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Nontrivial Velocity Distributions in Inelastic Gases

P. L. Krapivsky·E. Ben-Naim
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Abstract

We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In the freely evolving case, we find that the velocity distribution decays algebraically, P(v,t) ~ v^{-sigma} for sufficiently large velocities. We derive the exponent sigma(d,epsilon), which exhibits nontrivial dependence on both d and epsilon, exactly. In the forced case, the velocity distribution approaches a steady-state with a Gaussian large velocity tail.

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P. L. Krapivsky, E. Ben-Naim. 2001-11-06. Nontrivial Velocity Distributions in Inelastic Gases. https://doi.org/10.1088/0305-4470%2F35%2F11%2F103

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