Boundary conditions and normal state for a vibrated granular fluid

The steady state of a fluidized granular system confined between a vibrating wall and a reflecting one is analyzed in detail. The relationship between the velocity of the wall and the hydrodynamic profiles is established. In the limit of a large system, a peculiar normal state, independent of the details of the boundaries, is reached in the bulk. This state has a uniform pressure and a constant temperature gradient. Both quantities are not independent, but verify a closed constitutive relationship. The generality of this state and the relevant role it is expected to play in the description of vibrated granular systems is discussed.