Nonlinear diffusion and exclusion processes with contact interactions
Anthony E Fernando, Kerry A Landman, Matthew J Simpson
Physical Review E | AMER PHYSICAL SOC | Published : 2010
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 go..View full abstract
This work is supported by the Australian Research Council (ARC). Kerry Landman and Matthew Simpson thank the ARC. We thank Barry Hughes for helpful discussions and feedback.