Microscopic models of traveling wave equations

Reaction-diffusion problems are often described at a macroscopic scale by p artial derivative equations of the type of the Fisher or Kolmogorov-Petrovs ky-Piscounov equation. These equations have a continuous family of front so lutions, each of them corresponding to a different velocity of the front. B y 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 c onverges 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 on e to understand the origin of the logarithmic correction. (C) 1999 Publishe d by Elsevier Science B.V. All rights reserved.