Self-organized criticality in a two-dimensional rotating drum model

Baumann, G. W.; Wolf, Dietrich E.

doi:10.1103/physreve.54.r4504

Cited by 15 publications

(12 citation statements)

References 8 publications

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“…This and similar results for real sandpiles should, however, be taken with, well, a grain of salt [8]. A polydisperse granular material simulated in [6] shows a rather convincing power law with a shoulder like that in [1, Fig. 1(a)].…”

supporting

confidence: 79%

Flyvbjerg Replies:

Flyvbjerg

1996

Phys. Rev. Lett.

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Flyvbjerg Replies: Bundschuh and Lässig's results for the distributions of avalanche sizes and pile sizes between avalanches [1] are interesting, and useful for understanding the simplest possible self-organized critical (SOC) system [2], as well as more complex and realistic SOC systems. The difference between the results in [1] and [2] is due to different values for the parameter m. In [2] m 1, while in [1] m is 1 100 and 4274 0031-9007͞96͞77(20)͞4274(1)$10.00

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supporting

confidence: 79%

Flyvbjerg Replies:

Flyvbjerg

1996

Phys. Rev. Lett.

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“…Held et al (1990) found power-law distributions for small sandpiles but not for large sandpiles. A variety of other studies have been carried out (Puhl 1992, Frette 1993, Grumbacher et al 1993, Baumann and Wolf 1996, Densmore et al 1997, Hager et al 1997, Head and Rodgers 1997b. Laboratory studies of sandpiles have been reviewed by Nagel (1992) and Feder (1995).…”

Section: Cellular-automata Modelmentioning

confidence: 99%

Self-organized criticality

1999

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The concept of self-organized criticality was introduced to explain the behaviour of the sandpile model. In this model, particles are randomly dropped onto a square grid of boxes. When a box accumulates four particles they are redistributed to the four adjacent boxes or lost off the edge of the grid. Redistributions can lead to further instabilities with the possibility of more particles being lost from the grid, contributing to the size of each 'avalanche'. These model 'avalanches' satisfied a power-law frequency-area distribution with a slope near unity. Other cellular-automata models, including the slider-block and forest-fire models, are also said to exhibit self-organized critical behaviour. It has been argued that earthquakes, landslides, forest fires, and species extinctions are examples of self-organized criticality in nature. In addition, wars and stock market crashes have been associated with this behaviour. The forest-fire model is particularly interesting in terms of its relation to the critical-point behaviour of the sitepercolation model. In the basic forest-fire model, trees are randomly planted on a grid of points. Periodically in time, sparks are randomly dropped on the grid. If a spark drops on a tree, that tree and adjacent trees burn in a model fire. The fires are the 'avalanches' and they are found to satisfy power-law frequency-area distributions with slopes near unity. This forest-fire model is closely related to the site-percolation model, that exhibits critical behaviour. In the forest-fire model there is an inverse cascade of trees from small clusters to large clusters, trees are lost primarily from model fires that destroy the largest clusters. This quasi steady-state cascade gives a power-law frequency-area distribution for both clusters of trees and smaller fires. The site-percolation model is equivalent to the forest-fire model without fires. In this case there is a transient cascade of trees from small to large clusters and a power-law distribution is found only at a critical density of trees.

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“…In one variation instead of the addition of sand causing the stability imbalance necessary to bring about a critical state, a drum partially filled with sand is rotated. This has the effect of increasing the slope of the system until an avalanche occurs (past the critical value of the slope) [3].…”

Section: Historymentioning

confidence: 99%

Stairway to Self-Organized Criticality: SOC on a Slope using Relative Critical Heights

Davis¹

2008

AJUR

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A computational model of loose snow avalanches was studied as an example of Self-Organized Criticality (SOC). The distribution of the magnitudes of avalanches was measured for a stair-stepped system with various critical relative differences and system slopes. Depending on the configuration, the model showed either power law behaviors or a Gaussian distribution. For configurations that displayed power laws, the slope of the power law was dependent on the configuration of the system.

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Self-organized criticality in a two-dimensional rotating drum model

Cited by 15 publications

References 8 publications

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Self-organized criticality

Stairway to Self-Organized Criticality: SOC on a Slope using Relative Critical Heights

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