Fronts with a Growth Cutoff but Speed Higher than $v^*$

Details Fronts with a Growth Cutoff but Speed Higher than $v^*$ Fronts with a Growth Cutoff but Speed Higher than $v^*$

2002-04-05

arxiv.org/abs/cond-mat/0204131v3

Phys. Rev. E 66, 015206(R) (2002)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.66.015206

Fronts, propagating into an unstable state $\phi=0$, whose asymptotic speed $v_{\text{as}}$ is equal to the linear spreading speed $v^*$ of infinitesimal perturbations about that state (so-called pulled fronts) are very sensitive to changes in the growth rate $f(\phi)$ for $\phi \ll 1$. It was recently found that with a small cutoff, $f(\phi)=0$ for $\phi < \epsilon$, $v_{\text{as}}$ converges to $v^*$ 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 $\phi$ behind it, one can have $v_{\text{as}} > v^*$, {\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.

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