  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.
