Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts

Abstract

We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to \infty$, $D_f$ approaches zero as $1/{\ln }^{3}N$, where $N$ is the average number of particles per correlation volume in the stable phase of the front. This behaviour of $D_f$ stems from the shape fluctuations at the very tip of the front, and is independent of the microscopic model.

Some minor algebra corrected, to appear in Rapid Comm., Phys. Rev. E

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