Kinetics of Aggregation-Annihilation Processes

TL;DR

This paper studies the complex kinetics of systems where similar clusters merge and opposite clusters annihilate, revealing new behaviors, exact solutions, and scaling laws supported by simulations across multiple dimensions.

Contribution

It provides an exact mean-field solution for the cluster-mass distribution in aggregation-annihilation systems and explores their asymptotic behaviors and scaling laws.

Findings

Exact mean-field solution for cluster-mass distribution.

Novel scaling form for equal initial densities.

Dimension-dependent growth exponents in 1D.

Abstract

We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors and unusual conservation laws. On the mean-field level, an exact solution for the cluster-mass distribution is obtained. Asymptotically, this solution exhibits a novel scaling form if the initial species densities are the same while in the general case of unequal densities the process approaches single species aggregation. The theoretical predictions are compared with numerical simulations in 1D, 2D, and 3D. Nontrivial growth exponents characterize the mass distribution in one dimension.