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

Markos A. Katsoulakis, Andrew J. Majda, Dionisios G. Vlachos

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)250-278
Number of pages29
JournalJournal of Computational Physics
Volume186
Issue number1
DOIs
StatePublished - Mar 20 2003

Fingerprint

stochastic processes
Random processes
intermolecular forces
Asymptotic analysis
simulation
retaining
programming
Computer programming
Program processors
Desorption
desorption
vapor phases
deviation
Adsorption
requirements
Molecules
adsorption
Gases
Monte Carlo simulation
molecules

Keywords

  • Birth-death processes
  • Coarse-grained processes and coarse-grained Monte Carlo simulations
  • Detailed balance
  • Hierarchy of Monte Carlo algorithms
  • Large deviations

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. / Katsoulakis, Markos A.; Majda, Andrew J.; Vlachos, Dionisios G.

In: Journal of Computational Physics, Vol. 186, No. 1, 20.03.2003, p. 250-278.

Research output: Contribution to journalArticle

Katsoulakis, Markos A. ; Majda, Andrew J. ; Vlachos, Dionisios G. / Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. In: Journal of Computational Physics. 2003 ; Vol. 186, No. 1. pp. 250-278.
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