Mean-field theory of sandpile avalanches: From the intermittent- to the continuous-flow regime

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Abstract
We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity ω, the system undergoes a hysteresis cycle between an intermittent- and a continuous-flow regime. In the intermittent-flow regime, and approaching the transition, the avalanche duration exhibits critical slowing down with a temporal power-law divergence. Upon adding a white-noise term, and close to the transition, the distribution of avalanche durations is also a power law. The hysteresis, as well as the statistics of avalanche durations, are in good qualitative agreement with recent experiments in partly filled rotating cylinders.
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