Anisotropic Energy Distribution in Three-Dimensional Vibrofluidized Granular Systems

We examine the energy distribution in a three-dimensional model granular system contained in an open cylinder under the influence of gravity. Energy is supplied to the system by a vibrating base. We introduce spatially resolved, partial particle-particle ``dissipations'' for directions parallel and perpendicular to the energy input, respectively. Energy balances show that the total (integrated) ``dissipation'' is less than zero in the parallel direction while greater than zero in the perpendicular directions. The energy supplied to the perpendicular directions is dissipated by particle-wall collisions. We further define a fractional energy transfer, which in the steady state represents the fraction of the power supplied by the vibrating base that is dissipated at the wall. We examine the dependence of the fractional energy transfer on the number of particles, the velocity of the vibrating base, the particle-particle restitution coefficient, and the particle-wall restitution coefficient. We also explore the influence of the system parameters on the spatially dependent partial dissipations.