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The dynamics of a system composed of inelastic hard spheres or disks that areconfined between two parallel vertically vibrating walls is studied (thevertical direction is defined as the direction perpendicular to the walls). Thedistance between the two walls is supposed to be larger than twice the diameterof the particles so that the particles can pass over each other, but still muchsmaller than the dimensions of the walls. Hence, the system can be consideredto be quasi-two-dimensional (quasi-one-dimensional) in the hard spheres (disks)case. For dilute systems, a closed evolution equation for the one-particledistribution function is formulated that takes into account the effects of theconfinement. Assuming the system is spatially homogeneous, the kinetic equationis solved approximating the distribution function by a two-temperatures(horizontal and vertical) gaussian distribution. The obtained evolutionequations for the partial temperatures are solved, finding a very goodagreement with Molecular Dynamics simulation results for a wide range of theparameters (inelasticity, height and density) for states whose projection overa plane parallel to the walls is homogeneous. In the stationary state, wherethe energy lost in collisions is compensated by the energy injected by thewalls, the pressure tensor in the horizontal direction is analyzed and itsrelation with an instability of the homogenous state observed in thesimulations is discussed.

Confined granular gases under the influence of vibrating walls