Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles

被引:75
作者
Katsoulakis, MA
Vlachos, DG [1 ]
机构
[1] Univ Delaware, Dept Chem Engn, Newark, DE 19716 USA
[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
[3] Univ Delaware, Ctr Catalyt Sci & Technol, Newark, DE 19716 USA
关键词
D O I
10.1063/1.1616513
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q(2), where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q(3) for short potentials to q(4) for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made. (C) 2003 American Institute of Physics.
引用
收藏
页码:9412 / 9427
页数:16
相关论文
共 26 条
[1]  
[Anonymous], 1999, SCALING LIMITS INTER, DOI DOI 10.1007/978-3-662-03752-2
[2]   Metastability for the exclusion process with mean-field interaction [J].
Asselah, A ;
Giacomin, G .
JOURNAL OF STATISTICAL PHYSICS, 1998, 93 (5-6) :1051-1110
[3]   Theory and simulation of jump dynamics, diffusion and phase equilibrium in nanopores [J].
Auerbach, SM .
INTERNATIONAL REVIEWS IN PHYSICAL CHEMISTRY, 2000, 19 (02) :155-198
[4]   FAST WAVELET TRANSFORMS AND NUMERICAL ALGORITHMS .1. [J].
BEYLKIN, G ;
COIFMAN, R ;
ROKHLIN, V .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (02) :141-183
[5]  
Binder Kurt, 1986, Monte Carlo Methods in Statistical Physics, volume 7 of Topics in Current Physics, V7
[6]   NEW ALGORITHM FOR MONTE-CARLO SIMULATION OF ISING SPIN SYSTEMS [J].
BORTZ, AB ;
KALOS, MH ;
LEBOWITZ, JL .
JOURNAL OF COMPUTATIONAL PHYSICS, 1975, 17 (01) :10-18
[7]   BROWNIAN MOTION IN SPINODAL DECOMPOSITION [J].
COOK, HE .
ACTA METALLURGICA, 1970, 18 (03) :297-+
[8]  
Cover T. M., 2005, ELEM INF THEORY, DOI 10.1002/047174882X
[9]  
DEMASI A, 1994, NONLINEARITY, V7, P633, DOI 10.1088/0951-7715/7/3/001
[10]   Multiresolution wavelet coarsening and analysis of transport in heterogeneous media [J].
Ebrahimi, F ;
Sahimi, M .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 316 (1-4) :160-188