Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-02-20
Phys. Rev. E 66, 011309 (2002)
Physics
Condensed Matter
Statistical Mechanics
10 pages, 3 figures
Scientific paper
10.1103/PhysRevE.66.011309
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) ~ 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)=
Ben-Naim Eli
Krapivsky Paul. L.
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