Abstract
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.
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Brunet, É., Derrida, B. Effect of Microscopic Noise on Front Propagation. Journal of Statistical Physics 103, 269–282 (2001). https://doi.org/10.1023/A:1004875804376
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DOI: https://doi.org/10.1023/A:1004875804376