The Monte Carlo method in science and engineering

Computing in Science and Engineering

Volumn 8, Issue 2, 2006, Pages 9-19

  Amar, Jacques G ^a,b,c  

^a UNIVERSITY OF TOLEDO   (United States)

^b University of Toledo ^*  (United States)

^c Materials Research Society   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUILIBRIUM DISTRIBUTION; SYNCHRONOUS SUBLATTICE (SL) ALGORITHM;

ALGORITHMS; COMPUTER SIMULATION; KNOWLEDGE ENGINEERING; LARGE SCALE SYSTEMS; MICROPROCESSOR CHIPS;

MONTE CARLO METHODS;

EID: 33644648564     PISSN: 15219615     EISSN: None     Source Type: Journal    
DOI: 10.1109/MCSE.2006.34     Document Type: Article

References (58)

1. N.C. Metropolis et al., "Equation of State Calculations by Fast Computing Machines," J. Chemical Physics, vol. 21, 1953, pp. 1087-1092.
2. W. Wenzel and K. Hamacher, "Stochastic Tunneling Approach for Global Minimization of Complex Potential Energy Landscapes," Physical Rev, Letters, vol. 82, no. 15, 1999, pp. 3003-3007.
3. S. Kirkpatrick, CD. Gelatt, and M.P. Vecchi, "Optimization by Simulated Annealing," Science, vol. 220, no. 4598, 1983, pp. 671-680.
4. J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, 1992.
5. E. Marinari and G. Parisi, "Simulated Tempering: A New Monte Carlo Scheme," Europhysics Letters, vol. 19, 1992, pp. 451-458.
6. W.K. Hastings, "Monte Carlo Sampling Methods Using Markov Chains and Their Applications," Biometrika, vol. 57, no. 1, 1970, pp. 97-109.
7. A.A. Barker, "Monte Carlo Calculations of Radial Distribution Functions for a Proton-Electron Plasma," Australian J. Physics, vol. 18, no. 2, 1965, pp. 119-128.
8. I.R. McDonald, "NpT-Ensemble Monte Carlo Calculations for Binary Liquid Mixtures," MolecularPhysics, vol. 23, 1972, pp. 41-58.
9. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford Univ. Press, 2001.
10. G.E. Norman and V.S. Filinov, "Investigation of Phase Transitions by a Monte Carlo Method," High Temperature (USSR), vol. 7, 1969, pp. 216-222.
11. N.B. Wilding, "Computer Simulation of Fluid Phase Transitions," Am. I. Physics, vol. 69, no. 11, 2001, pp. 1147-1155.
12. D. Nicholson and N. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption, Academic Press, 1982.
13. A.Z. Panagiotopoulos et al., "Phase Equilibria by Simulation in the Gibbs Ensemble, Alternative Derivation, Generalisation and Application to Mixture and Membrane Equilibria," Molecular Physics, vol. 63, no. 4, 1988, pp. 527-538.
14. A.B. Bortz, M.H. Kalos, and J.L. Lebowitz, "A New Algorithm for Monte Carlo Simulation of Ising Spin Systems," J. Computational Physics, vol. 17, 1975, pp. 10-18.
15. J.D. Munoz, M.A. Novotny, and S.J. Mitchell, "Rejection-Free Monte Carlo Algorithms for Models with Continuous Degrees of Freedom," Physical Rev. E, vol. 67, no. 2, 2003, pp. 026101-1-026101-4.
16. M. Sweeny, "Monte Carlo Study of Weighted Percolation Clusters Relevant to the Potts Models," Physical Rev. B, vol. 27, no. 7, 1983, pp. 4445-4455.
17. R.H. Swendsen and J.-S. Wang, "Nonuniversal Critical Dynamics in Monte Carlo Simulations," Physical Rev. Letters, vol. 58, no. 2, 1987, pp. 86-88.
18. J.-S. Wang, O. Kozan, and R.H. Swendsen, "Sweeny and Gliozzi Dynamics for Simulations of Potts Models in the Fortuin-Kasteleyn Representation," Physical Rev. E, vol. 66, 2002, pp. 057101-1-057101-4.
19. C.M. Fortuin and P.W. Kasteleyn, "On the Random-Cluster Model I. Introduction and Relation to other Models," Physica, vol. 57, no. 4, 1972, pp. 536-564.
20. U. Wolff, "Collective Monte Carlo Updating for Spin Systems," Physical Rev. Letters, vol. 62, no. 4, 1989, pp. 361-364.
21. H.G. Evertz, G. Lana, and M. Marcu, "Cluster Algorithm for Vertex Models," Physical Rev. Letters, vol. 70, no. 7, 1993, pp. 875-878.
22. M. Troyer, S. Wessel, and F. Alet, "Flat Histogram Methods for Quantum Systems: Algorithms to Overcome Tunneling Problems and Calculate the Free Energy," Physical Rev. Letters, vol. 90, 2003, pp. 120201-1-120201-4.
23. C. Dress and W. Krauth, "Cluster Algorithm for Hard Spheres and Related Systems," J. Physics A: Mathematics and General, vol. 28, 1995, pp. L597-L601.
24. J. Liu and R. Luijten, "Rejection-Free Geometric Cluster Algorithm for Complex Fluids," Physical Rev. Letters, vol. 92, no. 3, 2004, pp. 035504-1-035504-4.
25. J. Liu and R. Luijten, "Generalized Geometric Cluster Algorithm for Fluid Simulation," Physical Rev. E, vol. 71, no. 12, 2004, pp. 066701-1-066701-12.
26. G.M. Torrie and J.P. Valleau, "Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling," J. Computational Physics, vol. 23, no. 2, 1977, pp. 187-199.
27. G.R. Smith and A.D. Bruce, "A Study of the Multi-Canonical Monte Carlo Method," J. Physics A: Mathematical and General, vol.28, 1995, pp. 6623-6643.
28. A.M. Ferrenberg and R.H. Swendsen, "New Monte Carlo Technique for Studying Phase Transitions," Physical Rev. Letters, vol. 61, no. 23, 1988, pp. 2635-2638.
29. F. Wang and D.P. Landau, "Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States," Physical Rev. Letters, vol. 86, no. 10, 2001, pp. 2050-2053.
30. F. Wang and D.P. Landau, "Determining the Density of States for Classical Statistical Models: A Random Walk Algorithm to Produce a Flat Histogram," Physical Rev. E, vol. 64, no. 5, 2001, pp. 056101-1-056101-16.
31. F.C Chuang et al., "Structure of Si(114) Determined by Global Optimization Methods," Surface Science, vol. 578, 2005, pp. 183-195.
32. R. Faller, Q. Yan, and J.J. de Pablo, "Multicanonical Parallel Tempering," J. Chemical Physics, vol. 116, no. 13, 2002, pp. 5419-5423.
33. W. Kohn and L.J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects," Physical Rev. A, vol. 140, no. 4A, 1965, PP.A1133-A1138.
34. D.M. Ceperley and B.J. Alder, "Ground State of the Electron Gas by a Stochastic Method," Physical Rev. Letters, vol. 45, no. 7, 1980, pp. 566-569.
35. J.P. Perdew and A. Zunger, "Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems," Physical Rev. B, vol. 23, no. 10, 1981, pp. 5048-5079.
36. 4," Physical Rev., vol. 138, no. 2A, 1965, pp. A442-A451.
37. D.M. Ceperley, G.V. Chester, and M.H. Kalos, "Monte Carlo Simulation of a Many-Fermion Study," Physical Rev. Vol., vol. 16, no. 7, 1977, pp. 3081-3099.
38. M.H. Kalos, D. Levesque, and L. Verlet, "Helium at Zero Temperature with Hard-Sphere and other Forces," Physical Rev. A, vol. 9, no. 5, 1974, pp. 2178-2195.
39. S.D. Ivanov, A.P. Lyubartsev, and A. Laaksonen, "Bead-Fourier Path Integral Molecular Dynamics," Physical Rev. E, vol. 67, 2003, pp. 066710-1-066710-11.
40. R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill, 1965.
41. A.F. Voter, "Introduction to the Kinetic Monte Carlo Method," to be published in Radiation Effects in Solids, K.E. Sickafus and E.A. Kotomin, eds., Springer, 2005.
42. K.A. Fichthorn and W.H. Weinberg, "Theoretical Foundations of Dynamical Monte Carlo Simulations," J. Chemical Physics, vol. 95, no. 2, 1991, pp. 1090-1096.
43. G.H. Vineyard, "Frequency Factors and Isotope Effects in Solid State Rate Processes," J. Physics and Chemistry of Solids, vol. 3, 1957, pp. 121-127.
44. J.L. Blue, I. Beichl, and F. Sullivan, "Faster Monte Carlo Simulations," Physical Rev. E, vol. 51, no. 2, 1995, pp. R867-R868.
45. T.S. Rahman et al., "Atomistic Studies of Thin Film Growth," Proc. SPIE, vol. 5009, 2004, pp. 1-14.
46. O. Trushin et al., "Self-Learning Kinetic Monte Carlo Method: Application to Cu(111)," Physical Rev. B, vol. 72, 2005, pp. 115401-1-115401-9.
47. K.M. Chandy and J. Misra, "Distributed Simulation: A Case Study in Design and Verification of Distributed Programs," IEEE Trans. Software Eng., vol. 5, no. 9, 1979, pp. 440-452.
48. B.D. Lubachevsky, "Efficient Parallel Simulations of Dynamic Ising Spin Systems," J. Computational Physics, vol. 75, no. 1, 1988, pp. 103-122.
49. G. Korniss et al., "From Massively Parallel Algorithms and Fluctuating Time Horizons to Nonequilibrium Surface Growth," Physical Rev. Letters, vol. 84, no. 6, 2000, pp. 1351-1354.
50. G. Korniss et al., "Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations," Science, vol. 299, 31 Jan. 2003, pp. 677-679.
51. G. Korniss, M.A. Novotny, and P.A. Rikvold, "Parallelization of a Dynamic Monte Carlo Algorithm: A Partially Rejection-Free Conservative Approach," J. Computational Physics, vol. 153, no. 2, 1999, pp. 488-508.
52. M. Kardar, G. Parisi, and Y.C. Zhang, "Dynamic Scaling of Growing Interfaces," Physical Rev. Letters, vol. 56, no. 9, 1986, pp. 889-892.
53. Y. Shim and J.G. Amar, "Hybrid Asynchronous Algorithm for Parallel Kinetic Monte Carlo Simulations of Thin Film Growth," J. Computational Physics, vol. 212, no. 1, 2006, pp. 305-317.
54. S.G. Eick et al., "Synchronous Relaxation for Parallel Simulations with Applications to Circuit-Switched Networks," ACM Trans. Modeling and Computer Simulation, vol. 3, no. 4, 1993, pp. 287-314.
55. B.D. Lubachevsky and A. Weiss, "Synchronous Relaxation for Parallel Ising Spin Simulations," Proc. 15th Workshop Parallel and Distributed Simulation (PADS'01), IEEE CS Press, 2001; http://lanl.arXiv.org/abs/cs.DC/ 0405053.
56. Y. Shim and J.G. Amar, "Rigorous Synchronous Relaxation Algorithm for Parallel Kinetic Monte Carlo Simulations of Thin Film Growth," Physical Rev. B vol. 71, 2005, pp. 115436-1-115436-12.
57. Y. Shim and J.G. Amar, "Semirigorous Synchronous Sublattice Algorithm for Parallel Kinetic Monte Carlo Simulations of Thin Film Growth," Physical Rev. B, vol. 71, 2005, pp. 125432-1-125432-13.
58. Y. Shim and J.G. Amar, "Growth Instability in Cu Multilayer Films Due to Fast Edge/Corner Diffusion," to be published in Physical Rev. B, 2006.