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

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

2003-04-16

arxiv.org/abs/cond-mat/0304371v3

Phys. Rev. E 68, 065202(R) (2003)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.68.065202

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 $1/\ln^3N$, 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.

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