Hard Sphere Dynamics for Normal and Granular Fluids

Details Hard Sphere Dynamics for Normal and Granular Fluids Hard Sphere Dynamics for Normal and Granular Fluids

2005-03-08

arxiv.org/abs/cond-mat/0503180v1

Physics

Condensed Matter

Soft Condensed Matter

Submitted for publication in the Proceedings of Workshop on Nonlinear Dynamics in Astronomy and Physics, eds. S. Gottesmann an

Scientific paper

10.1196/annals.1350.009

A fluid of N smooth, hard spheres is considered as a model for normal (elastic collisions) and granular (inelastic collisions) fluids. The potential energy is discontinuous for hard spheres so the pairwise forces are singular and the usual forms of Newtonian and Hamiltonian mechanics do not apply. Nevertheless, particle trajectories in the N particle phase space are well defined and the generators for these trajectories can be identified. The first part of this presentation is a review of the generators for the dynamics of observables and probability densities. The new results presented in the second part refer to applications of these generators to the Liouville dynamics for granular fluids. A set of eigenvalues and eigenfunctions of the generator for this Liouville dynamics is identified in a special "stationary representation". This provides a class of exact solutions to the Liouville equation that are closely related to hydrodynamics for granular fluids.

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