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Microscopic models of traveling wave equations

Authors
  • Brunet, Eric
  • Derrida, Bernard
Type
Published Article
Publication Date
May 22, 2000
Submission Date
May 22, 2000
Identifiers
DOI: 10.1016/S0010-4655(99)00358-6
arXiv ID: cond-mat/0005364
Source
arXiv
License
Unknown
External links

Abstract

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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