Formation of a finite-time singularity in diffusion-controlled annihilation dynamics

Abstract

I review the basic features of formation of the universal annihilationcatastrophe which develops in an open system, where speciesA and B diffuse from the bulk of a restricted medium and die on its surface (desorb) by the reaction. This phenomenon arises in the diffusion-controlled limit as a result of self-organizingexplosive growth (drop) of the surface concentrations of, respectively, slow and fastparticles (concentration explosion) and manifests itself in the form of an abruptsingular jump of the desorption flux relaxation rate. I present a systematic scalingtheory of passage through the point of singularity and demonstrate the results ofextensive numerical calculations illustrating its main features. In conclusion Idiscuss the conditions and possibilities of an experimental observation of theannihilation catastrophe and point out some prospective lines for its generalization.