skip to main content

Title: A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes

Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracymore » of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.« less
Authors:
 [1] ; ;  [2] ;  [3] ;  [1]
  1. Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215 (United States)
  2. Department of Mathematics, University of California, Santa Barbara (United States)
  3. 6712 South Hall, Department of Mathematics, University of California, Santa Barbara, CA 93106 (United States)
Publication Date:
OSTI Identifier:
22230872
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 259; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; APPROXIMATIONS; DIFFUSION; DIFFUSION EQUATIONS; GRAPH THEORY; MOLECULES; MONTE CARLO METHOD; POTENTIALS; REACTION KINETICS; STOCHASTIC PROCESSES; TWO-BODY PROBLEM