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Coarse-Grained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 653-682页

作者： Sasanka ARE Markos A. KATSOULAKIS anders szepessy Department of Mathematics and Statistics University of MassachusettsAmherstMA 01003-9305USA Department of Applied Mathematics University of Crete and Foundation of Research and TechnologyHellasHeraklion 71405Greece Matematiska Institutionen Kungliga Tekniska Hgskolan (Royal Institute of Technology)SE-100 44 StockholmSweden

Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes such as the diffusion of interacting particles on a surface, at a detailed atomistic level. However such algorithms are typically computationatly expensive and are restricted to fairly small spatiotemporal scales. One approach towards overcoming this problem was the development of coarse-grained Monte Carlo algorithms. In recent literature, these methods were shown to be capable of efficiently describing much larger length scales while still incorporating information on microscopic interactions and fluctuations. In this paper, a coarse-grained Langevin system of stochastic differential equations as approximations of diffusion of interacting particles is derived, based on these earlier coarse-grained models. The authors demonstrate the asymptotic equivalence of transient and long time behavior of the Langevin approximation and the underlying microscopic process, using asymptotics methods such as large deviations for interacting particles systems, and furthermore, present corresponding numerical simulations, comparing statistical quantities like mean paths, auto correlations and power spectra of the microscopic and the approximating Langevin processes. Finally, it is shown that the Langevin approximations presented here are much more computationally efficient than conventional Kinetic Monte Carlo methods, since in addition to the reduction in the number of spatial degrees of freedom in coarse-grained Monte Carlo methods, the Langevin system of stochastic differential equations allows for multiple particle moves in a single timestep.

关键词： Kinetic Monte Carlo methods Diffusion Fluctuations

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