Boltzmann equation for a granular capped rectangle in a thermalized bath of hard disks.
By using the Boltzmann approach, we study the steady-state dynamics of a granular capped rectangle placed in a two-dimensional bath of thermalized hard disks. Hard core collisions are assumed elastic between disks and inelastic between the capped rectangle and the disks, with a normal coefficient of restitution alpha < 1. Assuming a Gaussian ansatz for the probability distribution functions, we obtain analytical expressions for the granular temperatures. We show the absence of equipartition and investigate both the role of the anisotropy of the capped rectangle and of the relative ratio of the bath particles to the linear sizes of the capped rectangle. In addition, we investigate a model of a capped rectangle with two normal coefficients of restitution for collisions along the straight and curved surfaces of the capped rectangle. In this case one observes equipartition for a nontrivial ratio of the normal coefficient of restitutions.
Gomart
H
H
Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France.
Talbot
J
J
Viot
P
P