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

TL;DR

This paper provides exact solutions for one-dimensional anisotropic reaction-diffusion models involving coagulation and annihilation, demonstrating that anisotropy does not alter universal properties.

Contribution

It introduces a method of solving these models via mapping onto coagulating positive integer charges with synchronous cellular automaton dynamics.

Findings

Anisotropy does not affect universal properties of the models.

Exact large-time asymptotic particle densities are obtained.

Results are consistent with other models despite different dynamical rules.

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.