First-Passage Kinetic Monte Carlo method
2009 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 80, no 6, 066701- p.Article in journal (Refereed) Published
We present a new effcient method for Monte Carlo simulations of diusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditionalsmall diusion hops and propagates the diusing particles over long distances through asequence of super-hops, one particle at a time. By partitioning the simulation space into nonoverlappingprotecting domains each containing only one or two particles, the algorithm factorizesthe N-body problem of collisions among multiple Brownian particles into a set of much simplersingle-body and two-body problems. Ecient propagation of particles inside their protective domainsis enabled through the use of time-dependent Green's functions (propagators) obtained assolutions for the rst-passage statistics of random walks. The resulting Monte Carlo algorithmis event-driven and asynchronous; each Brownian particle propagates inside its own protectivedomain and on its own time clock. The algorithm reproduces the statistics of the underlyingMonte-Carlo model exactly. Extensive numerical examples demonstrate that for an importantclass of diusion-reaction models the new algorithm is effcient at low particle densities, whereother existing algorithms slow down severely.
Place, publisher, year, edition, pages
2009. Vol. 80, no 6, 066701- p.
Brownian motion; Green's function methods; Monte Carlo methods; N-body problems; reaction-diffusion systems
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:kth:diva-11570DOI: 10.1103/PhysRevE.80.066701ISI: 000273228000084ScopusID: 2-s2.0-72449169547OAI: oai:DiVA.org:kth-11570DiVA: diva2:277776
Uppdaterad från manuskript till artikel: 20100805
QC 201008052009-11-202009-11-202012-01-18Bibliographically approved