2010/04/27 by J. Javier Brey, J. J. Brey, M. I. García de Soria +2 · 22 citations
Engineering · Mathematics · Physics and Astronomy · #Boltzmann equation #Classical mechanics #Eigenfunction #Eigenvalues and eigenvectors #Gas Dynamics and Kinetic Theory #Granular flow and fluidized beds #Homogeneous #Inelastic collision #Kinetic energy #Kinetic theory #Maxwell–Boltzmann distribution #Mechanics #Particle Dynamics in Fluid Flows #Physics #Plasma #Quantum mechanics #Statistical physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.82.021303
published in Physical Review E 82(2), 021303 (American Physical Society) · Submitted to PRL (13/04/10)
arxiv created 2010/04/27 · openalex publication_date 2010/08/18 · arxiv updated 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Both the right and left eigenfunctions and eigenvalues of the linearized homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to the hydrodynamic modes are calculated. Also, some nonhydrodynamic modes are identified. It is shown that below a critical value of the parameter characterizing the inelasticity, one of the kinetic modes decays slower than one of the hydrodynamic ones. As a consequence, a closed hydrodynamic description does not exist in that regime. Some implications of this behavior on the formally computed Navier-Stokes transport coefficients are discussed.