1997/09/01 by Éric Brunet-Gouet, Eric Brunet, Bernard Derrida · 6 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Combinatorics #Constant (computer programming) #Cutoff #Dimension (graph theory) #Evolution and Genetic Dynamics #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Position (finance) #Quantum mechanics #Simple (philosophy) #Stability (learning theory) #cond-mat
paper · pdf · doi:10.1103/physreve.56.2597
published as Physical Review E 57 (1997) 2597-2604 · 12 pages, 3 figures
openalex publication_date 1997/09/01 · arxiv created 2000/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the effect of a small cutoff \ensuremathε on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff \ensuremathε is to select a single velocity that converges when \ensuremathε\ensuremath→0 to the one predicted by the marginal stability argument. For small \ensuremathε, the shift in velocity has the form K(ln\ensuremathε)^\ensuremath-2 and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite-size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.