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Power-law velocity distributions in granular gases

E. Ben-Naim·B. Machta·J. Machta
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Abstract

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.

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E. Ben-Naim, B. Machta, J. Machta. 2005-04-07. Power-law velocity distributions in granular gases. https://doi.org/10.1103/physreve.72.021302

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