The Mathematical Institute, University of Oxford, Eprints Archive

The importance of the Voronoi domain partition for position-jump reaction-diffusion processes on non-uniform rectilinear lattices

Yates, C A and Baker, R. E. (2013) The importance of the Voronoi domain partition for position-jump reaction-diffusion processes on non-uniform rectilinear lattices. Physical Review E, 88 (5). 05471.

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Abstract

Position-jump processes are used for the mathematical modeling of spatially extended chemical and biological systems with increasing frequency. A large subset of the literature concerning such processes is concerned with modeling the effect of stochasticity on reaction-diffusion systems. Traditionally, computational domains have been divided into regular voxels. Molecules are assumed well mixed within each of these voxels and are allowed to react with other molecules within the same voxel or to jump to neighboring voxels with predefined transition rates. For a variety of reasons implementing position-jump processes on irregular grids is becoming increasingly important. However, it is not immediately clear what form an appropriate irregular partition of the domain should take if it is to allow the derivation of mean molecular concentrations that agree with a given partial differential equation for molecular concentrations. It has been demonstrated, in one dimension, that the Voronoi domain partition is the appropriate method with which to divide the computational domain. In this Brief Report, we investigate theoretically the propriety of the Voronoi domain partition as an appropriate method to partition domains for position-jump models in higher dimensions. We also provide simulations of diffusion processes in two dimensions in order to corroborate our results.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1767
Deposited By: Sara Jolliffe
Deposited On:08 Feb 2014 13:21
Last Modified:29 May 2015 19:27

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