Annihilation Catastrophe: From Formation to Universal Explosion

TL;DR

This paper analyzes the universal annihilation catastrophe in an open diffusion system, revealing how surface concentrations explode and lead to abrupt flux jumps, with key dependencies on initial conditions and universality conditions.

Contribution

It provides a systematic analysis of the formation and characteristics of the universal annihilation catastrophe, including conditions for universality and detailed dependence on initial parameters.

Findings

Dependence of catastrophe time and amplitude on initial particle number

Identification of conditions for universality in the annihilation process

Characterization of the explosive growth of surface concentrations

Abstract

I present a systematic analysis of formation of the universal annihilation catastrophe which develops in an open system, where species $A$ and $B$ diffuse from the bulk of restricted medium and die on its surface (desorb) by the reaction $A + B \to 0$. This phenomenon arises in the diffusion-controlled limit as a result of self-organizing explosive growth (drop) of the surface concentrations of, respectively, slow and fast particles ({\it concentration explosion}) and manifests itself in the form of an abrupt singular jump of the desorption flux relaxation rate. As striking results I find the dependences of time and amplitude of the catastrophe on the initial particle number, and answer the basic questions of when and how universality is achieved.