Probabilistic ballistic annihilation with continuous velocity distributions
Abstract
We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability p, or undergo an elastic shock with probability 1p. Restricting to homogeneous systems, we provide in the scaling regime that emerges in the long time limit, analytical expressions for the exponents describing the time decay of the density and the rootmeansquare velocity, as continuous functions of the probability p and of a parameter related to the dissipation of energy. We work at the level of molecular chaos (nonlinear Boltzmann equation), and using a systematic Sonine polynomials expansion of the velocity distribution, we obtain in arbitrary dimension the first nonGaussian correction and the corresponding expressions for the decay exponents. We implement Monte Carlo simulations in two dimensions, which are in excellent agreement with our analytical predictions. For p<1, numerical simulations lead to the conjecture that unlike for pure annihilation (p=1), the velocity distribution becomes universal, i.e., does not depend on the initial conditions.
 Publication:

Physical Review E
 Pub Date:
 January 2004
 DOI:
 10.1103/PhysRevE.69.011303
 arXiv:
 arXiv:condmat/0309098
 Bibcode:
 2004PhRvE..69a1303C
 Keywords:

 45.05.+x;
 05.20.Dd;
 82.20.Nk;
 General theory of classical mechanics of discrete systems;
 Kinetic theory;
 Classical theories of reactions and/or energy transfer;
 Condensed Matter  Statistical Mechanics
 EPrint:
 10 pages, 9 eps figures included