Asymptotic behavior of the velocity distribution of driven inelastic gas with scalar velocities: analytical results

Abstract

We determine the asymptotic behavior of the tails of the steady state velocity distribution of a homogeneously driven granular gas comprising of particles having a scalar velocity. A pair of particles undergo binary inelastic collisions at a rate that is proportional to a power of their relative velocity. At constant rate, each particle is driven by multiplying its velocity by a factor $-r_w$ and adding a stochastic noise. When $r_w<1$, we show analytically that the tails of the velocity distribution are primarily determined by the noise statistics, and determine analytically all the parameters characterizing the velocity distribution in terms of the parameters characterizing the stochastic noise. Surprisingly, we find logarithmic corrections to the leading stretched exponential behavior. When $r_w=1$, we show that for a range of distributions of the noise, inter-particle collisions lead to a universal tail for the velocity distribution.

arXiv comment27 pages, 5 figures. J Stat Phys (2019)

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Cited by in corpus (5)

• Mpemba effect in driven granular Maxwell gases
• Mpemba effect in anisotropically driven inelastic Maxwell gases
• High-energy velocity tails in uniformly heated granular materials
• Asymptotic velocity distribution of a driven one dimensional binary granular Maxwell gas
• Mean-squared displacements of rough particles in polydisperse granular gases