2003/12/29 by James W. Dufty, Aparna Baskaran, Lorena Zogaib · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Coal Properties and Utilization #Environmental science #Gas Dynamics and Kinetic Theory #Gaussian #Granular flow and fluidized beds #Kinetic energy #Mechanics #Physics #Quantum mechanics #Statistical physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.051301
to be submitted to Phys. Rev. E
arxiv created 2003/12/29 · openalex publication_date 2004/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal "homogeneous cooling solution" after a few collisions. The homogeneous cooling solution (HCS) is studied in some detail and the exact solution is compared with known results for the hard sphere Boltzmann equation. It is shown that all qualitative features of the HCS, including the nature of overpopulation at large velocities, are reproduced by the kinetic model. It is also shown that all the transport coefficients are in excellent agreement with those from the Boltzmann equation. Also, the model is specialized to one having a velocity independent collision frequency and the resulting HCS and transport coefficients are compared to known results for the Maxwell model. The potential of the model for the study of more complex spatially inhomogeneous states is discussed.