2009/05/31 by Tomas Oppelstrup, T. Oppelstrup, V. V. Bulatov +9 · 102 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Algorithm #Anomalous diffusion #Brownian motion #Computer science #Diffusion #Dynamic Monte Carlo method #First-hitting-time model #Hybrid Monte Carlo #Kinetic Monte Carlo #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Mathematics #Monte Carlo algorithm #Monte Carlo method #Monte Carlo method in statistical physics #Monte Carlo molecular modeling #Nuclear physics research studies #Particle (ecology) #Particle filter #Physics #Propagator #Quantum Monte Carlo #Quantum mechanics #Random walk #Statistical physics #Statistics #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physreve.80.066701
published in Physical Review E 80(6), 066701 (American Physical Society) · Elaborates on Phys. Rev. Lett., 97:230602, 2006. Small revisions from prior version only
arxiv created 2009/10/13 · openalex publication_date 2009/12/01 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev. Lett. 97, 230602 (2006)], 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.