Concentration for One and Two Species One-Dimensional Reaction-Diffusion Systems

TL;DR

This paper explores similarity transformations linking various one-dimensional reaction-diffusion systems, enabling the generalization of results across models, and provides numerical insights into concentration behaviors and asymptotics.

Contribution

It introduces mappings between different reaction-diffusion models, including single and two-species systems, and offers numerical analysis of concentration dynamics.

Findings

Mappings between reaction-diffusion models are established.

Numerical results detail the influence of reaction rates on concentration.

Asymptotic behavior of two-species annihilation with symmetric initial conditions is characterized.

Abstract

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The coagulation (A + A -> A) or the annihilation (A + A -> 0) models can be mapped onto systems in which both processes are allowed. With the help of the coagulation-decoagulation model results for some death-decoagulation and annihilation-creation systems are given. We also find a reaction-diffusion system which is equivalent to the two species annihilation model (A + B ->0). Besides we present numerical results of Monte Carlo simulations. An accurate description of the effects of the reaction rates on the concentration in one-species diffusion-annihilation model is made. The asymptotic behavior of the concentration in the two species annihilation system (A + B -> 0) with symmetric initial conditions is studied.