### 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 language | English (US) |
---|---|

Article number | 066701 |

Journal | Physical Review E |

Volume | 80 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2009 |

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### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 80, no. 6, 066701. https://doi.org/10.1103/PhysRevE.80.066701

}

TY - JOUR

T1 - First-passage kinetic Monte Carlo method

AU - Oppelstrup, Tomas

AU - Bulatov, Vasily V.

AU - Donev, Aleksandar

AU - Kalos, Malvin H.

AU - Gilmer, George H.

AU - Sadigh, Babak

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=72449169547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72449169547&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.80.066701

DO - 10.1103/PhysRevE.80.066701

M3 - Article

VL - 80

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 6

M1 - 066701

ER -