Effect of microscopic noise on front propagation
type: Item
instance of: scholarly article
title: Effect of microscopic noise on front propagation
zbMATH Open document ID: 1018.82020
DOI: 10.1023/A:1004875804376
author: Éric Brunet
author: Bernard Derrida
published in: Journal of Statistical Physics
publication date: 2001-08-28T00:00:00Z
review text: We study the effect of the noise due to microscopic fluctuations on the position of a one-dimensional front propagating from a stable to an unstable region in the ``linearly marginal stability case''. By simulating a very simple system for which the effective number \(N\) of particles can be as large as \(N=10^{150}\), we measure the \(N\) dependence of the diffusion constant \(D_N\) of the front and the shift of its velocity \(v_N\). Our results indicate that \(D_N\sim (\log N)^{-3}\). They also confirm our recent claim that the shift of velocity scales like \(v_{\min}- v_N\simeq K(\log N)^{-2}\) and indicate that the numerical value of \(K\) is very close to the analytical expression \(K_{\text{approx}}\) obtained in our previous work using a simple cut-off approximation.
Mathematics Subject Classification ID: 82C80
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1638120
zbMATH Keywords: diffusion-reaction equation
zbMATH Keywords: wave-front
zbMATH Keywords: microscopic stochastic systems
zbMATH Keywords: noise
zbMATH Keywords: microscopic fluctuations
MaRDI profile type: Publication
full work available at URL: a:1004875804376
OpenAlex ID: W14972457
description: scientific article; zbMATH DE number 1638120