Energy and number of collisions fluctuations in inelastic gases

TL;DR

This paper investigates how inelastic collisions and collision number fluctuations in a 2D Inelastic Maxwell Model cause power-law energy fluctuations, influencing the velocity distribution tail over time.

Contribution

It reveals the asymptotic scaling of energy fluctuations and their impact on velocity distribution tails in inelastic gases.

Findings

Energy fluctuations decay as a power-law.

Fluctuations lead to a shrinking of phase space.

Velocity distribution tails are affected during long times.

Abstract

We study by numerical simulations the two-dimensional Inelastic Maxwell Model (IMM), and show how the inelasticity of collisions together with the fluctuations of the number of collisions undergone by a particle lead to energy fluctuations that decay like a power-law. These fluctuations are associated to a shrinking of the available phase space. We find the asymptotic scaling of these energy fluctuations and show how they affect the tail of the velocity distribution during long time intervals.