Grid computing applications in modeling and simulations of molecular nanomagnets and classical charged particles Michał Antkowiak Faculty of Physics, A. Mickiewicz University, Poznań, Poland European Institute of Molecular Magnetism, Florence, Italy P. Sobczak, G. Musiał, G. Kamieniarz, B. Błaszkiewicz
Grid computing applications in modeling and simulations of molecular nanomagnets and classical charged particles. Michał Antkowiak. P. Sobczak, G. Musiał, G. Kamieniarz, B. Błaszkiewicz. Faculty of Physics, A. Mickiewicz University, Pozna ń , Poland - PowerPoint PPT Presentation
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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).