Fronts with a Growth Cutoff but Speed Higher than $v^{\ast }$

Abstract

Fronts, propagating into an unstable state $\varphi =0$, whose asymptotic speed $v_{\text{as}}$ is equal to the linear spreading speed $v^{\ast }$ of infinitesimal perturbations about that state (so-called pulled fronts) are very sensitive to changes in the growth rate $f(\varphi )$ for $\varphi \ll 1$. It was recently found that with a small cutoff, $f(\varphi )=0$ for $\varphi <\epsilon$, $v_{\text{as}}$ converges to $v^{\ast }$ very slowly from below, as ${\ln }^{-2}\epsilon$. Here we show that with such a cutoff {\em and} a small enhancement of the growth rate for small $\varphi$ behind it, one can have $v_{\text{as}}>v^{\ast }$, {\em even} in the limit $\epsilon \to 0$. The effect is confirmed in a stochastic lattice model simulation where the growth rules for a few particles per site are accordingly modified.

4 pages, 4 figures, to appear in Rapid Comm., Phys. Rev. E

References in corpus (1)

• The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff

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