Journal of Statistical Physics

, Volume 103, Issue 1–2, pp 269–282 | Cite as

Effect of Microscopic Noise on Front Propagation

  • Éric Brunet
  • Bernard Derrida


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=10150, we measure the N dependence of the diffusion constant DN of the front and the shift of its velocity vN. Our results indicate that DN∼(log N)−3. They also confirm our recent claim that the shift of velocity scales like vmin−vN≃K(log N)−2 and indicate that the numerical value of K is very close to the analytical expression Kapprox obtained in our previous work using a simple cut-off approximation.

diffusion-reaction equation wave-front microscopic stochastic systems 


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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Éric Brunet
    • 1
  • Bernard Derrida
    • 1
  1. 1.Laboratoire de Physique StatistiqueÉcole Normale SupérieureParis Cédex 05France

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