Truncated Levy distributions in an inelastic gas

TL;DR

This paper investigates a one-dimensional granular gas model, demonstrating the existence of stationary states with infinite energy and showing that truncated Levy distributions describe particle velocities.

Contribution

It provides a theoretical proof of stationary solutions with infinite energy and confirms their quasi-stationary nature through numerical simulations using finite particles.

Findings

Stationary solutions characterized by infinite average energy exist.

Numerical simulations with finite particles show truncated Levy velocity distributions.

Quasi-stationary states are observed in the model.

Abstract

We study a one-dimensional model for granular gases, the so-called Inelastic Maxwell Model. We show theoretically the existence of stationary solutions of the unforced case, that are characterized by an infinite average energy per particle. Moreover, we verify the quasi-stationarity of these states by performing numerical simulations with a finite number of particles, thereby highlighting truncated L\'evy distributions for the velocities.