On the first Sonine correction for granular gases

TL;DR

This paper introduces a new method to accurately compute the first Sonine correction to the velocity distribution in granular gases, validated against numerical solutions and previous results, with implications for understanding non-Gaussian behavior.

Contribution

A novel approach for calculating the first Sonine correction in granular gases, improving accuracy over existing methods and analyzing linear approximation ambiguities.

Findings

The new method provides highly accurate results for small velocities.

Comparison shows consistency with previous analytical and numerical results.

Discussion of limitations in linear approximation methods for $a_2$.

Abstract

We consider the velocity distribution for a granular gas of inelastic hard spheres described by the Boltzmann equation. We investigate both the free of forcing case and a system heated by a stochastic force. We propose a new method to compute the first correction to Gaussian behavior in a Sonine polynomial expansion quantified by the fourth cumulant $a_2$. Our expressions are compared to previous results and to those obtained through the numerical solution of the Boltzmann equation. It is numerically shown that our method yields very accurate results for small velocities of the rescaled distribution. We finally discuss the ambiguities inherent to a linear approximation method in $a_2$.