When push comes to shove: Exclusion processes with nonlocal consequences
Axel A Almet, Michael Pan, Barry D Hughes, Kerry A Landman
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | ELSEVIER | Published : 2015
Abstract Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, whi..View full abstract
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Awarded by Australian Research Council
This work was supported by the Australian Research Council (DP1110100795 and DP140100339) and an Australian Mathematical Sciences Institute student vacation scholarship (A.A. Almet). We thank an anonymous reviewer for alerting us to the manuscript .