Annihilation Catastrophe: From Formation to Universal Explosion

Details Annihilation Catastrophe: From Formation to Universal Explosion Annihilation Catastrophe: From Formation to Universal Explosion

2005-07-14

arxiv.org/abs/cond-mat/0507323v2

Physics

Condensed Matter

Statistical Mechanics

13 pages, 8 figures, long length paper

Scientific paper

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.

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