Two scales in asynchronous ballistic annihilation

The kinetics of single-species annihilation, A + A -> 0, is investigated in which each particle has a fixed velocity which may be either +/-upsilon with equal probability, and a finite diffusivity. In one dimension, the interplay between convection and diffusion leads to a decay of the density which is proportional to t(-3/4). At long times, the reactants organize into domains of right- and left-moving particles, with the typical distance between particles in a single domain growing as t(3/4), and the distance between domains growing as t. The probability that an arbitrary particle reacts with its nth neighbour is found to decay as n(-5/2) for same-velocity pairs and as n(-7/4) for +- pairs. These kinetic and spatial exponents and their interrelations are obtained by scaling arguments. Our predictions are in excellent agreement with numerical simulations.