Spatial Organization in Two-Species Annihilation

The spatial structure of reactants in the two-species annihilation reaction A + B ~ 0 is described. In one dimension, we investigate the distribution of domain sizes and the distributions of nearest-neighbor distances between particles of the same and of opposite species. The latter two quantities are characterized by a new length scale which is intermediate to the domain size t 1./2 and the typical interparticle spacing t ~/4. A scaling argument suggests that the typical distaffce between particles of opposite species, or equivalently the gaps between domains, grows as t ~, with ~ = 3/8 and 1/3, respectively, in spatial dimension d= 1 and 2. The average density profile of a single domain is spatially nonuniform, with the density decaying to zero linearly as the domain edge is approached. This behavior permits a determination of the distribution of nearest-neighbor distances of same-species reactants. The corresponding moments of this distribution exhibit multiscaling which involves geometric averages of different powers of the domain size and the interparticle spacing.