  We investigate the dynamics of an ensemble of inelastic hard spheres confined
between two horizontal plates separated a distance smaller than twice the
diameter of the particles, in such a way that the system is
quasi-two-dimensional. The bottom wall is vibrating and, therefore, it injects
energy into the system in the vertical direction and a stationary state is
reached. It is found that, if the size of the plates is small enough, the
stationary state is homogeneous. Otherwise, a cluster of particles is
developed. The instability is understood by using some effective hydrodynamic
equations in the horizontal plane. Moreover, the theoretical prediction for the
size of the system above which it is unstable agrees very well with Molecular
Dynamics simulation results without any fitting parameter.
