Collision frequencies and energy flux in a dilute granular gas

Recent experimental study of a granular gas fluidized by vibrations in a low gravity environment has reported that the collision frequency nu(P) of the particles with the container boundary scales roughly like N-alpha with alpha=0.6 +/- 0.1, where N is the number of particles. Using numerical simulations, we show that this scaling is observed on a wide range of N, both for nu(P) and for the particle-particle collision frequency nu(c). Simple scaling arguments show that this behavior is related to the energy flux in the granular gas, from injection by the moving boundary to dissipation by inelastic collisions. We predict in the dilute limit that the collision frequencies scale such as root N are in fair agreement with experimental measurements.