grid computing applications in modeling and simulations of molecular nanomagnets and classical...
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Grid computing applications in modeling and simulations of molecular nanomagnets and classical charged particles
Michał Antkowiak
Faculty of Physics, A. Mickiewicz University, Poznań, PolandEuropean Institute of Molecular Magnetism, Florence, Italy
P. Sobczak, G. Musiał, G. Kamieniarz, B. Błaszkiewicz
Outline
Molecular nanomagnets Classical charged particles PEARL-AMU site
Molecular nanomagnets
• Quantum molecular rings
• Spin models and thermodynamic quantities
• Exact Diagonalization Technique
• Results for Cr – based rings
Cr8
(Cr8F8Piv16)
Cr9
[Pr2NH2][Cr9F9Cl2(Piv)17]
Cr7Cd
[(CH3)2NH2][Cr7CdF8{OOCC(CH3)3}16]
)sincos()(
)( =
B2
1||111=
xj
zj
zj
zj
zj
yj
yj
xj
xj
n
j
ssBgsD
ssJssssJ
H
Sj - spin operators (s=3/2)n – number of sitesB – magnetic field
The quantum molecular rings model
θ
HB TreZZTkF ,ln
BTBTB
F
T
FTC
F
-S ,,2
2
2
2
222 )()( zzBz SSg
•Free energy
•Specific heat C, susceptibility χ and entropy S as derivatives of the free energy
•Specific heat C and susceptibility χz as functions of the spin moments
Thermodynamic quantities
Exact diagonalization technique
•Size of the Hamiltonian matrix• Cr8: 48 x 48 (65536 x 65536 = 32GB)• Cr9: 49 x 49 (262144 x 262144 = 512GB)
•For θ=0• quasi diagonal form of the Hamiltonian• matrix blocks labeled by
• eigenvalues M of Sz
• Symmetry (a) of the eigenstate• Cr8: 48 blocks (max. size: 4068 x 4068 = 0.12GB)• Cr9: 52 blocks (max. size: 15180 x 15180 = 1.7GB)
•For θ≠0 -> only 2 blocks labeled by symmetry
Sizes of the Hamiltonian matrix blocks (Cr8)
Parallel programming tasks and models
MPI library Master-slave model Star-like
LPT algorithm
Processing times for different blocks (Cr8)
Speedup (Cr8) u = tseq/tpar
Efficiency (Cr8) E = u/p
Limited scalability
Results
Magnetisation Cr7Cd
Susceptibility
Susceptibility Cr7Cd
Susceptibility
Classical charged particles
• Subject of the research
• Models
• Genetic algorithm
• Results
Subject of the research
2D system Coulomb potential (1), 9≤N≤30 Logarithmic potential (2), 9≤N≤30
3D system Coulomb potential (1), 17≤N≤70 Logarithmic potential (2), 10≤N≤50
N
=i
N
=i
N
+ij= ji
jii
rr
qq+r=U
1
1
1 1
2
N
=i
N
=i
N
+ij= ji
jii
rr
qq+r=U
1
1
1 1
2 ln2(1) (2)
Uniform particles: qi = qj = 1
The classical charged particles models
2D system One chromosome = one solution One gene = one coordinate (x or y).
x1
x2
… xN Chromosome
y1
y2
… yN gene
Genetic algorithm method
Ns (generations): 106 - 107
S (chromosomes): 200 – 500Pc (crossing probability): 0.1 - 0.9Pm (mutation probability): 0.02 – 0.2
N=302D system results
N=302D system results
Ground-state configuration Metastable state configuration
Higher symmetry = lower energy
Conclusions
Despite more and more advanced algorithmslarge computing resources are still needed
More complicated systems = more computing resources(both quantum and classical)(ED – higher scalability)
Grid resources improve computational infrastructure and enable simulations of more complicated systems
G. Kamieniarz W. FlorekG. MusiałL. DębskiP. KozłowskiK. PacerD. TomeckaP. SobczakP. GąbkaL. KaliszanM. HaglauerT. ŚlusarskiB. BłaszkiewiczŁ. KucharskiM. Antkowiak
Team
19 CPUs (32 cores) AMD x86_64 Opteron Dual Core: 2.0 and 2.4 GHz Xeon Dual Core: 2.66GHz ~ 4 cores per node
Rpeak = 153 GFlops 41 GB RAM
4 GB – 12 GB per node 1.22 TB disc space Wien2k, FPLO, NWChem, Molpro, Turbomole,
numerical NAG library
PEARL-AMU site
PEARL-AMU node
Galera1344 x quad-core Xeon 2,33 GHz
Reef46 x dual-core Xeon EM64T 3GHz
Computing grants in HPC centers
JUMP448 x Power6 4.7 GHz
Acknowledgements
European Network of Excellence MAGMANet
Polish Ministry of Science and Higher Education
Thank you for your attention!
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