Microscopic models of traveling wave equations

Details Microscopic models of traveling wave equations Microscopic models of traveling wave equations

2000-05-22

arxiv.org/abs/cond-mat/0005364v1

Computer Physics Communications 121--122 (1999), 376-381

Physics

Condensed Matter

11 pages, 3 figures

Scientific paper

10.1016/S0010-4655(99)00358-6

Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov-Petrovsky-Piscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. By simulating systems of size up to N=10^(16) particles at the microscopic scale, where particles react and diffuse according to some stochastic rules, we show that a single velocity is selected for the front. This velocity converges logarithmically to the solution of the F-KPP equation with minimal velocity when the number N of particles increases. A simple calculation of the effect introduced by the cutoff due to the microscopic scale allows one to understand the origin of the logarithmic correction.

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