On high energy tails in inelastic gases

TL;DR

This paper investigates how high energy tails form in a one-dimensional inelastic gas model, revealing that continuous time dynamics lead to larger energy fluctuations and tail formation, supported by simulations and analytical methods.

Contribution

It introduces a time-discretized stochastic process for the Inelastic Maxwell Model, demonstrating the impact of continuous time on energy fluctuations and tail formation.

Findings

Continuous time results in larger energy fluctuations.

High energy tails are linked to the number of inelastic collisions.

Analytical and simulation results confirm the tail formation mechanism.

Abstract

We study the formation of high energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time- discretized version of the stochastic process, and show that continuous time implies larger fluctuations of the particles energies. This is due to a statistical relation between the number of inelastic collisions undergone by a particle and its average energy. This feature is responsible for the high energy tails in the model, as shown by computer simulations and by analytical calculations on a linear Lorentz model.