Catastrophe in diffusion-controlled annihilation dynamics: from formation to universal explosion.
We present a systematic theory of formation of the universal annihilation catastrophe which develops in an open system where species A and B diffuse from the bulk of a restricted medium and die on its surface (desorb) by the reaction A+B-->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 (concentration explosion), and manifests itself in the form of an abrupt singular jump of the desorption flux relaxation rate. As striking results we 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.
Shipilevsky
Boris M
BM
Institute of Solid State Physics, Chernogolovka, Moscow district, 142432, Russia.