Abstract
We apply a simple kinetic theory for a moderately dense gas of identical, slightly dissipative spheres to a nearly homogeneous shearing flow in a planetary ring. We phrase and solve a boundary-value problem for the determination the variation of the strength of the velocity fluctuations and the volume fraction normal to the mid-plane of the ring. We do this for a single value of the coefficient of restitution and several values of the optical depth and self-gravity. At a given value of the optical depth, we find two solutions, one of which is likely to be unstable. The stable solutions evolve towards a monolayer as the self-gravity increases.
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