value. The relevance of thesehypotheses is discussed in relation with existing botanical data.


5.11.70

An effective membrane model of the immunological synapse

Subhadip Raychaudhuri1,Arup K. Chakraborty2 and Mehran Kardar3

1,2Departmet of Chemical Engineering, University of California Berkeley, Berkeley USA3Department of Physics, Massachusetts Institute of Technology, Cambridge USA

The immunological synapse is a patterned collection of different types of receptors and ligands that forms at theintercellular junction between T lymphocytes (T cells) and antigen presenting cells (APCs) during recognition. Wederive a minimalist model for the immunological synapse formation that includes membrane mechanics, binding energyof receptors and ligands, and thermal fluctuations. Numerical simulations of the model show synaptic patterns witha stable central cluster of TCR proteins as observed for mature T cells, in vivo and in vitro. As we decrease theTCR protein concentration, the stable central cluster disappears and a dynamic multifocal pattern of TCR proteinsemerges. This explains why immature T cells (DP Thymocytes), where the initial TCR concentration is much lowercompared with that of the mature T cells, form such dynamic synapses. We show that the transition between the twodifferent classes of synaptic patterns, as the TCR concentration is decreased, is determined by the temperature andthe flexibility of the receptor-ligand bonds.




5.12.1

Two dimensional potential mapping-Monte Carlo Simulation

J.Meena Devi1 and K.Ramachandran2

1,2 School of Physics, Madurai Kamaraj University,Madurai-625021,India

Monte Carlo simulation to solve a Laplaces Equation for potential has been implemented here for simple configurationand compared with the real experiments. A two dimensional electrolytic tank model is constructed to verify thesesimulation results. The experiment is first carried out with three laminas placed vertically in a triangular shape andthree different voltages were applied. The voltages at different points inside the envelope of three laminas are measuredusing a multimeter. Instead of solving this by Laplace equation, using random numbers and the special algorithmdeveloped, the voltages are computed. The vertices of the triangle as seen from the electrolytic tank model are takenas the input. Let them be A , B and C . The point where measurement is to be done is taken as P and it is connectedwith vertices A, B and C to form three small triangles ABP, BCP, CAP. Randomly some point D is chosen using therandom number generator and it is checked in which small triangle it falls. NA, NB, NC is considered as number ofsuccesses out of N trials that fall within triangles ABP, BCP, CAP respectively. A suitable program is written for thisand executed for different trials. Then the voltage at point P from elementary statistics is calculated as VP = (NBNcVA + NANCVB + NANB VC) / (NANB+NBNC+NCNA) These results from the simulation program along withthe experimental results of electrolytic tank agree quite well.


5.12.2

Cluster weighted modeling and prediction of spatiotemporal systems

Anandamohan Ghosh1, V. Ravi Kumar2 and B. D. Kulkarni3

1,2,3 Chemical Engineering Division, National Chemical Laboratory, Pune 411 008, India.

The prediction of dynamics of spatiotemporal systems is difficult because of the large dimensionality that arises due toconsideration of the spatial domain and extension of data prediction methods developed for low-dimensional systemsis not applicable in a straightforward manner. Wavelet transforms offer superior spatial localization properties whileaccurately projecting the spatial features over long segments of data. The wavelet basis functions have been used inconjunction with probabilistic density estimators in cluster weighetd model for spatiotemporal data prediction. Themethodology developed has been exemplified for the Kuramoto-Sivashinsky (KS) equation and coupled map lattices(CML) as prototype spatially extended systems although the principles can be applied to any dynamical systemswithout any loss of generality.



5.12.3

Statistical-mechanical approaches for phase retrieval by the Q-Isingmodel

Yohei Saika1 and Hidetoshi Nishimori2

1 Department of Electrical Engineering, Wakayama National College of Technology, 77 Noshima, Nada, Gobo,Wakayama 644-0023, Japan

2 Department of Physics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro, Tokyo 152-8551, Japan

On the basis of statistical mechanics of the Q-Ising model, we formulate the problem of phase retrieval which isappearing in adaptive optics. Our method is based on the Bayes inference and we retrieve phases using a set ofnoisy phase differences observed at the sampling points on the grid of optical instruments. Then, we estimate theperformance of our method using the replica theory for the infinite-range model and the Monte Carlo simulation forthe two-dimensional realistic model in adaptive optics. The replica theory obtains the result that our method workswell when we appropriately tune parameters, if the Nyquist condition holds. Then, this result is confirmed by theMonte Carlo simulation for a typical sample in adaptive optics. On the other hand, when the aliasing occurs dueto under-sampling, the Monte Carlo simulation gives the result that phase retrieval is possible by our method if weuse the initial phase pattern generated by the smoothness condition. These results are summarized that phases areretrieved well, if we select the appropriate model of the true prior respective of the sensitivity of sampling.


5.12.4

Characteristics of Non-Gaussian Fluctuations in Financial Time Series

Baosheng Yuan1 and Kan Chen2

1,2 Department of Computational Science, Faculty of Science, National University of Singapore, Singapore 117543

We introduce a new approach to analyze financial time series using the distribution of conditional returns. With thisapproach we are able to demonstrate clear return/volatility clustering, scalability, and predictability in real financialtime series. We find that most financial time series can be described by a ”transient” dynamics with the Hurstexponent ∼ 0.6 at small time scales (T < Tc), and by a ”recurrent” dynamics with the Hurst exponent ∼ 0.5 atlarge time scales (T > Tc). Based on these emperical results, we construct a simple model incorporating short-timetrend-clustering and long-time mean-reversal. We show that the simulation data generated from the model possessmost important statistics of non-Gaussian fluctuations in real data. We expect the model be potentially useful foroption pricing.



5.12.5

Analytic study of wealth distribution function using a trading model

Arnab Das1 and Sudhakar Yarlagadda2

1,2 Saha Institute of Nuclear Physics, Calcutta, India

We develop a general formalism, similar to Boltzmann transport theory, to obtain the distribution function for wealthand income as a function of time. Within this framework, we analyze the wealth distribution in a society by proposinga model which involves two-party trading (with- and without-savings) among poor people while for the rich interactionwith wealthy entities (huge reservoir) is relevant. At equilibrium, the trading with large entities gives a Pareto-likepower law behavior in the wealth distribution while the two-party interaction yields a distribution similar to thatreported earlier by the present authors [Physica Scripta T106, 39 (2003)].


5.12.6

A framework that represents multiagent systems with co-evolvingdependence among agents

Suhan Ree1

1 Dept. of Industrial Information, Kongju National University, Chungnam, KOREA

In multiagent systems, the time evolution of the state of each agent is influenced by states of other agents, and whichagents each agent depends on at a given time is described by dependence among agents. In general, states of all agentsand the dependence among agents co-evolve with time. When the time scale for the evolution of the dependence iscomparable to that of the evolution of agents, a framework incorporating co-evolving dependence is necessary. Here weintroduce a discrete-time framework in which states of all agents and the dependence co-evolve in discrete timesteps.The evolution of the dependence is determined not only by states of all agents, but by given abstract rules as wellin some cases. This framework can be reduced to many exiting models such as cellular automata, network evolutionmodels, and some models describing many-body systems in nature. As an example, we choose a system of N randomwalkers in a two-dimensional lattice. Each random walker is given a number, which can be interpreted as an opinion,and interacts with others locally and by given abstract rules. After performing the simulation, we observe somestatistical properties of the system.

1 [email protected]


5.12.7

Frustrated lattice gas and its application to probabilistic informationprocessing

Jun-ichi Inoue1

1 Complex Systems Engineering, Graduate School of Enginnering, Hokkaido University, Kita-ku, Sapporo 060-8628,Japan

We applied a kind of spin glass — frustrated lattice gas [1] — to the problems of probabilistic information processing,namely, associative memories of stochastic neural network and Bayesian image restoration. For associative memories,we reformulate the Hopfield model so that each neuron in the network is created or annihilated dynamically.Consequently, the network changes its structure by controlling thermal noise and chemical potential. We investigatethe phase diagram of the system and obtain the chemical potential dependence of the optimal loading rate analytically.For Bayesian image restoration [2][3], we label each pixel using lattice gas variable ni = 0, 1 so as to represent ”edges”at the pixel labeled by ni = 0. Thus, we construct the prior distribution by the ferromagnetic lattice gas model. Weevaluate the performance of restoration by analysis of the mean-field model and applying so-called Belief propagationto standard images.

References :[1] A. Coniglio, J. Phys. IV France, 3 C1-1 (1993).[2] J. Inoue and K. Tanaka, J. Phys. A : Math. Gen., 37 p. 10997 (2003).[3] K. Tanaka, J. Inoue and D.M. Titterington, J. Phys. A : Math. Gen., 37 p. 11023 (2003).

1 [email protected]

5.12.8

Study the cardiorespiratory synchronization by using the empiricalmode decomposition method

Ming-Chya Wu1, Chin-Kun Hu2 and Chung-Kang Peng3

1,2 Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan3 Cardiovascular Division, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts

02215, USA

The empirical decomposition method (EMD) and the Hilbert spectral analysis are used to study the synchronizationbetween human heartbeat and respiration. The intrinsic mode functions (IMFs) obtained from EMD are regarded asrespiratory rhythms. Our results also reveal the existence of cardiorespiratory synchronization. The scheme we usedhere can also be applied in the studies of other physiological signals.



5.12.9

Power-law tail in income distribution

Arnab Chatterjee1 and Bikas K. Chakrabarti2

1,2 Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata700 064, India.

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and eachtrading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensityλ of agents, such that each agent saves a fraction λ of its money and trades with the rest. Introducing (quenched) savingpropensity of the agents, distributed widely between the agents (0 ≤ λ < 1), the system remarkably self-organizesto a critical Pareto distribution of money P (m) ∼ m−(ν+1) with ν ' 1. We analyse the robustness (universality) ofthe distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural onein the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines twocentury-old distributions: Gibbs (1901) and Pareto (1897) distributions. We discuss a class of similar simple modelsgiving a non-integral value of Pareto index. We compare these results with observations on wealth distributions ofvarious countries.


5.12.10

Optimization with hysteresis

Karoly Ferenc Pal1

1 Institute of Nuclear Research of the Hungarian Academy of Sciences, Bem ter 18/c, Debrecen, H-4026 Hungary

Magnetic samples may be demagnetized with an alternating external magnetic field of slowly decreasing amplitude.After the process the sample ends up in a state, which has not only a virtually zero magnetization, but also aremarkably low energy. Recently, we have proposed a quite general optimization algorithm based on this principle.For finding low energy states of disordered magnetic systems, the application of the algorithm is straightforward.We applied it successfully to Sherrington-Kirkpatrick and Edwards-Anderson spin glasses, for the former case thealgorithm performed especially well, it was able to find even ground states of fairly large samples. Extending thenotion of magnetic field, we generalized the method to a much wider range of optimization problems. We applied thisidea to instances of the traveling salesman problem. For every problem it was tried, the method performed as wellas one may reasonably expect from a general purpose heuristic optimization algorithm. We found it somewhat moreeffective than simulated annealing every time.

1 [email protected]


5.12.11

Double End Growth Walk

M. Ponmurugan1, V. Sridhar2 and K.P.N. Murthy3

1,2,3 Materials Science Division, IGCAR, Kalpakkam - 603 102

We propose a method(DGW) for generation of excluded volume lattice random walk of contour length comparable tothose of real polymer molecules. An essential feature of this method is that, a walk can be grown along either ends;the growth stops only when attrition sets in at both the ends. Employing this method, homopolymer configurationswere generated with number of monomers upto 200. We find there is a reduction of attrition by a factor of 3. Wecalculated the radius of gyration exponent, the entropy exponent and the cross over exponent for this ensemble. Wefound the walk belongs to the same universality class as self avoiding walks.


5.12.12

Multi-asset minority game

Ginestra Bianconi1 and Matteo Marsili 2

1,2 The Abdus Salam Center for Theoretical Physics,Trieste Italy

We discuss a simple model based on Minority Game in which players can choose to play in different assets. Themodel is evolved following a dynamics that minimize the predictability of both the assets.As in the canonical MinorityGame we observe a phase transition between a phase with zero predictability and a phase with non zero predictability.Moreover depending on the available information in the two assets the players choose to play preferentially in one ofthe two assets. We present simulations and we compare with analytical results of the model.



5.12.13

Finding Communities on Complex Networks via ”Max-flow, Min-cut”Theorem

Seung-Woo Son1, Hawoong Jeong2 and Jae Dong Noh3

1,2 Dept. Physics, Korea Advanced Institute of Science and Technology(KAIST), Daejeon, KOREA3 Dept. Physics, Chungnam National University, Daejeon, KOREA

Finding communities out of complex networks has many important applications including social science study. In thiswork, we developed a new community finding method based on the ”max-flow, min-cut” theorem in graph theory.The ”max-flow, min-cut” theorem is finding set of links which limits the flow when we try to send maximum trafficfrom a given source to sink node. Using this set of links, we can separate the network into two domains (source andsink domains, respectively). After repeating this process for all pairs of source and sink nodes, we suggest a methodto determine the number of communities in the network, simply by comparing the number of nodes in each domain.Based on this domain information, we find corresponding communities successfully. We also show that this method isapplicable to weighted networks with excellent performance.


5.12.14

Local structural organization of metabolic networks

Young-Ho, Eom1 and Hawoong, Jeong2

1,2Dept. of physics, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon, Korea

Metabolism, the sum of all chemical reactions within a living organism, is a very important complex cellular network.Although the global topological organization of metabolic networks is well understood, local structural organization isstill not clear. By analyzing subgraphs of metabolic networks of 43 organisms, we identified network motifs, which arestatistically significant subgraph patterns, of metabolic networks. This may indicate that these metabolic networkshave the local organization principle. In addition, we discussed local properties of each subgraph pattern and biologicalsignificance of each patterns.

[email protected]@kaist.ac.kr


5.12.15

A Random Matrix Theory Approach to Collective Behavior in FinancialMarkets

Vasiliki Plerou1, Parameswaran Gopikrishnan2, Bernd Rosenow3 and H. Eugene Stanley4

1,2,4 Center for Polymer Studies and Dept. Of Physics, Boston University, Boston MA 02215, USA3 Universitat du Koln, Germany

We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory(RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-minreturns of 1000 US stocks for the 2-yr period 1994–95 (ii) 30-min returns of 881 US stocks for the 2-yr period 1996–97,and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962–96. We test the statistics of the eigenvalues λi ofC against a “null hypothesis” — a random correlation matrix constructed from mutually uncorrelated time series.We find that a majority of the eigenvalues of C fall within the RMT bounds [λ−, λ+] for the eigenvalues of randomcorrelation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matricesand find good agreement with the results for the Gaussian orthogonal ensemble of random matrices — implyinga large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distributionof eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound displaysystematic deviations from the RMT prediction. In addition, we find that these “deviating eigenvectors” are stablein time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds toan influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whoseidentities correspond to conventionally-identified business sectors.


5.12.16

Scale-free network on a vertical plane.

G.Mukherjee1, S.S.Manna2 and Parongama Sen3

1,2 S.N.Bose National Centre for Basic Sciences,Salt Lake,Kolkata-700098,India.3 Dept.of Physics,University of Calcutta,Kolkata-700009,India.

A scale-free network is grown in the euclidean space with a global directional bias. On a vertical plane, nodes areintroduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodeswhich are below it using the attachment probability: πi(t) ∼ ki(t)`α. Our numerical results indicate that the directedscale-free network for α = 0 belongs to a different universality class compared to the isotropic scale-free network. Forα < αc the degree distribution is stretched exponential in general which takes a pure exponential form in the limit ofα → −∞. The link length distribution is calculated analytically for all values of α.



5.12.17

Ideal traffic dynamics and complementary non-ideal factor

Hyun Keun Lee1,Robert Barlovic2,Michael Schreckenberg3 and Doochul Kim4

1,4School of Physics, Seoul National University, Seoul 151-747, Korea2,3Theoretische Physik Fakult”at 4, Universit”at Duisburg-Essen, D-47048 Duisburg, Germany

An ideal traffic dynamics is designed under the limited acceleration and deceleration capabilities. The new dynamicsrealizes the common driving strategy (move fast as far as security allows) in the Cellular Automaton (CA) approach.The anticipation effect is formulated systematically due to the introduction of the deceleration capability, whichresults in physically meaningful collision-free dynamics. Three traffic states (free, synchronized, and jammed phases)are reproduced qualitatively. It is shown that the synchronized flow in this approach is a self-organized dynamicphase with its own stability. We next introduce human effect presumed responsible for the non-ideal actual driving.Driver’s overreaction to the local traffic condition is simply implemented in the model. Universal constants of trafficflow such as moving velocity of wide traffic jams and out-flux from them are realized while enhancing the quantitativefeatures of the three traffic states. Furthermore, time-headway below 1 sec is frequently observed in the free flow ofthis model, which is attributed to the platoons of freely moving vehicles. It is remarked that the time-headway below1 sec plentiful in the empirical free flow can be explained by such platoons without extraordinarily high flux in thefundamental diagram (platoon effect).

[email protected]

5.12.18

Collision dynamics of two barchan dunes simulated by a simple model

Atsunari Katsuki1, Hiraku Nishimori2, Noritaka Endo3 and Keisuke Taniguchi4

1 Department of physics and Cybermedia Center, Osaka University, Osaka 560-0043, Japan2 Department of Mathematical Sciences, Osaka Prefecture University, Sakai 599-8531, Japan

3,4 Department of Earth and Space Sciences, Osaka University, Osaka 560-0043, Japan

Collision processes of two crescentic shaped dunes called barchans are systematically studied using a simple computersimulation model. Two types of collision processes, which are coalescence and reorganization, obtained by the simu-lation shows good agreement with water tank experiments. We found that a realized type of collisions depends notonly on the mass ratio but also the lateral distance between barchans in initial conditions.Besides, a simple set ofdifferential equations to describe one-dimensional (1D) dunes collisions is introduced.The results calculated indicatedthat the main features of collision can be reproduce without lateral sand flux taken into account.



5.12.19

The friction forces as a critical feature to manufacture graded materialsapplying the brazil nut approach.

Jorge Fiscina1, Dragana Jankovic Ilic2 and Frank Muecklich3

1,2,3 Saarland University, Department of Materials Science. Geb. 22, 7. Etage. 66123 Saarbruecken, Germany.

W-Cu complex graded materials, with definite microstructures and millimeter gradients, were manufactured using theBrazil-nut approach (BNA). Since tungsten and copper are practically insoluble in solid-solid, this application of theBNA has major relevance. The granular matter bed is formed by W and Cu- agglomerates. The vibration treatmentunder wet air and gravity, is followed by the application of conventional powder metallurgy techniques. The frictionforces and restitution coefficients related to the granular mater bed depend strongly on the temperature and absolutehumidity of the wet air in which the vibration treatment is carried out. A change in the absolute humidity provokeselectrostatic charge fluctuations on the agglomerate surface and consequently on the agglomerate - agglomerate frictionforces. We study the regimes of motion as a function of the humidity by measuring the dilatation of the granularmatter bed through a laser dilatometer.


5.12.20

Random Walks on Complex Networks

Jae Dong Noh1 and Heiko Rieger2

1 Department of Physics, Chungnam National University, Deajeon 305-764, Korea2 Theoretische Physik, Universitat des Saarlandes, 66041 Saarbrucken, Germany

We investigate random walks on complex networks and derive an exact expression for the mean first passage time(MFPT) between two nodes. We introduce for each node the random walk centrality C, which is shown to to determineessentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spreadinformation over the network in a random process. Numerical simulations of an ensemble of random walkers movingon paradigmatic network models are performed to confirm the analytical prediction.



5.12.21

Multifractal analysis of time series of atmospheric pollutants

Alejandro Munoz Diosdado1, Jose Luis del Rio Correa2 and Victor Hugo Almanza Veloz3

1,3 Mathematics Department, UPIBI-IPN, Mexico City, MEXICO2 Physics Department, UAM-Iztapalapa, Mexico City, MEXICO

The multifractal analysis has been using intensively in the last years for the analysis of time series, such an analysishas revealed, for example, that the dynamics of many physiologic variables is multifractal, that is to say, if we wantto describe such time series we will need a set of fractal dimensions and not only a fractal dimension. In this work,we applied the multifractal formalism multifractal to time series of contaminant concentrations in the metropolitanarea of Mexico City. We have concentration data for several years of ozone, sulfur dioxide, carbon monoxide, nitrogendioxide, total suspended particles, particles smaller than 10 micrometers and lead. We considered time series with allthe concentration data, time series of daily maxima and time series of daily averages. The main obtained results arethe following ones: The time series of ozone, sulfur dioxide, carbon monoxide and nitrogen dioxide have a multifractalbehavior. The time series width of the multifractal spectrum of daily maxima is bigger than the time series width ofthe spectrum of daily averages; this seems to suggest that a relationship exists between the width of the spectrum andthe concentration of pollutants. Based on the multifractal analysis results we found that there is a tendency towardthe increment of the sulfur dioxide concentrations in the last years, reason why it is necessary to take measures to lowerthe concentrations of this pollutant. The work has been based on the analysis of the graphs of the Hausdorff dimensionversus the Holder exponent using the Chhabra and Jensen algorithm and the graphs of the Hausdorff dimension andthe Holder exponent versus the qth moment of the measure besides the calculation of the Shanon entropy.



5.12.22

Quantifying the Scale-free behavior of Price fluctuations and Volatility.

Parameswaran Gopikrishnan1, Vasiliki Plerou2, Xavier Gabaix3 and H. Eugene Stanley4

1 Center for Polymer Studies and Dept. of Physics, Boston University, Boston MA 02215 [ presently at: GoldmanSachs & Co., New York]

2,4 Center for Polymer Studies and Dept. of Physics, Boston University, Boston MA 022153 Department of Economics, MIT, Cambridge MA 02142, USA.

Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financialsystem huge databases now exist which facilitates the analysis of large fluctuations and the characterization of theirstatistical behavior. Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations instock price, trading volume, and the number of trades. Here we discuss the key statistics that describe large movementsin stock market activity and show that their distributions and certain correlation functions decay as power-laws withrather universal values of exponents. We also quantify the dependence of stock price fluctuations on demand andsupply. References: Gabaix, X., Gopikrishnan, P., Plerou, V. & Stanley, H.E. A theory of power law distributions infinancial market fluctuations. Nature 423, 267-70 (2003). Plerou, V., Gopikrishnan, P., Gabaix, X. & Stanley, H. E.Quantifying stock price response to demand fluctuations. Phys. Rev. E 66, 027104 (2002).


5.12.23

Structure of banking network

Hajime Inaoka1

1 Earthquake Research Institute, The University of Tokyo, Tokyo 113-0032, Japan

We analyzed a network structure formed by monetary transactions between financial institutions. The analyzed datais the records of transactions between current accounts owned by financial institutions at the Bank of Japan. Eachfinancial institution naturally defines a node of the network, while the links between a pair of financial institutions isdefined only when the frequency of the transactions between the pair exceeds a threshold. The network shows self-similarity described by a power-law degree distribution with an exponent close to 1. We also introduce a propagationfunction, which describes the propagation of the effect of a transaction on the network as a function of time. Thepropagation function follows a power law with the exponent 2. This indicates that the number of financial institutionsaffected by the effect of a transaction increases with the second power of time. The definition of the propagationfunction is similar to that of a number-radius relation, thus, the power law of the function implies a fractality of thenetwork.

1 [email protected]


5.12.24

Construction of Exact Invariants for Classical Dynamical systems inthree dimensions

Fakir chand1,Roshan Lal2 and S.C.Mishra3

1,3Deptt. of physics Kurukshetra University Kurukshetra2Deptt. of Computer science, Govt P.G. College Karnal

In the recent past there has been considerable interest in the study of TD & TID integrable classical dynamical systemsin one dimension and two dimensions. Construction of invariants for such systems facilitates the solution of non-lineardifferential equations. There exist at present no general method for testing the integrability of a given dynamical sys-tem. Here we present a general method for the construction of second constant of motion for three dimensional classicalsystem. A systematic mathematical method leads us to construct an exact invariant for classical dynamical system inhigher dimensions using a general potential equation. This potential equation provides a large class of integrable sys-tems. The above observations tempted us to extend to construct the invariant in three dimensions .Interestingly it hasbeen observed that the potential in separable in multiplication form as:- V(x1,x2,x3) = x1m x2n x3l In this case a fewremarks seem to be appropriate that the solution of the potential of above type satisfy only for m+n+l= -2. Some ofthe interesting combinations are maid to construct the second constant of motion for three dimension. These examplesare interesting because it represents a generalization of well known Fokas potential in three dimension . References:-1. Fokas, A.S.,and Lagerstrom, P.A.(1980) Journal of Mathematical Analysis and Applications.74,325. 2. Hietarinta,J.(1987) Physics Reports,147,87. 3. Kaushal R.S.,and Mishra S.C.(1986) Pramana (Journal of Physics),26,109. 4.Lakshamanan ,M and Sahadevan, R. (1984) Physics Letters,101A,189. 5. Leach,P.G.L(1981) Journal of MathematicalPhysics,22,465. 6. Whittaker,E.T.(1927).Analytical Dynamics, Cambridge University Press p.332. 7. S.C.Mishra,Reports on Mathematical Physics,Vol.32(1993) No.2

1fchand [email protected]@yahoo.com3fchand [email protected]

5.12.25

Financial Time Series from Minority Game

Fernando Fagundes Ferreira1 and Antonio Christian Silva2

1The Abdus Salam-International Centre for Theoretical Physics, Condensed Matter Section, Trieste, Italy2University of Maryland, Dep. of Physics, College Park, MD 20742

We have modeled the probability distribution of the return obtained from grand canonical Minority Game with theHeston model in different time scale. The qualitative agreement with real data encourage us to design an algorithm togenerate a financial times series based on the statistical property got from the real data. We discuss this new stylizedfact as well the crashes generated by the models studied here to show how a simple measure of risk can be defined. Wealso investigated a mixed population of agent with different investment and trading strategies focusing the analysison the agents behavior.

[email protected]@Glue.umd.edu


5.12.26

Energy Distribution in Human Travel Behavior

F.Brouers1 and A.C.Mataran-Torres2

1University of Liege, Department of Physics, B5, Liege 4000, Belgium2Instituto Superior de Cultura Fisica (ISCF), Santiago de Cuba, Cuba

Statistical methods have been introduced to understand and quantify human travel behavior. This has applications inurban and transport planning as well as in sport training. Maximum entropy techniques have been used to interpretthe energy consumption distribution. We show that the concept of generalized entropy and superstatistics can accountfor some universality found in this problem.

[email protected]

5.12.27

Modular synchronization in scale free networks

Eulsik Oh1, Kyoo Hyoung Rho2, Hyunsuk Hong3, Byungnam Kahng4 and Doochul Kim5

1,2,3,5 School of Physics, Seoul National University, Seoul, 151-742, Korea3 Shool of physics, Korea Institude for Advanced Study, Seoul, 130-722, Korea

While it was shown that many complex networks in real world comprise of modules, the cooperation among modulesand their collective behaviors have not been investigated yet. Here we study a synchronization-desynchronizationtransition on scale free networks by virtue of the modified Kuramoto model. We find that for the protein interactionnetwork and the community network model, inter-modular interactions are made through diverse pathways, so thatmost modules are synchronized with the same one phase. For the Internet and the hierarchy model, however, inter-modular interactions are made only through a few vertices, hubs, where phases synchronized intra-modularly arecanceled out. Thus each module is synchronized with their own phases



5.12.28

Detailed balance and imbalance at the greedy sites of a quenchedsandpile

Rumani Karmakar1,S. S. Manna2 and A. L. Stella3

1,2S.N. Bose National Centre for Basic Sciences, Block -JD, Sector-III, Salt Lake, Kolkata-700098.3INFM- Dipartimento di Fisica, Universita di Padova, I-35131 Padova, Italy.

Sandpile models with quenched random toppling matrices are studied on square lattice.With symmetric matricesavalanche statistics falls in the multiscaling BTW universality class. In the asymmetric case the simple scaling of theManna model is observed. The presence or absence of a detailed balance between the amount of sand released bya toppling site and the minimal quantity the same site must receive to become unstable, determine the appropriateuniversality class.


5.12.29

Double-stranded DNA Adsorption as a Quantum Three-body Problem

Zh.S. Gevorkian1, A.S. Gevorkyan2 and Chin-Kun Hu3

1 Yerevan Physics Institute, Yerevan, Armenia2 Institute for Informatics and Automation Problems, Yerevan, Armenia

3 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan

We show that a simple model for the adsorption of a double-stranded DNA (dsDNA) on a surface is equivalent to aquantum mechanical three-body problem which implies that an adsorbed state of the dsDNA on the surface is muchmore stable than that of a single polymer chain. Experimental manifestations of the obtained results are discussed.



5.12.30

Functional Complexity Measure for Networks

Hildegard Meyer-Ortmanns1

1 SES, International University Bremen, P.O.Box 750561, D-28725 Bremen, Germany

We propose a complexity measure that addresses the functional flexibility of networks. It is conjectured that thenumber of different functions a network can fulfill is reflected in topological features of the assigned graphs, resultingfrom the resolution of their vertices and a rewiring of their edges under certain constraints. The application will be aclassification of networks in artificial or biological systems, where functionality plays a central role.

1 [email protected]

5.12.31

Congestion in a communication network

Neelima Gupte1 and Brajendra K. Singh2

1,2 Dept. of Physics, IIT Madras, Chennai , 600036, India

We study network traffic dynamics in a simple two dimensional communication network with nodes which are connectedto all nearest neighbours and hubs which are connected to all nodes in a given area of influence. If the networkexperiences heavy traffic, i.e. a large number of messages are travelling on the network at the same time, congestionoccurs due to finite capacity of the nodes. We discuss strategies to manipulate hub capacity and hub connections torelieve hub congestion. We find that the betweenness centrality criterion provides a useful way of identifying hubswhich are most likely to cause congestion, and that the addition of assortative connections to the hubs of highestbetweenness centrality is the most efficient way of relieving hub congestion. This result could have useful applicationsin realistic networks.


5.12.32

Extensive Air Shower : A multifractal Process

Ashok Kumar Razdan1

1 Nuclear Research Laboratory , Bhabha Atomic Research Centre,Trombay Mumbai -400085, India

Extensive air showers (EAS) are produced when high energy cosmic rays enter atmosphere from space. We representEAS as a cantor process and study its multifractal nature. We also simulate EAS to compare multifractal nature ofsimulated showers to theoretically calculated ones.

1 [email protected]


5.12.33

Fracture and Phase Transitions on Small-World networks

Dong Hee Kim1,Beom Jun Kim2 and Hawoong Jeong3

1,3Department of Physics, Korea Advanced Institiute of Science and Technology, Daejeon, Republic of Korea2Department of Physics, Ajou Univeristy, Suwon, Republic of Korea

We numerically study the fiber bundle model on the Watts-Strogatz (WS) small-world networks subject to the localload-sharing rule. For the WS network of the size N at the rewiring probability P = 0, corresponding to the localregular one-dimensional network, we find that there exists a first-order phase transition at the critical value of theload σc ∼ 1/ ln N , i.e., σc = 0 in thermodynamic limit N → ∞. As P is increased, the first-order transition is againobserved at the critical point σc(N →∞) which shifts toward a nonzero finite value. These findings suggest that thefiber bundle model on the WS small-world network shows completely different behavior than that on the local regularnetwork


5.12.34

Speech Recognition by Using Statisticaly Independent Basis Functions

Hnio Henrique Arago Rgo1 and Allan Kardec Duailibe Barros2

1Departamento de Cincias Exatas, Centro Federal de Educao Tecnolgica do Maranho (DCE/CEFET-MA)2Departamento de Engenharia Eltrica, Universidade Federal do Maranho (DEE/UFMA)

The extraction of speech can be obtained by measures of a single or multiple-channels. In order to extract the speachin a single channel, we propose to use the speech features introducing the concept of efficient codification, that triesto imitate the way the auditory cortex gets information using the Independent Component Analysis (ICA) method,getting the basis functions of the input signal and retriving the estimated signal even when we add interferences toit. In order to obtain the extracted signal we use the Simulated Annealing optimization method. We also show theefficiency of the method in the presence of reverberation effects and the recovery of the speech signal by handling ofbasis function of other speech signals. This method can be used efficiently both to extract a single speech, as well ashighlighting new ways of approaching the speech/speaker recognition problem.

[email protected]@elo.com.br


5.12.35

Levy flights, non linear correlations, power laws and slow convergence

Iram Marcelo Gleria1, Annibal Figueiredo2, Raul Matsushita3 and Sergio DaSilva4

1 Department of Physics, Federal University of Alagoas2 Department of Physics, University of Brasilia

3 Department of Statistics, University of Brasilia4 Department of Economics, Federal University of Rio Grande Do Sul

We put forward that the sluggish convergence of truncated Levy flights to a Gaussian together with the scaling powerlaws in their probability of return to the origin can be explained by correlations in data. We analyze as well the problemof establishing the distance of a given distribution to the Gaussian. We show that whereas power laws in the secondmoment can be explained by linear correlation of pairs, sluggish convergence emerge from nonlinear autocorrelations.Our approach is exemplified with data from the British pound-US dollar exchange rate.


5.12.36

The Distribution and Scaling of return for KOSPI in Korean StockMarket

Jae Woo Lee1 and Kyoung Eun Lee2

1,2 Dept. of Physics, Inha University 253 Younghyun-dong, Nam-gu Incheon 402-751, Korea

We consider the distribution and the scaling of returns for KOSPI in Korean stock market. The central parts ofthe probability distribution function of returns are well described by the Lorentzian distribution function. However,the tails of the probability distribution function show the power-law behaviors. We also consider the multifractalcharacteristics of the returns. We calculate the generalized Hurst exponents for the return time series.



5.12.37

Geometry of minimum spanning trees on scale-free networks

Gabor Szabo1, Mikko Alava2 and Janos Kertesz3

1,3 Insitute of Physics, Budapest University of Technology, Hungary2 Laboratory of Physics, Helsinki University of Technology, Finland

The minimum spanning trees on scale-free graphs are shown to be scale-free as well, in the presence of random edgeweights. The probability distribution of the weights on the tree differs from regular lattices reflecting the typicallyshort distances (small-world property). We consider also the trees in the absence of such randomness and the ensuingmassive degeneracy, which is analyzed with graph theoretical arguments.


5.12.38

Power Law Distributions for Stock Prices in Korean Financial Market

Kyungik kim1 and Seong-Min Yoon2

1 Dept. of Physics, Pukyong National University, Pusan 608-737, Korea2 Division of Economics, Pukyong National University, Pusan 608-737, Korea

We study the distribution function and the cumulative probability for two assets, i.e. the KOSPI and the KOSDAQ,in Korean financial market. For our case, the distribution functions are consistent with the Zipfs law. It is particularlyshowed that the probability densities of price growth rates almost have the form of a exponential function. Ourobtained results are compared with those of numerical calculations of other nations.



5.12.39

Power Law Distributions for Current, Labor, and Property Incomes.

Kyungik kim1 and Seong-Min Yoon2

1Dept. of Physics, Pukyong National University, Pusan 608-737, Korea2Division of Economics, Pukyong National University, Pusan 608-737, Korea

We investigate the distribution function and the cumulative probability for Korean household incomes, i.e. the current,labor, and property incomes. The distribution functions are consistent with a power law. It is also found that theprobability density of income growth rates almost has the form of an exponential function. Our obtained results arecompared with those of other numerical calculations.

[email protected]@pknu.ac.kr

5.12.40

Effective ergodic convergence and optimization by local search heuristics

Manabu Hasegawa1

1 Institute of Engineering Mechanics and Systems, University of Tsukuba, Tsukuba 305-8573, Japan

A concept of effective ergodic convergence is applied to the design of local search algorithm for heuristic optimization.Exploration performance is evaluated by the degree of agreement among cost distributions cumulated in differentsearch histories. Numerical experiments are done on the Euclidean traveling salesman problems. First, the introducedmeasure is applied to the design of an adaptive scheduling in threshold algorithm such as simulated annealing. Thepresent adaptive scheduling works successfully for guiding the search processes to promising regions in the searchspace. Second, the measure is applied to the evaluation of diversification ability in hierarchically designed thresholdalgorithm such as the replica-exchange method. The enhancement of exploration performance can be observed in theexperimental time scale and this evaluation is expected to be useful for an adaptive design of threshold distributionand for an adaptive termination of the search processes.

1 [email protected]


5.12.41

Some Aspects of Application of Multiparticle Distribution Function toDescription of Steady Solar Wind

Natalia Romanovna Minkova1

1FTF, Tomsk State University, Lenin Ave., 36, Tomsk, 634050, Russia

The statistical approach based on the multiparticle distribution function is applied to the steady solar wind that isconsidered as a collisionless quasineutral fully ionized hydrogen plasma flow. The results are compared to one and twoparticle kinetic models and observational data for average parameters of the flow.

[email protected]

5.12.42

First Passage Properties of the Erdos-Renyi Random Graph

V. Sood1, S. Redner 2 and D.ben-Avraham3

1,2 Centre for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston,MA 02215, USA

3 Department of Physics, Clarkson University, Potsdam NY 13699, USA

We study the first-passage properties of the Erdos-Renyi random graph. An effective medium approximation isdeveloped to obtain the positive integer moments of the mean-first passage time and the mean commute time betweena pair of nodes. Within this approach, these moments are found to be independent of the fraction p of links. Thisprediction is tested by numerical simulation. However, the inverse first moment exhibits non-monotonic behavior onp that can be understood on physical grounds.

1 [email protected] [email protected] qd100clarkson.edu


5.12.43

Congestion Patterns in A Computer Network Model

Shan-Chien Chai1 and Yih-Yuh Chen2

1,2 Physics Department, National Taiwan University, Taipei, Taiwan, Republic of China

The congestion patterns occurring in a model computer network are reported in this work. The model network westudy is consisted of computer nodes located in a regular square lattice. When the source and destination routersin this network are located at the boundaries, as is done in the work of Ohira and Sawatari (Phys. Rev. E58, 193,(1998)), we find that the most congested sites are located at the center of the boundaries when phase transition beginsto set in but are located at the corners when the system is severely congested. This switch of congestion patterns willbe discussed in this work. We further study the congestion patterns when one imposes periodic boundary conditionbut allows the routers to be randomly scattered in the network. Specifically, we study how congestion is developedfor various router cluster geometries, and relate the findings with the results for the former model.



5.12.44

Equation of State of Supernova Matter

C. Das1 and R. Sahu2

1,2Dept. of Physics, Berhampur University, Berhampur - 760 007, India

Statistical mechanics is a formalism which has vast application in different branches of science. It is also used in nuclearastrophysics and in nuclear matter with considerable success. In this article we have tried to study the equation ofstate (EOS) of supernova matter using statistical mechanics. Usually massive stars ( M > M¯,where M¯ is the massof the sun) develop into supernova of type II at the end of their lives. Hydrogen burning is the chief source of energyin stars. As the star evolves, fusion of heavier nuclei like helium, carbon, silicon etc. takes place. The fusion continuesto heavier elements till the formation of iron since iron has the highest binding energy in the periodic table. Whenthe mass of iron exceeds the Chandrasekhar mass which is between 1.2 and 1.5 solar mass, the core of the star startsto collapse under its own gravity. At this point the pressure of electrons can not resist the gravitational contraction.In early collapse, inward movement is accelerated due to capture of electron. When the density of the core reaches 4X 1011 grams per cubic centimeter, neutrinoes are trapped in the core and core collapses homologously. This collapsecontinues till the density in the central part of the core reaches about normal nuclear matter density i.e 2.7 X 1014

grams per cubic centimeter. Nuclear matter is highly incompressible. Once the central part of the core reaches nuclearmatter density it offers powerful resistance to further compression. This strong resistance turns the stellar collapseinto an explosion. The remnant of this explosion is the neutron star. Within the first (0.1-1) second this star goesthrough rapid contrction and then it is identified as hot neutron star. At this stage it contains supernova matter andit is at temperature comparable to the fermi energies of its constituents. Statistical mechanics help us to understandthe properties of this matter. Here we have concentrated on the above matter consisting of neutrons, protons andelectrons. We also assume that the system is charge neutral. Two body density dependent effective nucleon nucleoninteraction [1] is used in our calculation. Electron is considered as a relativistic free particle and coulomb interactionis neglected. The starting point of our formalism is to calculate the thermodynamic potential per unit volume whichis given by

Ω = −P = −T ln trexp[− (H − µn)T

] (5.9)

Where H, P, T, µ and n are the hamiltonian, pressure, temperature, chemical potential and number density respectively.This thermodynamical potential can be expressed as linked cluster expansion analogous to zero temperature Bruckner-Goldstone expansion i.e

Ω = Ω0 + Ω1 + Ω2 + · · · (5.10)

Where Ω0, Ω1 and Ω2 are the contributions to thermodynamic potential due to unperturbed part, one-body partand two body part of the Hamiltonian. The details of our formalism is discussed in our earlier publications [2,3].We have performed our calculation for equation of state at finite temperatures T=10 MeV, 20 MeV and 30 MeV atvarious values of electron concentration Ye=.1 to .5 and nuclear matter density ρ=.025 to .8 fm−3. We have alsocalculated entropy per nucleon at various values of electron concentration and densities at temperatures 10 MeV to30 MeV. ¿From the analysis of our result of EOS we observe that for a fixed value of electron fraction, pressure riseswith density and also with temperature. We also find that on increasing the electron fraction from .1 to .5, pressurealso increases. We also mark that the increase of pressure with temperature is more on comparison to the increasein pressure with electron fraction. It may be as such that thermal energy play the dominant role over the electroncontribution. We observe that for a fixed value of electron fraction, entropy per nucleon decreases with increase indensity for temperature 10 MeV, 20 MeV and 30 MeV. But on increasing temperature, entropy increases which agreeswith the calculation made by T.Takatsuka et al [4]. However in our calculation on increasing electron concentrationfrom .1 to 0.5 entropy increases for T=20 MeV and 30 MeV for densities from .025 fm−3 to .8 fm−3. Where as attemperature T=10 MeV entropy increases on increasing electron fraction from Ye=.1 to .5 upto density 0.125 fm−3.Beyond that density, entropy increases with increase in electron fraction from Ye=.1 to .3 but from Ye=.4 to .5, itdecreases. It may be that on approching nuclear matter density, proton combines with electron resulting in decreasein entropy to some extent.

References :[1] R.K.Tripathi,J.P.Elliott and E.A.Sanderson Nucl.Phycs A380,483, (1982)[2] C.Das, R.K.tripathi and J.Cugnon Phy.Rev.Lett 56,1663,(1986)[3] C.Das, R.K.Tripathi and R.Sahu Phys. Rev. C45, 2217, (1992)[4] T.Takatsuka, S.Nishizaki and J.Hiura Prog.of.Theo.phys. 92, 779 (1994)

1chapala [email protected]


5.12.45

The Optimal path transition on Disordered Complex Networks

Sameet Sreenivasan1, Tomer Kalisky2, Lidia A. Braunstein3, Sergey V. Buldyrev4, Shlomo Havlin5,and H. Eugene Stanley6

1,4,6 Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA2,5 Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel

3 Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes3350,7600 Mar del Plata, Argentina

We study the transition between the strong and weak disorder regimes in the scaling properties of the optimal path lopt

on disordered Erdos Renyi (ER) random networks and Scale-Free (SF) networks. Each link i is associated with a weightτi = exp(ari) where ri is a random number taken from a uniform distribution between 0 and 1 and the parametera controls the strength of the disorder. For any finite a, there is a crossover network size N∗(a) or equivalently, acrossover length scale l∗(a) at which the transition occurs. We determine the functional dependence of N∗ or l∗ on a.


5.12.46

An empirical test for cellular automaton models of traffic flow

Andreas Schadschneider1,Wolfgang Knospe2,Ludger Santen3 and Michael Schreckenberg4

1Institut fur Theoretische Physik, Universitat zu K”oln D-50937 Koln, Germany2Theoretische Physik FB 10,

3Gerhard-Mercator-Universitat Duisburg, D-47048 Duisburg, Germany4Theoretische Physik, Universitat des Saarlandes, Postfach 151150, 66041 Saarbrucken, Germany

A large number of different cellular automata models have been proposed for modelling traffic flow. Based on astatistical analysis of empirical data from German highways we have developed a detailed microscopic test scenario.We compare several of the most common cellular automaton models and find that there are three levels of agreementwith the empirical data: 1) models that do not reproduce even qualitatively the most important empirical observations,2) models that are on a macroscopic level in reasonable agreement with the empirics, and 3) models that reproducethe empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed newlight on the relevant interactions in traffic flow.

• W. Knospe, L. Santen, A. Schadschneider, M. Schreckenberg: Phys. Rev. E65, 015101(R) (2002); E65, 056133(2002) and Phys. Rev. E (in press)

[email protected]@[email protected]@uni-duisburg.de


5.12.47

Typical properties of large random economies

Andrea De Martino1,Matteo Marsili2 and Isaac Perez Castillo3

1INFMUniversita di Roma La SapienzaP.le A. Moro 2, 00185 Roma (Italy)2The Abdus Salam International Centre for Theoretical PhysicsStrada Costiera 11, 34014 Trieste Italy

3Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven Celestijnenlaan 200D, 3001 Leuven (Belgium)

The optimal (‘equilibrium’) macroscopic properties of an economy with N industries endowed with different technolo-gies, P commodities and one consumer are derived in the limit thermodynamic limit with n=N/P fixed using thereplica method. When technologies are strictly inefficient, a phase transition occurs upon increasing n. For low n,the system is in an expanding phase characterized by the existence of many profitable opportunities for new technolo-gies. For high n, technologies roughly saturate the possible productions and the economy becomes strongly selectivewith respect to innovations. The phase transition and other significant features of the model are discussed in detail.When the inefficiency assumption is relaxed, the economy becomes unstable at high n. We argue that endogenoustechnological change drives the economy close to the critical point.


5.12.48

Triangular aribitrage in the foreign exchange market

Yukihiro Aiba1 and Naomichi Hatano2

1Department of Physics, University of Tokyo, Tokyo, Japan2Institute of Industrial Science, University of Tokyo, Tokyo, Japan

We show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets [1], analyzingthe time dependence of the yen-dollar rate, the dollar-euro rate, and the yen-euro rate. Based on the analysis, wepropose a model of foreign exchange rates with an interaction. The model includes effects of triangular arbitragetransactions as an interaction among the three rates. The model explains the actual data of the multiple foreignexchange rates well [1]. The model gives an explanation to an interesting feature of the fluctuation of foreign exchangerates [2]. The auto-correlation function of the fluctuation of the foreign exchange rates has been known to be negativein a short time scale [3]. Our model suggests that an important ingredient of the negative auto-correlation is thetriangular arbitrage [2, 4]. References [1] Y. Aiba et al, Physica A 310 (2002) 467-479. [2] Y. Aiba et al, PhysicaA 324 (2003) 253-257. [3] H. Takayasu, et al, in: M.M. Novak (Ed.), Fractal Properties in Economics, Paradigms ofComplexity, World Scientific, Singapore, 2000, pp. 243-258. [4] Y. Aiba et al, in: H. Takayasu (Ed.), The Applicationof Econophysics, Springer-Verlag Tokyo, 2004, pp.18-23

[email protected]@iis.u-tokyo.ac.jp

Index

Abascal Jose L. F., 82Abramson Guillermo, 335Agrawal Himanshu, 343, 350, 351Ahmed A. Z. Ziauddin, 138Ahn Yong-Yeol, 328, 342Aiba Yukihiro, 384Akihiko MINAMI, 68Akimov Vladimir, 326Alava Mikko, 265, 378Alcaraz Francisco C., 43Alet F., 24Alfinito Eleonora, 58, 307, 326Alinchenko Marina G, 276Altland Alexander, 109Alvarez Alvaro Dominguez, 89, 246Alves Tayroni Francisco de, 148Amit Daniel, 336, 349Amritkar R. E., 231Amritkar Ravindra E., 230Ananthakrishna G., 55, 61, 75, 93, 150, 206, 212, 282Ananthakrishna Garani, 228Andras Peter, 120Andrey Ladislav G., 142Andrey Pototsky,, 103Anikeenko Aleksey V, 276Ansumali Santosh, 77Anta Juan A., 269Aoki Hideo, 297Arcangelis Lucilla de, 170, 252Arenzon Jeferson J., 315Arimitsu Naoko, 235, 245Arimitsu T., 149Arimitsu Toshihico, 235, 245Arita Ryotaro, 297Arns Christoph, 104Arora B. M., 291Aste Tomaso, 90, 134Au-Yang Helen, 41, 45Auernhammer G. K., 54Azad Rajeev, 345

Bachmann Michael, 358Bagchi Biman, 81, 251, 280, 300, 342Bagchi Debjani, 153Balasubramanian Sundaram, 280Balcan Duygu, 126Balibar S., 7Bandyopadhyay Ranjini, 258

Bandyopdhyay Ranjini, 90Banerjee Bidisha, 346Bansil Rama, 257Barabasi A L, 3Baranowski Rafal, 229, 234Barbetta Camilla Ratto, 275Barbosa Marcia C, 48, 96Barbosa Marcia C., 278BArkai Eli, 79Barkai Eli, 107, 309Barlovic Robert, 368Barma Mustansir, 59, 159, 209Barqun L. Fernndez, 182Barrat Alain, 133, 218Barros Allan Kardec Duailibe, 376Barthelemy Marc, 133Bashkirtseva Irina, 231Baskaran Aparna, 83Basu Abhik, 74, 169Basu Kasturi, 118Batchelor M T, 42Baumgaertner A., 325Bec Jeremie, 73Beims Marcus Werner, 185Belyi Viatcheslav V., 198ben-Avraham D., 380Benecke Arndt, 127, 340Berche Bertrand, 178, 318Berche Pierre-Emmanuel, 318Berciu Mona, 109Berg Bernd A, 171Bergersen Birger, 357Berkovits Richard, 313Bert F., 31Bhattacharjee J. K., 163, 230Bhattacharjee Jayanta K., 161Bhattacharjee Jayanta Kumar, 186, 200, 215Bhattacharjee Somendra M., 34Bhattacharya Dipanjan, 348Bhattacharya Swati, 215Bhattacharyya Sarika Maitra, 324Bhattad Pradeep, 260Bhatt R. N., 109Bhimalapuram* Prabhakar, 331Bhuiyan G. M., 138Bianconi Ginestra, 365Binder Kurt, 23, 84, 245Biroli Giulio, 114

385

386 INDEX

Biswal B., 46Biswas Shyamal, 163Blythe R. A., 150Bobadilla Juan R., 322Bodenschatz Eberhard, 18Boettcher Stefan, 312Bohn Steffen, 70, 359Bolhuis Peter G., 88Borthwick M. A., 258Bose Indrani, 334Bouchaud J.-P., 31Bradley Phil, 49, 115Braun Petr, 109Braunstein Lidia A., 314, 383Brener Efim, 69Bresme Fernando, 269Brey J. Javier, 83Brouers F, 283, 373Brouers F., 139, 141Brovchenko Ivan, 52, 100Brown F.C.S., 358Brujic J., 244Brujic Jasna, 97Bryk Taras, 244Buceta Ruben C., 314Budini Adrian A., 198Buldyrev Sergey V., 85, 383Burnecki Krzysztof, 144Bu Shouliang, 233Bustamante C., 34

Caceres Manuel, 240Caceres Manuel O., 198Cagin Tahir, 254Cahkraborty Somendra Nath, 240Cain Philipp, 108Calleja E. de la, 213Camera Giancarlo La, 336, 349Candia A. de, 125Candia Antonio de, 114, 339Canfield P.C., 304Canosa Norma, 296Canosa Norma B., 110Carlos, 233Carrillo J.L., 213Carvalho Kelly, 353Castellano Claudio, 151Castelnovo Claudio, 223Castillo Isaac Perez, 384Caupin F., 7Cavagna Andrea, 116Cellai D., 267CERNOCH Peter, 270Chacon Enrique, 287Chaddah P., 157Chai Shan-Chien, 381Chakrabarti Bikas K., 160, 320, 364

Chakrabarti Buddhapriya, 71, 97, 210, 319Chakrabarti Dwaipayan, 300Chakrabarti Jaydeb, 214Chakraborty Arup K., 359Chakraborty Bulbul, 212Chakraborty Satyabrata, 228Chakravarty Charusita, 85, 238, 240Chamon C., 29Chamon Claudio, 223Chan C. K., 345Chand Fakir, 372Chandra Navin, 329Chandra V. Ravi, 289Chang Iksoo, 330, 352Chang Shu-Chiuan, 47, 147Chan Hue Sun, 122Chapagain Prem P, 351Chaplot S. L., 152, 165Chaplot S.L., 140Chatelain Christophe, 318Chatterjee Arnab, 364Chatterjee Sakuntala, 209Chatterji Apratim, 266Chattopadhyay M. K., 157Chaudhuri Abhishek, 224, 239Chaudhuri Debasish, 161, 284Chaudhuri Pinaki, 91Checa Ramiro, 287Chen Chi-Ning, 347Chen Chien-Fu, 167Chen Jeff Z.Y., 121Chen Kan, 234, 361Chen X. S., 282Chen Xingzhi, 200Chen Yih-Yuh, 381Chen Yonghong, 79Cheon Mookyung, 330, 352Cherepinsky Vera, 121Chernenko Ivan, 205Choi Moo Young, 167Cho Masanori, 264, 265, 333Cho Namiko, 264, 265, 333Chou Chung-I, 261, 347Choudhury N., 165Chou Tom, 148, 207, 356, 357Chowdhury Debashish, 129, 327Chowdhury Jayeeta, 290Chung Kwanghoon, 330, 352Ciamarra Massimo Pica, 81Ciliberti Stefano, 312Cohen E.G.D., 1, 59Colby Ralph H., 90Collin Delphine, 34Coniglio A., 125Coniglio Antonio, 114, 243, 252, 339Cont David dei, 40Controzzi Davide, 55

INDEX 387

Coppersmith Susan, 302Corberi Federico, 151Cornu F., 10Correa Jose Luis del, 370Cortada Maria, 269Costa-Kramer J.L., 106costa Bismarck Vaz da, 158Costa Ismael, 194Couder Yves, 70, 226, 359Coutinho-Filho Mauricio D., 316Coutinho Lenilson Pereira dos, 177Craig Erin, 190Crisanti Andrea, 117Crochik Leonardo, 183Cross M. C., 75Cuevas H., 267Cugliandolo L. F., 29Curado Evaldo Mendona Fleury, 170Curti Emanuele, 336, 349Cwilich Gabriel, 195

D’Orsogna Maria R., 148Daillant J., 25Dalton Fergal, 87Dana Syamal Kumar, 228Dan Debasis, 125Das Arnab, 362Das C., 382Das Dibyendu, 158Das Dyutiman, 290Dasgupta Chandan, 5, 71, 91, 181, 210Dasgupta I., 298DaSilva Sergio, 377Das Moumita, 61, 71, 93Das Palash, 161Das Subir K., 245Das Subir Kumar, 84Das Tushar Kanti, 242Datta Sumita, 292Dauchot Olivier, 112Dawson Kenneth A., 49, 115Dayal Prakash, 110, 302Debnath Ananya, 263Deem Michael W., 343Deen R., 277Deloubriere Olivier, 58Denteneer P.J.H., 28Deo Nivedita, 139Derenyi Imre, 123, 321Derrida Bernard, 6De Rumi, 75, 212Deserno Markus, 96Devi J.Meena, 360Dhar Abhishek, 190Dhar Deepak, 62, 66, 132Diaz M., 106Diehl Alexandre, 168

Diehl H. W., 12Dietrich S., 101, 102, 154Dietrich Siegfried, 89, 103, 246Dijkstra M., 264Ding Mingzhou, 79Diosdado Alejandro Munoz, 370Domnic Merkt,, 103Donado F., 213Dong W., 282Dufty James W., 83Dupuis A., 26Dupuis V., 31Dutta Amit, 108, 163Dutta Debabrata, 230Dutta Sreedhar B., 155Dutta Subhrajit, 166Dutta Tapati, 285

Eisenriegler Erich, 56Endo Noritaka, 368Eom Young-Ho,, 366Epstein T., 17Erp Titus Sebastiaan van, 67Erzan Ayse, 126Eskildson M.R., 304Evans Martin, 14, 192, 208Evans R., 264, 284

Fabrice Thalmann, 122Fari nas-S’anchez Ana Isabel, 178Farrelly Francis, 87Fasolo Moreno, 92, 261Feigel’man M. V., 27Feitosa Klebert, 86Feldman Dima E., 99Ferguson Allison, 212Fernndez J. Rodrguez, 182Ferreira Fernando Fagundes, 372Fielding Suzanne M, 220Fierro Annalisa, 114, 243, 252Figueiredo Annibal, 377Filho R.N. da Costa, 222Fineberg Jay, 17Fink T.M.A., 358Fiscina Jorge, 240, 369Fisher Daniel S., 114Fisher Matthew P. A., 50Forsten-Williams Kimberly, 334Fouladvand Mohmmad Ebrahim, 135Franzese Giancarlo, 85, 170Franz Silvio, 117, 310Freire J. A., 299Freire Rodrigo Teixeira Santos, 158Frey Erwin, 22, 169Frisch Uriel, 73Frydman Aviad, 313Fuentes M. A., 210

388 INDEX

Fujihara Akihiro, 187Fujimoto Masafumi, 140, 164Fujisaka Hirokazu, 352Furukawa Akira, 96

G.V.Shivashankar, 346, 348Gabaix Xavier, 371Gabrielli Pier Giuseppe, 192, 292Gabrielli Simone, 192, 292Gade Prashant M., 232Gado Emanuela Del, 252Galleas Wellington, 149Galvan Pedro Bernaola, 345Gama M. M. Telo, 91Gama M. M. Telo da, 24Gamba A., 125Gamba Andrea, 196, 339Ganapathy Rajesh, 92Gang Hu, 18Garcia-Mochales P., 106Garg Arti, 293Garg N., 179GASPARD Pierre, 63G Ayappa K, 102Gayathri V.S., 162Gazzillo Domenico, 241, 242Geiger Alfons, 52, 100Gendiar Andrej, 186Gerstman Bernard S, 351Gevorkian Zh.S., 374Gevorkyan A.S., 374Ghoshal S.K., 184Ghosh Anandamohan, 360Ghosh Shankar, 63Giacomelli Giovanni, 195Giacometti Achille, 241, 242Giampaolo Salvatore Marco, 146Giberti Claudio, 196, 236Gier Jan de, 39Gillespie D., 332Gitterman M., 172G Kripa., 337Glazier James A., 125Gleiter Herbert, 250, 271, 277Gleria Iram Marcelo, 377Glocke Stefan, 44Goh K.-I., 35Goh Kwang-Il, 132Gokhale M. R., 291Goldbart Paul M., 111, 290Goldbaum Pedro, 42Goldhirsch Isaac, 203Goldman Daniel I., 81Golestanian Ramin, 26Gomila Gabriel, 326Goncalves Lindberg Lima, 148, 177, 201Gonnella Giuseppe, 221

Gonzalez A., 141, 238Gopalakrishnan Manoj, 166, 334Gopikrishnan Parameswaran, 367, 371Gorban Alexander, 340Govezensky Tzipe, 322Govindarajan Rama, 76, 219Granato E., 222Grant Martin, 211Gregorio Paolo De, 49, 115Grempel Daniel, 308Grigera Tomas S., 312Grodon C., 264Grover A. K., 94Grover A.K., 304Gruber Christian, 61Guan Xi-Wen, 42Gupta Umesh, 184Gupte Neelima, 375Guttmann Anthony J., 13

Haake Fritz, 109Ha Bae-Yeun, 121Halter Martin, 321Ha Meesoon, 154, 159Hamer Chris J., 106Hammann J., 31Hanney Tom, 192, 208Han Rong-Sheng, 261, 347Hansen Alex, 160Hansen Jean-Pierre, 88HANSEN PER LYNGS, 328Harabayashi Minoru, 47Harden J. L., 258Harden James L., 90Harnau L., 102, 253Haro Mariano Lopez de, 201Hasegawa Manabu, 379Hashmi Ghazala, 121Hasmy A., 106Hatano Naomichi, 156, 384Hatwalne Yashodhan, 97, 126Havlin Shlomo, 36, 313, 383Hayakawa Hisao, 191Hayashi T., 149Hayryan Shura, 181Heidarian D., 28Heidarian Dariush, 288, 311Heller Urs M, 171Henkel Malte, 171Henriques Vera, 48Henriques Vera Bohomoletz, 275Heo Jiyoung, 255Heo Muyoung, 352Heras Daniel de las, 278Hernndez A. Calvo, 239Hernandez-Machado Aurora, 221Hernandez-Saldana Hugo, 305, 322

INDEX 389

Herrmann Hans, 80HESS Siegfried, 271Heusler Stefan, 109He Yong, 107Higgins M. J., 94Hilfer R., 46Hilhorst Henk J., 58Hinze G., 272Hiroto Kuninaka, 70Hisao Hayakawa, 70H Krishnan S, 102Holm C., 96Hong Hyunsuk, 167, 373Horbach Jurgen, 245Horbach Juergen, 84, 266Hori Motoo, 44Huang Hsu-Sheng, 261, 347Huang Ming-Chang, 172Hu Chin-Kun, 181, 363, 374Hyde Stephen T., 134Hyunggyu Park,, 173

Idowu Olusola C., 120III William A. Goddard, 254, 255Ilic Dragana Jankovic, 369Imamura Takashi, 211, 220Inaoka Hajime, 371Inoue Jun-ichi, 320, 363Inui Norio, 287Iqbal Naseer, 145Isambert Herve, 122Ishiguro R., 7Isobe Masaharu, 219Ito Nobuyasu, 15, 176Ivashin Anatoly Petrovich, 155, 256Iwaki Takashi, 274Izmailian Nickolay, 43Izrailev Felix M., 305

Julicher Frank, 4Jacobsen Jesper Lykke, 158Jafarpour Farhad H, 169Jagla Eduardo A., 216Jain Sanjay, 124Jaiswal D., 94Jalan Sarika, 231Jalil Mansoor Bin Abdul, 200Janke W., 46Janke Wolfhard, 318, 358Jarzynski Chris, 34Jaurez Gabriela Baez, 199Jayannavar A. M., 202Jayaprakash Ciriyam, 234Jayasri D., 248J De Coninck, 101Jedlovszky Pal, 276Jensen Mogens H., 124

Jeong Hawoong, 217, 328, 342, 366, 376Jeong Hawoong,, 366Jia L. C., 345Jimenez-Angeles Felipe, 286Jimenez Sergio, 317Johal Ramandeep S., 141John Alexander, 129Johnson D. L., 244Joos Bela, 300Jorg Thomas, 317Jose Marco V., 322Jose Prasanth P, 251Julicher Frank, 123Junior Wilson Marques, 208

K. Balamurali Krishna Mayya, 230Konig P.-M., 22Kabakcioglu Alkan, 126Kador L., 309Kager Wouter, 41Kahng B., 35Kahng Byungnam, 130, 132, 373Kalda Jaan, 74Kalelkar Chirag, 229Kalisky Tomer, 383Kaneko Yoshifumi, 66Kanter Ido, 131Kantor Yacov, 25Kardar Mehran, 359Karlin Iliya V, 77Karmakar B., 291Karmakar Rajesh, 334Karmakar Rumani, 374Karmakar Sachindra Nath, 290Kaski Kimmo, 131KASONO Katsumi, 268Kasono Katsumi, 176Kastner Michael, 53Katsuki Atsunari, 368Kaul S. N., 182Kaupuzs J, 164Kawasaki Mitsuhiro, 78Kemper Andreas, 186, 288Kenkre V. M., 210Kennett Malcolm P, 109Kertesz Janos, 131, 305, 378Khakhar D. V., 80Khandkar M. D., 159Kharlamov George Vladimirovich, 241Kharwanlang R S, 188Kim Beom Jun, 320, 376Kim D., 35Kim Dong-Hee, 342Kim Dong Hee, 376Kim Doochul, 132, 368, 373Kim Jin Min, 283kim Kyungik, 378, 379

390 INDEX

Kim Pan-Jun, 217Kim Suhkmann, 352Kim Yup, 283Kinzel Wolfgang, 131Kitahara Kazuo, 44Kitsunezaki So, 215Klumper Andreas, 44Klotsa Daphne, 321Knackstedt Mark, 104Knospe Wolfgang, 383Knoth Hans, 84Knott Michael, 122Kobe Sigismund, 302Kobryn A.E., 149Koenig Peter, 138Koga Kenichiro, 331Kolton Alejandro B., 308Kondrat S., 253Konishi Yoshinao, 287Konno Norio, 287, 297Kosterlitz J.M., 222Ko Tae-Wook, 217Kovalevsky Michail Yurievich, 155, 256Krishnamurthy H R, 28, 91, 293Krishnan Raishma, 202Krishna Sandeep, 329Kroger Martin, 271Krzakala Florent, 310Kuhl U., 295, 314Kulkarni Aditi, 260Kulkarni B. D., 360Kumar A.V. Anil, 206Kumar Anil, 153Kumaran V., 72, 197Kumar D., 293Kumar Deepak, 68, 294Kumar N., 63Kumar Niraj, 216Kumar P. B. Sunil, 250, 337Kumar P.B. Sunil, 120Kumar P.B.Sunil, 337Kumar S., 182Kumar Sanjay, 349Kumar Sanjeev, 118Kumar V. Ravi, 360Kunc K., 179Kunwar Ambarish, 129, 327Kuperman Marcelo N., 335Kurbah L, 188Kwon Sungchul, 154

LACOSTE David,, 262Ladieu F., 31Lafarga Pedro Tarazona, 64Laghate M., 179Lago Santiago, 269Lai Pik-Yin, 300, 345

Lakatos Greg, 207, 357Lakshmi K. C., 337Lakshmi K.C., 337Lal Roshan, 372Lamura Antonio, 221Landau David P., 53Lang D. T. N., 291Lannert Courtney, 50Lara Antonio H., 81Larkin A. I., 27Larralde Hernan, 60Lassig Michael, 332LAU Andy,, 262Lawlor A., 267Lawlor Aonghus, 49, 115Lazo Matheus J., 43Leandre R, 196Lebovka Nikolai I., 285Lee Andrew T., 81Lee Changhan, 283Lee D.-S., 35Lee Hwee Kuan, 53, 200Lee Hyun Keun, 368Lee Jae Woo, 180, 377Lee Kyoung Eun, 377Lee Ting-Kuo, 261, 347Leheny R. L., 258Leheny Robert L., 90Leone Michele, 310Leopoldo, 233Leuzzi Luca, 117Levine Alex J., 319Levin Yan, 20, 278Levrel L., 24Leyvraz Francois, 60Liang Dennis, 90, 258Liaw Tsong-Ming, 172Lichtenstein A. I., 298Lifshitz Ron, 75Lima Jose Pimentel de, 148, 177Lin Chai-Yu, 167Linke Heiner, 190Lin Shiang-Tai, 254Lippiello Eugenio, 151Li Wentian, 345Llano Manuel de, 294Logvinova Lyubov Viktorovna, 155, 256LOMHOLT MICHAEL L., 328Lookman Turab, 174Louis Ard A., 88Lozada-Cassou Marcelo, 286Lubensky T.C., 6Luding Stefan, 17Ludwig Karl, 257Lu Kunquan, 250, 271, 277Luna-Acosta Germ’n A., 314Luna-Acosta German A., 295

INDEX 391

Luzet D., 25Luz M. G. E., 130, 299Lyagushin Sergey, 206Lynden Steven J., 120

Muller Sebastian, 109Mendez-Bermudez J.A., 295MacDowell Luis G., 82Machta Jonathan, 50Maciolek Anna, 103Madhusudana N. V., 95, 97Maeda Kei-ichi, 226Maggs A.C., 24Mahmoodi-Baram Reza, 80Maiti Prabal K., 254, 255Maiti Prabal Kumar, 95Maiti Santanu Kumar, 290Majumdar Pinaki, 118Majumdar Satya N., 36, 59Makse Hernan, 273Makse Hernan A., 71, 244Mamasakhlisov Yeugeni Shamil, 181Manekar M. A., 157Manna S.S., 367, 374Manoharan Maalika Priyadarshini, 219Marakani Srikant, 225Marchetti M. Cristina, 30Marconi Umberto Marini Bettolo, 218Marconi Veronica I., 183, 216Markowich Peter Alexander, 295Marques Carlos, 246Marsili Matteo, 134, 365, 384Martınez-Raton Yuri, 279Martin-Mayor Victor, 317Martinez Julia Taguena, 201Martino Andrea De, 384Martins Marcio J., 144Martins Marcio Jose, 146, 149Martins Paulo Henrique, 156Marty Guillaume, 112Maruyama Kaneyasu, 224Mataran-Torres A C, 373Matskevich Valentina Tadeuscevna, 256Matsushita Raul, 377Matteo Tiziana Di, 90, 134Mattutis H.G., 46Maurer Jean, 226Mayer Peter, 301Mayor Victor Martin, 312Mazenko Gene F., 225Mazumder Aprotim, 346McCoy Barry, 9McCullagh G. D., 267McKane Alan, 199Mecke K., 25Mecke Klaus, 11, 104, 138, 157Mederos Luis, 278

Medina A., 239Medina E., 106Medvedev Nikolai N, 276Mehrotra Ravi, 68Melkikh Alexey Veniaminovich, 341Mendes J. F. F., 64Mendes Jose Fernando Ferreira, 143Mendez-Sanchez Rafael, 322Mendoza M.E., 213Menon G. I., 189Menon Gautam I, 242Menon Gautam I., 120, 250, 318Menon Narayanan, 86Menon Reghu, 153Messina Rene, 96Meyer-Ortmanns Hildegard, 171, 375MIAO LING, 328Michael Bestehorn,, 103Mikami Masuhiro, 163Minkova Natalia Romanovna, 380Mishra Bud, 119, 121Mishra Pramod Kumar, 349Mishra Sailesh, 298Mishra S C, 372Mitra Dhrubaditya, 73, 78Mitra Manidipa, 289Mitsudo Tetsuya, 191Mittal R., 152, 165Miura Yoshinori, 264, 265, 323, 333Miyazima Sasuke, 224Mizusaki T., 7Mochrie S. G. J., 258Mocuta Cristian, 157Mohanty P.S., 89, 259Mohanty Pradeep Kumar, 160Mohapatra Chandra Shekhar, 118Monasterio Carlos Mejia, 60Mondal Enakshi, 168Mongillo Gianluigi, 336, 349Moon Eun-Joung, 352Moon Hie-Tae, 217Mora S., 25Morelli Luis G., 335Morgado Rafael, 194, 316Morozov Vladimir Fedor, 181Morriss Gary P., 227Moura Francisco A. B., 316Mudi Anirban, 238Muecklich Frank, 240, 369Muguruma Chizuru, 163Muhuri Sudipto, 336Mujumdar Sushil, 309Mukherjee Arnab, 342Mukherjee G., 367Mukhopadhyay Swagatam, 111, 290Munoz Miguel A., 54Muraca Diego, 314

392 INDEX

Murayama Yoshihiro, 193Murthy K. P. N., 247–249, 311, 319Murthy K.P.N., 365Mussardo Giuseppe, 55

Nagar Apoorva, 59Nagar Deepshikha Jaiswal, 304Nagel Sidney, 21Naik Vijay M., 260Naik VM, 281Nakamura Yuichi, 156NALLET Frederic, 270Nandi Amitabha, 230Narasimhan S. L., 311, 319Narasimha R, 219Narayan Onuttom, 190Naudts Jan, 142Naumov A. V., 309Nave Emilia La, 51Ndawana Macleans L., 303Neves Armando G. M., 341Nicodemi Mario, 114Nicoldemi Mario, 243Nie Huifen, 257Nienhuis Bernard, 40, 41, 65, 82Nishimori HIdetoshi, 113Nishimori Hidetoshi, 306, 315, 361Nishimori Hiraku, 368Nishinari Katsuhiro, 129Nishino Tomotoshi, 186Nishiyama Yoshihiro, 165Nobre Fernando Dantas, 170Noh Jae Dong, 366, 369NOIREZ Laurence, 270

Oelkers N, 42Oettel Martin, 89, 246, 272Oh Eulsik, 373Ohtsuki Toshiya, 187Okabe Yutaka, 53, 200Okamoto Yuko, 163Oka Takashi, 297Okazaki Akihiko, 224Oleinikova Alla, 52, 100Olivares-Robles Miguel A., 199Oliveira Fernando A., 194Oliveira Fernando A. de, 316Oliveira J. G., 64Olmsted Peter D, 220Onnela Jukka-Pekka, 131ONO Ikuo, 268Onuki Akira, 4, 68, 96Orland Henri, 31Orpe Ashish V., 80Oshanin G., 154Ostojic Srdjan, 65, 82Ou-Yang Zhong-can, 250, 271, 277

Ozeki Yukiyasu, 176, 313

Pai Ramesh V., 105Palacios J.J., 106Palassini Matteo, 116pal Dilip, 304Pal Karoly Ferenc, 364Pal Subrata, 280Panagiotopoulos Athanassios Z., 168Pandit Rahul, 73, 78, 105, 229Pando, 233Panja Debabrata, 82Panja Debabrate, 65Paolotti Daniela, 218Paredes Ricardo, 178Parisi Giorgio, 113, 117, 312Parker D., 31Park Heung Sik, 154Park Heungsik, 180Park Hyunggyu, 154, 159, 167, 180Park Jeong-Man, 236, 343Parry Andrew O., 6, 100, 286Partha M. K., 222Pascal Tod A., 255Pasquale Ferdinando de, 146Pastor-Satorras Romualdo, 54, 133Pastore Giorgio, 242Pathak K.N., 60Patricio P., 91Pauchard Ludovic, 359Paul Alok K. R, 263Peixoto Tiago P., 133Peletminskii Alexander, 203Peletminskii Sergey, 203, 204Peliti Luca, 332Peng Chung-Kang, 363Penna F, 64Pennetta Cecilia, 58, 307, 326Perez-Gaviro Sergio, 317Perez Luis S. Froufe, 195Perez M.A., 213Periorellis Panayiotis, 120Perk Jacques H. H., 41Perk Jacques H.H., 45Petaja Viljo, 265Petri Alberto, 87Pianegonda Salete, 278Picco Marco, 113Pietronero Luciano, 87Pitard Estelle, 303Pitolli Luca, 87Planes Antoni, 141Plascak Joao Antonio, 156, 158Plerou Vasiliki, 367, 371Plischke Michael, 190Poire Eugenia Corvera, 221Poniewierski A., 253

INDEX 393

Ponmurugan M., 365Ponomarenko L. A., 291Pontuale Giorgio, 87Popescu M. N., 101, 154Pradhan Punyabrata, 62Pradhan Srutrshi, 160Prado Carmen P. C., 133Prakash J Ravi, 253Prasad R., 293Priezzhev V. B., 17Prost Jacques, 123Pruisken A. M. M., 291Prykarpatsky Anatoliy, 237Puglisi Andrea, 218Pujol Pierre, 223Puri Sanjay, 15

Rakos Attila, 197Raghavendra S, 128Raghuram Nandula, 124Ramachandran K., 360Ramakrishnan S., 94Ramanadham M., 319Ramaniah L. M., 179Ramasco Jose J., 171Ramasesha S., 289Ramaswamy R, 230Ramaswamy R., 186Ramaswamy Ram, 200Ramaswamy Ramakrishna, 77, 345, 350, 351Ramaswamy Sriram, 61, 63, 71, 93, 126Rameshan P., 235Ramkrishnan S., 304Rana M. D. Masud, 138Randeria Mohit, 293Ranganthan S., 60Rangarajan Govindan, 79Ranjith P., 250Rao Madan, 123, 126, 162, 336, 337Rao Mala N., 140Raposo E. P., 130Rascon Carlos, 286Raut Janhavi S., 260Rawat Pawan Kumar, 298Raychaudhuri Subhadip, 359Ray Deb Shankar, 225Ray P., 189Ray Purusattam, 69Razdan Ashok Kumar, 375Redner S., 380Ree Suhan, 362Reggiani Lino, 58, 326Reichert Harald, 157Rgo Hnio Henrique Arag, 376Rho Kyoo Hyoung, 373Ribeiro Giuliano Augustus Pavan, 146Richard Christoph, 40

Ridaura Hernan Larralde, 199Rieger Heiko, 265, 369Ritort Felix, 34Rizzo Tommaso, 117, 119Robledo Alberto, 20, 305Roco J.M.M., 239Rodriguez-Ponce Inmaculada, 225Roemer Rudolf A, 108, 301, 321Roemer Rudolf A., 303Rogers J. L., 75Rolley E., 7Roman F.L., 238Romero-Enrique J. M., 6Romero-Enrique Jose Manuel, 100ROMERO-ROCHIN VICTOR, 285Rondoni Lamberto, 196, 236Roopa T., 357Rosa Jane, 185Rosenow Bernd, 367Rossignoli Raul, 296Rossignoli Raul D., 110Roth R., 22, 264, 284, 332Roth Roland, 138Rottler J., 24Rowlands George, 170Roy Arun, 95Roychowdhury Swapan, 81Roy Ratnadeep, 69Roy S. B., 157Roy Siddhartha, 329Roy Soumen Kumar, 166, 168Ruffo Stefano, 58Ryashko Lev, 231, 232

S.S Ashwin, 318S.Y. Bhide, 282Saadatfar Mohammad, 90Sabhapandit Sanjib, 302Saenz Juan Jose, 195Saha-Dasgupta Tanusri, 298Sahu Kirti Chandra, 76Sahu R., 382Saika Yohei, 361Sain Anirban, 121, 211Sairam T., 249Saito Takuya, 274Sakai Kazumitsu, 44Sakashita Hirofumi, 264, 265, 323, 333Sakellariou Arthur, 90Salyuk Yuriy, 206Samal Areejit, 124Samanta Himadri Shekhar, 186, 200Sammadar Soma, 329Sanchez Rafael Mendez, 199Sankararaman Sumithra, 120Sano M., 345Sano Masaki, 193, 353

394 INDEX

Sano Osamu, 66, 84Santen Ludger, 383Santo K. P., 262, 331Santos Constantino A. da, 171Santos M. C., 130Santos Maria A., 171Santos Rita Maria Zorzenon, 338Santra S. B., 162, 191Sanyal Devashish, 189Sanz Eduardo, 82Sapienza Riccardo, 309Sapoval B., 191Sarjala Matti, 265Sasamoto Tomohiro, 211, 220Sasa Shin-ichi, 78Sastry Srikanth, 111, 318Sastry V. S. S., 247–249Sator Nicolas, 252Sato Yasuomi Daishin, 175Satyanarayana S.V.M., 325Satyavathi N., 247Sawada T., 259Saxena Avadh, 174Scalettar R.T., 28Schutz Gunter M., 197Schadschneider Andreas, 62, 129, 186, 288, 383Schanze H, 314Schick Michael, 33Schmidt M., 277Schmittmann Beate, 166Schofield A. B., 272Schreckenberg Michael, 368, 383Schreiber Michael, 303Schulz-Baldes Hermann, 301Schupper Nurith, 173Schutz Gunter M, 57Schwabl Franz, 225Sciortino Francesco, 51, 268Scopigno Tullio, 83Seas A., 182Sebastain K. L., 262Sebastian K. L., 263, 331SEGOVIA JOSE GPE., 285Sekhar G. P. Raja, 222Sellitto Mauro, 315Sen A., 152Senden Tim J., 90Sen Diptiman, 108, 289Sengupta Ankush, 242Sengupta Surajit, 161, 224, 239, 242, 284Sen Parongama, 367Senthilkumar D. V., 232Serena P.A., 106Serini Guido, 339Seul Michael, 121Shah A. P., 291Shalini, 124

Sharma Puneet, 60Sharma S. M., 179Shen Dianhong, 250, 271, 277Shenoy Subodh R., 174Shibata Hiroshi, 76Shibata Sawako, 333Shivashankar G.V., 357Shivashankar G V, 329, 346, 348, 350Shnerb Nadav, 173Shukla N. N., 293Shukla P., 189Shukla Prabodh, 188Shukla S. K., 293Silva Antonio Christian, 372Silva R., 213Silvestre N. M., 91Simha R. Aditi, 126Sindt O., 244Singha Subhendu B, 66Singh Brajendra K., 375Singh Navinder, 185Singh R. K. Brojen, 294Singh Rajiv R. P., 106Singh Yashwant, 349Sinha Deepak, 348Sinha S., 162Sinha Sitabhra, 128Sinha Sudeshna, 232Sinha Supurna, 260Sinha Tapas Kumar, 207, 298, 354–356Skvortsov M. A., 27Slanina Frantisek, 134Slyusarenko Yuriy, 204Smith Graham, 127Smith Steve, 34Sneppen Kim, 32, 124Sokhey K. J. S., 157Sokolovsky Alexander, 202–206Sokolovsky Sergey, 205Sollich Peter, 92, 261, 301Solomon Chirstophe, 27Somsikov, 137Song Chaoming, 71, 273Soni G V, 350Son Seung-Woo, 342, 366Sood A. K., 92Sood A.K., 63Sood Ajay K, 91Sood Ajay K., 61, 71Sood V., 380Sotolongo-Costa O, 283Sotolongo-Costa O., 139, 141Sourlas Nicolas, 113Sparber Christof, 295Spatschek Robert, 69Spineanu Florin, 143, 194Spohn Herbert, 13

INDEX 395

Sreekala S., 55, 150Sreenivasan Katepalli R., 19Sreenivasan Sameet, 383Sreeram P. A., 224Sridhar V., 365Stockmann H.-J., 295Stanley H. Eugene, 2, 85, 367, 371, 383Stauffer Dietrich, 327Steinhart Milos, 257Stella A. L., 374STEPANEK Petr, 270Stockmann H.-J., 314Stollenwerk Nico, 344Strelniker Yakov M., 313Stupka Anton, 202Su-Chan Park,, 173Succi Sauro, 77Sugiyama Asuka, 47, 145Sukhorukov Eugene, 193Sumedha, 132Sunthar P, 253Suresh SJ, 281Suzuki Hidenori, 47, 145, 147Suzuki Masuo, 47, 145, 147Swinney Harry L., 81Szabo Gabor, 378Szamel Grzegorz, 118Szollosi Gergely, 321

Tauber Uwe C., 58Taitelbaum Haim, 67, 99Takasu Masako, 263Takeda Koujin, 113, 306, 315Takesue Shinji, 191Takeya H., 304Talia S. Di, 125Talia Stefano Di, 339Taniguchi Keisuke, 368Taniguchi Tooru, 227Tanimoto Satoshi, 187Tankeshwar K., 60Tarafdar Sujata, 285Tarazona Pedro, 287Tartaglia Piero, 51, 268Tarzia Marco, 114, 243Tata B. V. R., 98Tata B.V.R., 89, 259Tatekawa Takayuki, 226Tauber Uwe C., 334Tejero Carlos F., 86Tewari Shubha, 212Thakur A. D., 94Thakur A.D., 304Thalmann Fabrice, 246Thomas M., 284Tiana Guido, 124Tinoco I., 34

To Kiwing, 21Tome Tania, 183, 353Tomita Jungo, 263Toninelli Cristina, 114Toninelli Fabio Lucio, 117, 310Torrens Francisco, 180Toyabe Shoichi, 353Trebst Simon, 302Tria Francesca, 332Tripathy G., 64Tripathy Goutam, 216Trivedi N., 28Trivedi Nandini, 288, 311Troyer Matthias, 110, 302Tsallis C, 10Tsao Heng-Kwong, 121Tullio, 83Turner Matthew S, 321TUZAR Zdenek, 270

Uchida Nariya, 214Uchiyama Satoki, 352Ueno T., 7Ugawa Akiko, 84Ullrich B., 272Unger Tamas, 305Urabe Chiyori, 217Uwe Thiele,, 103

V.I.Anisimov, 298Vaidehi Nagarajan, 255Vainer Yu. G., 309Vainstein Mendeli H., 316Valls Oriol T., 181Valsakumar M. C., 235Valsakumar M.C., 98Vandembroucq Damien, 56Vanicek Jiri, 296Vazquez Federico, 199Vega-Redondo Fernando, 134Vega Carlos, 82Velasco Enrique, 278Velasco S., 238, 239Veloz Victor Hugo Almanza, 370Velytsky Alexander, 171Venu K., 247Vergassola Massimo, 19Verma Mahendra K., 227Vernia Cecilia, 196, 236Verrocchio Paolo, 312Vespignani Alessandro, 133Vicsek T., 37Vieira Andre Pinho, 201Vincent E., 31Vishnoi Anchal, 350, 351Vishveshwara Smitha, 50, 290Visser A. de, 291

396 INDEX

Viswanathan G. M., 130Vivek, 350, 351Vives Eduard, 141Vlad Madalina, 143, 194Volk N., 277Volkov Nikolay Aleksandrovich, 274Vollmer D., 54, 272, 277Vollmer J., 54Voloshin Vladimir P, 276Vorontsov-Velyaminov Pavel Nikolaevich, 274Voros Janos, 321

Wada Hirofumi, 193Waltz Francois Leyvraz, 199Wang Bing-Hong, 135, 233Wang Fugao, 53Wang Guofeng, 254Wang Hongqiang, 86Wang Jian-Sheng, 57Wang Ping, 71, 244, 273Wang Zhen-Gang, 324Wan Xin, 109Washenberger Mark J., 58Watanabe Midori, 333Wei Tzu-Chieh, 290Werner Wendelin, 8Weron Aleksander, 144Wessel Stefan, 302White J.A., 238Widom Benjamin, 331Wiegmann P., 11Wiersma Diederik, 309Wiese Kay, 12Willbrand K., 358Williams Ellen D., 16Wolf Dietrich E., 305Wuertz Diethelm, 302Wu Ming-Chya, 363Wu Yi-Wen, 261, 347

Xhu Xing, 250, 271, 277Xiang T., 15Xu Aiguo, 221

Yamamoto Hiroshi, 187Yamanaka J., 89, 259Yamazaki Yoshitake, 250, 271, 277Yarlagadda Sudhakar, 289, 362Yashonath S., 206, 282Yeomans J. M., 26Yokota Terufumi, 308Yoon Seong-Min, 379Yoshikawa Kenichi, 274Young Malcolm P., 120Young Peter, 29Yuan-Chung Cheng, 79Yuan Baosheng, 361

Yurchenko Anton Alekseevich, 274Yusuf S.M, 304

Zaccarelli Emanuela, 268Zanette Damian H., 335Zannetti Marco, 151Zebrowski Jan Jacek, 229, 234Zecchina Riccardo, 36Zewail Ahmed H., 324Zheng W. M., 282Zheng Weihong, 106Zhou Chenggang, 109Zhou Yi, 119Zhou Zicong, 300Zia R. K. P., 166Ziff Robert M., 45Zinovyev Andrei, 127, 340Zippelius A., 12Zippelius Annette, 111Zon Ramses van, 59Zuckermann Martin, 190Zumdieck A., 75

contentsstatphys22/abstractbook.pdfcontents 1 lectures by boltzmann award recipients 1 2 plenary...

Documents