Diffusion-controlled death of AA-particle and BB-particle islands at propagation of the sharp annihilation front A+B→0A + B \to 0

We consider the problem of diffusion-controlled evolution of the system $A$-particle island - $B$-particle island at propagation of the sharp annihilation front $A+B\to 0$. We show that this general problem, which includes as particular cases the sea-sea and the island-sea problems, demonstrates rich dynamical behavior from self-accelerating collapse of one of the islands to synchronous exponential relaxation of the both islands. We find a universal asymptotic regime of the sharp front propagation and reveal limits of its applicability for the cases of mean-field and fluctuation fronts.Comment: 4 revtex pages, 1 jpg figure. Submitted to Phys. Rev.

Diffusion-controlled annihilation A+B→0A + B \to 0: The growth of an AA particle island from a localized AA-source in the BB particle sea

We present the growth dynamics of an island of particles $A$ injected from a localized $A$-source into the sea of particles $B$ and dying in the course of diffusion-controlled annihilation $A+B\to 0$. We show that in the 1d case the island unlimitedly grows at any source strength $\Lambda$, and the dynamics of its growth {\it does not depend} asymptotically on the diffusivity of $B$ particles. In the 3d case the island grows only at $\Lambda > \Lambda_{c}$, achieving asymptotically a stationary state ({\it static island}). In the marginal 2d case the island unlimitedly grows at any $\Lambda$ but at $\Lambda < \Lambda_{*}$ the time of its formation becomes exponentially large. For all the cases the numbers of surviving and dying $A$ particles are calculated, and the scaling of the reaction zone is derived.Comment: 5 REVTEX pages, no figure

Diffusion-controlled annihilation A+B→0A + B \to 0 with initially separated reactants: The death of an AA particle island in the BB particle sea

We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of particles in the island is large enough, then at any system's dimensionality $d$ the death of the majority of particles occurs in the {\it universal scaling regime} within which $\approx 4/5$ of the particles die at the island expansion stage and the remaining $\approx 1/5$ at the stage of its subsequent contraction. In the quasistatic approximation the scaling of the reaction zone has been obtained for the cases of mean-field ($d \geq d_{c}$) and fluctuation ($d < d_{c}$) dynamics of the front.Comment: 4 RevTex pages, 1 PNG figure and 1 EPS figur

Catastrophe in diffusion-controlled annihilation dynamics: general scaling properties

We present a systematic analytical and numerical study of the annihilation catastrophe phenomenon 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 → 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. In the recent work [B.M. Shipilevsky, Phys. Rev. E 76, 031126 (2007)] a closed scaling theory of catastrophe development has been given for the asymptotic limit when the characteristic time scale of explosion becomes much less than the characteristic time scales of diffusion of slow and fast particles at an arbitrary ratio of their diffusivities 0 <p< 1. In this paper we consider the behavior of the system at strong difference of species diffusivities p ≪ 1 and reveal a rich general pattern of catastrophe development for an arbitrary ratio of the characteristic time scales of explosion and fast particle diffusion. As striking results we find remarkable scaling properties of catastrophe evolution at the crossover between two limiting regimes with radically different dynamics