Minimal model for avalanches in granular systems

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Abstract
A nonlinear model for the dynamics of avalanches in granular systems is presented. It is based on mean-field equations for the particle velocity and the angle of the surface of the granular system. The friction force is discontinuous at zero velocity and increases monotonically with the square of the velocity. The model explains the main features of the dynamics of avalanches in analytical detail. It also explains the logarithmic decay behavior of the angle of the pile in the presence of vibrations as found experimentally by Jaeger et al. [Phys. Rev. Lett. 62, 40 (1990)].