Kinetic Integrals in the Kinetic Theory of dissipative gases

TL;DR

This paper introduces a computer algebra-based method for analytically evaluating kinetic integrals in the kinetic theory of dissipative gases, enabling the computation of properties like velocity moments and transport coefficients that are otherwise difficult to calculate manually.

Contribution

A novel analytical method using computer algebra for evaluating kinetic integrals in granular gases, simplifying complex calculations.

Findings

Computed velocity distribution moments for granular gases

Derived transport coefficients analytically

Demonstrated the method's effectiveness for complex integrals

Abstract

The kinetic theory of gases, including Granular Gases, is based on the Boltzmann equation. Many properties of the gas, from the characteristics of the velocity distribution function to the transport coefficients may be expressed in terms of functions of the collision integral which we call kinetic integrals. Although the evaluation of these functions is conceptually straightforward, technically it is frequently rather cumbersome. We report here a method for the analytical evaluation of kinetic integrals using computer algebra. We apply this method for the computation of some properties of Granular Gases, ranging from the moments of the velocity distribution function to the transport coefficients. For their technical complexity most of these quantities cannot be computed manually.