Avalanche dynamics in a pile of rice

Frette, Vidar; Christensen, Kim; Malthe‐Sørenssen, Anders; Feder, Jens; Jøssang, Torstein; Meakin, Paul

doi:10.1038/379049a0

Cited by 457 publications

(444 citation statements)

References 16 publications

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“…Qualitatively similar observations were made in an experimental setup measuring the avalanche distributions in rice piles (7,8) . The measured distributions crucially depend on the geometrical properties of the rice grains, i.e., their friction.…”

Section: It Follows Thatsupporting

confidence: 57%

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

Hauert

Nagler

Schuster

2004

Journal of Statistical Physics

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The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log 10 N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N . Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.

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Section: It Follows Thatsupporting

confidence: 57%

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

Hauert

Nagler

Schuster

2004

Journal of Statistical Physics

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“…al [32] and Frette et. al [26]. The former was for coalescence of bubbles in a bubble raft, while the latter was observed in sliding grains in rice piles.…”

Section: P(n) = λ Exp(−λn) (4)mentioning

confidence: 99%

“…There is a variety of physical systems which exhibit avalanches, ranging from earthquakes [24] and random fuse networks [25] to piles of rice [26]. However, their statistics are usually described by power-laws of the form p(n) ∼ n −α , where the exponent α has a value between 1 and 2.…”

Section: P(n) = λ Exp(−λn) (4)mentioning

confidence: 99%

Statistics and topological changes in 2D foam from the dry to the wet limit

Dunne

Bolton²,

Weaire

et al. 2017

Philosophical Magazine

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“…The stochasticity in toppling rules models phenomenologically the variation of grain sizes, roughness etc. that are found in real experiments on granular media [47]. In the next section, we shall describe a different variation which makes the model non-abelian.…”

Section: The Abelian Distributed Processors Modelmentioning

confidence: 99%

The Abelian sandpile and related models

Dhar

1999

Physica A: Statistical Mechanics and its Applications

298

291

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The Abelian sandpile model is the simplest analytically tractable model of self-organized criticality. This paper presents a brief review of known results about the model. The abelian group structure of the algebra of operators allows an exact calculation of many of its properties. In particular, when there is a preferred direction, one can calculate all the critical exponents characterizing the distribution of avalanche-sizes in all dimensions. For the undirected case, the model is related to q → 0 state Potts model. This enables exact calculation of some exponents in two dimensions, and there are some conjectures about others. We also discuss a generalization of the model to a network of communicating reactive processors. This includes sandpile models with stochastic toppling rules as a special case. We also consider a non-abelian stochastic variant, which lies in a different universality class, related to directed percolation.

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Avalanche dynamics in a pile of rice

Cited by 457 publications

References 16 publications

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

Statistics and topological changes in 2D foam from the dry to the wet limit

The Abelian sandpile and related models

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