2009/03/30 by J. Javier Brey, P. Maynar, M. I. García de Soria +1 · 2 citations
Engineering · Physics and Astronomy · #Environmental science #Granular flow and fluidized beds #Heat and Mass Transfer in Porous Media #Mechanics #Particle Dynamics in Fluid Flows #Physics #Statistical physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.051305
arxiv created 2009/03/30 · openalex publication_date 2009/05/18 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white-noise term. Balance equations for the fluctuating hydrodynamic fields are derived. New fluctuating forces appear as compared with the elastic limit. The particular case of the transverse velocity field is investigated in detail. Its fluctuations can be described by means of a Langevin equation, but exhibiting two main differences with the Landau-Lifshitz theory: the noise is not white, and its second moment is not determined by the shear viscosity. This shows that the fluctuation-dissipation relations for molecular fluids do not straightforwardly carry over to inelastic gases. The theoretical predictions are shown to be in good agreement with molecular-dynamics simulation results.