Shift in the velocity of a front due to a cut-off

Details Shift in the velocity of a front due to a cut-off Shift in the velocity of a front due to a cut-off

2000-05-22

arxiv.org/abs/cond-mat/0005362v1

Physical Review E 57 (1997) 2597-2604

Physics

Condensed Matter

12 pages, 3 figures

Scientific paper

10.1103/PhysRevE.56.2597

We consider the effect of a small cut-off epsilon on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cut-off epsilon is to select a single velocity which converges when epsilon tends to 0 to the one predicted by the marginal stability argument. For small epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.

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