An exact and efficient first passage time algorithm for reaction diffusion processes on a 2D-lattice

JOURNAL OF COMPUTATIONAL PHYSICS

卷:256

Article

Bezzola, Andri¹  Bales, Benjamin B.¹  Alkire, Richard C.²  Petzold, Linda R.^1,3 

[1] Univ Calif Santa Barbara, Dept Mech Engn, Santa Barbara, CA 93106 USA

[2] Univ Illinois, Dept Chem Engn, Urbana, IL 61801 USA

[3] Univ Calif Santa Barbara, Dept Comp Sci, Santa Barbara, CA 93106 USA

关键词: Reaction-diffusion;    Stochastic algorithm;    First passage time;    Nucleation and growth;    Electrodeposition;    Discrete Laplacian;   

DOI  :  10.1016/j.jcp.2013.08.053

来源: Elsevier

【 摘 要 】

We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096 x 4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free