Effect of Microscopic Noise on Front Propagation – Archive ouverte HAL

Éric BrunetBernard Derrida 1, 2

Éric Brunet, Bernard Derrida. Effect of Microscopic Noise on Front Propagation. Journal of Statistical Physics, Springer Verlag, 2001, 103 (1-2), pp.269-282. ⟨10.1023/A:1004875804376⟩. ⟨hal-03282975⟩

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.

  • 1. UPMC - Université Pierre et Marie Curie - Paris 6
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques