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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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Citation： |
Sasanka ARE,Markos A. KATSOULAKIS,Anders SZEPESSY.Coarse-Grained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles[J].Chinese Annals of Mathematics B,2009,30(6):653~682 |
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Net amount： 1364 |
Authors： |
Sasanka ARE; Markos A. KATSOULAKIS; Anders SZEPESSY; |
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| Abstract： |
Kinetic Monte Carlo methods provide a powerful computational tool for the
simulation of microscopic processes such as the diffusion of interacting particles on a sur-
face, at a detailed atomistic level. However such algorithms are typically computationally
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 equa-
tions 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 sys-
tems, 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 free-
dom in coarse-grained Monte Carlo methods, the Langevin system of stochastic differential
equations allows for multiple particle moves in a single timestep. |
Keywords： |
Kinetic Monte Carlo methods, Diffusion, Fluctuations |
Classification： |
82B24, 82B26, 82B80 |
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