Self-similar evolution of the A-island-B-island system at diffusion-controlled propagation of the sharp annihilation front: exact asymptotic solution for arbitrary species diffusivities.
We consider the problem of 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 present an exact asymptotic solution of this problem for the general case of an arbitrary ratio of species diffusivities D. This elegant analytic solution describes self-similar evolution of the island-island system at equal particle numbers of A and B species that decay by the law N∝t(-β(D)) with a nonuniversal exponent β(D), which is determined by a self-consistent condition of the front velocity selection and varies from β(D→0)∝D(-1/2)→∞ to β(D→∞)=1/2. In the quasistatic approximation, we derive nontrivial laws of the front width growth, which define the applicability limits of the presented solution for the cases of mean field and fluctuation fronts.
Shipilevsky
Boris M
BM
Institute of Solid State Physics, Chernogolovka, Moscow District 142432, Russia.
D001704:Biopolymers / Q000737:chemistry*; D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical
D001704:Biopolymers