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Hard Sphere Dynamics for Normal and Granular Fluids
Author(s) -
DUFTY JAMES W.,
BASKARAN APARNA
Publication year - 2005
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1196/annals.1350.009
Subject(s) - hard spheres , classical mechanics , eigenfunction , physics , eigenvalues and eigenvectors , phase space , spheres , hamiltonian mechanics , hamiltonian (control theory) , newtonian dynamics , observable , generator (circuit theory) , statistical physics , granular material , mathematics , quantum mechanics , power (physics) , mathematical optimization , astronomy
A bstract : A fluid of N smooth, hard spheres is considered as a model for normal (elastic collision) and granular (inelastic collision) fluids. The potential energy is discontinuous for hard spheres so that 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 system 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.