Bruna, M. and Chapman, S. J. (2012) Diffusion of multiple species with excludedvolume effects. Journal of Chemical Physics . (Submitted)

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Abstract
Stochastic models of diffusion with excludedvolume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter species competition emerges at the population level. Each individual is described as a finitesize hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear crossdiffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excludedvolume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and selfdiffusion. Simulations of the discrete system show good agreement with the analytic results.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1645 
Deposited By:  Peter Hudston 
Deposited On:  05 Jan 2013 10:23 
Last Modified:  29 May 2015 19:20 
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