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.

scholarly journals Entropy production and self-organized (sub)criticality in earthquake dynamics

2010 ◽  
Vol 368 (1910) ◽  
pp. 131-144 ◽  
Author(s):  
Ian G. Main ◽  
Mark Naylor
Keyword(s):  
Numerical Model ◽  
Entropy Production ◽  
Power Law ◽  
Subcritical State ◽  
Earthquake Dynamics ◽  
Broad Bandwidth ◽  
Rupture Area ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Definition Of

We derive an analytical expression for entropy production in earthquake populations based on Dewar’s formulation, including flux (tectonic forcing) and source (earthquake population) terms, and apply it to the Olami–Feder–Christensen numerical model for earthquake dynamics. Assuming the commonly observed power-law rheology between driving stress and remote strain rate, we test the hypothesis that maximum entropy production (MEP) is a thermodynamic driver for self-organized ‘criticality’ (SOC) in the model. MEP occurs when the global elastic strain is near-critical, with small relative fluctuations in macroscopic strain energy expressed by a low seismic efficiency, and broad-bandwidth power-law scaling of frequency and rupture area. These phenomena, all as observed in natural earthquake populations, are hallmarks of the broad conceptual definition of SOC (which has, to date, often included self-organizing systems in a near but strictly subcritical state). In the MEP state, the strain field retains some memory of past events, expressed as coherent ‘domains’, implying a degree of predictability, albeit strongly limited in practice by the proximity to criticality and our inability to map the natural stress field at an equivalent resolution to the numerical model.

Self-Organized Criticality and Dynamic Instability of Microtubule Growth

1995 ◽  
Vol 50 (9-10) ◽  
pp. 739-740 ◽  
Author(s):  
Peter Babinec ◽  
Melánia Babincová
Keyword(s):  
Power Law ◽  
Dynamic Instability ◽  
Relative Number ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Microtubule Growth

Abstract We have shown that the distribution of lengths of site nucleated microtubules obey an algebraic power law relationship D(s) = As-τ, where D(s) is relative number of microtubules with length 5, A and τ are constants. This relationship indicates the possibility of a self-organized criticality in the dynamic instability of microtubule growth

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.

Power-Law Phenomena in Adhesive De-Bonding

1996 ◽  
Vol 458 ◽  
Author(s):  
G. Kendall ◽  
P. J. Cote ◽  
D. Crayon ◽  
F. J. Bonetto
Keyword(s):  
Power Law ◽  
Characteristic Length ◽  
Power Laws ◽  
Structural Features ◽  
Fractal Nature ◽  
Pressure Sensitive Adhesive ◽  
Self Organized ◽  
Pressure Sensitive ◽  
Self Organized Criticality ◽  
Glass Interface

ABSTRACTAcoustic emission (AE) events were recorded during the peeling of pressure-sensitive adhesive (PSA) tape from a silicate glass surface. The distributions of AE event durations and energies are found to have the form of power laws. Power-law dependencies (hyperbolic distributions) are recognized as a consequence of self-organized criticality (SOC), resulting from the absence of any characteristic length or time scales. In these studies, standard optical microscopy was used to characterize the fractal nature of the PSA-glass interface. The present results suggest that it is the inherent static structural features found at the fractal PSA-glass interface which produce the observed hyperbolic distributions in AE events, rather than a true SOC process.

SELF-ORGANIZED CRITICALITY AND THE BARKHAUSEN EFFECT IN AMORPHOUS AND POLYCRYSTALLINE METALS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 934-937 ◽  
Author(s):  
PAUL J. COTE ◽  
LAWRENCE V. MEISEL
Keyword(s):  
Power Law ◽  
Barkhausen Effect ◽  
Self Organized ◽  
Polycrystalline Metals ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Spatially Extended ◽  
Self Organized Criticality ◽  
Dissipative Dynamical Systems ◽  
Pulse Energies

An investigation of the possibility that the Barkhausen effect in amorphous and polycrystalline ferromagnets is an example of self-organized criticality is described. Since the theory of self-organized criticality was introduced by Bak, Tang, and Weisenfeld to explain the behavior of spatially extended, dissipative, dynamical systems the Barkhausen effect is a natural candidate for such a description. The data are consistent with self-organized critical behavior: the power spectral densities depend on frequency f as 1/fa and the distribution of pulse energies are well described by a power law analogous to the Gutenberg-Richter law for earthquakes. Alternative explanations for power law dependences are also presented.

SELF-ORGANIZED CORONA GRAPHS: A DETERMINISTIC COMPLEX NETWORK MODEL WITH HIERARCHICAL STRUCTURE

2019 ◽  
Vol 22 (06) ◽  
pp. 1950019
Author(s):  
ROHAN SHARMA ◽  
BIBHAS ADHIKARI ◽  
TYLL KRUEGER
Keyword(s):  
Power Law ◽  
Small World ◽  
Self Organization ◽  
Scale Free ◽  
Self Organized ◽  
Power Law Exponent ◽  
Growing Networks ◽  
Growing Network ◽  
Hierarchical Pattern ◽  
Corona Graphs

In this paper, we propose a self-organization mechanism for newly appeared nodes during the formation of corona graphs that define a hierarchical pattern in the resulting corona graphs and we call it self-organized corona graphs (SoCG). We show that the degree distribution of SoCG follows power-law in its tail with power-law exponent approximately 2. We also show that the diameter is less equal to 4 for SoCG defined by any seed graph and for certain seed graphs, the diameter remains constant during its formation. We derive lower bounds of clustering coefficients of SoCG defined by certain seed graphs. Thus, the proposed SoCG can be considered as a growing network generative model which is defined by using the corona graphs and a self-organization process such that the resulting graphs are scale-free small-world highly clustered growing networks. The SoCG defined by a seed graph can also be considered as a network with a desired motif which is the seed graph itself.

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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