First-passage kinetic Monte Carlo method

Tomas Oppelstrup, Vasily V. Bulatov, Aleksandar Donev, Malvin H. Kalos, George H. Gilmer, Babak Sadigh

Research output: Contribution to journalArticle

Abstract

We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper, our algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of superhops, one particle at a time. By partitioning the simulation space into nonoverlapping protecting domains each containing only one or two particles, the algorithm factorizes the N -body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Green's functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the algorithm is efficient at low particle densities, where other existing algorithms slow down severely.

Original languageEnglish (US)
Article number066701
JournalPhysical Review E
Volume80
Issue number6
DOIs
StatePublished - Dec 1 2009

Fingerprint

Kinetic Monte Carlo
Monte Carlo method
kinetics
statistics
two body problem
many body problem
propagation
Statistics
N-body Problem
Reaction-diffusion Model
random walk
Event-driven
Monte Carlo Algorithm
clocks
Reaction-diffusion
Propagator
Green's functions
simulation
Green's function
Partitioning

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Oppelstrup, T., Bulatov, V. V., Donev, A., Kalos, M. H., Gilmer, G. H., & Sadigh, B. (2009). First-passage kinetic Monte Carlo method. Physical Review E, 80(6), [066701]. https://doi.org/10.1103/PhysRevE.80.066701

First-passage kinetic Monte Carlo method. / Oppelstrup, Tomas; Bulatov, Vasily V.; Donev, Aleksandar; Kalos, Malvin H.; Gilmer, George H.; Sadigh, Babak.

In: Physical Review E, Vol. 80, No. 6, 066701, 01.12.2009.

Research output: Contribution to journalArticle

Oppelstrup, T, Bulatov, VV, Donev, A, Kalos, MH, Gilmer, GH & Sadigh, B 2009, 'First-passage kinetic Monte Carlo method', Physical Review E, vol. 80, no. 6, 066701. https://doi.org/10.1103/PhysRevE.80.066701
Oppelstrup T, Bulatov VV, Donev A, Kalos MH, Gilmer GH, Sadigh B. First-passage kinetic Monte Carlo method. Physical Review E. 2009 Dec 1;80(6). 066701. https://doi.org/10.1103/PhysRevE.80.066701
Oppelstrup, Tomas ; Bulatov, Vasily V. ; Donev, Aleksandar ; Kalos, Malvin H. ; Gilmer, George H. ; Sadigh, Babak. / First-passage kinetic Monte Carlo method. In: Physical Review E. 2009 ; Vol. 80, No. 6.
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