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arXiv · 1207.6135

Reaction-Diffusion Processes with Nonlinear Diffusion

P. L. Krapivsky
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Abstract

We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two natural inhomogeneous realizations. The two-species annihilation process is investigated in the situation when the reactants are initially separated, namely each species occupies a half space. In particular, we determine the growth law of the width of the reaction zone. The single-species annihilation process is studied in the situation when the spatially localized source drives the system toward the non-equilibrium steady state. Finally we investigate a dissolution process with a localized source of diffusing atoms which react with initially present immobile atoms forming immobile molecules.

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P. L. Krapivsky. 2012-10-29. Reaction-Diffusion Processes with Nonlinear Diffusion. https://doi.org/10.1103/physreve.86.041113

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