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Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime

V. G. Benza·Franco Nori·Oscar Pla
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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 regimes. 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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V. G. Benza, Franco Nori, Oscar Pla. 1993-10-23. Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime. https://doi.org/10.1103/physreve.48.4095

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