scholarly journals Apparent Power Laws Can Occur without Criticality

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1486
Author(s):  
Lawrence S. Schulman
Keyword(s):  
Power Laws ◽  
Self Organized ◽  
Self Organized Criticality

Power laws often lead to the conclusion that self-organized criticality is at work. This is not the case, and power laws can also occur away from criticality or can occur for other reasons.

scholarly journals Associating an Entropy with Power-Law Frequency of Events

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 940 ◽  
Author(s):  
Evaldo Curado ◽  
Fernando Nobre ◽  
Angel Plastino
Keyword(s):  
Information Theory ◽  
Forest Fires ◽  
Ground State ◽  
State Energy ◽  
Power Laws ◽  
Natural Systems ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Isothermal Processes ◽  
Entropic Index

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy S q . The relevant parameters become: (i) The entropic index q, which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ε 0 , in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature T q with k T q ∝ ε 0 (i.e., isothermal processes, for a given q), in analogy with those in the class of self-organized criticality, which are known to occur at fixed temperatures. Typical examples are analyzed, like earthquakes, avalanches, and forest fires, and in some of them, the entropic index q and value of T q are estimated. The knowledge of the associated entropic form opens the possibility for a deeper understanding of such phenomena, particularly by using information theory and optimization procedures.

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.

scholarly journals Modelling the outer radiation belt as a complex system in a self-organised critical state

2005 ◽  
Vol 12 (6) ◽  
pp. 993-1001 ◽  
Author(s):  
N. B. Crosby ◽  
N. P. Meredith ◽  
A. J. Coates ◽  
R. H. A. Iles
Keyword(s):  
Radiation Belt ◽  
Outer Part ◽  
Power Laws ◽  
Threshold Value ◽  
Electron Radiation ◽  
Outer Electron ◽  
Outer Radiation Belt ◽  
Frequency Distributions ◽  
Self Organized ◽  
Self Organized Criticality

Abstract. The dynamic behaviour of the outer electron radiation belt makes this area of geo-space a candidate for the concept of self-organized criticality. It is shown here that frequency distributions of measured outer electron radiation belt data are well-represented by power-laws over two decades. Applying the concept of self-organized criticality to interpret the shape of the distributions suggests another approach to complement existing methods in the interpretation of how this complicated environment works. Furthermore sub-grouping the radiation belt count rate data as a function of spatial location or temporal interval (e.g. L-shell, magnetic local time, solar cycle, ...) shows systematic trends in the value of the slope of the power-laws. It is shown that the inner part of the outer radiation belt is influenced in a similar manner to the outer part, but in a less profound way. Our results suggest that the entire outer radiation belt appears to be affected as the sum of its individual parts. This type of study also gives the probability of exceeding a given threshold value over a given time; limiting the size of "an event". The average values could then be compared with models used in spacecraft design.

scholarly journals Morphogenesis of an institution on a lattice game

1998 ◽  
Vol 2 (3) ◽  
pp. 209-213 ◽  
Author(s):  
Elettra Agliardi ◽  
Emanuele Giovannetti
Keyword(s):  
Social Interactions ◽  
Power Laws ◽  
Self Organized ◽  
Transient Period ◽  
Self Organized Criticality ◽  
Degree Of Differentiation ◽  
High Degree ◽  
Lattice Game

In this paper we study the morphogenesis of an institution when local social interactions are taken into account. The structure we obtain has characteristics of “self-organized criticality”. After a transient period the system self-organizes into a configuration which is compatible with a high degree of differentiation among different sites and generates typical power laws.

DYNAMICAL EXPLANATION FOR THE EMERGENCE OF POWER LAW IN A STOCK MARKET MODEL

1996 ◽  
Vol 07 (01) ◽  
pp. 65-72 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON ◽  
GIVAT RAM
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Wealth Distribution ◽  
Power Laws ◽  
Stationary Regime ◽  
Market Model ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sand Piles

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

Correlation between Barkhausen noise and mechanical sensitivity in FINEMET-type materials

2009 ◽  
Vol 24 (1) ◽  
pp. 130-134 ◽  
Author(s):  
G. Eszenyi ◽  
S. Szabó ◽  
L. Harasztosi ◽  
F. Zámborszky ◽  
J. Nyéki ◽  
...  
Keyword(s):  
Power Laws ◽  
Distribution Functions ◽  
Barkhausen Noise ◽  
Mechanical Sensitivity ◽  
Composite State ◽  
Noise Parameters ◽  
Self Organized ◽  
Heat Treated ◽  
Self Organized Criticality ◽  
Nanocrystalline Composite

FINEMET-type (Fe75Si15NbBCu) ribbons were heat treated, and their magnetic properties were analyzed. Permeability, thermal, and mechanical sensitivities were measured by commonly used industrial methods, and these properties were correlated with measured magnetic Barkhausen noise parameters. Distributions of peak area, A, and peak noise energy, E, were evaluated. Distribution functions of noise parameters, P(x), were in good agreement with the theory of self-organized criticality (SOC), satisfying power laws in the form P(x)∼x−α. It is found that the noise did not considerably depend on the temperature sensitivity parameter and on the permeability of ribbons. However, a useful correlation between the noise parameters and mechanical sensitivity has been observed. Minimal noise was detected for samples with negligible mechanical sensitivity in an amorphous-nanocrystalline composite state obtained by a heat treatment at 853 K.

scholarly journals Record dynamics of evolving metastable systems: theory and applications

2021 ◽  
Vol 94 (1) ◽  
Author(s):  
Paolo Sibani ◽  
Stefan Boettcher ◽  
Henrik Jeldtoft Jensen
Keyword(s):  
Physical Aging ◽  
Complex Dynamics ◽  
Power Laws ◽  
Hierarchical Systems ◽  
Relaxation Effects ◽  
Self Organized ◽  
Rapid Changes ◽  
Continuous Time Random Walks ◽  
Self Organized Criticality ◽  
Metastable Systems

Abstract Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as “physical aging”, but from the vantage point of RD, the evolution of a class of systems of physical, biological, and cultural origin is rooted in a hierarchically structured configuration space and can, therefore, be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self-Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time-series, and connects it to the statistics of quakes in metastable hierarchical systems, arguing that the relaxation effects of quakes can generally be described by power laws unrelated to criticality. Several different applications of RD have been developed over the years. Some of these are described, showing the basic RD hypothesis and how the log-time homogeneity of quake dynamics, can be empirically verified in a given context. The discussion summarizes the paper and briefly mentions applications not discussed in detail. Finally, the outlook points to possible improvements and to new areas of research where RD could be of use. Graphic Abstract

scholarly journals Are Giant Pulses Evidence of Self-Organized Criticality?

1996 ◽  
Vol 160 ◽  
pp. 179-180 ◽  
Author(s):  
Matthew D. T. Young ◽  
Brian G. Kenny
Keyword(s):  
Power Laws ◽  
Crab Pulsar ◽  
Statistical Distributions ◽  
Millisecond Pulsar ◽  
Recent Discussion ◽  
Scale Invariant ◽  
Giant Pulse ◽  
Self Organized ◽  
Giant Pulses ◽  
Self Organized Criticality

The statistical distributions of certain giant pulse (GP) properties appear to be well described by power laws. This suggests that the emission mechanism that produces giant pulses is a scale-invariant one. In turn this may indicate that the source of the GPs is in a state of self-organized criticality (SOC). For a recent discussion of SOC see Sornetteet al. (1995).Prior to this conference, the only pulsars reported to exhibit GPs were the Crab pulsar, PSR B0531+21 (Lundgrenet al. 1995), and the millisecond pulsar PSR B1937+21 (Cognardet al. 1996). However, at the conference it was reported that giantmicropulseshad recently been observed from PSR J0437–4715 (Ables and McConnell, this volume). In all cases the statistical distributions of observed GP heights and/or fluxes are found to be well described by simple power laws. The arguments in this note apply to all these pulsars.

scholarly journals Managing Complexity in Socio-Economic Systems

2009 ◽  
Vol 17 (2) ◽  
pp. 423-438 ◽  
Author(s):  
Dirk Helbing
Keyword(s):  
Complex Systems ◽  
Driving Forces ◽  
Production Systems ◽  
Power Laws ◽  
Self Organization ◽  
Economic Systems ◽  
Hierarchical Systems ◽  
Cascading Effects ◽  
Self Organized ◽  
Self Organized Criticality

This contribution summarizes some typical features of complex systems such as non-linear interactions, chaotic dynamics, the ``butterfly effect’’, phase transitions, self-organized criticality, cascading effects, and power laws. These imply sometimes quite unexpected, counter-intuitive, or even paradoxical behaviors of socio-economic systems. A typical example is the faster-is-slower effect. Due to their tendency of self-organization, complex systems are often hard to control. Instead of trying to control their behavior, it would often be better to pursue the approach of guided self-organization, i.e. to use the driving forces of the system rather than to fight against them. This is illustrated by the example of hierarchical systems, which need to fulfill certain principles in order to be efficient and robust in an ever-changing environment. We also discuss the important role of fluctuations and heterogeneity for the adaptability, flexibility and robustness of complex systems. The presentation is enriched by a number of examples ranging from decision behavior up to production systems and disaster spreading.

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