1999/09/01 by Eric Brunet, Bernard Derrida · 50 citations
Mathematics · Physics and Astronomy · #Cutoff #Exact solutions in general relativity #Length scale #Logarithm #Scale (ratio) #Simple (philosophy) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Traveling wave #Wave equation #cond-mat #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/s0010-4655(99)00358-6
published in Computer Physics Communications 121-122, 376-381 (Elsevier BV) · 11 pages, 3 figures
openalex publication_date 1999/09/01 · arxiv created 2000/05/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.