Effect of microscopic noise on front propagation
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.
scientific article; zbMATH DE number 1638120