Hydrodynamics of probabilistic ballistic annihilation

Abstract

We consider a dilute gas of hard spheres in dimension $d\ge 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic energy are conserved quantities. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse grained description (density, momentum and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.

19 pages, 3 eps figures included

References in corpus (16)

• Randomly Driven Granular Fluids: large scale structure
• The Inelastic Maxwell Model
• Close-packed floating clusters: granular hydrodynamics beyond the freezing point?
• Transport coefficients of a heated granular gas
• Hydrodynamic theory for granular gases
• Transport coefficients of d-dimensional inelastic Maxwell models
• Shear viscosity for a moderately dense granular binary mixture
• Stochastic Ballistic Annihilation and Coalescence
• Ballistic Annihilation
• Kinetics and scaling in ballistic annihilation
• Dynamics of ballistic annihilation
• On the validity of the Boltzmann equation to describe low density granular systems
• Search for universality in one-dimensional ballistic annihilation kinetics
• Probabilistic ballistic annihilation with continuous velocity distributions
• Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
• Some exact results for Boltzmann's annihilation dynamics

Cited by in corpus (7)

• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description
• Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics
• Dynamics of Annihilation II: Fluctuations of Global Quantities
• Kinetic description of a Rayleigh Gas with annihilation
• A Kac model for kinetic annihilation
• Existence of self-similar profile for a kinetic annihilation model