Exact Solutions of Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

Abstract

We report exact results for one-dimensional reaction-diffusion models A+A -> inert, A+A -> A, and A+B -> inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasized anisotropy of hopping rates; no changes in universal properties were found, due to anisotropy, in all three reactions. The method of solution employed mapping onto a model of coagulating positive integer charges. The dynamical rules were synchronous, cellular-automaton type. All the asymptotic large-time results for particle densities were consistent, in the framework of universality, with other model results with different dynamical rules, when available in the literature.

28 pages in plain TeX + 2 PostScript figures

References in corpus (4)

• Exact Results for Diffusion-Limited Reactions with Synchronous Dynamics
• Model of Cluster Growth and Phase Separation: Exact Results in One Dimension
• Fast-diffusion mean-field theory for k-body reactions in one dimension
• Discrete to Continuous-Time Crossover due to Anisotropy in Diffusion-Limited Two-Particle Annihilation Reactions

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