Coarse-Grained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles |
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Authors: | Sasanka ARE Markos A KATSOULAKIS and Anders SZEPESSY |
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Institution: | 1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305, USA 2. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305, USA; Department of Applied Mathematics, University of Crete and Foundation of Research and Technology-Hellas, Heraklion 71405, Greece 3. Matematiska Institutionen, Kungliga Tekniska Hogskolan (Royal Institute of Technology), SE-100 44 Stockholm, Sweden |
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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 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. |
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Keywords: | Kinetic Monte Carlo methods Diffusion Fluctuations |
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