Flowing sand: A physical realization of directed percolation.

@article{Hinrichsen1999FlowingSA,
  title={Flowing sand: A physical realization of directed percolation.},
  author={Haye Hinrichsen and Andrea Jim{\'e}nez-Dalmaroni and Yadin Rozov and Eytan Domany},
  journal={Physical Review Letters},
  year={1999},
  volume={83},
  pages={4999-5002}
}
We introduce and investigate a simple model to describe recent experiments by Douady and Daerr on flowing sand. The model reproduces experimentally observed compact avalanches, whose opening angle decreases linearly as a threshold is approached. On large scales the model exhibits a crossover from compact directed percolation to directed percolation; we predict similar behavior for the experimental system. We estimate the regime where "true" directed percolation morphology and exponents will be… 
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References

Physics of dry granular media
Preface. 1. Static Packings. 2. Deformation of the Packing. 3. Particle-Particle Interactions. 4. Shape of the Granular Heap. 5. Theory of Rapid Flows. 6. Avalanches and Inclined Chutes. 7. Flow in