Flowing Sand—A Possible Physical Realization of Directed Percolation

@article{Hinrichsen2000FlowingSP,
  title={Flowing Sand—A Possible Physical Realization of Directed Percolation},
  author={Haye Hinrichsen and Andrea Jim{\'e}nez-Dalmaroni and Yadin Rozov and Eytan Domany},
  journal={Journal of Statistical Physics},
  year={2000},
  volume={98},
  pages={1149-1168}
}
A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches, leading to a crossover from compact to ordinary directed percolation… 
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7 Citations
Background Citations
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7 Citations

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Approximation for directed percolation in d=1+1.
  • C. Sire
  • Mathematics
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  • 2002
TLDR
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References

SHOWING 1-10 OF 12 REFERENCES
Flowing sand: A physical realization of directed percolation.
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…
Emergent Spatial Structures in Critical Sandpiles
We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of…
Two types of avalanche behaviour in granular media
The nature of the transition between static and flowing regimes in granular media, provides a key to understanding their dynamics. When a pile of sand starts flowing, avalanches occur on its inclined…
Collision-induced friction in the motion of a single particle on a bumpy inclined line.
  • Dippel, Batrouni, Wolf
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
By means of molecular-dynamics simulations, this work investigates the elementary process of avalanches and size segregation by surface flow in two dimensions: a single ball confined to moving along an inclined line consisting of balls and finds that it is very regular and consists of many small bounces on each ball on the line.
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…
Disordered one-dimensional contact process
New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure…
Temporally Disordered Bond Percolation on the Directed Square Lattice.
  • Jensen
  • Materials Science
    Physical review letters
  • 1996
TLDR
Analysis of the series revealed that the critical exponent $\ensuremath{\beta}$ and critical point ${p}_{c}$ change continuously with the strength of the disorder.
Reggeon field theory (Schlögl's first model) on a lattice: Monte Carlo calculations of critical behaviour
Self-organized criticality: An explanation of the 1/f noise.
We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical…
Equivalence of Cellular Automata to Ising Models and Directed Percolation
Time development of cellular automata in $d$ dimensions is mapped onto equilibrium statistical mechanics of Ising models in $d+1$ dimensions. Directed percolation is equivalent to a cellular…
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