A method for choosing the computational cell in stochastic reaction-diffusion systems

Hye-Won Kang
Mathematical Biosciences Institute, The Ohio State University

(September 29, 2011 10:30 AM - 11:30 AM)

A method for choosing the computational cell in stochastic reaction-diffusion systems

Abstract

In this talk, I will discuss how to discretize space in the stochastic model for chemical reaction-diffusion networks based on the chemical master equation. A system with reaction and diffusion is modeled using a continuous time Markov jump process. Diffusion is described as a jump to the neighboring computational cell with proper spatial discretization. Considering the steady-state mean and variance of the number of molecules of each species in each computational cell, an upper bound for the computational cell size for spatial discretization will be suggested. Then, I will show conditions for the exponential convergence of concentration to its uniform solution in the corresponding PDE model for chemical reaction-diffusion networks. Conditions obtained from the PDE model give an estimate for the maximal compartment size for space discretization in the stochastic model. This is a joint work with Hans G. Othmer and Likun Zheng at the University of Minnesota.