Recent developments in the physics of granular matter [1, 2] motivate the analysis of the effects of dissipative interactions on the structure of stationary states. The series of theoretical models described below is sufficiently simple to allow rigorous analytic analysis to be performed, but it contains at the same time some features relevant to the theory of granular flows. Thus, a description of coupling to a vibrating base via stochastic boundary conditions, or dissipative binary collisions are ingredients of the models considered.
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