MEAN-FIELD THEORY OF SANDPILE AVALANCHES - FROM THE INTERMITTENT-FLOWTO THE CONTINUOUS-FLOW REGIME

We model the dynamics of avalanches in granular assemblies in partly f illed rotating cylinders using a mean-field approach. We show that, up on varying the cylinder angular velocity omega, the system undergoes a hysteresis cycle between an intermittent- and a continuous-flow regim e. In the intermittent-flow regime, and approaching the transition, th e avalanche duration exhibits critical slowing down with a temporal po wer-law divergence. Upon adding a white-noise term, and close to the t ransition, the distribution of avalanche durations is also a power law . The hysteresis, as well as the statistics of avalanche durations, ar e in good qualitative agreement with recent experiments in partly fill ed rotating cylinders.