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.

Forest Fires

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Forest Fire ◽  
Forest Fires ◽  
Model Simulation ◽  
Percolation Cluster ◽  
Natural Process ◽  
Wildfire Management ◽  
Fire Model ◽  
Self Organized ◽  
Forest Fire Model ◽  
Self Organized Criticality

This chapter explores how a “natural” process generates dynamically something that is conceptually similar to a percolation cluster by using the case of forest fires. It first provides an overview of the forest-fire model, which is essentially a probabilistic cellular automata, before discussing its numerical implementation using the Python code. It then describes a representative simulation showing the triggering, growth, and decay of a large fire in a representative forest-fire model simulation on a small 100 x 100 lattice. It also considers the behavior of the forest-fire model as well as its self-organized criticality and concludes with an analysis of the advantages and limitations of wildfire management. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

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.

Fractality and Self-Organized Criticality of Wars

Fractals ◽  
1998 ◽  
Vol 06 (04) ◽  
pp. 351-357 ◽  
Author(s):  
D. C. Roberts ◽  
D. L. Turcotte
Keyword(s):  
Forest Fire ◽  
Power Law ◽  
Forest Fires ◽  
Size Dependence ◽  
Fire Model ◽  
Self Organized ◽  
Battle Deaths ◽  
Forest Fire Model ◽  
Alternative Measures ◽  
Self Organized Criticality

This paper considers the frequency-size statistics of wars. Using several alternative measures of the intensity of a war in terms of battle deaths, we find a fractal (power-law) dependence of number on intensity. We show that the frequency-size dependence of forest fires is essentially identical to that of wars. The forest-fire model provides a basis for understanding the distribution of forest firest in terms of self-organized criticality. We extend the analogy to wars in terms of the initial ignition (outbreak of war) and its spread to a group of metastable countries.

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.

STATISTICAL PROPERTIES OF SOLAR FLARES AND COMPARISON TO OTHER IMPULSIVE ENERGY RELEASE EVENTS

2009 ◽  
Vol 23 (28n29) ◽  
pp. 5609-5618 ◽  
Author(s):  
FABIO LEPRETI ◽  
VLADIMIR G. KOSSOBOKOV ◽  
VINCENZO CARBONE
Keyword(s):  
Solar Flare ◽  
Energy Release ◽  
Solar Flares ◽  
Statistical Properties ◽  
Universal Curve ◽  
Mhd Turbulence ◽  
Natural Systems ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Impulsive Processes

Impulsive energy release events are observed in many natural systems. Solar flares are certainly among the most remarkable examples of such processes. In the last years the study of solar flare statistical properties has received considerable attention in the context of solar flare models based on different approaches, such as Self Organized Criticality (SOC) or magnetohydrodynamic (MHD) turbulence. In this talk the main statistical properties of solar flares will be presented and compared to those of other well known impulsive processes, such as earthquakes and soft γ-ray flashes occurring on neutron stars. It is shown that the these phenomena are characterized by different statistics that cannot be rescaled onto a single, universal curve and that this holds even for the same phenomenon, when observed in different periods or at different locations. Our results indicate apparent complexity of impulsive energy release processes, which neither follow a common behavior nor could be attributed to a universal physical mechanism.

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.

Self-organized criticality of forest fires in China

2001 ◽  
Vol 46 (13) ◽  
pp. 1134-1137 ◽  
Author(s):  
Song Weiguo ◽  
Fan Weicheng ◽  
Wang Binghong
Keyword(s):  
Forest Fires ◽  
Self Organized ◽  
Self Organized Criticality

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.

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