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

TL;DR

This paper analytically investigates the asymptotic tails of the steady state velocity distribution in a driven inelastic granular gas with scalar velocities, revealing the dominant role of noise statistics and universal behaviors under certain conditions.

Contribution

It provides analytical results characterizing the tail behavior of the velocity distribution in driven inelastic gases, including the effects of noise and collision parameters.

Findings

Tails are primarily determined by noise statistics when r_w<1.

Logarithmic corrections to stretched exponential tails are identified.

Universal tail behavior emerges at r_w=1 for various noise distributions.

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.