A branching process model for sand avalanches |
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Authors: | Ricardo García-Pelayo Iván Salazar William C Schieve |
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Institution: | (1) Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems, Physics Department, University of Texas at Austin, 78712 Austin, Texas |
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Abstract: | An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one. |
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Keywords: | Self-organized criticality avalanches branching processes dynamical critical phenomena 1/f noise |
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