Flux through a hole from a shaken granular medium

We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, vmax, controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of vmax. The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of vmax. The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system.