Precollisional velocity correlations in a hard-disk fluid with dissipative collisions.

Velocity correlations are studied in granular fluids, modeled by the inelastic hard sphere gas. Making a density expansion of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the evolution of the reduced distributions, we predict the presence of precollisional velocity correlations. They are created by the propagation through correlated sequences of collisions (ring events) of the velocity correlations generated after dissipative collisions. The correlations have their origin in the dissipative character of collisions, being always present in granular fluids. The correlations, that manifest microscopically as an alignment of the velocities of a colliding pair produce modifications of collisional averages, in particular, the virial pressure. The pressure shows a reduction with respect to the elastic case as a consequence of the velocity alignment. Good qualitative agreement is obtained for the comparison of the numerical evaluations of the obtained analytical expressions and molecular dynamics results that showed evidence of precollisional velocity correlations [R. Soto and M. Mareschal, Phys. Rev. E 63, 041303 (2001)].