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

Complex dynamics of interacting fronts in a simple A+B→C reaction-diffusion system

Pattern interaction has so far been restricted to systems with relatively complex reaction schemes, such as activator-inhibitor systems, that lead to rich spatio-temporal dynamics. Surprisingly, a simple second-order chemical reaction is capable of generating similar complex phenomena, such as attractive or repulsive interaction modes between the localized reaction zones (or fronts). We illustrate the latter statement both analytically and numerically with two initially separated A+B→C reaction-diffusion fronts when the solution of B is initially confined between two solutions of A. The nature of the front-front interaction changes from an attractive type to a repulsive one above a critical distance separating the two fronts initially. The complexity of the pattern dynamics emerges here due to finite-size effects. A scaling law relating the critical distance d_{c} above which the repulsion occurs and kinetic parameters gives insights into (i) extracting those parameters from experiments for bimolecular reactions and (ii) the control strategy of periodic patterns.

Evolution of the A-particle island-B-particle island system at propagation of the sharp annihilation front A+B-->0

We consider diffusion-controlled evolution of the A-particle island-B-particle island system in a semi-infinite medium at propagation of the sharp annihilation front A+B-->0. We show that depending on the initial particle number ratio, the system demonstrates three asymptotic regimes: self-accelerating collapse of one of the islands, synchronous power-law relaxation of both islands, and exponential death of one of the islands at a constant velocity of front propagation. We find asymptotic scaling laws of evolution in these regimes and reveal the limits of their applicability for the cases of mean field and fluctuation fronts.