Catastrophe in diffusion-controlled annihilation dynamics: from formation to universal explosion

Death of an A -particle island in the B -particle sea: propagation and evolution of the reaction front A+B<-->C

We present a systematic theory of propagation and evolution of the reaction front A+B<-->C in the reaction-diffusion system where an island of particles A is surrounded by the uniform sea of particles B . In the first part of the work we give a systematic analysis of the crossover from the irreversible to reversible regime of front propagation in terms of the quasistatic approximation (QSA) and derive the key condition for the island death in the quasiequilibrium front regime. We show that the same as in the case of pure annihilation A+B-->0 the QSA enables the description of the quasiequilibrium front propagation only to a critical point t{c} on approaching to which the QSA is violated. In the second part of the work under the assumption of a sufficiently large forward reaction constant k we derive the perturbative expansion in powers of 1k which gives the asymptotically exact description of the quasiequilibrium front evolution up to t-->infinity. We demonstrate that below some critical value of the reduced backward reaction constant g<g{c} there appear two turning points on the front trajectory, the first of which arises at the sharp localized front stage and is due to the finite number of island particles whereas the second is a consequence of radical transformation of the front structure at the passage through the critical point (delocalization of the front). We find a remarkable property of self-similarity of the passage through the critical point, we derive scaling laws for such passage and show that in the limit g-->0 these laws lead to a striking phenomenon of an abrupt delocalization of the front.

Diffusion-controlled death of A -particle and B -particle islands at propagation of the sharp annihilation front A+B-->0

We consider the problem of diffusion-controlled evolution of the A -particle-island- B -particle-island system at propagation of the sharp annihilation front A+B-->0 . We show that this general problem, which includes as particular cases the sea-sea and island-sea problems, demonstrates rich dynamical behavior from self-accelerating collapse of one of the islands to synchronous exponential relaxation of both islands. We find a universal asymptotic regime of the sharp-front propagation and reveal the limits of its applicability for the cases of mean-field and fluctuation fronts.