2005/03/04 by Francois Coppex, François Coppex, Michel Droz +1
Engineering · Materials Science · Physics and Astronomy · #Granular flow and fluidized beds #Material Dynamics and Properties #Particle Dynamics in Fluid Flows #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.021105
published as Phys. Rev. E 72, 021105 (2005) · 24 pages, 10 eps figures included
arxiv created 2005/03/04 · openalex publication_date 2005/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard spherelike dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very-hard-particle (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against direct Monte Carlo simulations. Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.