Abstracts Submitted for Talks and Posters(final version)

Dynamics Days 201130th Annual International Conference

on Nonlinear Dynamics

January 5-8, 2011

The Carolina InnChapel Hill, North Carolina

Invited Speakers

Rosalind Allen Bruno AndreottiMartine Ben AmarAndrea BertozziKaren DanielsBarbara DrosselJerry GollubPhilip HolmesEdgar Knobloch

Jurgen KurthsWolfgang LosertAmala MahadevanTakashi NishikawaCorey O'HernEd OttJeffrey RogersLeah ShawLawrie Virgin

http://www.math.duke.edu/conferences/DDays2011

Deadlines:

Contributed presentations: November 15, 2010

Conference registration: December 1, 2010

Schedule

Wednesday, January 5, 20111

8:45 Opening Remarks

9:00 – 10:40 Session 1, Chair: Joshua Socolar, Duke University

9:00 I3 – Statistical Mechanics of Packing: From Proteins to Cells to GrainsCorey O’Hern, Yale University

9:40 I2 – Spatially localized structures in two dimensionsEdgar Knobloch, University of California, Berkeley

10:20 C1 – An Elementary Model of Torus CanardsAnna Barry, Boston University

10:40 Break

11:00 – 12:40 Session 2, Chair: Thomas Witelski, Duke University

11:00 I6 – The Path to Fracture: Dynamics of Broken Link Networks in Granular FlowsWolfgang Losert, University of Maryland

11:40 C2 – Flexibility Increases Energy Efficiency of Digging in Granular SubstratesDawn Wendell, MIT

12:00 I4 – Ripples, dunes, bars and meandersBruno Andreotti, ESPCI

12:40 Lunch

2:00 – 4:00 Session 3, Chair: Joshua Socolar, Duke University

2:00 I5 – The Nonlinear Population Dynamics of Pacific SalmonBarbara Drossel, University of Darmstadt

2:40 I8 – Erosional Channelization in Porous MediaAmala Mahadevan, Boston University

3:20 C3 – Determining the onset of chaos in large Boolean networksAndrew Pomerance, University of Maryland

3:40 C4 – Exploring mesoscopic network structure with communities of linksJames Bagrow, Northeastern University

4:00 Break

4:20 – 5:20 Session 4, Chair: Thomas Witelski, Duke University

4:20 I7 – Swarming by Nature and by DesignAndrea Bertozzi, UCLA

5:00 C5 – Sub-wavelength position-sensing using a wave- chaotic cavity with nonlinear feedbackHugo Cavalcante, Duke University

5:20 Break for Dinner

1General Guidelines: Invited presentations are 40 minutes total (35 minutes presentation, 5 minutes questions), Contributed presentationsare 20 minutes total (16 minutes presentation, 4 minutes questions), space for poster presentations is limited to a maximum size of 4 feet by4 feet for each poster.

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Thursday, January 6, 2011

9:00 – 9:40 Session 5, Chair: Robert Behringer, Duke University

9:00 I1 – Still Running! Recent Work on the Neuromechanics of Insect LocomotionPhillip Holmes, Princeton University

9:40 C6 – Fluid rope tricksStephen Morris, University of Toronto

10:00 C7 – Three-dimensional structure of a sheet crumpled into a sphereAnne Dominique Cambou, University of Massachusetts, Amherst

10:20 Break

10:40 – 12:00 Session 6, Chair: Edward Ott, University of Maryland

10:40 I9 – Evolutionary Dynamics for Migrating PopulationsRosalind Allen, University of Edinburgh

11:20 C8 – Predicting criticality and dynamic range in complex networks: effects of topologyDaniel Larremore, University of Colorado at Boulder

11:40 C10 – Creating Morphable Logic Gates using Logical Stochastic Resonance in an Engineered Gene Regu-latory NetworkAnna Dari, Arizona State University

12:00 Lunch

2:00 - 3:40 Session 7, Chair: Brian Utter, James Madison University

2:00 I10 – Stochastic Extinction along an Optimal PathLeah Shaw, College of William and Mary

2:40 C9 – Chaos Elimination of Fluctuations in Quantum Tunneling RatesLouis Pecora, Naval Research Laboratory

3:00 I14 – Dynamics and Interactions of Swimming CellsJerry Gollub, Haverford College

3:40 – 7:30 Break for afternoon and dinner

7:30 – 8:10 Session 8, Chair: Karen Daniels, NCSU

7:30 I12 – Low Dimensional Dynamics in Large Systems of Coupled OscillatorsEdward Ott, University of Maryland

8:15 –10:00 Poster Session 1 - Setup and Desserts

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Friday, January 7, 2011

9:00 – 10:20 Session 9, Chair: Joshua Socolar, Duke University

9:00 I13 – Nonlinear programs and DARPAJeffrey Rogers, DARPA

9:40 C11 – Measuring Information Flow in Anticipatory SystemsShawn Pethel, U.S. Army RDECOM

10:00 C12 – Time delays in the synchronization of chaotic coupled systems with feedbackJose Rios Leite, Universidade Federal de Pernambuco

10:20 Break

10:40 – 12:20 Session 10, Chair: Thomas Witelski, Duke University

10:40 I11 – Compensatory structures in network synchronizationTakashi Nishikawa, Clarkson University

11:20 C13 – Folding: the nonlinear step in fluid mixingDouglas Kelley, Yale University

11:40 C14 – Trapping of Swimming Particles in Chaotic Fluid FlowNicholas Ouellette, Yale University

12:00 Lunch

2:00 – 4:00 Session 11, Chair: Joshua Socolar, Duke University

2:00 I15 – Network of Networks and the Climate SystemJurgen Kurths, University of Potsdam

2:40 C15 – What is the front velocity in wave propagation without fronts? Epidemics on complex networksprovide an answerDirk Brockmann, Northwestern University

3:00 I16 – Shape instability of growing tumorsMartine Ben Amar, University of Paris

3:40 C16 – Reconstruction of Cardiac Action Potential Dynamics using Computer Modeling with Feedback fromExperimental DataLaura Munoz, Cornell University

4:00 – 6:00 Poster Session 2

6:00 Break for dinner

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Saturday, January 8, 2011

9:30 – 10:30 Session 12, Chair: Robert Behringer, Duke University

9:30 I17 – Faults & Earthquakes as Granular Phenomena: Controls on Stick-Slip DynamicsKaren Daniels, North Carolina State University

10:10 C17 – Effects of Shape on DiffusionRob Shaw, Santa Fe Complex

10:30 Break

10:50 – 11:50 Session 13, Chair: Michael Shearer, NCSU

10:50 C18 – Crowd behavior: Synchronization of multistable chaotic systems by a common external forceAlexander Pisarchik, Centro de Investigaciones en Optica

11:10 I18 – Rocking and RollingLawrie Virgin, Duke Univ. Engineering

11:50 End of Conference. Have a safe trip home!

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Invited Talks

• Models for bacterial population dynamics and evolutionRosalind Allen, University of Edinburgh

• Ripples, dunes, bars and meandersBruno Andreotti, ESPCI

• Swarming by Nature and by DesignAndrea Bertozzi, UCLAThe cohesive movement of a biological population is a commonly observed natural phenomenon. With theadvent of platforms of unmanned vehicles, such phenomena has attracted a renewed interest from the engineeringcommunity. This talk will cover a survey of the speaker’s research and related work in this area ranging fromaggregation models in nonlinear PDE to control algorithms and robotic testbed experiments. We conclude witha discussion of some interesting problems for the applied mathematics community.

• Shape instability of growing tumorsMartine Ben Amar, University of Paris

• Faults & Earthquakes as Granular Phenomena: Controls on Stick-Slip DynamicsKaren Daniels, North Carolina State UniversityGranular and continuous materials fail in fundamentally different ways, yet inherently discontinuous natural faultmaterials have often been modeled as continuum processes. A long-standing question is whether the granularnature of fault material such as gouge plays a major role in controlling seismicity and periodicity in geologicalfaults. In both natural faults and granular experiments, the ability of the material to rearrange in response tostrain is an important effect on its effective strength. I will describe laboratory experiments on a photoelasticgranular aggregate which allow us to investigate these particle-scale controls on bulk behaviors. By adjusting thepressure and/or volume of the system, we are able to control both the size-distribution of stick-slip events (eitherpower-law or exponential) and their periodicity/aperiodicity. In addition, we find scaling relations connectingthe size and duration of individual events which permit comparison with mean-field models of failure.

• The Nonlinear Population Dynamics of Pacific SalmonBarbara Drossel, University of Darmstadt

• The Path to Fracture: Dynamics of Broken Link Networks in Granular FlowsWolfgang Losert, University of Maryland

• Dynamics and Interactions of Swimming CellsJerry Gollub, Haverford University

• Still Running! Recent Work on the Neuromechanics of Insect LocomotionPhilip Holmes, Princeton UniversityI will describe several models for running insects, from an energy-conserving biped with passively-sprung legs toa muscle-actuated hexapod driven by a neural central pattern generator (CPG). Phase reduction and averagingtheory collapses some 300 differential equations that describe this neuromechanical model to 24 one-dimensionaloscillators that track motoneuron phases. The reduced model accurately captures the dynamics of unperturbedgaits and the effects of impulsive perturbations, and phase response and coupling functions provide improvedunderstanding of reflexive feedback mechanisms. Specifically, piecewise-holonomic constraints due to intermittentfoot contacts confers asymptotic stability on the CPG- driven feedforward system, the natural dynamics featuresa slow subspace that permits maneuverability, and leg force sensors modulate firing patterns to mitigate largeperturbations. More generally, I will argue that both simple models and large simulations are necessary to under-stand such complex systems. The talk will draw on joint work with Einat Fuchs, Robert Full, Raffaele Ghigliazza,Raghu Kukillaya, Josh Proctor, John Schmitt, Justin Seipel and Manoj Srinivasan. Research supported by NSFand the J. Insley Blair Pyne Fund of Princeton University.

• Spatially localized structures in two dimensionsEdgar Knobloch, UC Berkeley

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Many continuum systems in physics exhibit a spatially localized response to spatially homogeneous forcing. Theresulting structures are frequently called dissipative solitons. In this talk I will describe the phenomenon ofhomoclinic snaking that is responsible for the presence of these states, together with the associated snakes-and-ladders structure of the snaking region, i.e. the parameter region containing such localized structures. I willdescribe this behavior in both one and two spatial dimensions, focusing on the growth of the structures as onefollows branches of localized structures from small to large amplitude. I will illustrate the results using bothmodel equations such as the Swift-Hohenberg equation and “real” systems such as binary fluid convection.

• Network of Networks and the Climate SystemJurgen Kurths, University of PotsdamWe introduce a novel graph-theoretical framework for studying the interaction structure between sub-networksembedded within a complex network of networks. This allows us to quantify the structural role of single vertices orwhole sub-networks with respect to the interaction of a pair of subnetworks on local, mesoscopic, and global topo-logical scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatologicaldata. Here we use the concept of network of networks by introducing climate subnetworks representing differentheights in the atmosphere. Parameters of this network of networks, as cross-betweenness, uncover relations toglobal circulation patterns in oceans and atmosphere. The global scale view on climate networks offers promisingnew perspectives for detecting dynamical structures based on nonlinear physical processes in the climate system.

• Erosional Channelization in Porous MediaAmala Mahadevan, Boston UniversityWe explore the evolution of erosional channels induced by fluid flow in a granular porous medium. When thefluid-induced stresses exceed a critical threshold, grains are dislodged and transported with the flow, therebyaltering the porosity of the medium. This in turn affects the local hydraulic conductivity and pressure in themedium and results in the growth and development of channels that preferentially conduct the flow. We proposea continuum multiphase model that captures the formation of erosional channels by coupling the spatiotemporalevolution of the granular and liquid phases to the dynamical properties of the fluid and porous substrate.

• Compensatory structures in network synchronizationTakashi Nishikawa, Clarkson UniversitySynchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion,depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by thenetwork has resisted comprehensive characterization within the prevailing paradigm that interactions facilitatingpair-wise synchronization also facilitate collective synchronization. Here we challenge this paradigm and showthat networks with best complete synchronization, least coupling cost, and maximum dynamical robustness,have arbitrary complexity but quantized total interaction strength, which constrains the allowed number ofconnections. It stems from this characterization that negative interactions as well as link removals can be usedto systematically improve and optimize synchronization properties in both directed and undirected networks.For networks of nonidentical maps, we show that these compensatory modifications to the network structure canlead to complete synchronization, despite the heterogeneity of the dynamical units. These results extend therecently discovered compensatory perturbations in metabolic networks to the realm of oscillator networks anddemonstrate why “less can be more” in network synchronization.

• Statistical Mechanics of Packing: From Proteins to Cells to GrainsCorey O’Hern, Yale UniversityOver the past ten years, my research group has focused on understanding the statistical mechanics of jammedparticulate systems such as colloidal glasses and granular materials. Using a variety of computational and theoret-ical techniques, we have found many fascinating results for nonequilibrium systems that do not occur in thermalliquids and solids. Examples include the breakdown of equi-probability of microstates as in the microcanonicalensemble and strongly nonharmonic response of granular solids even for vanishingly small vibrations. In addition,we have shown that geometric and packing constraints often determine the key structural, mechanical, and evendynamical properties of jammed systems. More recently, my research group has been investigating to what extentpacking constraints play a role in determining biological structures and interactions. I will highlight our studies

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of the conformational dynamics of intrinsically disordered proteins, the binding affinity of repeat proteins andtheir cognate peptides, and the size, shape, and mobility of epithelial cells in monolayers.

• Low Dimensional Dynamics in Large Systems of Coupled OscillatorsEdward Ott, University of MarylandThe issue of determining the emergent collective behavior of these systems is of great practical and basic concern.Examples include chirping crickets, pedestrian induced shaking of footbridges, control of circadian rythm by thesuperchiasmatic nucleus, pacemaker cells in the heart, chemical oscillators, birdsong, coupled lasers, Josephsonjunction circuits, bubbly fluids, neuronal oscillations in the brain and many others. A convenient characterizationof the individual oscillators is the phase oscillator description where the state of each oscillator is given solely bya single phase variable. The simplest example is the Kuramoto model. In the past, models of this type have beeninvestigated primarily via direct numerical computation for the time evolution of all the many coupled equationsdescribing the system. In this talk I will describe an exact analytical technique [1] that reduces the study ofthe emergent collective macroscopic behavior of these systems to the solution of just a few ordinary differentialequations. In particular, it is found that all initial conditions are attracted to an invariant manifold in the statespace [2], and evalution on this manifold is governed by a low dimensional dynamical system. The technique iswidely applicable, and I will indicate some examples where it has already been employed to uncover the attractorsand bifurcations of large oscillator systems.[1] E.Ott and T.M.Antonsen, Chaos (2008).[2] E.Ott and T.M.Antonsen, Chaos (2009).

• Nonlinear Programs and DARPAJeffrey Rogers, DARPA

• Stochastic Extinction along an Optimal PathLeah Shaw, College of William and MaryExtinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation.The extinction process follows an optimal path that maximizes the probability of extinction. We show that theoptimal path is maximally sensitive to initial conditions and thus can be detected using finite-time Lyapunovexponents. Several stochastic population models are presented, and the extinction process is examined in adynamical systems framework.

• Rocking and RollingLawrie Virgin, Duke Univ. EngineeringA system at rest is subject to the sudden application of (harmonic) forcing. The resulting transient dynamicresponse may typically lead to various kinds of periodic behavior or chaos. However, if an underlying potentialenergy well in which the system lives is limited in extent, then the system may exit the local vicinity of the initialequilibrium, and perhaps go off to infinity. This talk will focus on two types of mechanical system in which weseek to characterize the likelihood of an extreme outcome: a ball that rolls on a curved surface, and a rectangularblock that rocks on a table. These systems are relatively easy to model, and easy to build experimentally, buttheir behavior is often highly erratic and unpredictable.

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Contributed Talks

Exploring mesoscopic network structure withcommunities of links, James Bagrow, Northeast-ern UniversityComplex networks have recently received much at-tention as a productive way to study diverse phenom-ena ranging from biological interactions in the cellto societal-wide activities in human dynamics. Oneimportant problem is the identification of Commu-nities, mesoscopic-scale groups of densely connectednodes. These groups may correspond to functionallyrelated proteins, or to the social circles that peoplemove through in their daily lives. Finding commu-nities is usually considered a partitioning problem,where each node is placed into exactly one commu-nity. Yet nodes often fulfill multiple structural andfunctional roles in the network, meaning that com-munities overlap and nodes belong to multiple com-munities. We show that it is still possible to studyoverlapping structure with a partition, by forminggroups of links rather than nodes. This has distinctadvantages and achieves accurate results accordingto empirical measures. We also describe how somebasic assumptions about communities may not al-ways hold, with important dynamical and functionalconsequences.

An Elementary Model of Torus Canards, AnnaBarry, Boston UniversityWe study the recently-discovered phenomena of toruscanards. These are a higher-dimensional generaliza-tion of the classical canard orbits familiar from pla-nar systems, and arise in fast-slow systems of or-dinary differential equations in which the fast sub-system contains a saddle-node bifurcation of peri-odic orbits. Torus canards spend long times nearslowly-varying families of attracting periodic orbitsand then near slowly-varying families of repelling pe-riodic orbits, in alternation. We carry out a detailedstudy of torus canards in an elementary third-ordersystem that consists of a rotated van der Pol equa-tion in which the rotational symmetry is broken byincluding a phase-dependent term in the slow com-ponent of the vector field. In the regime of fast ro-tation, the torus canards behave much like their pla-nar counterparts. In the regime of slow rotation,the phase dependence creates rich torus canard dy-namics. Similar dynamics have been observed in amathematical model of action potential generationin Purkinje cells. Stable torus canard solutions ex-

ist for open sets of parameter values, correspond toamplitude-modulated spiking of the neural dynam-ics, and arise exactly in the transition region betweenrapid spiking and bursting in this model.

What is the front velocity in wave propagationwithout fronts? - Epidemics on complexnetworks provide an answer, Dirk Brockmann,Northwestern UniversityThe spatiotemporal patterns of infectious diseasesthat spread nowadays typically lack a well definedwave front as human mobility is multi-scale. Thestructure of emergent patterns is difficult to assessquantitatively, in particular spreading speeds are dif-ficult to define and compare in different scenarios.We present a novel way to look at contagion phe-nomena on complex networks using the underlyingtopological structure of the network. Shortest-pathdistances and arrival times are used to redefine thevelocity of spreading patterns. We extend the idea ofa wavefront that can be directly observed in simplenetworks like a regular lattice to the class of com-plex networks which in traditional views exhibit com-plicated patterns. This method substantially sim-plifies the way dynamics are analyzed and explainswhy patterns in complex modeling approaches sharemany similarities. Disease dynamics on various com-plex networks ranging from artificial to real humanmobility networks show the benefit of representingthe spatio-temporal patterns based on topologicalfeatures of the network.

Sub-wavelength position-sensing using a wave-chaotic cavity with nonlinear feedback, HugoCavalcante, Duke UniversityHugo L. D. de Souza Cavalcante, Seth D. Cohen,Daniel J. Gauthier, Department of Physics, DukeUniversity, Durham, NC, USAWe develop a new dynamical system that consists ofa nonlinear element whose output is passed througha wave-chaotic cavity and then fed back to the non-linear element. The nonlinearity of the system isprovided by a transistor-based circuit. The circuit’sinput and output voltage couple to the radiation in-side the cavity through broadband antennas, and themultipath reflections of the signal inside the cav-ity constitute multiple delayed-feedback loops. Thepath lengths and coupling strengths of these feed-back delays depend sensitively on the position of asub-wavelength scatterer placed into the cavity. The

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primary purpose of this work is to show that quan-tities observable in the dynamics, such as bifurca-tions points or frequencies of oscillation, are linearlyproportional to the position of this scatterer object.Fixing the position of this scatterer, we generate a bi-furcation in the system’s dynamics by scanning thebias voltage of the nonlinear circuit. We find thatthe bifurcation point is sensitive to displacementsof the scatterer position as small as 10 micrometers(see poster by Seth D. Cohen et al.). Because offluctuations on system’s parameters this method al-lows for one-dimensional position-tracking with res-olution of 60 micrometers. This last number is 2,500times smaller than the minimum wavelength of radi-ation inside the cavity (15 cm). Alternatively, we canmeasure the frequency of a periodic oscillation as afunction of the object position. We have found thatthe frequency also changes continuously and allowssimilar tracking of the scatterer position. These tech-niques may find potential applications in radio-basedsub-wavelength imaging and sensors with through-wall capabilities. We gratefully acknowledge the sup-port of the ONR MURI “Exploiting Nonlinear Dy-namics for Novel Sensor Networks”.

Three-dimensional structure of a sheet crumpledinto a sphere, Anne Dominique Cambou, Univer-sity of Massachusetts, AmherstWe probe the interior of thin aluminum sheets hand-crumpled into three-dimensional balls to character-ize the resulting structure that has low volume frac-tion but high resistance to further compression. Weuse X-ray computerized microtomography to deter-mine the location of the sheet in the volume. Froma reconstruction of the X-ray images, we performfully three-dimensional analyses of their curvature,orientation, and local stacking. In order to iden-tify possible anisotropy and inhomogeneity imposedby the method of crumpling, we present an analy-sis of the radial dependence of these metrics of thegeometry. Our results reveal that the internal three-dimensional geometry of a crumpled ball is in manyrespects isotropic and homogeneous. However, wefind inhomogeneously distributed local nematic or-dering by the layering of the folded sheet into par-allel stacks. We also present ongoing work on thedynamics of the crumpling process.

Creating Morphable Logic Gates using LogicalStochastic Resonance in an Engineered GeneRegulatory Network, Anna Dari, Arizona StateUniversity

The idea of Logical Stochastic Resonance (LSR) isadapted and applied to an gene regulatory network(GRN) in the bacteriophage λ. The resultant com-puting device is able to work as an AND or OR gateinterchangeably in the presence of noise. Noise iscritical for the existence and operation of the gates.We have computed the gate “performance” as a func-tion of noise intensity and shown that the biologicalsystem output is the logical combination of the twodata inputs for a range of noise intensities, and theGRN phage λ can switch from the AND to OR gateas desired; this switching can be accomplished, for afixed external noise level, by adjusting other deter-ministic system parameters. LSR on a GRN, thathas the capability of being reconfigured, could becombined, in near future, with other logic modules(done by different sets of input/output signals) to in-crease the computational power and functionality ofan engineered GRN. Such networks may allow pre-dictable and robust control in fluctuating cellular en-vironments and thereby have a significant impact inthe design of synthetic biological systems such as re-cently created bacterial cells controlled by chemicallysynthesized genomes.

Folding: the nonlinear step in fluid mixing, DouglasKelley, Yale UniversityEfficient large-scale mixing of an impurity in a fluiddepends on stretching and folding–together they ex-pand the periphery of material volumes, allowingmolecular diffusion to mix efficiently. The linearstep in this process, stretching, has been studied ex-tensively with tools like finite-time Lyapunov expo-nents. But folding, corresponding to nonlinear defor-mation of materials volumes, has been more difficultto study. We use nonlinearity of the folding trans-formation to separate it from stretching and studyboth steps independently. Our data come from aquasi-two-dimensional laboratory flow in which wemeasure the velocity of roughly 30,000 Lagrangianparticles per frame. At short deformation times, lin-ear stretching dominates, but once fluid elementshave elongated, nonlinear folding becomes rapidlystronger and begins to dominate the deformation.The relative strength of the two processes also variesstrongly in space. Our analysis takes a first step be-yond the analysis of nonlinear mixing with purelylinearized measures. This work is supported by theNational Science Foundation.

Predicting criticality and dynamic range in com-plex networks: effects of topology, Daniel

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Larremore, University of Colorado at BoulderWe study the effect of network structure on the dy-namical response of networks of coupled discrete-state excitable elements which are stochasticallystimulated by an external source. Such systems havebeen used as toy models for the dynamics of somehuman sensory neuronal networks and neuron cul-tures. The collective dynamics of such systems de-pends on the topology of the connections in the net-work. Here we develop a general theoretical approachto study the effects of network topology on dynamicrange, which quantifies the range of stimulus inten-sities resulting in distinguishable network responses.We find that the largest eigenvalue of the weightednetwork adjacency matrix governs the network dy-namic range. Specifically, a largest eigenvalue equalto one corresponds to a critical regime with maxi-mum dynamic range. This result appears to hold forrandom, all-to-all, and scale free topologies, and isrobust to the inclusion of time delays and refractorystates. We gain deeper insight on the effects of net-work topology using a nonlinear analysis in terms ofadditional spectral properties of the adjacency ma-trix. We find that homogeneous networks can reach ahigher dynamic range than those with heterogeneoustopology. Our analysis, confirmed by numerical sim-ulations, generalizes previous studies in terms of thelargest eigenvalue of the adjacency matrix. These re-sults provide a better understanding of the sourcesof enhanced dynamic range of neuronal networks andmay be applicable to the study of other systems thatcan be modeled as a network of coupled excitableelements (e.g., epidemic propagation).

Fluid rope tricks, Stephen Morris, University ofTorontoA thread of viscous fluid, like honey, falling ontoa surface undergoes a buckling instability known asthe “rope coiling effect”. The thread spontaneouslywraps itself into helical loops before the fluid settlesonto the surface. We will discuss a generalization ofthis classic problem, known as the “fluid mechani-cal sewing machine”, in which the surface is replacedby a moving belt. The belt breaks the rotationalsymmetry of the rope coiling, leading to an astonish-ing zoo of states as a function of the belt speed andnozzle height. We constructed a precision apparatusthat can systematically explore this zoo and identifythe modal structure of, and bifurcations between, thevarious “stitch patterns”.

Reconstruction of Cardiac Action Potential Dy-

namics using Computer Modeling with Feed-back from Experimental Data, Laura Munoz,Cornell UniversitySudden cardiac arrest is a leading cause of death inthe industrialized world. Most cases of sudden car-diac arrest are due to ventricular fibrillation (VF),a lethal heart arrhythmia. Closed-loop observer de-sign techniques are relevant to the study of arrhyth-mias, since such methods could be used to improvethe performance of anti-arrhythmic electrical stim-ulus protocols, or to provide enhanced informationto researchers who investigate arrhythmias during invitro or in vivo experiments. In this study, an ob-server has been developed based on a mathematicalmodel of cardiac action potential (AP) dynamics, inorder to reconstruct unmeasured quantities, such asAP durations (APDs) at locations away from sens-ing electrodes. Tools for observer analysis and designwere applied to a two-variable Karma model of APdynamics, and it was confirmed that cellular mem-brane potential data could be used to reconstructthe state of a single-cell system, and that Luenbergerfeedback could stabilize the observer for a multi-cellsystem. Next an observer with 1D spatial geometrywas tested with microelectrode membrane potentialdata from a 2.1cm in vitro canine Purkinje fiber. Itwas shown that the observer produced more accurateAPD estimates than the model by itself. The abilityof feedback to stabilize the observer about differentcategories of AP patterns in multi-cell systems willbe discussed.

Trapping of Swimming Particles in Chaotic FluidFlow, Nicholas Ouellette, Yale UniversitySmall motile particles in fluid environments are wellknown to show a wide variety of complex behav-iors, ranging from pattern formation to the drivingof macroscopic flow. Less is known, however, aboutthe dynamics of swimming particles in flows that area priori nontrivial and chaotic. Using a simple com-putational model, we study the behavior of pointlike,spherical particles that have their own intrinsic ve-locity and are advected by a two-dimensional chaoticflow field. We show that small but finite values ofthe intrinsic swimming speed can sometimes lead toweaker particle transport, as swimmers can becomestuck for long times in traps that form near the el-liptic islands of the underlying flow field.

Chaos Elimination of Fluctuations in QuantumTunneling Rates, Louis Pecora, Naval ResearchLaboratory

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We study quantum tunneling in various shaped,two-dimensional, flat, double wells by calculatingthe energy splitting between symmetric and anti-symmetric state pairs. For shapes that have regularor nearly regular classical behavior (e.g. rectangu-lar or circular wells) we find that tunneling rates fornearby energy states vary over wide ranges. Ratesfor energetically close quantum states can differ byseveral orders of magnitude. As we transition to wellshapes that admit more classically chaotic behaviorthe range of tunneling rates narrows, often by an or-der of magnitude or more. For well shapes in whichthe classical behavior appears to be fully chaotic thetunneling rates’ range narrows to about a factor of 3or so between the smallest and largest rates in a widerange of energies. This dramatic narrowing appearsto come from destabilization of periodic orbits in theregular wells that produce the largest and smallesttunneling rates which eliminates large fluctuations.We have developed a theory based on a random planewave approximation which quantitatively reproducesthe changes in tunneling rate distributions seen in thenumerical results and explains their statistics.

Measuring Information Flow in AnticipatorySystems, Shawn Pethel, U.S. Army RDECOMWe report that the apparent direction of informationflow in an anticipatory (predictive) network dependson measurement resolution. Transfer entropy esti-mates from low resolution data show net informa-tion flow away from an anticipatory element whilehigh resolution measurements show the flow towardsit. At low resolutions anticipatory elements will ap-pear to be driving the network dynamics even whenthere is no possibility of such an influence. Becausecoarse graining is generally required for the estima-tion of transfer entropy this effect is likely to be en-countered. We present numerical results for coupledmaps and analytical results for a Markov chain modeland discuss a feature that can be used to detect thepresence of anticipatory dynamics.

Crowd behavior: Synchronization of multistablechaotic systems by a common external force,Alexander Pisarchik, Centro de Investigaciones enOpticaIt was noted long time ago that individuals being in acrowd lose their personality and act synchronously asa common system. While psychologists and sociolo-gists give different explanations for this phenomenon,an alternative approach is to consider individuals asdynamical systems, and say that they are affected

by the same external force if they are looking ator listening to the same object (a leader, a govern-ment, a football game, a rock concert, a movie, etc.).When the individuals think alike, so that collectiveor crowd behavior can be expected, we may say theyare synchronized. In sociology, synchronization phe-nomena are very relevant to better understand themechanisms underlying the formation of social col-lective behaviors, such as the sudden emergence ofnew ideas, habits, fashions or leading opinions. Tofind out what kind of state might be associated withpeople’s opinions and emotions, we first need an an-swer to: What kind of motion can be related to thebrain functioning? Numerous experiments with neu-ronal activity and electroencephalograms (EEG) in-dicate that their dynamics exhibit many characteris-tics inherent to chaos; this means that the overall sys-tem which gives rise to the EEG potentials, namelythe brain, is in a chaotic state. Moreover, many re-searchers have confirmed that multistability is inher-ent to neuronal behavior and manifests itself in manybrain functions, such as audio and visual perception,and is even responsible for memory. An externalforce, generally chaotic or stochastic provokes jumpsbetween coexisting attractors and create a new syn-chronization state. We study this synchronizationproblem with prototype bistable chaotic Rossler os-cillators subject to a common chaotic or noisy force.Depending on the coupling strength, different syn-chronization states are distinguished and analyzedfor both cases.

Determining the onset of chaos in large Booleannetworks, Andrew Pomerance, University of Mary-landBoolean networks are discrete dynamical systems inwhich the state (zero or one) of each node is updatedat each time t to a state determined by the states attime t−1 of those nodes that have links to it. Thesesystems have been extensively studied as models ofgenetic control in cells and neuronal systems. Oneimportant property of these systems is that they ex-hibit ordered and chaotic dynamics, with a transitionbetween the two regimes. This transition has beenwell-studied in the limit of random network topolo-gies, however little is known about their behavior inrealistic topologies such as those found in biologicalsystems. In this talk we present a criterion that pre-dicts the onset of chaotic dynamics in a wide varietyof networks with realistic topological features, suchas in-/out-degree correlation, assortativity, commu-

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nity structure, and small motifs. In addition, a gen-eralization of this criterion can be applied to net-works with special update rules, such as thresholdrules or canalizing rules.

Time delays in the synchronization of chaotic cou-pled systems with feedback, Jose Rios Leite, Uni-versidade Federal de PernambucoIsochrony and time leadership was studied in the syn-chronized excitable behavior of coupled chaotic sys-tems. Each unit of the system had chaos due tofeedback with a fixed delay time. The inter-unitscoupling signal had a second, independent, charac-teristic time. Synchronized excitable spikes presentisochronous, time leading or time lagging behav-ior whose stability is shown to depend on a sim-ple relation between the feedback and the couplingtimes. Experiments on the synchronized low fre-quency fluctuations of two optically coupled semicon-ductor lasers and numerical calculations with cou-pled laser equations verify the predicted stabilityconditions for synchronization. Synchronism withintermittent time leadership exchange was also ob-served and characterized [1].[1] Jhon F. Martinez Avila and J. R. Rios Leite,“Time delays in the synchronization of chaotic cou-pled lasers with feedback,” Opt. Express 17, 21442-21451 (2009)

Effects of Shape on Diffusion, Rob Shaw, Santa FeComplexThe motion of point particles undergoing randommotions is well-understood; particle density can beconsidered a field, governed by the ordinary diffu-sion equation. The assumption that the infinitesimalparticles do not interact leads to densities evolvingaccording to a local and linear differential operator.But as soon as the motions of extended objects areconsidered, we may see unexpected effects due tononlocal interactions, and deviations from standardFickian diffusion. In fact, simple diffusive flow ofshapes in confined spaces can be used in the con-struction of rectifiers, and other machines, on a mi-croscopic scale. This is perhaps relevant in the highlycrowded environment of the cytoplasm of living cells.Any sorting, or other operation, which can be ac-complished in a simple gradient flow, without theexpenditure of ATP, would be highly advantageous.As a particular example, we examine rectification ofion flows in cellular membrane channels. While ionchannels in today’s living systems are highly sophis-ticated devices, we show that much of the function-

ality, including rectification, can be achieved simplywith the geometrical constraints arising from ex-tended objects in close proximity. No electrostaticbinding, or additional cellular mechanisms are nec-essarily required. The configuration space of a setof closely packed rigid objects can become convo-luted, with many dead-end alleys. If the system issubjected to a shear, or gradient, it may naturallytend to settle in such a dead-end, and have to backup, or retrace its path, in order to proceed further.Thus metastable states, requiring a fluctuation toescape, can commonly arise, and a configuration canbecome locally locked. The requirement that the sys-tem backtrack to unlock distinguishes this processfrom ordinary jamming. There is no friction per se.We will present simple models of this process. Evena Hamiltonian system of rigid extended objects inequilibrium can have complications. Ergodicity tellsus that, in the long run, all configurations must beequally likely. But the space of configurations, sub-ject to boundary conditions, may be constrained.Though the probability of being in any particularconfiguration is the same, the likelihood of gettingin and out of a tight fit can be greatly reduced. Forexample, an object near a wall or a corner is morelikely to remain for a time in a local area than anobject in the bulk. Such extended residence timescan affect reaction rates of molecules kept in prox-imity. We will suggest spatially dependent statisticsto measure this effect. We will present several exam-ples, including simulations of hard disks in confinedgeometries, as well as dimers and other shapes mov-ing on a lattice, and a few physical demonstrations.ReferencesN. Packard and R. Shaw, arxiv.org:cond-mat/0412626 (2004)R. Shaw, N. Packard, M. Schroter and H. L. Swin-ney, PNAS 104, p. 9580 (2007)R. Shaw and N. Packard, Phys Rev Lett 105, 098102(2010)

Flexibility Increases Energy Efficiency of Diggingin Granular Substrates, Dawn Wendell, MITThe mechanics of digging through granular materialsoften neglect the inhomogeneities present in granularpackings. However, this variety of forces implies thatthere are more and less efficient ways to traverse thegranular substrate. This work investigates changesin energy requirements for thin diggers in granularmaterials by varying the mechanical flexibility of thediggers. We find that there is an optimal amount of

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flexibility in the digger that leads to deeper depthsthan rigid diggers for the same digging energy. Ex-

perimental results are compared to theory to explainwhy flexibility increases digging efficiency.

Posters

Robustness of modular network and overlappingcommunities, Yong-Yeol Ahn, Northeastern Uni-versityOur life relies on a wide variety of properly func-tioning complex systems, from our cells to social or-ganizations. Such complex systems often take theform of network that contains overlapping modules.For instance, the protein-protein interaction net-work contains protein complexes (modules), whichoften overlap—sharing elements (proteins). Here, westudy the robustness of the networks with functional,overlapping modules using percolation theory. Weshow that the network of modules may fall apartwell before the network of elements does. Our resulthas important implications on the robustness and dy-namics of real-world networks, and may explain howmissing information hides pervasive overlap betweencommunities in real networks.

Chaotic Ionization of Bidirectionally Kicked Ryd-berg Atoms, Korana Burke, University of Califor-nia MercedA highly excited Rydberg atom exposed to peri-odic alternating external electric field pulses exhibitschaotic behavior. The ionization of this system isorganized by a homoclinic tangle attached to a fixedpoint at infinity. We present and explain the re-sults from two experiments designed to probe thestructure of the phase space turnstile. The first ex-periment focuses on observing a step-function-likebehavior of the ionization fraction as a function ofthe strength and period of the applied electric fieldpulses. The second experiment observes the periodicdips in survival probability as a function of the posi-tion of the starting electron ensemble in phase space.

Homoclinic Snaking in Plane Couette Flow, JohnBurke, Boston UniversityPlane Couette flow is a shear flow driven by twoparallel plates moving in opposite directions. Thesimple geometry makes it an ideal system in whichto study the transition from a simple laminar flowto complicated turbulent dynamics. On small peri-odic domains, there are several exact equilibrium andtraveling wave solutions to the Navier-Stokes equa-tions which are known to play a key role in guiding

this transition to turbulence, and in the turbulenceitself. Less is known about the transition to tur-bulence on larger domains. I describe several newclass of exact solutions of plane Couette flow whichare spatially localized in one direction, resemblingseveral wavelengths of the known spatially periodicsolutions embedded in a laminar background. Un-der continuation in Reynolds number, the localizedsolutions exhibit a sequence of saddle-node bifurca-tions similar to the homoclinic snaking phenomenon,which has been studied extensively in much simplerPDEs such as the Swift-Hohenberg equation. Theselocalized solutions represent a step toward general-izing the dynamical systems picture for turbulenceto extended flows. John Burke, Boston UniversityJohn Gibson, University of New Hampshire TobiasSchneider, Harvard University

Jet-Induced Granular 2-D Crater Formation withHorizontal Symmetry Breaking, Abe Clark,Duke UniversityWe investigate the formation of a crater in a 2-D bedof granular material by a jet of impinging gas, moti-vated by the problem of a retrograde rocket landingon a planetary surface. As the strength and height ofthe jet are varied, the crater is characterized in termsof depth and shape as it evolves, as well as by thehorizontal position of the bottom of the crater. Thecrater tends to grow logarithmically in time, a resultwhich is common in related experiments. We alsoobserve an unexpected horizontal symmetry break-ing at certain well-defined conditions. We presentdata on the evolution of these asymmetric states andattempt to give insights into the mechanism behindthe symmetry-breaking bifurcation. This horizontalsymmetry breaking is highly suggestive of a pitch-fork bifurcation, and we give evidence to classify itas forward or backward in different regimes of oper-ation. As we will demonstrate, the formation of anasymmetric crater could be of considerable practicalconcern for lunar or planetary landers, particularlyin the case of a backward pitchfork bifurcation, whichis characterized by hysteresis and very rapid transi-tions.

Couette Shear for Elliptical Particles Near

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Jamming, Somaiyeh Farhadi, Duke UniversityWe have performed 2D Couette shear experimentson systems of photoelastic particles. The particlesare identical ellipses with aspect ratio 2. We usethe photoelastic property of the disks to obtain theforces acting on a particle. We use two cameras to si-multaneously image the particle motion and the pho-toelastic force response. Using ellipses enables us tounderstand the effect of particle shape asymmetryon the large-scale behavior on the rheological behav-ior of granular systems near jamming. Of particu-lar interest are the nematic ordering of the ellipses,the formation of shear bands and the nature of forcetransmission.

Measuring information flow in anticipatorysystems, Daniel Hahs, US Army RDECOMWe report that the apparent direction of informationflow in an anticipatory (predictive) network dependson measurement resolution. Transfer entropy esti-mates from low resolution data show net informa-tion flow away from an anticipatory element whilehigh resolution measurements show the flow towardsit. At low resolutions anticipatory elements will ap-pear to be driving the network dynamics even whenthere is no possibility of such an influence. Becausecoarse graining is generally required for the estima-tion of transfer entropy this effect is likely to be en-countered. We present numerical results for coupledmaps and analytical results for a Markov chain modeland discuss a feature that can be used to detect thepresence of anticipatory dynamics.

Experimental and theoretical evidence for fluctu-ation driven activations in an excitable chem-ical system, Harold Hastings, Hofstra UniversityAn excitable medium is a system in which smallperturbations die out, but sufficiently large per-turbations generate large “excitations”. Biologicalexamples include neurons and the heart; the lat-ter supports waves of excitation normally generatedby the sinus node, but occasionally generated byother mechanisms. The ferroin-catalyzed Belousov-Zhabotinsky reaction is the prototype chemical ex-citable medium. We present experimental and the-oretical evidence for that random fluctuations cangenerate excitations in the Belousov-Zhabothinskyreaction. Although the heart is significantly differ-ent, there are some scaling analogies.

Bifurcations of 2D Rayleigh-Taylor UnstableFlames, Elizabeth Hicks, University of Chicago

A premixed flame moving against a sufficientlystrong gravitational field becomes deformed and cre-ates vorticity. If gravity is strong enough, this vor-ticity is shed and deposited behind the flame front.We present two-dimensional direct numerical simula-tions of this vortex shedding process and its effect onthe flame front for various values of the gravitationalforce. The flame and its shed vortices go throughthe following stages as gravity is increased: no vor-ticity and a flat flame front; long vortices attached toa cusped flame front; instability of the attached vor-tices and vortex shedding (Hopf bifurcation); disrup-tion of the flame front by the shed vortices, causingthe flame to pulsate; loss of left/right symmetry (pe-riod doubling); dominance of Rayleigh-Taylor insta-bility over burning (torus bifurcation); and, finally,complex interactions between the flame front and thevortices. We consider the first few bifurcations of thesystem in detail. The initial vortex shedding (theHopf bifurcation) is similar to the first stages of thevon Karman vortex street in that both processes aredescribed by the Landau equation. For higher valuesof gravity, this vortex shedding disturbes the flamefront the flame speed begins to oscillate. We showtime series analyses of the flame speed for variousvalues of gravity and show that a period doublingbifurcation and a torus bifurcation occur. These bi-furcations are related to changes in the behavior ofthe flame front itself. We also present calculations ofthe embedding dimension and the largest Lyapunovexponent to help characterize the growing complex-ity of the system.

Pattern formation in coating flows of suspensions,Justin Kao, Massachusetts Institute of TechnologyWe investigate Landau-Levich coating of a solid wallby a suspension. When the suspended particle sizeexceeds the liquid film thickness, capillarity inducesattractions between particles, and pinning of parti-cles against the wall. Experiments show small-scaleclustering of particles, a strongly nonlinear relation-ship between the particle coating density and thewall speed, and under certain conditions, heteroge-neous coating with long-range correlations in the par-ticle density. We show that a continuum model basedon the Cahn-Hilliard formalism generates similar be-havior.

Spike-Time Reliability of Pulse-Coupled Oscilla-tor Networks, Kevin Lin, University of ArizonaA network is reliable if its response to repeated pre-sentations of a given stimulus is essentially repro-

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ducible. Reliability is of interest in, e.g., compu-tational neuroscience, since the degree to which anetwork is reliable constrains its ability to encodeinformation via precise patterns of spikes. In thiswork, we formulate the problem of reliability usingthe theory of random dynamical systems. We presentan analysis of certain layered network architectures(commonly used in neuroscience), and show how net-work conditions determine the reliability of such net-works.

Depinning of localized structures in a forced dis-sipative system, Yi-Ping Ma, University of Cali-fornia, BerkeleyThe 1:1 forced complex Ginzburg-Landau equation(FCGLE) is a forced dissipative system that exhibitsbistability between equilibria and thus admits 1Dtraveling front solutions. A localized state consist-ing of an inner equilibrium embedded in an outerequilibrium can be formed by assembling two iden-tical fronts back-to-back. The speed of the frontcan be computed using an ODE in the comovingframe, regardless of the temporal stability of the in-ner equilibrium in the original PDE. When the innerequilibrium is modulationally unstable, there existsa parameter interval within which the outer equi-librium remains pinned to a periodic state that bi-furcates from the inner equilibrium. The bifurca-tion structure of these steady states is referred toas defect-mediated snaking [1]. This growth mecha-nism nucleates rolls of periodic states at the centerof the wave train and thus differs from standard ho-moclinic snaking where rolls are nucleated at the lo-cation of the bounding fronts. Outside the snakinginterval, these fronts move (or “depin”) such thatrolls are created or destroyed via successive phaseslips. These phase slips occur in the center of thewave train for slow depinning and off center for fastdepinning. Fast depinning is a strongly nonlinearphenomenon that resembles wave propagation con-fined by an artificial boundary. Slow depinning maybe partially explained by a weakly nonlinear theoryand reveals subtle differences between the dynamicsnear the two limits of the snaking interval.References[1] Y.-P. Ma, J. Burke, and E. Knobloch, Defect-mediated snaking: A new growth mechanism for lo-calized structures, Physica D 239 (2010), pp. 1867–1883.[2] Y.-P. Ma and E. Knobloch, Depinning of localizedstructures in a forced dissipative system, in prepara-

tion (2010).

Clustering of particles in turbulence, JulianMartinez Mercado, University of TwentePreferential concentration of particles occurs fre-quently in nature, playing an important role in avariety of processes: from cloud formation, sedimen-tation to plankton distribution in oceans. Even inhomogenous isotropic turbulence, particles do notdistribute homogeneously. In this work we study par-ticle clustering in homogenous isotropic turbulenceboth numerically and experimentally. Experimentsare carried out in the Twente Water Tunnel. ParticleTracking Velocimetry is employed to obtain 2D and3D positions of light particles (bubbles). We conducta Voronoi analysis on the experimental and numeri-cal data to obtain area and volume distributions ofthe Voronoi cells. From numerics we can also com-pute these distributions for tracers and heavy par-ticles. Both in numerics and experiments, area andvolume distributions show a different behavior froma random Poisson process, implying that clusteringis present. In addition, the effect of Stokes numberon the clustering behavior can be studied using thenumerics.

Invariant manifolds in chaotic advection-reaction-diffusion pattern formation, Kevin Mitchell, Uni-versity of California, MercedAuthors: John Mahoney (UC Merced), KevinMitchell (UC Merced), Tom Solomon (Bucknell)Invariant manifolds are organizing structures cen-tral to the problem of transport in chaotic advec-tion, having been applied extensively in periodicallydriven systems and more recently extended, in theform of Lagrangian coherent structures, to fluidsthat are not strictly time-periodic. Here, we con-sider reaction-diffusion dynamics in systems that aresimultaneously undergoing chaotic advection. Thiscan be viewed as a simplified model such diversesystems as combustion dynamics in a chaotic flow,microfluidic chemical reactors, and blooms of phy-toplankton and algae. Prior experimental and nu-merical work has shown that such systems generate“burning fronts” with a remarkably rich structure,including the mode locking of the front profile to thedriving frequency. Here, we demonstrate how the in-variant manifolds useful in chaotic advection can begeneralized to accommodate the additional reaction-diffusion dynamics. The generalized manifolds existin an extended phase space that is of larger dimen-sion than the fluid itself. We show how these man-

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ifolds provide a clear criterion for the existence ofmode-locking and are essential for explaining the pat-terns of the mode-locked fronts. Finally, we presentrecent experimental results on the direct laboratorymeasurement of such manifolds.

Fluctuations in an agitated granular liquid, KiriNichol, Leiden University / North Carolina StateUniversityA container of glass beads behaves as a solid - thebeads cannot rearrange. However, if the particles aresheared by a spinning disk in the bottom of the vesselthe system begins to behave like a liquid: low-densityobjects float in the grains at the depth predicted byArchimedes’ Rule and moving objects experience vis-cous drag. But what is the microscopic cause of thisliquid-like behavior? And does our granular liquidbehave microscopically like a real liquid? We haveinvestigated the microscopic behavior of the grainsby studying the motion of a probe floating in thegrains. The position of the probe fluctuates - andwe find that the character of the fluctuations can beBrownian or subdiffusive depending on the shape ofthe shear band that excites the fluctuations. Finally,we demonstrate that the time scale of the fluctua-tions sets the time scale of the viscosity, suggestingthat fluctuations are the cause of the liquid-like be-haviour in sheared granular matter.

Stability and Bifurcations in a Dynamical SystemAssociated with Membrane Kinetics Underly-ing Cardiac Arrhythmias, Irina Popovici, USNAThis presentation aims to describe the bifurcations,stability properties and basins of attraction of a dy-namical system introduced by Kline and Baker tomodel the response to stimulation of a cardiac cell(or electrically coupled multi-cellular preparation).The two-dimensional system is controlled by five pa-rameters: four kinetic parameters (two amplitudes,two rate constants) and the stimulus period. Amongperiodic orbits, the escalators and the alternans areof particular interest to the medical community. Ourresults describe their properties, focusing on the im-pact of varying the stimulus period from slower tofaster cardiac rhythms. We also describe bifurca-tions associated with changing the kinetic parame-ters within a 4-dimensional region of (mathemati-cally) admissible values, with emphasis on the dis-similarities between the properties of the low orderand high-order escalators.

Nonlinear Waves in Granular Crystals, Mason

Porter, University of OxfordI will discuss recent investigatations of highly non-linear solitary waves in granular chains using numer-ical computations, analytical calculations, and ex-periments. I will provide an introduction to granularchains, and then I will focus on the dynamics of in-trinsic localized modes (aka, discrete breathers) indiatomic chains and chains with defects.

Density-dependent particle clustering on a Fara-day wave, Ceyda Sanli, University of TwenteCeyda Sanli, Devaraj van der Meer, and DetlefLohse. Physics of Fluids Group, Department of Sci-ence and Technology, J.M. Burgers Center for FluidDynamics and IMPACT, University of Twente, 7500AE Enschede, The Netherlands.Floating granular particles on a standing Faradaywave accumulate at the nodal points of the wave dueto the wave drift [1]. By the help of the increasingimportance of the capillary attraction, in the denselimit the motion of the particles becomes complex.Understanding the resultant spatial distribution ofthe particles and the clustering is of fundamentalimportance to characterize such a complex system,and brings a different perspective to the granularflow of particles on surface waves. We experimen-tally observe that surprisingly the particles positioncan be changed by increasing the particle concen-tration. Our hydrophilic naturally buoyant granularparticles, clustering at the antinodes for low concen-trations, form clusters at the nodes for higher con-centrations. Different kind of structures e.g. com-pact, almost circular clusters, more deformed clus-ters, such as elongated or filamentary structures, ormore heterogeneous patterns are observed at differ-ent positions on the wave at an intermediate den-sity of the antinode-node transition. We study thechanges in the spatial distribution and the organi-zation of the particles at the antinode-node transi-tion by calculating the Minkowski functionals, whichis a powerful technique being used to analyze thegeometry and the topology of the pattern forma-tions in e.g. astrophysics, whereas its applicationgrows in various other areas such as biophysics, col-loidal physics, and recently in granular physics [2,3].We apply the Minkowski functionals by consideringthe point patterns approach: The discs of radius raround each particle center are drawn and then r isvaried. We find that it is possible to quantify thedifferent types of clustering by the varieties of de-cays in the Minkowski functional with respect to r,

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e.g. the sharp decays are due to the almost circularclusters, whereas the smooth decays are due to moredeformed clusters and heterogeneous patterns.[1] G. Falkovich et al. Nature 435, 1045 (2005).[2] K. Michielsen et al. Phys. Reports 347, 461(2001).[3] H. Mantz et al. J. Stat. Mech. P12015 (2008).

The Buckley-Leverett Equation with DynamicCapillary Pressure, Michael Shearer, North Car-olina State UniversityThe Buckley-Leverett equation for two phase flow inporous media is modified by including a dependenceof capillary pressure on the rate of change of satu-ration. This model, due to Gray and Hassanizadeh,results in a nonlinear partial differential equation.Phase plane analysis, including a separation functionto measure the distance between invariant manifolds,is used to determine when the equation supportstraveling waves corresponding to undercompressiveshocks. The Riemann problem for the underlyingconservation law is solved and the structures of thevarious solutions are confirmed with numerical sim-ulations of the partial differential equation.

Spatiotemporal Dynamics of Calcium-Driven Al-ternans in Cardiac Tissue, Per Sebastian Skardal,University of Colorado at BoulderCardiac alternans are a potentially fatal phenomenondefined as a beat-to-beat alternation of action po-tential duration or calcium concentration in cardiactissue. Alternans can be either voltage or calciumdriven, with distinct qualitative differences in theirspatiotemporal dynamics due to the quick diffusionof voltage across tissue. Understanding the spa-tiotemporal dynamics of alternans in tissue is im-portant because tissue near phase reversals is partic-ularly vulnerable to phenomena like wave break-upand re-entry. Unlike voltage-driven alternans whereamplitude equations have been successfully used, forexample, to analyze alternans control schemes, thespatiotemporal dynamics of calcium-driven alternansremains poorly understood. We model the coupleddynamics of calcium and voltage alternans in tissueusing coupled beat-to-beat continuous maps. Thesemaps include spatial diffusive coupling of voltage andthe dependence of signal conduction velocity (CVrestitution) on alternans dynamics. We analyze theresulting dynamics numerically and analytically. Asthe degree of calcium instability is increased, thereis a transition from no alternans to smooth travelingwaves analogous to that observed in voltage-driven

alternans. As the degree of calcium instability is in-creased further, we observe a novel bifurcation fromsmooth traveling waves to a stationary discontinu-ous pattern. This transition is characterized by aboundary layer dividing regions of opposite phasewhose thickness decreases, together with the wavevelocity, as the transition point is approached. Atthis point the thickness of this layer and the ve-locity vanish, and the pattern becomes discontinu-ous. Scaling predictions for the dependence of thewavelength of smooth and discontinuous patterns ofspatially discordant alternans on conduction veloc-ity restitution are derived analytically and verifiednumerically. Our findings extend our theoretical un-derstanding of spatiotemporal dynamics of alternansto the important case of calcium-driven alternans.

Fingering instability down the outside of a verti-cal cylinder, Linda Smolka, Bucknell UniversityWe present an experimental and numerical study ofthe dynamics of a gravity-driven contact line of athin viscous film traveling down the outside of a ver-tical cylinder of radius R. In all of our experimentswith cylinder radii ranging between 0.159 and 3.81cm, the contact line becomes unstable to a finger-ing pattern. Observations are compared to inclinedplane experiments in order to understand the influ-ence curvature plays on the fingering pattern. Us-ing lubrication theory, we derive a model for the filmheight that includes gravitational and surface tensioneffects and examine the structure and linear stabil-ity of the contact line using traveling wave solutions.For Bond number (Bo) greater than or equal to or-der 10 our model predicts that curvature’s influenceis negligibly weak as the shape and stability of thecontact line converge to the behavior one observes fora vertical plane. For Bo greater than or equal to 1.3,the most unstable and cutoff wave modes and max-imum growth rate scale like Bo0.45, indicating thecontact line becomes more unstable as gravitationaleffects increase or, for a fixed fluid, as the cylinderradius increases. The linear stability of the contactline changes at the critical value Boc = 0.56, suchthat, above Boc the contact line is unstable and be-low Boc it is stable to fingering. We find excellentagreement between the number of fingers that formalong the contact line and the range of wavelengthsmeasured in experiments with the range of unstablemodes and wavelengths predicted by our model.

The Buckley-Leverett Equation with DynamicCapillary Pressure, Kimberly Spayd, North Car-

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olina State UniversityThe Buckley-Leverett equation for two phase flow inporous media is modified by including a dependenceof capillary pressure on the rate of change of satu-ration. This model, due to Gray and Hassanizadeh,results in a nonlinear partial differential equation.Phase plane analysis, including a separation functionto measure the distance between invariant manifolds,is used to determine when the equation supportstraveling waves corresponding to undercompressiveshocks. The Riemann problem for the underlyingconservation law is solved and the structures of thevarious solutions are confirmed with numerical sim-ulations of the partial differential equation.

Suspensions of Maps to Flows, John Starrett, NewMexico Institute of Mining and TechnologyThe surface of section map is a construction that al-lows us to analyze certain properties of a flow in n di-mensional space by examining a map in n−1 dimen-sions. We can also go the other way by suspendingmaps to flows, although the utility is not so obvious.We describe several different methods for suspend-ing maps to flows, including the suspension of onedimensional maps to semi-flows equivalent to flowson templates and numerical methods to suspend twodimensional maps to three dimensional flows usingonly a few carefully chosen periodic points of themap.

The Effect of Network Structure on the Path toSynchronization in Large Systems of CoupledOscillators, John Stout, North Carolina State Uni-versity(With Matthew Whiteway)The Kuramoto Model has been used extensively asa tool for understanding the dynamics of large sys-tems of oscillators that are either coupled globally,locally, or through a complex network. We are in-terested in the path that systems of networked oscil-lators take to global synchronization as the couplingstrength between oscillators is increased. We employthe Kuramoto Model to study the effects of networksize, degree distribution, and natural frequency dis-tribution on the dynamics of these systems. A recentstudy has shown that small clusters of synchronizedoscillators form before the entire system transitionsto a state of global coherency. The main result fromour work is that this local synchronization is largelyindependent of both the size and natural frequencydistribution of the system, and is instead highly de-pendent on the average number of links per oscillator,

becoming less prominent as this average increases.

Brownian movement in complex asymmetric peri-odic potential under the influence of “green”noise, Mikhail Sviridov, Moscow Institute of Physicsand TechnologyThe idea of the molecular motor has been put for-ward by M. Smoluchowski and R. Feynman. Upto now this problem has wide development. Thephysics of this phenomenon consists in different “dif-fusion velocities” of a Brownian particle in oppositedirections if a periodic structure action (for exam-ple, a biomolecule or other long chemical chain) isdescribed by a non-symmetric potential. However,for many stochastic systems this problem has stillnot been treated thoroughly. In particular, we cannote that external colored noises are seldom consid-ered. Most often the motion of a Brownian parti-cle is studied for the case when the system is sub-jected to the action of white noise. However, whitenoise is just a convenient abstraction for mathemat-ical calculations. In practical situations noise is col-ored with a spectral density commonly decreasingwith frequency. We conditionally call this kind ofnoise as “red” noise. The well-known red noise is theOrnstein-Uhlenbeck random process. (We are notconsidering the case of flicker noise). In this workwe consider noise when the spectral density of theexternal broadband noise is equal to zero on the ze-roth frequency. In our previous work [1] such a noiseis been called as “green” noise. Similar noise canoriginate if a molecule is lighted by the black-bodyradiation, or is influenced by thermal phonons noisein low-dimensional structures, or at a phase modu-lation of a potential, etc. For the analytical study ofgreen noise action, we use an approach based on aKrylov-Bogoliubov averaging method. For the caseof green noise this theory is modified to study theaction of noise with arbitrary intensity. We showthat a certain effective potential can be built whichdetermines the basic features of the system dynam-ics. Numerical simulations for many systems corrob-orate this fact. Further, we compare two numericalcases. The first one corresponds to the case of greennoise, which is the time-derivative of the Ornstain-Uhlenbeck process. In the second example we takethe initial Ornstain-Uhlenbeck process as red noise.We show that there are the complex potentials thatthe system does not work as a molecular motor in thecase of red noise, i.e. the average motion of the parti-cle does not exhibit a drift in a given direction. How-

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ever, if green noise operates on the same system, thesystem will play a role of the molecular motor whichis effective enough. We demonstrate this fact by ahistograms for 100 realisations of these processes.[1] S. A. Guz and M. V. Sviridov. Brownian motionwith “green” noise in a periodic potential. Phys.Lett. A 240 (1998) 43-49.

Synchronization in Finite-Memory DynamicalSystems, Nicholas Travers, University of Califor-nia, DavisNicholas F. Travers and James P. Crutchfield Com-plexity Sciences Center Mathematics DepartmentPhysics Department University of California at DavisDavis, CA 95616When studying chaotic dynamical systems it is of-ten helpful to use probabilistic models, even if theunderlying dynamics are deterministic. In particu-lar, hidden Markov models are often used to modeltime series data from dynamical systems and sub-shifts derived from symbolic dynamics. Our workconcerns a class of hidden Markov models known asepsilon-machines. Specifically, we are interested inthe synchronization problem: How well can an ob-server infer the internal state of the machine throughobservations of its output? We find, in general,that an observer synchronizes exponentially fast forany finite-state epsilon-machine. For those that ad-mit a finite-length synchronization word, we pro-vide an analytical method for calculating the syn-chronization rate. These results have importantconsequences for prediction: The synchronizationrate upper-bounds the convergence rate of finite-length approximations of the Kolmogorov-Sinai en-tropy. (See http://arxiv.org/abs/1008.4182 andhttp://arxiv.org/abs/1011.1581.)

Reactive mixing of initially isolated scalars: esti-mation of mix-down time, Yue-Kin Tsang, TheChinese University of Hong KongRecently, there is much interest in the chaotic mixingof two reactive scalars that are initially separated bya third inert fluid. Such configuration is relevant tothe process of broadcast spawning in marine biologyand the modeling of chemical reactions in the atmo-sphere. The reactants, sperm and egg in the formercase and atmospheric chemicals in the latter, are re-leased at separate locations and brought into contactby the flow. An important quantity in this problemis the mix-down time, i.e. time taken for the reac-tants to come into contact and start to react. Usinga Lagrangian chaotic flow, we study the dependence

of the mix-down time on the diffusivity of the reac-tants and the initial separation between them. Weshall present a theory relating the mix-down time tothe finite-time Lyapunov exponent of the flow.

Stabilization of chaotic spiral waves during car-diac ventricular fibrillation using feedbackcontrol, Ilija Uzelac, Vanderbilt UniversityIlija Uzelac and John Wikswo, Vanderbilt University,and Richard Gray, Food and Drug AdminstrationThe cardiac arrhythmias that lead to ventricularfibrillation arise from electrical spiral waves rotat-ing within the heart with a characteristic periodtau. A single drifting spiral wave can degenerateinto a chaotic system of multiple spiral waves andventricular fibrillation. Earlier attempts to controlcardiac chaos (Garfinkel et al., Science, 1992) uti-lized the Ott, Grebogi and York (OGY) algorithm(Physical Review Letters, 64: 1196 (1990)) to de-liver timed stimuli to a segment of isolated cardiactissue and convert a drug-induced arrhythmia intoperiodic beating. However, it is not clear whetherthis strategy can defibrillate an entire heart. We takean alternative approach wherein early spiral wavedetection and termination are used to prevent ven-tricular fibrillation from developing after the appear-ance of spiral waves. Time-delayed feedback control(TDFC) is a well known approach for stabilizing un-stable periodic orbits embedded in chaotic attractors(Pyragas, Phys. Lett. A, 170: 421 (1992). We hy-pothesize that an unstable cardiac spiral wave withperiod tau can be stabilized by applying a TDFCsignal that represents the difference between the cur-rent state of the system and the state of the sys-tem a time tau earlier, weighted by an experimen-tally obtained scaling factor. Implementing this ap-proach will require precise, closed-loop control of theelectrical charge delivered to the heart during thecardioversion/defibrillation process. To do this, wehave developed a 2 kW arbitrary-waveform voltage-to-current converter (V2CC) with a 1 kHz bandwidththat can deliver up to 5 A at 400 V for 500 ms, anda photodiode system for recording in real time anoptical electrocardiogram, OECG(t). The feedbacksignal driving the V2CC will be the time-difference(OECG(t) - OECG(t−T ), where we hypothesize thatT is τ , the period of the spiral wave. We use phasesingularity mapping to identify the appearance of ro-tors and spiral waves and to verify their stabilizationand termination through cardioversion/defibrillationshocks. One limitation of TDFC is a possible sensi-

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tivity to the choice of a single feedback delay andamplitude, and it may be necessary to utilize in-formation from many previous states of the system(Pyragas, Phys. Lett. A, 323 (1995)). The advan-tage of our hardware is that it will be straightfor-ward to implement a variety of algorithms to gener-ate the feedback signal, if necessary with a complexwave form. The TDFC approach may dramaticallydecrease defibrillation voltages by using a defibrilla-tion waveform that is customized to the particulararrhythmic event, unlike commercial capacitor de-fibrillation devices with fixed, decaying exponentialwaveforms. Supported in part by National Institutesof Health grant R01 HL58241-11 through the Amer-ican Recovery and Reinvestment Act of 2009, andthe Vanderbilt Institute for Integrative BiosystemsResearch and Education.

Dynamic Structure Factor and Transport Coeffi-cients of a Homogeneously Driven GranularFluid in Steady State, Katharina Vollmayr-Lee,Bucknell University, USAWe study the dynamic structure factor of a gran-ular fluid of hard spheres, driven into a station-ary nonequilibrium state by balancing the energyloss due to inelastic collisions with the energy inputdue to driving. The driving is chosen to conservemomentum, so that fluctuating hydrodynamics pre-dicts the existence of sound modes. We present re-sults of computer simulations which are based on anevent driven algorithm. The dynamic structure fac-tor F (q, ω) is determined for volume fractions 0.05,0.1 and 0.2 and coefficients of normal restitution 0.8and 0.9. We observe sound waves, and compare ourresults for F (q, ω) with the predictions of generalizedfluctuating hydrodynamics which takes into accountthat temperature fluctuations decay either diffusivelyor with a finite relaxation rate, depending on wavenumber and inelasticity. We determine the speedof sound and the transport coefficients and comparethem to the results of kinetic theory.

Entrainment of a Thalamocortical Neuron to Peri-odic Sensorimotor Signals, Dennis Guang Yang,Drexel UniversityWe study a 3D conductance-based model of a singlethalamocortical (TC) neuron in response to sensori-motor signals. In particular, we focus on the entrain-ment of the system to periodic signals that alternatebetween ‘on’ and ‘off’ states lasting for time T1 andT2, respectively. By exploiting invariant sets of thesystem and their associated invariant fiber bundles

that foliate the phase space, we reduce the 3D sys-tem to a 2D map, based on which we analyze thebifurcations of the entrained limit cycles as the pa-rameters T1 and T2 vary.

A mathematical model of the decline of religion,Haley Yaple, Northwestern UniversityPeople claiming no religious affiliation constitute thefastest growing religious minority in many countriesthroughout the world. Americans without religiousaffiliation comprise the only religious group growingin all 50 states; in 2009 those claiming no religionrose to 15 percent nationwide, with a maximum inVermont at 34 percent. Here we use three simpli-fied models of competition for members between so-cial groups to explain historical census data on thegrowth of religious non-affiliation in nine countriesworldwide. All three models coincide in the limitof an all-to-all social network, but surprisingly, per-turbations dividing the network into cliques do notchange the qualitative dynamics. According to thesemodels, a single parameter quantifying the perceivedutility of adhering to a religion determines if the un-affiliated group will grow in a society. The modelspredict that for societies in which the perceived util-ity of not adhering is greater than the utility of ad-hering, religion will be driven toward extinction.

Switching from steady-state to chaos via pulsetrains in an optoelectronic oscillator, KristineCallan, Duke UniversityAuthors: Kristine E. Callan, Lucas Illing, DavidRosin, Daniel J. Gauthier, and Eckehard SchollWe investigate an optoelectronic oscillator comprisedof commercially available components which, due tothe presence of a feedback loop and nonlinear ele-ment, displays a variety of dynamical behaviors [1,2]. For a particular choice of slope of the nonlinearity,the (noise-free) model describing our system showsthat the steady-state is linearly stable for all valuesof the feedback gain. We find, however, that this qui-escent state coexists with a chaotic attractor. Onecan switch from the quiescent state to the chaoticwith a finite-size perturbation, causing the produc-tion of an initially periodic train of pulses spacedby the time-delay of the feedback loop with a pulseduration (full width at half maximum) of less than200 ps. Eventually, the pulse spacing and amplitudebecome irregular, resulting in fully developed broad-band chaos with a featureless power spectrum. Wederive a one-dimensional map that accurately pre-dicts the amplitude of the perturbation necessary to

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push the system to the coexisting chaotic attractor,via a pulse train, as a function of the feedback gain.For a given noise level, this map also predicts thevalue of the gain for which the system leaves the qui-escent state for all operating points of the nonlinear-ity. This result could have general implications forthe stability of time-delay systems, for which coex-isting states are common. In addition, the system’spropensity for producing periodic trains of pulses isalso being investigated further, and stable pulsing so-lutions with durations of less than 200 ps have beenrealized experimentally.[1] M. Peil, et al., Phys. Rev. E 79, 026208 (2009)[2] K. E. Callan, et al., Phys. Rev. Lett. 104, 113901(2010).

Brownian Motion By Switching Unstable Dissipa-tive Systems, Eric Campos Canton, Instituto Po-tosino de InvestigacionIt is known that the Brownian motion is the move-ment generated by a particle suspended in a fluid.Then, the Brownian motion of a particle underthe same condition has to behave identically, andthe behavior just chance if the initial conditionschance. Thus, we address the following question:Is the Brownian motion a chaotic or random pro-cess? There are two comments: The first commentis about that the Brownian motion has been modeledas a stochastic process because it is easy to model aprocess where nobody knows what happen in the col-lision between particles. The second comment, thecollision between two particles can be modeled andit is a deterministic process, so the collision betweenseveral particles is a deterministic process too. Thenif we know the exact number of collision between theparticle and others we will be able to model the ex-act trajectory of the particles. It is found that, ingeneral, Chua’s trajectories behave as a Brownianmotion for small time scales, while they can displaya white noise-like behavior or be dominated by har-monic oscillations for large time scales. The Chua’ssystem is a PWL system which yields two scrolls.The generalization of PWL system can be seen in[1, 2]. The aim of this work is to introduce Brow-nian motion as the central object of deterministicprocess and discuss its properties, putting particularemphasis on the sample path properties. Switchingpiece wise linear systems exhibit a chaotic behaviorreflected by a strong divergence of trajectories witharbitrarily close initial condition. In this way, sim-ilar to trajectories from Brownian motion, chaotic

trajectories by PWL systems can be seen as noisewith some degree of correlation. This work focuseson the study of chaotic behavior with similar proper-ties that Brownian motion. The chaotic time seriesare studied by using detrended fluctuation analysisand wavelet transform, which are a methods designedfor the detection of correlations in stochastic time se-ries.References[1] E. Campos-Canton, I. Campos-Canton, J. S.Gonzalez Salas and F. Cruz Ordaz, A parameter-ized family of single-double-triple-scroll chaotic oscil-lations, Rev. Mex. de Fıs., Vol. 54, pp411-415 (2008).[2] E. Campos-Canton, R. Femat, J.G. Barajas-Ramırez and G. Solıs-Perales, ”Multiscroll attractorsby switching systems”, CHAOS, Vol. 20, 013116,(2010).

Phase space method for target ID, Thomas Carroll,Naval Research LabChaotic signals are very sensitive to the effects of fil-tering. In radar or sonar, scattering from a targetis a linear process that may be described as a fil-ter. I have found that interaction of a chaotic signalwith a target produces a characteristic distribution ofneighbors in phase space which may be used to iden-tify the target. The particular distribution of pointsdepends on the rate of compression for the chaoticsignal and on the target characteristics. I show re-sults of numerical simulations and simple microwaveexperiments.

Hamiltonian monodromy, Chen Chen, College ofWilliam and MaryWe say that a system exhibits monodromy if wetake the system around a closed loop in its spectrumspace, and we find that the system does not comeback to its original state. We report a method forexperimental realization of a newly discovered dy-namical manifestation of monodromy by investigat-ing the behavior of atoms in a trap. The trapping po-tential has long range attraction to and short rangerepulsion from the center. Calculations include twoparts. First, we consider atoms as classical parti-cles for which we can choose any desired set of initialconditions. As was shown previously for differentsystems, when we take the system around a mon-odromy circuit, a loop of initial conditions evolvesinto a topologically different loop. Second, we in-corporate the limitations that would appear in ex-perimental implementation. The atoms have a rangeof initial angles, initial angular momenta, and initial

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energies. Our work shows how real atoms can bedriven by real forces around a monodromy circuit,and thereby shows how one can observe dynamicalmonodromy in a laboratory. Finally, we extend clas-sical dynamical monodromy to quantum dynamicalmonodromy by examining wave function evolutionunder comparable conditions.

Exploring the dynamics of CRISPR loci length:How much can a bacterium remember aboutviruses that infected it?, Lauren Childs, GeorgiaInstitute of TechnologyA novel bacterial defense system against invadingviruses, known as Clustered Regularly InterspacedShort Palindromic Repeats (CRISPR), has recentlybeen described. Unlike other bacterial defense sys-tems, CRISPRs are virus-specific and heritable, pro-ducing a form of adaptive immune memory. Specificbacterial DNA regions, CRISPR loci, incorporate onaverage 30 copies of unique short ( 20 base pair)regions of viral DNA which then allow the bacte-ria to detect, degrade and have immunity to viruseswith matching sub-sequences. Ideally, the number ofunique viral-copied regions a bacterial CRISPR locicontains would grow indefinitely to allow immunityto a large number of viruses. However, the numberof these short viral-copied regions in the CRISPRloci of any bacteria appears to be limited. We usea birth-death master-equation model to explore thegrowth and decay of the length of the CRISPR lociand thus the number of short viral-copied regions.

The role of crossover recombination, inversion,and gene linkage in determining gene spac-ing in a chromosome., Brian Clark, Illinois StateUniversityThe human genome consists of approximately 30,000genes and other elements of DNA distributed over 23pairs of chromosomes. Genes may be linked togetherin so far as they code for proteins that taken to-gether can represent a single trait. Here we examinethe role of crossover recombination between individ-ual strands of DNA and inversion within a singlestrand of DNA in determining the spacing betweentwo genes linked through their fitnesses via a com-putational simulation. Our model includes a popu-lation of haploid individuals with n genes per singlestrand of DNA. Two of the genes are linked throughtheir fitness function, which can be additive, mul-tiplicative, stochastic, or constant. Individuals areallowed to reproduce according to a function of theirfitnesses. When two individuals are selected for re-

production, they each undergo an inversion with rateRi and then are allowed to crossover with rate Rc.Only offspring with two genes for the specified traitsurvive reproduction. We record the changes in genespacings as the system evolves and show that the sys-tem has a small number of attractors who’s stabilityis a function of inversion and crossover rates. We alsoshow that genes linked with multiplicative fitnessesare more likely to be found closer together than geneslinked with additive fitnesses, when starting from aspecific set of initial gene positions.

Bifurcations from sub-wavelength changes in awave chaotic cavity with nonlinear feedback,Seth Cohen, Duke UniversitySeth D. Cohen, Hugo L. D. de Souza Cavalcante,Daniel J. Gauthier, Department of Physics, DukeUniversity, Durham, NC, USABroadband chaos has been observed previously in asimple transistor-based nonlinear circuit with time-delayed feedback through a single coaxial cable [1].We replace this coaxial cable with a multipath de-lay system consisting of broadband antennas placedinside a stadium-shaped cavity. This creates a newnonlinear feedback system where the multipath re-flections of the radio waves inside the cavity becomethe delayed feedback loops of the dynamical sys-tem. By translating the location of a sub-wavelengthscatterer that is also placed in the cavity, the pathlengths and coupling strengths of these feedback de-lays change. From scatterer movements as little as 10micrometers, we observe bifurcations in the system?soutput voltage between periodic, quasi-periodic, andchaotic attractors. The primary purpose of this workis to describe the bifurcations observed in this multi-path, time-delay dynamical system. The minimal de-tectable change in scatterer position is 15,000 timessmaller than the minimum wavelength of radiationinside the cavity (15 cm). By exploiting this noveltechnique for sub-wavelength sensitivity, we hope toimprove traditional methods of intrusion detectionsystems and tracking devices with through-wall ca-pabilities. We gratefully acknowledge the support ofthe ONR MURI “Exploiting Nonlinear Dynamics forNovel Sensor Networks”.[1] L. Illing and D. J. Gauthier, Chaos 16, 033119(2006).

Exact Folded-Band Oscillator, Ned Corron, US ArmyRDECOMWe present a novel, low-dimensional chaotic oscil-lator that exhibits an exact folded-band attractor.

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That is, analytic returns of the oscillator waveformexactly satisfy a one-dimensional, unimodal map.The oscillator is a hybrid dynamical system includ-ing both a continuous differential equation and a dis-crete switching condition. Between switching events,the oscillator is linear and solvable, and we derivean exact analytic expression relating peak returns.For this oscillator, we find the successive maximareturn map is conjugate to a one-dimensional skewtent map, thereby proving the waveform is chaoticand characterized by a simple, noninvertible fold.Furthermore, the chaotic waveform admits a linearrepresentation using a fixed basis pulse, for which asimple matched filter is defined. As such, we claimthis oscillator is well suited for chaotic radar andcommunication applications, and we show a physi-cal realization as an electronic circuit. Experimentaldata is presented that confirms the effectiveness ofthe physical implementation.

Electroporation in a three-dimensional, time-dependent model of a skeletal muscle fiber,Jonathan Cranford, Duke UniversityElectroporation, in which strong electric pulses cre-ate transient pores in the cell membrane, holdspromise for improving delivery of DNA to skeletalmuscle fibers in gene therapy applications. However,the results of electroporation-mediated gene deliveryin fibers are difficult to predict, as electroporation isa nonlinear process. Current models of fibers assumethat electroporation is proportional to the magni-tude of only the transverse component of the electricfield. This study investigates the full spatiotempo-ral dynamics of electroporation using a new time-dependent model of a 3-D muscle fiber. The modelassumes a cylindrical fiber and two point source elec-trodes positioned parallel to the fiber in an isotropicconductive solution. The membrane of the fiber re-sponds to strong transmembrane potential (Vm) bydeveloping electropores at a rate that is an exponen-tial function of the square of Vm. The model accountsfor the creation of electropores by solving at eachlocation on the fiber membrane an ODE that gov-erns pore density N . Outputs of model simulationare the time evolution of Vm and N over the entirefiber membrane, which are compared to electropo-ration predicted from a linear, non-electroporatingversion of the model. The linear model shows thatthe largest magnitude of Vm and the largest regionof elevated Vm occur on the side of the fiber facingthe electrodes. Thus, the linear model implies that

both the pore density N and the region of elevatedN should be greater on the side of the fiber facingthe electrodes. However, the nonlinear model showsthat the magnitudes of Vm and N are approximatelyequal at the sides of the fiber facing and opposite tothe electrodes, and that the region of elevated N isgreater at the side of the fiber opposite to the elec-trodes. Therefore, the nonlinear model of an elec-troporating fiber produces different results than thelinear, non-electroporating model.

Force Network in a 2D Frictionless EmulsionModel System, Kenneth Desmond, Emory Univer-sityWe confine oil-in-water emulsion droplets betweentwo parallel plates to create a quasi-two-dimensionalmodel system to study the jamming transition. Thismodel system is analogous to granular photoelasticdisks with the exception that there is no static fric-tion between our droplets. To study the jammingtransition we compress the droplets in small incre-ments and investigate how the force network evolveswith increasing area fraction, where the forces aremeasured using a calibration technique we have de-veloped. The forces in our system are spatial hetero-geneous with a probability distribution that is simi-lar to that found for photoelastic disks. We also findthat the probability distribution of the forces narrowswith area fraction, and that the correlation length ofthe largest forces is only few particle diameters.

Homogeneous linear shear of a two dimensionalgranular system, Joshua Dijksman, Duke Univer-sityUsing a novel shear device, we experimentally studythe response of dry granular materials to quasi-staticshear. Our apparatus is capable of creating linearstrain profiles over the entire width of the two dimen-sional shear cell. By eliminating the usual tendencyof granular shear to localize in non-uniform shearbands, we can study the poorly understood natureof granular flows in great detail. We employ photoelastic particles, fluorescent labelling and high reso-lution imaging to obtain information about particlepositions, rotation and inter particle forces. We dis-cuss our results in the context of the jamming sce-nario and also look at various measures capable ofelucidating the physics of dense granular flows.

An Information-Theoretic Analysis of CompetingModels of Stochastic Computation, ChristopherEllison, UC Davis

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Finitary, stationary stochastic processes are analyzedin terms of the convergence of state-block and block-state entropies. The latter are compared to previ-ously known convergence properties of the Shannonblock entropy. We find that synchronization is de-termined by both the process’s internal organizationand by an observer’s model of it. With regard to thechoice of model, a natural classification scheme is de-fined in terms of minimality, synchronizability, andunifilarity. In particular, we characterize informa-tion in the model that is not justified by the data—gauge information—and asymptotically inaccessibleinformation encoded about the future—oracular in-formation. Finally, we draw out a duality betweensynchronization properties and a process’s controlla-bility. (See arXiv:1007.5354.)

Universal Shapes Formed by Two InteractingCracks, Melissa Fender, NCSUBrittle failure through multiple cracks occurs in awide variety of contexts, from microscopic failuresin dental enamel and cleaved silicon to geologicalfaults and planetary ice crusts. In each of these sit-uations, with complicated curvature and stress ge-ometries, pairwise interactions between approachingcracks nonetheless produce characteristically curvedfracture paths known in the geologic literature as enpassant cracks. While the fragmentation of solids viamany interacting cracks has seen wide investigation,less attention has been paid to the details of indi-vidual crack-crack interactions. We investigate theorigins of this widely observed crack pattern usinga rectangular elastic plate which is notched on eachlong side and then subjected to quasistatic uniaxialstrain from the short side. The two cracks prop-agate along approximately straight paths until thepass each other, after which they curve and releasea lenticular fragment. We find that, for materialswith diverse mechanical properties, the shape of thisfragment has an aspect ratio of 2:1, with the lengthscale set by the initial cracks offset s and the timescale set by the ratio of s to the pulling velocity. Thecracks have a universal square root shape, which weunderstand by using a simple geometric model andthe crack-crack interaction.

Applying the Loschmidt Echo and Fidelity Decayto Classical Waves in a Wave Chaotic Systemwith a Nonlinear Dynamic Response, MatthewFrazier, University of Maryland, College ParkThe quantum mechanical concepts of LoschmidtEcho and Fidelity measure the effect of perturbations

on the quantum wave system. In previous work, weextended these concepts to classical waves, such asacoustic and electromagnetic, to realize a new remotesensor scheme [1, 2]. The sensor makes explicit use oftime- reversal invariance and spatial reciprocity in awave chaotic system to sensitively and remotely mea-sure the presence of small perturbations to the sys-tem. The loss of fidelity is measured through a classi-cal wave-analog of the Loschmidt echo by employinga single-channel time-reversal mirror to rebroadcasta probe signal into the perturbed system [3]. Theoperation of the time-reversal mirror itself benefitsfrom the wave chaotic scattering in the system. Wecompare and contrast the detection power and com-putational efficiency of our sensor with other tech-niques such as correlation and/or mutual informa-tion of probing signals. We also introduce the use ofexponential amplification of the probe signal to par-tially overcome the effects of propagation losses; onthe other hand, time windowing of the probe signal,along with the exponential amplification, is demon-strated to be effective to vary the spatial range ofsensitivity to perturbations, and the extent to whichthe spatial range of the sensors can be varied is dis-cussed. Experimental results are presented for theacoustic version of the sensing techniques studied.Now, we take this work in a different direction byconsidering the case in which there is a device witha nonlinear response inside a wave chaotic electro-magnetic system. In addition to the chaos that em-anates from the sensitive dependence of the ray tra-jectories to initial conditions, there is now a classi-cal nonlinearity in the system that creates new re-sponses. Preliminary results of this modification toour existing work are also presented. Work funded byONR MURI grant N000140710734, the AFOSR un-der grant FA95501010106, and by the IC Post-Docprogram.[1] B. T. Taddese, et al., Appl. Phys. Lett. 95, 114103(2009).[2] B. T. Taddese, et al., J. Appl. Phys. 108, 1 (2010).[3] S. M. Anlage, et al., Acta Physica Polonica A 112,569 (2007).

Evolutionary stability of an optimal strategy forhabitat selection, Theodore Galanthay, Universityof Colorado - BoulderEcologists have long sought to make sense of the ob-served distributions of organisms. In the majority ofthese theoretical habitat selection models, scientistshave assumed that organisms move in response to fit-

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ness differences between patches (for discrete spacemodels) or a fitness gradient (in continuous spacemodels). More recently, scientists studying habitatselection have recognized the importance of incorpo-rating in models the individual behavioral forces thatinfluence these population distributions. While it iswidely assumed in habitat selection models that in-dividuals move to maximize their fitness, it remainsunclear what type of movement mechanisms mightin fact produce higher fitness. We ask what type ofmovement mechanisms might lead to higher fitnessby analyzing a mechanistic single-species two-patchhabitat selection model. We compute analyticallya movement strategy that demonstrates that higherfitness is not achieved by moving solely in responseto fitness-dependent cues. We show that this evo-lutionarily stable strategy (ESS) is a continuouslystable strategy (CSS). We propose that there mightexist a movement strategy that is a blend of random,fitness-dependent, and habitat-dependent movementthat maximizes a species’ fitness. Therefore, we con-sider three different movement mechanisms: discretediffusion, fitness-, and habitat-dependent movement.We ask, is it evolutionarily advantageous for a speciesto move based on fitness (i.e. per capita reproductivegrowth) differences, habitat differences, or a mixtureof these? We use standard evolutionary game the-ory to find the answer to this question. We discovera candidate evolutionarily stable strategy for a dis-crete two-patch habitat system and apply the tools ofadaptive dynamics to show by numerical simulationthat this strategy is an ESS and also convergencestable.

Quantifying the Complexity of KauffmanNetworks, Xinwei Gong, Duke UniversityIn a 2004 article, Shalizi et al proposed a statisticalmeasure that quantifies the complexity of spatially-extended dynamical systems. They define complex-ity as the amount of information required for optimalprediction of system’s dynamics, and describe an al-gorithm for measuring the complexity given timeseries data for all components in a discrete system.The results of applying the algorithm to 1D and2D cellular automata agree with intuitive expecta-tions. We study this complexity measure for randomBoolean networks in which every node has an inde-gree and an outdegree of 2. We show that for a givendistribution of logic functions, the complexity is afunction of the steady-state bias of the network andnot simply related to its sensitivity to perturbations.

Subrcritical Fracture of Porous Media, AlessioGuarino, Universite de la Polynesie FrancaiseWe study the lifetime of a porous media submittedto a constant subcritical stress. We present a modelbased on a 2D spring network with thermal fluctu-ations were the porosity is represented by missingsprings. Numerical results are compared to experi-mental data of fracture of porous media submittedto three-point flexion.

Dynamic Modeling and Simulation of a RealWorld Billiard, Alex Hartl, North Carolina StateUniversityAlex Hartl, North Carolina State University BruceMiller, Texas Christian University Scientists are in-terested in gravitational billiards since they exhibit avariety of dynamical phenomena in nonlinear Hamil-tonian systems. The system typically consists of aparticle undergoing elastic collisions within a bound-ary, where the particle follows a ballistic trajectorybetween collisions. This paper considers the morerealistic situation of an inelastic, rotating, gravita-tional billiard in which there are retarding forces dueto air resistance and friction. In this case the motionis not conservative, and the billiard is a sphere of fi-nite size. Here we present a dynamical model thatcaptures the relevant dynamics required for describ-ing the motion of a real world billiard for arbitraryboundaries. An application of the model considersparabolic, wedge and hyperbolic billiards that aredriven sinusoidally. Direct comparisons are madebetween the model’s results and experimental datapreviously collected. Although several studies haveinvestigated the effect of variable elasticity in rela-tion to the gravitational billiard, this study is thefirst to incorporate rotational effects and additionalforms of energy dissipation.

Chaos in semiconductor at hellical instability,Khadjimurat Ibragimov, Institute of Physics Dagh-estan Sc. Centre of Russian A. S.

Isochronous chaos synchronization of delay-coupled optoelectronic oscillators, Lucas Illing,Reed CollegeWe study experimentally chaos synchronizationof nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. A sin-gle such optoelectronic oscillator can generate a widerange of dynamical behaviors, including fast andhigh-dimensional chaos. Coupling three oscillators in

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a chain, we find that the outer two oscillators alwayssynchronize isochronally. In contrast, isochronoussynchronization of the mediating middle oscillator isfound only when certain matching conditions for thetime delays and coupling strengths are satisfied. Ourexperimental results are in good agreement with the-ory.

Quantum and classical pumping using ultracoldatoms, Megan Ivory, College of William and MaryCan electrons be pumped from one reservoir to an-other without a difference in the electrical potential?Various theoretical schemes have been predicted, butno experiments have successfully implemented them.We examine the analogous question for neutral parti-cles: can ultracold atoms be pumped from one reser-voir to another without an external potential differ-ence? We are running numerical simulations to iden-tify experimental schemes which are capable of yield-ing large currents using time-varying potential barri-ers or wells in the channel connecting the reservoirs.Our simulations use either quantum or classical me-chanics, and explore symmetric and anti-symmetricdouble barrier and double well pumps with rectan-gular and Gaussian potentials. We show that fora non-uniform distribution of initial momentum, wecan expect significant classical pumping in additionto quantum pumping. Also, in some regions, the dy-namics show sensitive dependence upon initial con-ditions, and regions of fractal behavior are evident.We present preliminary results for various schemes,and suggest experimental parameters for testing thetheoretical predictions using ultracold atoms.

Application of periodic orbit theory to chaoscomputing, Behnam Kia, Arizona State UniversityChaos computing is introduced as a method to con-struct functions based on intrinsic complicated dy-namics of chaotic systems. The data inputs are en-coded as the parameters or the initial conditions ofa chaotic dynamical system and the resulting sys-tem state represents the output of the computation.By controlling how inputs are mapped to outputs,a specific function can be constructed. So far noclear connection has been demonstrated between thestructure of the dynamics and the computation thatthe dynamical system can perform. In this poster wedescribe, model and predict chaos computing basedon the dynamics of the underlying chaotic system.Here we model the dynamical system by use of itsbasic unstable periodic orbits (UPOs). Then we usethese UPOs and their stability in terms of eigenval-

ues to obtain the functions that the chaotic systemcan construct and also to estimate the stability ofthese functions against noise.

Pattern formation of grains in oscillatory frluidflows, Daphne Klotsa, University of BathGranular experiments in oscillatory fluids have beenobserved to form patterns dominated by hydrody-namic interactions [1,2]. We are studying a sys-tem consisting of a collection of macroscopic stain-less steel spheres undergoing horizontal vibration ina Newtonian fluid at intermediate Reynolds num-bers (between 5-200). The particles are initially ina dispersed configuration and evolve into an orderedchain structure, aligned perpendicular to the direc-tion of oscillation. We have developed computer sim-ulations to model such a system and have validatedthem against experiments. The nonlinear averagefluid flow (steady streaming) around pairs and chainsof interacting particles has been computationally cal-culated and shown to be the driving force behind thepattern formation.[1] G.A. Voth et al., PRL 88, 234301 (2002).[2] R. Wunenburger et al., Phys. Fluids 14, 2350(2002).

Understanding the Dynamics of Flames usingTime Series Analysis, Christopher Kulp, Ly-coming CollegeProper balancing of air-fuel mixing is one of themost important factors in designing and controllinghigh efficiency, low-emission burners for process heatand power production. As utilization of alternativenon-petroleum-based fuels has increased (especiallybiomass derived fuels) in boilers, engines, and gasturbines, the need to develop improved burner di-agnostics and controls to maintain high efficiencyand minimum emissions of pollutants and greenhousegases has escalated significantly. In this poster, wepresent preliminary results in our work to developsimple algorithms and models for using video imag-ing to measure and understand the dynamic state ofgas-air flames as key burner parameters are adjusted.In particular, we are interested in understanding howthe spatio-temporal behavior of these flames changesas the air-to-fuel ratio (AFR) is varied through criti-cal values (e.g., the stoichiometric point), where ma-jor global shifts in the dynamics are known to occur.We are interested in quantitatively tracking thosechanges with optical sensors (e.g., digital videogra-phy) and developing approaches for real-time feed-back controls. In the present experimental work, we

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record video images of flames from a gas-air Mekerburner with a fixed AFR and with a slowly changingAFR. We generate time series from the video record-ings and perform various statistical analyses to whichdescribe the state of the flame during the video. Inthis poster, we explain how we generate time seriesfrom the video and show some preliminary statisticalresults.

A new algorithm for detection of apnea in in-fants in neonatal intensive care units, HoshikLee, College of William and MaryApnea is a very common problem for premature in-fants: apnea of prematurity (AOP) occurs in > 50%of babies whose birth weight is less than 1500 g,and AOP is found in almost all babies who are <1000g at birth. Current respiration detectors of-ten fail to detect apnea, and also give many falsealarms. We have created a new algorithm for detec-tion of apnea. Respiration is monitored by continu-ous measurement of chest impedance (CI). However,the pulsing of the heart also causes fluctuations inCI. We developed a new adaptive filtering system toremove heart activity from CI, thereby giving muchmore reliable measurements of respiration. The newapproach is to rescale the impedance measurement toheartbeat-time, sampling 30 times per interbeat in-terval. We take the Fourier transform of the rescaledsignal, bandstop filter at 1 per beat to remove fluc-tuations due to heartbeats, and then take the inversetransform. The filtered signal retains all propertiesexcept the impedance changes due to cardiac fillingand emptying. This proves particularly effective dur-ing some severe episodes of apnea. While the infantis not breathing, the reduced oxygen levels slow theheart rate considerably, and the increased volumesof blood during each cycle lead to sizable changesin impedance that can be mistaken for breaths bythe conventional detection algorithms. The clinicalresult is that the monitor reports that the breathingrate is equal to the heart rate when in fact there is nobreathing at all. We use the new algorithms as a ba-sis for detecting apneas in a large and growing dataset from the University of Virginia Neonatal Inten-sive Care Unit, and we study apnea characteristicsin a variety of clinical scenarios.

Symmetry and Stability in Network DynamicalSystems, Anika Lindemann, Colby CollegeIn the study of network dynamical systems, the the-orems of linear algebra enable us to connect localstructural properties to the dynamical properties of

the network as a whole. In particular, for the case ofsymmetric networks, we can identify structural mo-tifs that confer instability to the entire network; ad-dition or removal of other pieces of the network can-not restore stability. For networks with simple edge-weight distributions, these motifs lead to a completecharacterization of stability. In this presentation, wewill outline these theoretical discoveries and discusstheir application to more general networks.

Probabilistic Maxima in Basins of Attrac-tion of Coexisting States in a NoisyMultistableSystem, Brenda Martinez, Universi-dad de GuadalajaraWhen talking about the size of the basins of attrac-tion of coexisting states in a noisy multistable sys-tem, one can only refer to its probabilistic properties.In this context, the most probable size of basins of at-traction of some coexisting states exhibits an obviousmaxima with respect to the noise amplitude. The ev-idence of this maxima is demonstrated through thestudy of the Henon map with three coexisting at-tractors: period 1, period 3, and period 9. By apply-ing periodic modulation to a system parameter, wefind the connection between this resonance and thefundamental frequency of the corresponding attrac-tor. Noise, periodic modulation, and a combinationof both can provide an efficient control of the globalstructure of phase space of a system with multiplecoexisting attractors.

Pinned and Twisted Scroll Rings in an ExcitableChemical System, Bradley Martsberger, DukeAuthors: B. Martsberger, Z. Jimenez, O. SteinbockThree dimensional spiral waves, called scroll waves,rotate around a one-dimensional space curve calleda filament. In some cases a filament may form aclosed loop. Typical long term behavior of a closedloop scroll ring is a complete collapse leading to theextinction of the scroll wave. In media containing un-excitable heterogeneities, all or some part of the fila-ment can become attached to the heterogeneity pre-venting the collapse of the spiral. Such phenomenonhas been observed in cardiac systems. In the casewhere a portion of the filament is pinned, rotationfrequency differences create stationary gradients inthe rotation phase, called twist. Twist patterns andtheir frequencies agree with solutions of the forcedBurgers’ equation revealing insights into the nonlin-ear phase coupling of scroll waves.

Localization phenomena arising from spatially pe-

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riodic forcing, Jonathan McCoy, Colby CollegeLocalized structure formation is a striking featureof many spatially extended nonlinear systems. Wefind, in an experiment on spatially periodic forcingof thermal convection patterns in a large aspect ratiofluid layer, that frustration arising from the forcinggenerates an unexpected assortment of kink, ringlet,and worm structures. In this presentation, we of-fer a unified interpretation of these localized patternmotifs and explore its consequences for our under-standing of the transition to spatiotemporal chaos.This work was supported by the National ScienceFoundation under grant no. DMR-0305151 and bythe Max Planck Society.

Instability in a Sheet of Birds, Nicholas Mecholsky,University of MarylandFlocks of birds and other aerial animals are often ob-served in coordinated sheets of individuals that canmove wildly in the air. This poster investigates suchsheet-like behavior. Using a continuum model for aflock of individuals, we find equilibria where the den-sity goes to zero at a finite extent for several differentforms of the pressure. We then investigate the sta-bility of a sheet of individuals. We find that motionof the flock along the direction of the sheet is alwaysunstable for the pressures that we investigate.

Control of chaos by a weak perturbation in an im-pact oscillator., Everton Medeiros, Universidadede Sao PauloWe control chaotic orbits in an impact oscillator byapplying a weak periodic perturbation. The param-eters of the controlled periodic orbits compose newperiodic windows in the bi-dimensional parameterspace. These new periodic windows are displacedin the parameter space by varying the perturbationamplitude. We identify periodic and chaotic attrac-tors by their largest Lyapunov exponents.

Estimating the time scales for the evolution ofrobustness under almost-neutral drift, GarrettMitchener, College of CharlestonMany biochemical mechanisms are robust: multiplereactions serve to control them, so a mutation thatdamages one reaction but leaves others intact leavesthe organism fully functional. Abstractly, considera species with some beneficial feature whose mech-anism is vulnerable to a mutation. The two phe-notypes are identical except for a slight difference inthe quality of their offspring, so natural selection willbe unable to distinguish them on short time scales,

hence the term “almost-neutral drift”. A differentmutation that makes the mechanism more robustcould take over the population. Let us define theterms ‘type 0’ for the baseline genotype, ‘type 1’ for agenotype that has an advantageous feature but is onemutation away from losing it, and ‘type 2’ for a geno-type that has the same feature and is robust against asingle mutation. We are interested in what happensto a population of mostly type 1 agents with minorityof type 2 agents. A Markov chain can represent thesedynamics on a finite population exactly. It turns outto be rather likely that starting from a single type 2agent in a population of all type 1, the robust formwill go extinct, after which the advantageous featurewill eventually go extinct as well. However, condi-tioned on the event that the robust form does takeover, it takes on average a relatively short time to doso. Furthermore, details of the selection-mutation al-gorithm have a significant impact on these results. Iwill present numerical and theoretical results for thecircumstances under which the protective mutationtakes over the population based on these models

Application of Nonlinear Data Analysis to Locat-ing Disease Clusters, Linda Moniz, Johns HopkinsUniversityThis research centers on a new definition of a dis-ease cluster and detection of these clusters in realtime series of counts of clinic visits for respiratoryailments. Previous definitions of clustering concen-trated on the spatial definition (coincident detection)and ignored the dynamical one (shared dynamics be-tween locations). Thus, many statistical methodsfor finding disease clusters are prone to false alarmswhen the detection thresholds are tuned to high sen-sitivity. We show that our new definition of clus-tering together with a three-stage detection methodcan differentiate between actual clusters and geo-spatially coincident detections. This is preliminaryresearch intended for proof-of-concept but shows thatthe method is promising; it has high sensitivity andfewer false alarms than a current ”state of the art”method for detecting disease clusters.

Robustness of multi-layer networks composed ofmixed oscillators, Kai Morino, The University ofTokyoKai Morino, Gouhei Tanaka, and Kazuyuki AiharaCoupled oscillators have been used to understandmany real-world phenomena, e.g., behaviors in net-works of biological oscillatory elements. Since liv-ing things eventually die and lose their activity, be-

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haviors of mixed populations composed of activeand inactive elements are interesting phenomena.Daido and Nakanishi investigated globally couplednetworks composed of active and inactive oscillators[1]. They found an aging transition: when the pro-portion of inactive oscillators in the total popula-tion increases beyond a critical value, global oscil-lations vanish away. Following this seminal work,aging transitions in networks composed of several el-ements have been studied with homogeneous struc-tures. However it is known that many biological net-works are heterogeneous, for example, the corticalcolumn with a multi-layer structure. Therefore itshould be important to investigate the aging transi-tion in heterogeneous networks. The critical value ofthe aging transition point can be associated with adegree of robustness to changes of network elementsfrom active to inactive. In our study, we investigatethe robustness of multi-layer networks with mixedpopulations through aging transitions. We show thatnetworks increase or decrease their robustness de-pending on interlayer couplings. In addition, we findthat an increase of mismatches of oscillator types (ac-tive or inactive) among locally connected oscillatorsreduces the robustness of the networks with meanfield, chain, and diffusion couplings. Moreover, wediscuss the robustness of networks with more thantwo layers. This research is partially supported bythe FIRST program from JSPS.[1] H. Daido and K. Nakanishi, Phys. Rev. Lett. 93,104101(2004).

Noise-induced Phenomena in Two Strongly Pulse-coupled Resonate-and-Fire Neuron Models,Kazuki Nakada, Kyushu Institute of TechnologyIn this work, we consider the effects of dynamicalnoise in a continuous dynamical system on its dis-crete return map. Specifically, we have analyzed asystem of two pulse coupled resonate-and-fire neuron(RFN) models and the synchronization phenomenaand chaotic behavior by using Firing Time DifferenceMap (FTDM), which is the return map constructedfrom one dimensional maps with regard to the fir-ing time difference between two RFN models. Wefirstly demonstrate that the global stability of burstsynchronization in anti- and out-of-phase and Type Iintermittent chaos. Secondly, we show noise-inducedphenomena occurs in the system with additive whiteGaussian noise on threshold voltage. Finally, we con-sider the the robustness of chaos in biological neu-rons.

Intermittent Jamming in Quasi-2D MicrofunnelsCarlos Ortiz, North Carolina State UniversityBoth athermal granular jamming and thermal glasstransitions have recently received extensive atten-tion. We experimentally investigate the jammingtransition in a quasi-2D system of nearly hard-sphere, micron-sized particle suspension in a densityand index-matched medium flowing through a mi-crofunnel. We observe the packing fraction driventransition from a gas-like to a liquid-like to a solid-like phase. At sufficiently high packing fractions weobserve intermittent jamming under constant pres-sure driving. Further increase in the packing frac-tion forms a stable solid-like jammed phase whichis disordered on long-ranges, and susceptible to re-melting by reverse flow, agitation, and diffusion. Bydisplaying properties of both athermal granular jam-ming and thermal glass transitions, our experimentprovides a useful testing ground for understandingthe jamming transition as a unifying framework.

The effect of force chains on near-field soundpropagation, Eli Owens, North Carolina State Uni-versityGranular materials are inherently heterogeneous,leading to challenges in formulating accurate modelsof sound propagation. In order to quantify acousticresponses in space and time, we perform experimentsin a photoelastic granular material in which the in-ternal stress pattern (in the form of force chains)is visible. We utilize two complementary methods,high-speed imaging and piezoelectric transduction,to provide particle-scale measurements of both theamplitude and speed of an acoustic wave in the near-field regime. We observe that the wave amplitude ison average largest within particles experiencing thelargest forces, particularly in those chains radiatingaway from the source, with the force-dependence ofthis amplitude in qualitative agreement with a sim-ple Hertzian-like model. In addition, we are ableto directly observe transient force chains formed bythe opening and closing of contacts during propaga-tion which do not follow this trend. The speed ofthe leading edge of the pulse is consistent with pre-dictions and experiments for one-dimensional chains.The slower speed of the peak response suggests thatit contains waves which have traveled over multiplepaths even in this near-field region. These effectshighlight the importance of particle-scale behaviorsin determining the acoustical properties of granularmaterials, and point to possibilities for characteriz-

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ing force chain networks using acoustical techniques.

Phase Synchronization of Directly CoupledBoolean Chaos Oscillators, Myung Park, Univer-sity of Maryland / IREAPSynchronization phenomena has been extensivelyinvestigated in various applications including en-crypted communication, ultra-wideband radio fre-quency sources, and short-range sensor networks.Among the different types of synchronization, iden-tical synchronization is considered as the completecoincidence of states in coupled systems. A gener-alized synchronization for drive-response systems, isdefined as the presence of a functional relation be-tween the states of the drive and response systems.Finally, phase synchronization means phase lockingin the drive and response systems, while the ampli-tudes of the coupled systems remain chaotic. In thiswork, we study phase synchronization of our pre-viously studied Boolean chaotic oscillator, consist-ing of one ring oscillator, one XOR , and two de-lay buffers to compare with the experimental results.This Boolean chaos oscillator also has been modelledusing the BSIM3 transistor model. We constructeda Boolean chaos oscillator using commercially avail-able high-speed logic gates in a feedback loop to gen-erate chaotic behaviors. The temporal evolution ofthe voltage at a point demonstrates a broad powerspectrum extending to 1.5 GHz. In addition, bi-furcations occur with the supply voltage. PreviousBoolean chaos oscillators [1] have been studied usingthe Boolean delay equation by Ghil et al. [2]. Becausephysical components of logic gates consist of multi-ple transistors, BSIM3 transistor model [3] is morepromising for an analog analysis of the system dy-namics. The circuits are coupled with a resistor andmeasured at the same node in the two circuits. Toquantify the coupling strength, a coupling coefficientK is defined as the inverse of resistance. To describethe phase synchronization, we used a Hilbert trans-form of an output voltage for quantifying the phases.For both simulation and experiment, the phase dif-ference between circuits is calculated and measured.For weak coupling, a histogram of phase difference isuniformly distributed whereas the histogram of phasedifference in strong coupling shows a relatively nar-row peak. The standard deviation of the histogram isused as an indicator of how the dynamics of synchro-nization change in terms of the coupling strength.References[1] “Boolean Chaos”, Rui Zhang, et al., Physics Re-

view E, 80, 045202R, 2009[2] “Boolean delay equations. II. Periodic and aperi-odic solutions”, M.Ghil, et al., Journal of StatisticalPhysics, Vol 41, No 1-2, 1985[3] Simulated using Advanced Design Systems 2008

Algortithm for Planar 4-Body Problem CentralConfigurations with Given Masses, EduardoPina, Universidad Autonoma MetropolitanaA particular solution to the Four-Body problem inthe plane is obtained from the elliptic motion of thefour bodies keeping a central configuration. An al-gorithm to compute the six distances between par-ticles of a planar Four-Body central configuration ispresented according to the following schema. An or-thocentric tetrahedron is computed as a function ofgiven masses, it is rotated by two angles (to be tunedvariables) around the center of mass until a directionorthogonal to the plane of configuration coincideswith axis 3. The four coordinates of the verticesof the tetrahedron along this direction are identifiedwith the weighted directed areas of the central con-figuration. The central configuration correspondingto these weighted directed areas is computed givingrise to four masses and corresponding distances. Thegiven masses are compared with the computed ones.The two angles of the rotation are tuned until thegiven masses coincide with the computed. The cor-responding distances of this last computation deter-mine the central configuration.

Mixing properties of a granular monolayer, JamesPuckett, North Carolina State UniversityIn a dense driven granular system, the particle dy-namics are often quantified by the self-diffusion co-efficient, but this measure discards topological infor-mation important for measuring mixing. The topo-logical entropy, Sbraid, has been used in fluid sys-tems to measure the entanglement of particle space-time trajectories (Thiffeault, PRL, 2005). We ex-perimentally investigate the effect of boundary con-dition (constant pressure or constant volume) andinter-particle friction on the dynamics of a granu-lar liquid. The bidisperse monolayer of hard disksrests on a low friction air table and is driven bybumpers on the perimeter. We track the trajectoriesof the particles and observe that the braid entropy isa well-defined quantity: the logarithm of the braid-ing factor grows linearly in time. Both the diffusioncoefficient and Sbraid decrease with either increasingvolume fraction or confining pressure, and we exam-ine the extent to which the braid entropy provides

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additional information about the state of the system.

Cyclic simple shear in a two-dimensional granularsystem, Jie Ren, Duke UniversityWe study the evolution of a 2D granular system con-sisting of frictional photo-elastic disks under largenumbers of small-amplitude cyclic shear cycles. Weare particularly interested in the reversibility of thesystem under cyclic shear. The experiments are car-ried out on a specially designed apparatus whichcan create quasi-static, nearly uniform simple shear.By using photo-elastic particles and a fluorescent la-belling technique, we obtain information about dis-placement, rotation and contact forces for each par-ticle following each small strain. We also obtain thesystem-level behaviour over many shear cycles. Tobetter understand the nature of jamming, we havecarried out shearing runs that explore various ini-tial states which are initially unjammed, isotropicallyjammed or anisotropically jammed, and we comparethe results for different initial states.

Nonlinear synchronization of the Polar Regions?climatic oscillations over the last ice age: Aworking hypothesis, Jose Rial, UNC-Chapel HillAn important clue to understand global climate dy-namics is the apparent connection between the cli-mates of the Polar Regions revealed by ice core pa-leoclimate proxies of the last ice age, which con-firm the existence of a temperature bipolar seesaw(Antarctica warms while Greenland cools) whose ori-gin is still poorly understood. Using a heuristic low-dimensional climate model and an earth model ofintermediate complexity to back it up, it is shownthat the polar connection is likely caused by syn-chronization (frequency and phase locking) of theclimate oscillations from the two poles. Polar syn-chronization appears analogous to Huygens?s clas-sic problem describing the synchrony of two non-identical pendulum clocks coupled by weak elasticforces along the wall on which they hung. Here Iassume that polar climate fluctuations can each berepresented by a self-sustained nonlinear relaxationoscillator (Huygens’s clock), each with its own nat-ural frequency and feedbacks, influencing each otherthrough dissipative coupling proportional to the tem-perature and heat storage gradients between northand south Atlantic ocean and atmosphere (the com-mon wall). Synchronization of polar climate oscilla-tions explains recent data from the southern oceanshowing abrupt temperature change in anti-phasewith Greenland’s Dansgaard-Oeschger (DO) fluctu-

ations, it explains Antarctica’s temperature lead onabrupt warming episodes of the DO, and the lineardependence between the duration of stadial (cold)intervals in the north and peak temperature in thesouth. The synchronization model explains the bipo-lar climatic seesaw and makes two testable predic-tions: recordings of northern mean ocean tempera-ture should exist that are in anti-phase to Antarcticice core records, and southern temperature recordsshould exist that are in anti-phase to Greenland’sDO records. Though the former has yet to be found,evidence for the latter was recently obtained in theSouth Atlantic.

Effect of strength-interval relationship on cardiacrhythm dynamics in a one-dimensional map-ping model, Caroline Ring, Duke UniversityAuthors: Caroline L. Ring MS, David G. SchaefferPhD, Wanda Krassowska Neu PhDCardiac muscle cells respond to electrical stimuliabove a certain threshold strength by producing ac-tion potentials (APs), during which the cells con-tract. A cell’s response to a train of stimuli appliedat some constant pacing rate (basic cycle length,or BCL) may be characterized by the durations ofthe resulting train of action potentials (action po-tential duration, or APD). A regular APD responseresults in the normal, organized contraction of theheart to pump blood. An irregular or chaotic APDresponse can result in deadly cardiac arrhythmia.Therefore, the mechanisms by which irregular APDdynamics arise are of great interest. APD dynam-ics can be studied using a mapping model, in whichAPD is a function of one or more previous APDs.APD dynamics in mapping models are more eas-ily analyzed than in detailed physiological AP mod-els described by many ODEs. We consider a one-dimensional mapping model, in which APD is a func-tion of one previous APD, and BCL is a parame-ter of the function: APDn+1 = F (APDn; BCL) Atpresent, there are two routes to irregular dynamics(ID) in one-dimensional mapping models. First, IDarises from period-doubling bifurcations. The slopeof F increases with decreasing BCL, causing APDbehavior to move from period-1 to period-2 (alter-nans, 2:2) to period-4, and so on to chaos. Second,as BCL decreases, APD becomes shorter than theshortest APD at which the map function F is de-fined. This leads to phase-locking responses of cap-tured and missed beats: an AP for every stimulus(1:1), for every two stimuli (2:1), every three stimuli

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(3:1), and so on. The range of APDs over which Fexists for a given BCL is determined by the strength-interval (S-I) curve. The S-I curve gives the relation-ship between S, the minimum stimulus strength nec-essary to elicit an AP, and BCL-APD, the intervalbefore the next stimulus: S = G(BCL-APDn) Themap function F exists on the intervals of APD wherethe stimulus strength lies above the S-I curve, anddoes not exist elsewhere. If map iteration reachesan APD where F does not exist for a given BCL,then the beat is missed and the next APD will begoverned by F for 2*BCL, until an APD is reachedwhere either F for 2*BCL does not exist (in whichcase the next APD will be governed by F for 3*BCL),or F for BCL again exists (in which case the beat iscaptured). Depending on the position and stabil-ity of the fixed points of these map functions, andthe boundaries of these functions, APD may aperi-odically “jump” between map functions forever, pro-ducing sustained ID. Previous hypotheses hold thatthis mechanism can only cause ID if the S-I curveis triphasic, and the stimulus strength lies betweenthe local minimum and local maximum of the S-Icurve — giving rise to a gap in the map function F.Our work, however, shows that ID can be obtainedin a one-dimensional mapping model without a gapin F (i.e. when the S-I curve is not triphasic). Wehave reproduced irregular dynamics (ID) in a sim-ple, two-current mathematical model of the cardiacaction potential. By asymptotic analysis, we havesimplified the full model (consisting of two nonlin-ear ODEs) to a one-dimensional nonlinear map withBCL as a parameter. We considered three shapes ofthe S-I curve: monophasic, biphasic, and triphasic.We examined BCL between 150 ms and 1000 ms,and stimulus strengths between 0.1 and 0.3 (scaledvoltage units). APD behavior was characterized over1000 beats for each combination of S-I curve shape,BCL, and stimulus strength. Map iterations pro-duced sustained ID for BCLs between 210 and 220ms. For BCLs ranging from 150-200 ms, APD behav-ior moved from 6:2 to 3:1. For BCLs ranging from230-1000 ms, behavior moved from 2:1 to 1:1. For themonophasic S-I curve, sustained ID was observed atBCL = 210-220 ms for all stimulus strengths. Forbiphasic and triphasic S-I curves, sustained ID wasonly observed at these BCLs at stimulus strengthsabove 0.15; for lower stimulus strengths, transientID was observed for about 100 beats, resolving to2:1 behavior. Analysis of the mapping model dy-

namics shows that the development of sustained IDdepends not only on the stability of fixed points ofthe map, but also on the change in the extent of themap function F from beat to beat. The change inthe extent of F arises because the S-I curve dependson the previous APD. Since F exists only where thechosen stimulus strength lies above the S-I curve, theextent of F changes depending on the previous APD.Our results suggest another possible mechanism forirregular APD dynamics under constant pacing. Ouranalysis of ID in a one-dimensional mapping modelmay elucidate underlying mechanisms of irregularcardiac rhythms observed in our experiments, andmay inform the study of new methods of diagnosingor preventing cardiac arrhythmias.

Frequency-comb generation with an opto-electronic oscillator, David Rosin, TechnischeUniversitat Berlin, Duke UniversityAuthors: David Rosin, Kristine E. Callan, Daniel J.Gauthier, Eckehard SchollWe experimentally observe several pulsing and burst-ing solutions in a high-speed, time-delay opto-electronic oscillator [1], which is comprised ofcommercially available components.The pulses andbursts are spaced by submultiples of the time-delayof the feedback loop. We are especially interestedin a solution with only one pulse per time delay.The regime in parameter space where the pulse trainsolution exists is mapped out experimentally and iscompared to numerical simulations of the underlyingmathematical model. We find a bifurcation betweena pulsing solution with wide pulses, with a durationof 1 ns, and narrow pulses, with a duration of 350ps. The related bifurcation threshold is measuredin the parameter space. The pulse train with thenarrowest pulses, with a duration of 180 ps, corre-sponds to a frequency comb which extends furtherthan 8 GHz, the bandwidth of the oscilloscope used.We also measure the phase noise of the fundamen-tal frequency of the comb for different time delays.Theoretically, we show that the system is likely toproduce pulses because, for periodic solutions, itshows strong similarities to the generic FitzHugh-Nagumo model. The system could be used as aninexpensive frequency comb generator, which alsomakes it technologically attractive.[1] K. E. Callan, L. Illing, Z. Gao, D. J. Gauthier,and E. Scholl. Broadband chaos generated by anopto-electronic oscillator. Phys. Rev. Lett. 104,113901 (2010).

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Deformable self-propelled domain in a three-dimensional excitable reaction-diffusionsystem, Kyohei Shitara, Kyoto UniversityOur understanding of active matter has been ad-vanced for the last few decades. Particularly, self-propelled objects have attracted considerable at-tention because these are related with various non-equilibrium phenomena. For example, there are lotsof biological phenomena such as motion of bacteria,moving cells, dynamics of a school of swimming fishor a flock of flying birds and so on. Furthermore,a self-driven oil droplet has been observed experi-mentally [1]. Dynamics of a self-propelled domainin a reaction-diffusion system has been investigatedby a numerical simulation [2]. There is, however,few theory considering the effect of deformation ofself-propelled particles. Ohta and Ohkuma haveproposed a model of self-propelled particles whichdeform when the propagating velocity is increased[3]. It has been shown that a single deformable self-propelled particle has a bifurcation from a straightmotion to a rotating motion in two dimensions.Quite recently, we have derived, by a singular pertur-bation method, the set of time-evolution equationsof a deformable self propelled domain starting froman excitable reaction diffusion system both in twoand three dimensions [4]. The shape of domain prop-agating at a constant velocity has been determined.Solving this set of equations numerically in threedimensions, we have found a new bifurcation froma rotating motion to a helical motion caused by abiaxial deformation [5] and the parameter regimewhere the helical motion appears has been explored.[1] C. D. Bain, G. D. Burnett-Hall, and R. R. Mont-gomerie: Nature (london) 372, 414 (1994).[2] K. Krischer and A. Mikhailov: Phys. Rev. Lett.73, 3165 (1994).[3] T. Ohta and T. Ohkuma: Phys. Rev. Lett. 102,154101 (2009).[4] T. Ohta, T. Ohkuma, and K. Shitara: Phys. Rev.E 80, 056203 (2009).[5] T. Hiraiwa, K. Shitara and T. Ohta: Soft Matter(2011), DOI:10.1039/C0SM00856G (in press).

Excitable Nodes on Random Networks: Structureand Dynamics, Thounaojam Umeshkanta Singh,Jawaharlal Nehru University, New DelhiAuthors: Th. Umeshkanta Singh, K. Manchanda,R. Ramaswamy, School of Physical Sciences, Jawa-harlal Nehru University, New Delhi 110 067, India,and A. Bose, School of Physical Sciences, Jawahar-

lal Nehru University and Department of Mathemat-ical Sciences, New Jersey Institute of Technology,Newark, NJ 01702 USAThe generation of rhythmic activity in complex sys-tem arises from interaction between the components.We study the interplay of topology and dynamics ofexcitable nodes on random networks. Each node isa cellular automaton which can be active (positiveintegers), silent (zero), or refractory (negative inte-gers), and dynamical evolution proceeds via a setof loading rules. In simple loading (SL), a silentnode becomes active when it receives an input fromatleast one of its active neighbors whereas in major-ity rule (MR), a majority of neighbors are requiredto be in active state for a silent node to become ac-tive. We address the question of whether a partic-ular network design or motif confers dynamical ad-vantage, and which other intrinsic properties of thenode promote rhythmic activity. Closed pathwaysare necessary for propagation of activity with SL,while for MR, isolated minimal cycles are required.As a consequence, SL supports more dynamical ac-tivity than MR in random networks. In situationwhere the nodes have longer active duration relativeto their refractory state, the presence of cycles is notrequired; instead a link between the nodes can sup-port activity in the network.

Identification of delays and discontinuity points ofunknown systems by using synchronization ofchaos, Francesco Sorrentino, University of Marylandat College Park and Universita degli Studi di NapoliParthenopeI present an approach in which synchronization ofchaos is used to address identification problems. Thegoal is to synchronize a receiver system whose param-eters can be adaptively evolved to a sender chaoticsystem with a set of unknown parameters. By seek-ing synchronization between the sender and the re-ceiver, the adaptive strategy is able to reconstructthe set of unknown parameters of the sender. Ishow the usefulness of this approach in identifying(i) the discontinuity points of systems described bypiecewise equations and (ii) the delays of systems de-scribed by delay differential equations.ReferencesF. Sorrentino, “Identification of delays and disconti-nuity points of unknown systems by using synchro-nization of chaos”, Phys. Rev. E, 81, 066218 (2010)

Relation between Autonomous Boolean and ODEModels of a Gene Regulatory Network,

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Mengyang Sun, Duke UniversityWe present an autonomous Boolean network (ABN)model based on the ODE model of von Dassow etal [2000] for the Drosophila segment polarity generegulatory network. The ABN model highlights tim-ing and logic constraints that are hidden in ODEmodels. In the ABN model the binary output valueof each node is governed by Boolean functions andupdate times are encoded in delay parameters as-sociated with each link. Given the ODE network,we construct a corresponding ABN by adjusting thetopology, logic functions and delay parameters. Weshow that this ABN can reproduce the stable seg-mentation pattern observed in experiments, and wederive the constraints satisfied by successful choicesof time delay parameters.

Theory and experiment of fast non-deterministicrandom bit generation with on-chip chaoslasers, Satoshi Sunada, NTT Communication Sci-ence LaboratoriesRandom bit generation is important for many ap-plications, such as cryptography, numerical compu-tation, and stochastic modeling. In particular, fastgeneration of unpredictable truly random bit se-quences is very important to achieve high security ofcommunication systems. Recently, random bit gen-eration using chaos in semiconductor lasers has beendeveloped in order to obtain unpredictable truly ran-dom bit sequences extremely fast [1]. In this system,chaotic oscillation of high frequency above the orderof GHz is produced from the lasers with optical de-layed feedback. Random bit sequences are generatedby sampling and converting the fast chaotic signalsinto binary signals at fast rates over one gigabit persecond, much faster than any other physical randombit generator. While many experimental demonstra-tions of random bit generation with chaotic lasershave been reported [1-3], the role of chaos in gener-ating random bits has not yet been studied theoreti-cally. True random behaviors can never be obtainedonly from the chaotic dynamics subject to determin-istic laws. It is important to elucidate the mechanismof the physical random bit generation with chaoticlasers and the origin of its intrinsic randomness. Inthis presentation, we theoretically show that non-deterministic random bits can be generated due tothe combination of the mixing property of a chaoticlaser system and microscopic noises. The origin ofthe randomness is microscopic quantum noises dueto spontaneous emission. The mixing property of the

chaotic laser system transforms microscopic noisesto macroscopic random signals. The process of thetransformation and the randomness of the generatedbit sequences are numerically investigated by usingstandard chaotic semiconductor laser model equa-tions (Lang-Kobayashi equations) with microscopicnoises. On the basis of the theoretical and numericalconsiderations, we designed chaos laser devices suit-able for fast random bit generation and fabricatedthe devices on a semiconductor chip with photonicintegration technologies. We experimentally demon-strate that random bit sequences passed standardstatistical test suites for randomness can be gener-ated at fast rates up to 2 Gbps using the chaos laserdevices.[1] A. Uchida, K. Amano, M. Inoue, K. Hirano, S.Naito, H. Someya, I. Oowada, T. Karashige, M.Shiki, S. Yoshimori, K. Yoshimura, and P. Davis,“Fast physical bit generation with chaotic semicon-ductor lasers,” Nature Photonics, Vol.2 (12), 728-732(2008).[2] I. Kanter, Y. Aviad, I. Reidler, E. Cohen, M.Rosenbluh, “An optical ultrafast random bit gener-ator,” Nature Photonics, Vol.4 (1), 58-61, (2010).[3] A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris,and D. Syvridis, “Implementation of 140 Gb/s truerandom bit generator based on a chaotic photonicintegrated circuit,” Opt. Express Vol. 18 (18), pp.18763-18768 (2010).

Blowout bifurcation and spatial mode excitationin the bubbling transition to turbulence, JoseDanilo Szezech, Universidade de Sao PauloThe transition to turbulence (spatio-temporal chaos)in a wide class of spatially extended dynamical sys-tem is due to the loss of transversal stability of achaotic attractor lying on a homogeneous manifold(in the Fourier phase space of the system), causingspatial mode excitation. Since the latter manifestsas intermittent spikes this has been called a bubblingtransition. We present numerical evidences that thistransition occurs due to the so-called blowout bi-furcation, whereby the attractor as a whole losestransversal stability and becomes a chaotic saddle.We used a nonlinear three-wave interacting modelwith spatial diffusion as an example of this transi-tion.

Jamming of Granular Flow in a Two-DimensionalHopper, Junyao Tang, Duke UniversityWe seek an understanding of the physics of jammingin hopper flow, using high speed spatio-temporal

35

video data for photoelastic disks flowing through atwo-dimensional hopper. We have found experimen-tal support for the hypothesis that jamming events ofgranular flow in a hopper is approximately a Poissonprocess. The mean flow time between two consecu-tive jams increases rapidly while the hopper openingincreases, but it is insensitive to changes of the hop-per wall angle. Through particle tracking and pho-toelastic measurements, we measure stress field, ve-locity field and density field, as well as fluctuationsof each during the flow. Current work focuses oncombining these results to give further insights intothe relation between mean flow properties and jam-ming and their dependence on hopper configuration.These data are part of an IFPRI-NSF Collaboratoryfor comparing physical data and simulations.

Avalanching and shear of vibrated granular/granular-fluid mixtures, Brian Utter, James Madison Uni-versityThe behavior of dense granular materials can becharacterized by the continuous forming and break-ing of a strong force network resisting flow. Thisjamming/unjamming behavior is typical of a vari-ety of systems and is influenced by factors such asgrain packing fraction, applied shear stress, and therandom kinetic energy of the particles. Statisticalmeasures are desired to characterize the state of thesystem. We present experiments on shear strengthof granular and granular-water mixtures under theinfluence of external vibrations, one parameter thatleads to unjamming. We use low vibration (< 1g)and slow shear and measure avalanching statistics ina rotating drum and the torque required to move astirrer through a sand/water mixture. We find thatexternal vibration (i) increases granular strength atsmall vibrations in the dry system, (ii) removes his-tory dependence (memory), and (iii)decreases shearstrength at all accessible saturation levels in thesand-fluid system. Additionally, shear strength isfound to be smallest for both dry and completelysaturated mixtures. For moderate saturation levels,the variability of the data is small. Additional on-going experiments are probing beyond G = 1 andexploring jamming and surface chemistry effects inthe flow of granular/fluid mixtures.

Velocity Vector Field Pattern in a 2x2 gameof Human Subject Experimental EconomicsExperiment, Zhijian Wang, Zhejiang UniversityTaking the detailed balance condition (H. PeythanYoung 2005) or/and the time reversal transforma-

tion (Baiesi, Maes and Wynants 2009) into consider-ation, we present the Bertrand-Edgeworth-Shapleycycle (Cason, Friedman and Wagener 2005) in atwo-dimensional 5 × 5 lattices space based on ourdata from laboratory experimental economics exper-iments. We have, total 96 subject attended, 12 in-dependent sessions and in each session 4 Up-Downplayers and 4 Right-Left players play a 2 × 2 gamewith the payoff matrix of [(5, 0)(0, 5); (0, 5)(5, 0)] inpairs over 300 periods under random matching pro-tocol. We suggest that, a social Markov jumping instrategy space is a velocity vector, and then it can bemeasured. By analyzing our experimental data, wefind that these vectors form a significant spiral vectorfield in the 5 × 5 lattices space. Filtering out the de-tailed balance (or called as traffics process by physi-cist), we get a clear dynamic pattern (Fig.3(b,c,d,e)).We also find a ring-mountainshaped distribution ofthe time anti-symmetric Markov jumping in thetwo-dimensional space (Fig.3(f)). Both algebra ma-trix analysis and geometrical presentation methodreach the same result. These findings, together withthe method, suggest considerable connections be-tween evolutionary game theory and experimentaleconomics.

The Effect of Network Structure on the Path toSynchronization in Large Systems of CoupledOscillators, Matt Whiteway, University of Okla-homaThe Kuramoto Model has been used extensively asa tool for understanding the dynamics of large sys-tems of oscillators that are either coupled globally,locally, or through a complex network. We are in-terested in the path that systems of networked oscil-lators take to global synchronization as the couplingstrength between oscillators is increased. We employthe Kuramoto Model to study the effects of networksize, degree distribution, and natural frequency dis-tribution on the dynamics of these systems. A recentstudy has shown that small clusters of synchronizedoscillators form before the entire system transitionsto a state of global coherency. The main result fromour work is that this local synchronization is largelyindependent of both the size and natural frequencydistribution of the system, and is instead highly de-pendent on the average number of links per oscillator,becoming less prominent as this average increases.

Voltage interval mappings for activity transitionsin neuron models for elliptic bursters, JeremyWojcik, Georgia State University and Neuroscience

36

InstituteWe perform a thorough bifurcation analysis ofa mathematical elliptic bursting model, using acomputer-assisted reduction to equation-free, one-dimensional Poincare mappings for a voltage inter-val. We examine the bifurcations that underlie thecomplex activity transitions between tonic spiking,bursting, mixed-mode oscillations as well as quies-cence; in the Fitzhugh-Rinzel model and we compareour findings with two biologically relevant models forelliptic bursters; a bursting adaption of the classi-cal Hodgkin-Huxley model, and a realistic Rubin-Terman model for the external segment of the GlobusPallidus. We illustrate the wealth of information thatcan be derived from continuous Poincare mappings,both qualitatively and quantitatively, which cannotbe found directly from discrete mappings generatedfrom the flow.

A free energy simulation approach to the study ofequilibrium modulated phases, Kai Zhang, DukeUniversitySpatially periodic patterns that result from equilib-rium or out-of-equilibrium processes are observed ina variety of physical and chemical systems. Whileidentifying pattern formation of nonequilibrium phe-nomena, such as Rayleigh-Benard convection, usu-ally involves directly solving for the nonlinear timeevolution, equilibrium modulated phases, such as mi-crophases in diblock copolymers, correspond to min-imizing a Landau-Ginzburg free energy for a givenmorphology and periodicity. Any study of the mi-crophase dynamical self-assembly thus requires a de-tailed understanding of the underlying equilibriumphase behavior. Microphase separation has beenextensively studied by theoretical analysis, experi-ments, coarse-grained numerical optimizations andparticle-based simulations. However, due to the highfree energy barriers that separate the various phases,identifying the stable morphologies and periodicityin microphase-forming systems is difficult on the ac-cessible experiment and simulation time scale. Wedevelop a simulation methodology based on thermo-dynamic integration by which we can obtain the ab-solute free energy of different modulated phases. Weadopt the method in a Monte Carlo simulation oftwo microphase-forming spin systems, i.e., the ax-ial next-nearest-neighbor Ising (ANNNI) model andthe Ising-Coulomb (IC) model. The accurate equi-librium phase diagram prediction in those systemsdemonstrates that our method successfully circum-

vents the long-existing problem of kinetic arrest inthe study of equilibrium modulated phases.

Bistability and Oscillations in Fluid Networks,John Geddes, Franklin W. Olin College of Engineer-ingFluid networks in which the resistance to flow de-pends on the fluid in a nonlinear fashion are quitecommon. Some examples include the flow of bloodthrough the microcirculation, the flow of bubbles ordroplets through microfluidic devices, or the flow ofmagma through a volcanic chamber. Over the lastfew years we have developed a general theory for suchfluid networks which takes into account two mainsources of nonlinearity: the dependence of the localresistance on the fluid, and the partition rule for thefluid at network nodes. We have demonstrated the-oretically that bistability and oscillations are to beexpected, and we have confirmed these predictions inexperiments on several model systems. In this pre-sentation we will describe the nonlinear dynamics offluid networks, and present our latest experimentalstudies.

Nonlinear Dynamics and Methods of Investiga-tion of Chaotic Time Series in the Brain,Nayoung Koh, University of Califoria, IrvineWook Hee Koh, Department of Physics, Hanseo Uni-versity, Seosan, Chungcheongnam-do, Korea, Nay-oung Koh, Department of Anatomy and Neurobiol-ogy, University of California, Irvine, California, USA,Minjeong Koh, School of Social and Behavioral Sci-ences, Irvine Valley College, Irvine, California, USAA complex biological system, such as the brain, can-not be fully understood in the context of physiol-ogy through the application of purely reductionisticmethods due to the dynamical nature in its func-tion based upon collective behavior as a whole ratherthan simply the sum of its individual components.Numerous investigators in neuroscience have demon-strated the importance and the necessity of the useof analytical tools, such as chaos theory, to explainthe nonlinear phenomena of higher brain functionsfrom information processing to perception and mem-ory. The elementary processing units in the brain areneurons which are connected to each other in an in-tricate pattern. The neuronal signals consist of shortelectrical pulses, so-called action potentials or spikes.A chain of action potentials emitted by a single neu-ron is called a spike train which occurs at regularor irregular intervals. The form of the action po-tential does not carry any information. Rather, it

37

is the number and the timing of spikes that encodeand transmit stimulus information. Therefore, it isessential to analyze in depth the time series of spiketrain in order to understand the properties of corticalnetworks and higher brain function. Here, we intro-duce the concepts of nonlinear dynamics underlying

a spike train as well as the methods for time-seriesanalysis, such as return maps and surrogate strat-egy. We also present simulation results obtained byusing our numerical codes of spiking neuron mod-els designed to examine the nonlinear properties ofneuronal firing pattern.

38

Index

A free energy simulation approach to the study of equi-librium modulated phases, Zhang, 37

A mathematical model of the decline of religion, Yaple,21

A new algorithm for detection of apnea in infants inneonatal intensive care units, Lee, 28

Algortithm for Planar 4-Body Problem Central Config-urations with Given Masses, Pina, 31

An Elementary Model of Torus Canards, Barry, 9An Information-Theoretic Analysis of Competing Mod-

els of Stochastic Computation, Ellison, 24Application of Nonlinear Data Analysis to Locating Dis-

ease Clusters, Moniz, 29Application of periodic orbit theory to chaos computing,

Kia, 27Applying the Loschmidt Echo and Fidelity Decay to

Classical Waves in a Wave Chaotic System witha Nonlinear Dynamic Response, Frazier, 25

Avalanching and shear of vibrated granular/granular-fluid mixtures, Utter, 36

Bifurcations from sub-wavelength changes in a wave chaoticcavity with nonlinear feedback, Cohen, 23

Bifurcations of 2D Rayleigh-Taylor Unstable Flames,Hicks, 15

Bistability and Oscillations in Fluid Networks, Geddes,37

Blowout bifurcation and spatial mode excitation in thebubbling transition to turbulence, Szezech, 35

Brownian Motion By Switching Unstable DissipativeSystems, Canton, 22

Brownian movement in complex asymmetric periodicpotential under the influence of “green” noise,Sviridov, 19

Chaos Elimination of Fluctuations in Quantum Tunnel-ing Rates, Pecora, 11

Chaos in semiconductor at hellical instability, Ibragi-mov, 26

Chaotic Ionization of Bidirectionally Kicked RydbergAtoms, Burke, 14

Clustering of particles in turbulence, Mercado, 16Compensatory structures in network synchronization,

Nishikawa, 7Control of chaos by a weak perturbation in an impact

oscillator., Medeiros, 29Couette Shear for Elliptical Particles Near Jamming,

Farhadi, 15

Creating Morphable Logic Gates using Logical Stochas-tic Resonance in an Engineered Gene Regula-tory Network, Dari, 10

Crowd behavior: Synchronization of multistable chaoticsystems by a common external force, Pisarchik,12

Cyclic simple shear in a two-dimensional granular sys-tem, Ren, 32

Deformable self-propelled domain in a three-dimensionalexcitable reaction-diffusion system, Shitara, 34

Density-dependent particle clustering on a Faraday wave,Sanli, 17

Depinning of localized structures in a forced dissipativesystem, Ma, 16

Determining the onset of chaos in large Boolean net-works, Pomerance, 12

Dynamic Modeling and Simulation of a Real World Bil-liard, Hartl, 26

Dynamic Structure Factor and Transport Coefficientsof a Homogeneously Driven Granular Fluid inSteady State, Vollmayr-Lee, 21

Dynamics and Interactions of Swimming Cells, Gollub,6

Effect of strength-interval relationship on cardiac rhythmdynamics in a one-dimensional mapping model,Ring, 32

Effects of Shape on Diffusion, Shaw, 13Electroporation in a three-dimensional, time-dependent

model of a skeletal muscle fiber, Cranford, 24Entrainment of a Thalamocortical Neuron to Periodic

Sensorimotor Signals, Yang, 21Erosional Channelization in Porous Media, Mahadevan,

7Estimating the time scales for the evolution of robust-

ness under almost-neutral drift, Mitchener, 29Evolutionary stability of an optimal strategy for habitat

selection, Galanthay, 25Exact Folded-Band Oscillator, Corron, 23Excitable Nodes on Random Networks: Structure and

Dynamics, Singh, 34Experimental and theoretical evidence for fluctuation

driven activations in an excitable chemical sys-tem, Hastings, 15

Exploring mesoscopic network structure with communi-ties of links, Bagrow, 9

39

Exploring the dynamics of CRISPR loci length: Howmuch can a bacterium remember about virusesthat infected it?, Childs, 23

Faults & Earthquakes as Granular Phenomena: Con-trols on Stick-Slip Dynamics, Daniels, 6

Fingering instability down the outside of a vertical cylin-der, Smolka, 18

Flexibility Increases Energy Efficiency of Digging in Gran-ular Substrates, Wendell, 13

Fluctuations in an agitated granular liquid, Nichol, 17Fluid rope tricks, Morris, 11Folding: the nonlinear step in fluid mixing, Kelley, 10Force Network in a 2D Frictionless Emulsion Model Sys-

tem, Desmond, 24Frequency-comb generation with an opto-electronic os-

cillator, Rosin, 33

Hamiltonian monodromy, Chen, 22Homoclinic Snaking in Plane Couette Flow, Burke, 14Homogeneous linear shear of a two dimensional granular

system, Dijksman, 24

Identification of delays and discontinuity points of un-known systems by using synchronization of chaos,Sorrentino, 34

Instability in a Sheet of Birds, Mecholsky, 29Intermittent Jamming in Quasi-2D Microfunnels, Ortiz,

30Invariant manifolds in chaotic advection-reaction-diffusion

pattern formation, Mitchell, 16Isochronous chaos synchronization of delay-coupled op-

toelectronic oscillators, Illing, 26

Jamming of Granular Flow in a Two-Dimensional Hop-per, Tang, 35

Jet-Induced Granular 2-D Crater Formation with Hori-zontal Symmetry Breaking, Clark, 14

Localization phenomena arising from spatially periodicforcing, McCoy, 29

Low Dimensional Dynamics in Large Systems of Cou-pled Oscillators, Ott, 8

Measuring information flow in anticipatory systems, Hahs,15

Measuring Information Flow in Anticipatory Systems,Pethel, 12

Mixing properties of a granular monolayer, Puckett, 31Models for bacterial population dynamics and evolution,

Allen, 6

Network of Networks and the Climate System, Kurths,7

Noise-induced Phenomena in Two Strongly Pulse-coupledResonate-and-Fire Neuron Models, Nakada, 30

Nonlinear Dynamics and Methods of Investigation ofChaotic Time Series in the Brain, Koh, 37

Nonlinear Programs and DARPA, Rogers, 8Nonlinear synchronization of the Polar Regions? cli-

matic oscillations over the last ice age: A work-ing hypothesis, Rial, 32

Nonlinear Waves in Granular Crystals, Porter, 17

Pattern formation in coating flows of suspensions, Kao,15

Pattern formation of grains in oscillatory frluid flows,Klotsa, 27

Phase space method for target ID, Carroll, 22Phase Synchronization of Directly Coupled Boolean Chaos

Oscillators, Park, 31Pinned and Twisted Scroll Rings in an Excitable Chem-

ical System, Martsberger, 28Predicting criticality and dynamic range in complex net-

works: effects of topology, Larremore, 10Probabilistic Maxima in Basins of Attraction of Coexist-

ing States in a Noisy MultistableSystem, Mar-tinez, 28

Quantifying the Complexity of Kauffman Networks, Gong,26

Quantum and classical pumping using ultracold atoms,Ivory, 27

Reactive mixing of initially isolated scalars: estimationof mix-down time, Tsang, 20

Reconstruction of Cardiac Action Potential Dynamicsusing Computer Modeling with Feedback fromExperimental Data, Munoz, 11

Relation between Autonomous Boolean and ODE Mod-els of a Gene Regulatory Network, Sun, 34

Ripples, dunes, bars and meanders, Andreotti, 6Robustness of modular network and overlapping com-

munities, Ahn, 14Robustness of multi-layer networks composed of mixed

oscillators, Morino, 29Rocking and Rolling, Virgin, 8

Shape instability of growing tumors, Ben Amar, 6Spatially localized structures in two dimensions, Knobloch,

6Spatiotemporal Dynamics of Calcium-Driven Alternans

in Cardiac Tissue, Skardal, 18

40

Spike-Time Reliability of Pulse-Coupled Oscillator Net-works, Lin, 15

Stability and Bifurcations in a Dynamical System As-sociated with Membrane Kinetics UnderlyingCardiac Arrhythmias, Popovici, 17

Stabilization of chaotic spiral waves during cardiac ven-tricular fibrillation using feedback control, Uzelac,20

Statistical Mechanics of Packing: From Proteins to Cellsto Grains, O’Hern, 7

Still RunningRecent Work on the Neuromechanics of Insect Lo-

comotion, Holmes, 6Stochastic Extinction along an Optimal Path, Shaw, 8Sub-wavelength position-sensing using a wave-chaotic

cavity with nonlinear feedback, Cavalcante, 9Subrcritical Fracture of Porous Media, Guarino, 26Suspensions of Maps to Flows, Starrett, 19Swarming by Nature and by Design, Bertozzi, 6Switching from steady-state to chaos via pulse trains in

an optoelectronic oscillator, Callan, 21Symmetry and Stability in Network Dynamical Systems,

Lindemann, 28Synchronization in Finite-Memory Dynamical Systems,

Travers, 20

The Buckley-Leverett Equation with Dynamic CapillaryPressure, Shearer, 18

The Buckley-Leverett Equation with Dynamic CapillaryPressure, Spayd, 18

The effect of force chains on near-field sound propaga-tion, Owens, 30

The Effect of Network Structure on the Path to Syn-chronization in Large Systems of Coupled Os-cillators, Stout, 19

The Effect of Network Structure on the Path to Syn-chronization in Large Systems of Coupled Os-cillators, Whiteway, 36

The Nonlinear Population Dynamics of Pacific Salmon,Drossel, 6

The Path to Fracture: Dynamics of Broken Link Net-works in Granular Flows, Losert, 6

The role of crossover recombination, inversion, and genelinkage in determining gene spacing in a chro-mosome., Clark, 23

Theory and experiment of fast non-deterministic ran-dom bit generation with on-chip chaos lasers,Sunada, 35

Three-dimensional structure of a sheet crumpled into asphere, Cambou, 10

Time delays in the synchronization of chaotic coupledsystems with feedback, Leite, 13

Trapping of Swimming Particles in Chaotic Fluid Flow,Ouellette, 11

Understanding the Dynamics of Flames using Time Se-ries Analysis, Kulp, 27

Universal Shapes Formed by Two Interacting Cracks,Fender, 25

Velocity Vector Field Pattern in a 2x2 game of HumanSubject Experimental Economics Experiment,Wang, 36

Voltage interval mappings for activity transitions in neu-ron models for elliptic bursters, Wojcik, 36

What is the front velocity in wave propagation with-out fronts? - Epidemics on complex networksprovide an answer, Brockmann, 9

41

Author Index

Ahn, 14Allen, 6Andreotti, 6

Bagrow, 9Barry, 9Ben Amar, 6Bertozzi, 6Brockmann, 9Burke, 14

Callan, 21Cambou, 10Canton, 22Carroll, 22Cavalcante, 9Chen, 22Childs, 23Clark, 14, 23Cohen, 23Corron, 23Cranford, 24

Daniels, 6Dari, 10Desmond, 24Dijksman, 24Drossel, 6

Ellison, 24

Farhadi, 15Fender, 25Frazier, 25

Galanthay, 25Geddes, 37Gollub, 6Gong, 26Guarino, 26

Hahs, 15Hartl, 26Hastings, 15Hicks, 15Holmes, 6

Ibragimov, 26Illing, 26

Ivory, 27

Kao, 15Kelley, 10Kia, 27Klotsa, 27Knobloch, 6Koh, 37Kulp, 27Kurths, 7

Larremore, 11Lee, 28Leite, 13Lin, 15Lindemann, 28Losert, 6

Ma, 16Mahadevan, 7Martinez, 28Martsberger, 28McCoy, 29Mecholsky, 29Medeiros, 29Mercado, 16Mitchell, 16Mitchener, 29Moniz, 29Morino, 29Morris, 11Munoz, 11

Nakada, 30Nichol, 17Nishikawa, 7

O’Hern, 7Ortiz, 30Ott, 8Ouellette, 11Owens, 30

Park, 31Pecora, 11Pethel, 12Pina, 31Pisarchik, 12

42

Pomerance, 12Popovici, 17Porter, 17Puckett, 31

Ren, 32Rial, 32Ring, 32Rogers, 8Rosin, 33

Sanli, 17Shaw, 8, 13Shearer, 18Shitara, 34Singh, 34Skardal, 18Smolka, 18Sorrentino, 34Spayd, 19Starrett, 19Stout, 19Sun, 35Sunada, 35Sviridov, 19Szezech, 35

Tang, 35Travers, 20Tsang, 20

Utter, 36Uzelac, 20

Virgin, 8Vollmayr-Lee, 21

Wang, 36Wendell, 13Whiteway, 36Wojcik, 37

Yang, 21Yaple, 21

Zhang, 37

43