Coagulation reaction in low dimensions: Revisiting subdiffusive A+A reactions in one dimension

TL;DR

This paper develops a theoretical framework for the coagulation reaction A+A -> A involving subdiffusive particles in one dimension, validated by simulations, revealing the growth of interparticle gaps and correcting previous misconceptions.

Contribution

The paper introduces a new theory for subdiffusive coagulation reactions in one dimension, accurately describing both early and asymptotic behaviors, and clarifies the role of interparticle gaps.

Findings

Theory matches numerical simulations for concentration over time.

Interparticle gaps grow with time, influencing anomalous kinetics.

Corrects previous misconceptions about the reaction dynamics.

Abstract

We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous kinetics'') and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.