Power-law velocity distributions in granular gases

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.

11 pages, 9 figures

References in corpus (4)

• Dynamics of Freely Cooling Granular Gases
• Exchange Driven Growth
• Self-Similarity in Random Collision Processes
• Stationary states and energy cascades in inelastic gases

Cited by in corpus (7)

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• The rich behavior of the Boltzmann equation for dissipative gases
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• Granular gases under extreme driving
• Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
• Application of the Gillespie algorithm to a granular intruder particle
• A Collisional-Energy-Cascade Model for Nonthermal Velocity Distributions of Neutral Atoms in Plasmas