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J. Schmidt, F. Spahn, O. Petzschmann (Universitaet Postsdam, Germany), Heikki Salo (University of Oulu, Finland)
We model temperature and density profiles for a dilute planetary ring, based on the hydrodynamic balance equations for momentum and energy of granular flows. Within our approximation the ring consists of inelastic smooth spheres of unique size and mass, while the fluxes of mass, momentum and energy are linear functions of the gradients of density, velocity and temperature. The phase space distribution function is an isotropic Gaussian with additive corrections that are first order in these gradients (Jenkins and Richman, Arch. Ration. Mech. Anal., 87 (1985)). The resulting system of coupled differential equations leads to temperature and density profiles, which depend on the coefficient of restitution, a measure for the inelasticity of the particle collisions, the optical depth and the shear rate. We compare the results to those of the kinetic approach to ring dynamics (Simon and Jenkins, Icarus, 110 (1994)) , where the non-isotropic nature of the ring system is taken into account by use of a triaxial Gaussian velocity distribution. Furthermore we present event driven N-particle simulations that confirm the numerical results.
The author(s) of this abstract have provided an email address for comments about the abstract: jschmidt@uni-potsdam.de