Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics
arXiv:0801.2299 · doi:10.1103/PhysRevE.77.051127
Abstract
We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\em ballistic annihilation} therefore constantly looses particles. The dynamics of perturbations around the free decay regime is investigated from the spectral properties of the linearized Boltzmann operator, that characterize linear excitations on all time scales. The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients. We finally present the results of Molecular Dynamics simulations that validate the theoretical predictions.
22 pages
References in corpus (5)
- Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
- Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
- First-order Chapman--Enskog velocity distribution function in a granular gas
- Probabilistic ballistic annihilation with continuous velocity distributions
- Hydrodynamics of probabilistic ballistic annihilation