SHIFT IN THE VELOCITY OF A FRONT DUE TO A CUTOFF

We consider the effect of a small cutoff epsilon on the velocity of a traveling wave in one dimension. Simulations done over more than ten o rders of magnitude as well as a simple theoretical argument indicate t hat the effect of the cutoff epsilon is to select a single velocity th at converges when epsilon-->0 to the one predicted by the marginal sta bility argument. For small epsilon, the shift in velocity has the form K(ln epsilon)(-2) and our prediction for the constant K agrees very w ell with the results of our simulations. A very similar logarithmic sh ift appears in more complicated situations, in particular in finite-si ze effects of some microscopic stochastic systems. Our theoretical app roach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or simi lar equations.