First-Passage Kinetic Monte Carlo method

Uppdaterad från manuskript till artikel: 20100805 QC 20100805
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.

NATURVETENSKAP Fysik Den kondenserade materiens fysik hsv//swe
NATURAL SCIENCES Physical Sciences Condensed Matter Physics hsv//eng
Brownian motion; Green's function methods; Monte Carlo methods; N-body problems; reaction-diffusion systems
Defects and diffusion
Defekter och diffusion

Ingår i:Physical Review E. Statistical, Nonlinear, and Soft Matter Physics80:6, s. 066701-1063-651X1095-3787

Av författaren/redakt...: Oppelstrup, Toma ...; Bulatov, Vasily ...; Donev, Aleksanda ...; Kalos, Malvin H.; Gilmer, George H ...; Sadigh, Babak

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