Kinetic Integrals in the Kinetic Theory of dissipative gases

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.Comment: 32 page

Rolling as a continuing collision

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles \epsilon, which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient \mu_{roll} for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allow to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction