2002/02/20 by E. Ben-Naim, E. Ben‐Naim, P. L. Krapivsky · 6 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Granular flow and fluidized beds #Particle Dynamics in Fluid Flows #cond-mat.soft #cond-mat.stat-mech #nlin.CG
paper · pdf · doi:10.1103/physreve.66.011309
published as Phys. Rev. E 66, 011309 (2002) · 10 pages, 3 figures
arxiv created 2002/02/20 · openalex publication_date 2002/07/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the velocity distribution is characterized by an algebraic large-velocity tail, P(v,t) approximately v(-sigma). The exponent sigma(d,epsilon), a nontrivial root of an integral equation, varies continuously with the spatial dimension d and the dissipation coefficient epsilon. Although the velocity distribution follows a scaling form, its moments exhibit multiscaling asymptotic behavior. Furthermore, the velocity autocorrelation function decays algebraically with time, A(t)=<v(0).v(t)> approximately t(-alpha), with a nonuniversal dissipation-dependent exponent alpha=1/epsilon. In the forced case, the steady state Fourier transform is obtained via a cumulant expansion. Even in this case, velocity correlations develop and the velocity distribution is non-Maxwellian.