Titre du document / Document title

Coarse-grained Langevin approximations and spatiotemporal acceleration for kinetic Monte Carlo simulations of diffusion of interacting particles

Auteur(s) / Author(s)

Are Sasanka ⁽¹⁾ ; Katsoulakis Markos A. ^{(1 2)} ; Szepessy Anders ⁽³⁾ ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

⁽¹⁾ Department of Mathematics and Statistics, University of Massachusetts, MA, Amherst, USA
⁽²⁾ Department of Applied Mathematics, University of Crete and Foundation of Research and Technology-Hellas, 71405, Heraklion, Greece
⁽³⁾ Matematiska Institutionen, Kungliga Tekniska Högskolan (Royal Institute of Technology), SE-100 44, Stockholm, Sweden

Résumé / 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 surface, 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 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.

Revue / Journal Title

Chinese annals of mathematics. Series B    ISSN  1572-9133 

Source / Source

2009, vol. 30, n^o6, pp. 653-682 [30 page(s) (article)]

Langue / Language

Anglais

Editeur / Publisher

Springer, Heidelberg, ALLEMAGNE  (2002) (Revue)

Mots-clés d'auteur / Author Keywords

Kinetic Monte Carlo methods

;

Diffusion

;

Fluctuations

;

Localisation / Location

35400060359107.0008