Michał Antkowiak

1. Grid computing applications in modeling and simulations of molecular nanomagnets and classical charged particles MichałAntkowiak P. Sobczak, G. Musiał, G. Kamieniarz, B. Błaszkiewicz Faculty of Physics, A. Mickiewicz University, Poznań, Poland European Institute of Molecular Magnetism, Florence, Italy

2. Outline • Molecular nanomagnets • Classical charged particles • PEARL-AMU site

3. Molecular nanomagnets • Quantum molecular rings • Spin models and thermodynamic quantities • Exact Diagonalization Technique • Results for Cr – based rings

4. Cr8 (Cr8F8Piv16)

5. Cr9 [Pr2NH2][Cr9F9Cl2(Piv)17]

6. Cr7Cd [(CH3)2NH2][Cr7CdF8{OOCC(CH3)3}16]

7. θ The quantum molecular rings model Sj - spin operators (s=3/2) n – number of sites B – magnetic field

8. Thermodynamic quantities • Free energy • Specific heat C, susceptibility χ and entropy S as derivatives of the free energy • Specific heat C and susceptibility χzas functions of the spin moments

9. 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

10. Sizes of the Hamiltonian matrix blocks (Cr8)

11. Parallel programming tasks and models • MPI library • Master-slave model • Star-like • LPT algorithm

12. Processing times for different blocks (Cr8)

13. Speedup (Cr8) u = tseq/tpar

14. Efficiency (Cr8) E = u/p Limited scalability

15. Results

22. Magnetisation Cr7Cd

23. Susceptibility

24. Susceptibility Cr7Cd

25. Susceptibility

30. Classical charged particles • Subject of the research • Models • Genetic algorithm • Results

31. Subject of the research

32. The classical charged particles models • 2D system • Coulomb potential (1), 9≤N≤30 • Logarithmicpotential(2), 9≤N≤30 • 3D system • Coulomb potential(1), 17≤N≤70 • Logarithmicpotential(2), 10≤N≤50 Uniform particles:qi = qj= 1 (1) (2)

33. Genetic algorithm method • 2D system • One chromosome = one solution • One gene = one coordinate (x or y). x1 x2 … xN Chromosome y1 y2 … yN gene Ns (generations): 106 - 107 S (chromosomes): 200 – 500 Pc (crossing probability): 0.1 - 0.9 Pm (mutation probability): 0.02 – 0.2

34. 2D system results • N=30

35. 2D system results • N=30 Ground-state configuration Metastable state configuration Higher symmetry = lower energy

36. Conclusions • Despite more and more advanced algorithms large 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

37. Team G. Kamieniarz W. Florek G. Musiał L. Dębski P. Kozłowski K. Pacer D. Tomecka P. Sobczak P. Gąbka L. Kaliszan M. Haglauer T. Ślusarski B. Błaszkiewicz Ł. Kucharski M. Antkowiak

38. PEARL-AMU site • 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

39. PEARL-AMU node

40. Computing grants in HPC centers Reef 46 x dual-core Xeon EM64T 3GHz Galera 1344 x quad-core Xeon 2,33 GHz JUMP 448 x Power6 4.7 GHz

41. Acknowledgements • European Network of Excellence MAGMANet • Polish Ministry of Science and Higher Education

42. Thank you for your attention!