Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems

  • Authors:

  • Markos A. Katsoulakis;Andrew J. Majda;Dionisios G. Vlachos

  • Affiliations:

  • Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA;Courant Institute of Mathematical Sciences and Center for Atmosphere and Ocean Sciences, New York University, New York, NY;Department of Chemical Engineering and Center for Catalytic Science and Technology, University of Delaware, Newark, DE

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

Quantified Score

Hi-index 31.48

Visualization

Abstract

In this paper we present a new class of coarse-grained stochastic processes and Monte Carlo simulations, derived directly from microscopic lattice systems and describing mesoscopic length scales. As our primary example, we mainly focus on a microscopic spin-flip model for the adsorption and desorption of molecules between a surface adjacent to a gas phase, although a similar analysis carries over to other processes. The new model can capture large scale structures, while retaining microscopic information on intermolecular forces and particle fluctuations. The requirement of detailed balance is utilized as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. We carry out a rigorous asymptotic analysis of the new system using techniques from large deviations and present detailed numerical comparisons of coarse-grained and microscopic Monte Carlo simulations. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or the CPU time per executed event compared to microscopic Monte Carlo simulations.