Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems

2013/04/29 by Denis S. Grebenkov, Denis Grebenkov, Grebenkov, Denis
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Diffusion and Search Dynamics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech #physics.comp-ph

paper · pdf · doi:10.48550/arxiv.1304.7807

arxiv created 2013/04/29 · openalex publication_date 2013/04/29 · arxiv updated 2013/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to study various probabilistic characteristics (harmonic measure, first passage/exit time distribution, reaction rates, search times and strategies, etc.) and to solve the related partial differential equations. The adaptive character and flexibility of FRWs make them particularly efficient for simulating diffusive processes in porous, multiscale, heterogeneous, disordered or irregularly-shaped media.

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