scholarly journals Self-organized criticality in a rice-pile model

1996 ◽  
Vol 54 (5) ◽  
pp. R4512-R4515 ◽  
Author(s):  
Luís A. Nunes Amaral ◽  
Kent Bækgaard Lauritsen
Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 650-662 ◽  
Author(s):  
L. PIETRONERO

Irreversible fractal growth models like DLA and DBM have confronted us with theoretical problems of a new type that cannot be described in terms of the standard concepts like field theory and the renormalization group. The Fixed Scale Transformation is a theoretical scheme of a new type that is able to treat these problems in a reasonably systematic way. The idea is to focus on the dynamics at a given scale and to compute accurately the correlations at this scale by suitable lattice path integrals. The use of scale invariant growth rules then allows the generalization of these correlations to coarse-grained cells of any size and therefore to obtain the fractal dimension. We summarize the present status of the FST approach by focusing on the most recent results about the scale invariant dynamics of DLA/DBM. The possible extensions to other problems like the sand pile model (self-organized-criticality) and simplified models of turbulence will also be considered.


2021 ◽  
Vol 144 ◽  
pp. 110665
Author(s):  
Alexander V. Milovanov ◽  
Jens Juul Rasmussen ◽  
Bertrand Groslambert

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Kévin Perrot ◽  
Thi Ha Duong Phan ◽  
Trung Van Pham

International audience Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.


2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.


2020 ◽  
Vol 75 (5) ◽  
pp. 398-408
Author(s):  
A. Y. Garaeva ◽  
A. E. Sidorova ◽  
N. T. Levashova ◽  
V. A. Tverdislov

Author(s):  
M. E. J. Newman ◽  
R. G. Palmer

Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.


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