scholarly journals Universal Accretion Growth Using Sandpile Models

2015 ◽  
Vol 11 (S315) ◽  
Author(s):  
Srabani Datta ◽  
Ralph Spencer ◽  
Shane McKie
Keyword(s):  
Molecular Clouds ◽  
Velocity Structure ◽  
Power Law Distribution ◽  
Self Similarity ◽  
Scale Free ◽  
Fluid Turbulence ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sandpile Models

AbstractThe Bak Tang Weisenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around the system till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power- law distribution in cascade sizes having slope -5/3. This self-similarity of structure is synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions in fluid turbulence. In this paper, we show that this is a naturally occuring universal process giving rise to scale - free structures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a wide range of objects including molecular clouds, accretion disks and perhaps galaxies.

Modeling Research on Spatiotemporal Dynamics of the Hippocampus

1997 ◽  
Vol 07 (01) ◽  
pp. 187-198 ◽  
Author(s):  
Haijian Sun ◽  
Lin Liu ◽  
Chunhua Feng ◽  
Aike Guo
Keyword(s):  
Pyramidal Cells ◽  
Behavioral Pattern ◽  
Spatiotemporal Dynamics ◽  
Epileptic Focus ◽  
Power Law Distribution ◽  
Ca1 Pyramidal Cells ◽  
Self Organized ◽  
Hippocampal Ca1 ◽  
Self Organized Criticality ◽  
Neurological Insult

The spatiotemporal dynamics of the hippocampus is studied. We first propose a fractal algorithm to model the growth of hippocampal CA1 pyramidal cells, together with an avalanche model for information transmission. Then the optical records of an epileptic focus in the hippocampus are analyzed and simulated. These processes indicate that the hippocampus normally stays in self-organized criticality with a harmonious spatiotemporal behavioral pattern, that is, showing 1/f fluctuation and power law distribution. In case of a neurological insult, the hippocampal system may step into supercriticality and initiate epilepsy.

scholarly journals Observational evidence in favor of scale-free evolution of sunspot groups

2018 ◽  
Vol 618 ◽  
pp. A183
Author(s):  
A. Shapoval ◽  
J.-L. Le Mouël ◽  
M. Shnirman ◽  
V. Courtillot
Keyword(s):  
Weibull Distribution ◽  
Power Law ◽  
Large Range ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Spatio Temporal ◽  
Computational Procedures ◽  
Definition Of ◽  
Sunspot Groups

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. Aims. In this paper we reconsider this question, and are led to the opposite conclusion. Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group. Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/Vβ increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

Complexity and Criticality

2020 ◽  
pp. 42-50
Author(s):  
Helmut Satz
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Critical Point ◽  
Correlation Length ◽  
Critical Behavior ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Free Behavior

Complex systems and critical behavior in complex system are defined in terms of correlation between constituents in the medium, subject to screening by intermediate constituents. At a critical point, the correlation length diverges—as a result, one finds the scale-free behavior also observed for bird flocks. This behavior is therefore possibly a form of self-organized criticality.

scholarly journals Renormalization scheme for self-organized criticality in sandpile models

1994 ◽  
Vol 72 (11) ◽  
pp. 1690-1693 ◽  
Author(s):  
L. Pietronero ◽  
A. Vespignani ◽  
S. Zapperi
Keyword(s):  
Renormalization Scheme ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Sandpile Models

SELF-ORGANIZED CRITICALITY MODEL FOR EARTHQUAKES: QUIESCENCE, FORESHOCKS AND AFTERSHOCKS

1999 ◽  
Vol 09 (12) ◽  
pp. 2249-2255 ◽  
Author(s):  
S. HAINZL ◽  
G. ZÖLLER ◽  
J. KURTHS
Keyword(s):  
Power Law ◽  
B Value ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Self Organized ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality ◽  
Clustering Of Events ◽  
Foreshock Activity

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge–Knopoff model. Analogously to the original model, our model displays a robust power law distribution of event sizes (Gutenberg–Richter law). The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are accompanied by a precursory quiescence and by localized fore- and aftershocks. The increase of foreshock activity as well as the decrease of aftershock activity follows a power law (Omori law) with similar exponents p and q. All empirically observed power law exponents, the Richter B-value, p and q and their variability can be reproduced simultaneously by our model, which depends mainly on the level of conservation and the relaxation time.

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