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
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Cited by in corpus (6)
- Stability analysis of the homogeneous hydrodynamics of a model for a confined granular gas
- Lattice models for granular-like velocity fields: Hydrodynamic limit
- Energy fluctuations in a randomly driven granular fluid
- Dynamics of Annihilation II: Fluctuations of Global Quantities
- A Kac model for kinetic annihilation
- Fluctuations in the Uniform Shear Flow state of a granular gas