Subdiffusive fluctuations of "pulled" fronts with multiplicative noise

Details Subdiffusive fluctuations of "pulled" fronts with multiplicative noise Subdiffusive fluctuations of "pulled" fronts with multiplicative noise

2000-04-06

arxiv.org/abs/cond-mat/0004102v2

Phys. Rev. E 62 (2000) R13-R16

Physics

Condensed Matter

4 pages, 1 figure. Final version with minor changes

Scientific paper

10.1103/PhysRevE.62.R13

We study the propagation of a ``pulled'' front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently large $t$ creates a diffusive wandering of the front position about its mean, we predict that for so-called pulled fronts, the fluctuations are subdiffusive with root mean square wandering $\Delta(t) \sim t^{1/4}$, {\em not} $t^{1/2}$. The subdiffusive behavior is confirmed by numerical simulations: For $t \le 600$, these yield an effective exponent slightly larger than 1/4.

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