2005/04/07 by E. Ben-Naim, E. Ben‐Naim, Benjamin B. Machta +2
Engineering · Materials Science · Physics and Astronomy · #Granular flow and fluidized beds #Material Dynamics and Properties #Particle Dynamics in Fluid Flows #cond-mat.soft #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1103/physreve.72.021302
published as Phys. Rev. E 72, 021302 (2005) · 11 pages, 9 figures
arxiv created 2005/04/07 · openalex publication_date 2005/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The kinetic theory of granular gases is studied for spatially homogeneous systems. At large velocities, the equation governing the velocity distribution becomes linear, and it admits stationary solutions with a power-law tail, f (v) approximately v(-sigma) . This behavior holds in arbitrary dimension for arbitrary collision rates including both hard spheres and Maxwell molecules. Numerical simulations show that driven steady states with the same power-law tail can be realized by injecting energy into the system at very high energies. In one dimension, we also obtain self-similar time-dependent solutions where the velocities collapse to zero. At small velocities there is a steady state and a power-law tail but at large velocities, the behavior is time dependent with a stretched exponential decay.