Front Propagation up a Reaction Rate Gradient

Details Front Propagation up a Reaction Rate Gradient Front Propagation up a Reaction Rate Gradient

2005-08-28

arxiv.org/abs/cond-mat/0508663v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.72.066126

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fl uctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the front velocity depe ndence on bulk particle density, showing that the velocity indeed diverge s in the infinite density limit. The form in which diffusion is impleme nted, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence.

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