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Nonlinear diffusion and exclusion processes with contact interactions

Fernando, Anthony, Landman, Kerry A., & Simpson, Matthew (2010) Nonlinear diffusion and exclusion processes with contact interactions. Physical Review E (PRE), 81(1), 011903-1---11903-11.

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Abstract

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Impact and interest:

14 citations in Scopus
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19 citations in Web of Science®

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ID Code: 38942
Item Type: Journal Article
Additional URLs:
Keywords: Exclusion process, Nonlinear diffusion
DOI: 10.1103/PhysRevE.81.011903
ISSN: 1539-3755
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Institutes > Institute of Health and Biomedical Innovation
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2010 American Physical Society
Deposited On: 01 Dec 2010 08:04
Last Modified: 01 Mar 2012 00:28

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