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arXiv · 0905.1083

Fisher waves in the strong noise limit

Oskar Hallatschek·K. S. Korolev
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Abstract

We investigate the effects of strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute the wave velocity in one and two spatial dimensions, for which we find a linear and a square-root dependence of the speed on the particle density. Instead of smooth sigmoidal wave profiles, we observe fronts composed of a few rugged kinks that diffuse, annihilate, and rarely branch; this dynamics leads to power-law tails in the distribution of the front sizes.

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Oskar Hallatschek, K. S. Korolev. 2009-05-07. Fisher waves in the strong noise limit. https://doi.org/10.1103/physrevlett.103.108103

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