Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Relevance of the Voronoi domain partition for position-jump reaction-diffusion processes on nonuniform rectilinear lattices
Christian Adam Yates

Last modified: 2014-06-09


Position-jump processes are used for the mathematical
modelling of spatially extended chemical and biological systems with
increasing frequency. A large subset of the literature concerning such
processes is concerned with modelling 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 neighbouring 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. I will demonstrate that the Voronoi domain
partition is the appropriate method with which to divide the
computational domain, under the assumption of a fixed functional form for the transition rates.
In this talk, I will investigate theoretically the propriety of the
Voronoi domain partition as an appropriate method to partition domains for position-jump models and provide simulations of diffusion processes in order to corroborate our results.