Two-Scale Annihilation

Abstract

The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ 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 $n^{\mathrm{th}}$ neighbor 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.

revtex, 5 pages, 5 figures, also available from http://arnold.uchicago.edu/~ebn

References in corpus (2)

• Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions
• Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas

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