Simulation of stochastic diffusion via first exit times

JOURNAL OF COMPUTATIONAL PHYSICS

卷:300

Article

Lotstedt, Per¹  Meinecke, Lina¹ 

[1] Uppsala Univ, Div Comp Sci, Dept Informat Technol, SE-75105 Uppsala, Sweden

关键词: Stochastic simulation;    Diffusion;    Unstructured mesh;   

DOI  :  10.1016/j.jcp.2015.07.065

来源: Elsevier

【 摘 要 】

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free