scholarly journals Self-organized criticality: Does it have anything to do with criticality and is it useful?

2001 ◽  
Vol 8 (4/5) ◽  
pp. 193-196 ◽  
Author(s):  
D. L. Turcotte
Keyword(s):  
Forest Fires ◽  
Mantle Convection ◽  
Deterministic Chaos ◽  
Diffusion Limited Aggregation ◽  
Self Organized ◽  
Diffusion Limited ◽  
Self Organized Criticality ◽  
Self Similar ◽  
Similarities And Differences ◽  
And Diffusion

Abstract. Three aspects of complexity are fractals, chaos, and self-organized criticality. There are many examples of the applicability of fractals in solid-earth geophysics, such as earthquakes and landforms. Chaos is widely accepted as being applicable to a variety of geophysical phenomena, for instance, tectonics and mantle convection. Several simple cellular-automata models have been said to exhibit self-organized criticality. Examples include the sandpile, forest fire and slider-blocks models. It is believed that these are directly applicable to landslides, actual forest fires, and earthquakes, respectively. The slider-block model has been shown to clearly exhibit deterministic chaos and fractal behaviour. The concept of self-similar cascades can explain self-organized critical behaviour. This approach also illustrates the similarities and differences with critical phenomena through association with the site-percolation and diffusion-limited aggregation models.

FRACTAL TECTONICS AND EROSION

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 491-512 ◽  
Author(s):  
DONALD L. TURCOTTE
Keyword(s):  
Diffusion Limited Aggregation ◽  
Self Organized ◽  
Diffusion Limited ◽  
Drainage Networks ◽  
Fractal Statistics ◽  
Self Organized Criticality ◽  
Alternative Approaches ◽  
Block Models ◽  
Advective Diffusion ◽  
Frequency Magnitude

Tectonic processes build landforms that are subsequently destroyed by erosional processes. Landforms exhibit fractal statistics in a variety of ways; examples include (1) lengths of coast lines; (2) number-size statistics of lakes and islands; (3) spectral behavior of topography and bathymetry both globally and locally; and (4) branching statistics of drainage networks. Erosional processes are dominant in the development of many landforms on this planet, but similar fractal statistics are also applicable to the surface of Venus where minimal erosion has occurred. A number of dynamical systems models for landforms have been proposed, including (1) cellular automata; (2) diffusion limited aggregation; (3) self-avoiding percolation; and (4) advective-diffusion equations. The fractal statistics and validity of these models will be discussed. Earthquakes also exhibit fractal statistics. The frequency-magnitude statistics of earthquakes satisfy the fractal Gutenberg-Richter relation both globally and locally. Earthquakes are believed to be a classic example of self-organized criticality. One model for earthquakes utilizes interacting slider-blocks. These slider block models have been shown to behave chaotically and to exhibit self-organized criticality. The applicability of these models will be discussed and alternative approaches will be presented. Fragmentation has been demonstrated to produce fractal statistics in many cases. Comminution is one model for fragmentation that yields fractal statistics. It has been proposed that comminution is also responsible for much of the deformation in the earth’s crust. The brittle disruption of the crust and the resulting earthquakes present an integrated problem with many fractal aspects.

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.

Boundedness and Other Theories for Complex Systems

2013 ◽  
pp. 108-125
Keyword(s):  
Initial Conditions ◽  
Traditional Approach ◽  
Deterministic Chaos ◽  
Mathematical Object ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Universal Properties ◽  
The One ◽  
Global Invariant ◽  
Sensitivity To Initial Conditions

A comparison between the concept of boundedness on the one hand, and the theory of self-organized criticality (SOC) and the deterministic chaos on the other hand, is made. The focus is put on the methodological importance of the general frame through which an enormous class of empirical observations is viewed. The major difference between the concept of boundedness and the theory of self organized criticality is that under boundedness, the response comprises both specific and universal part, and thus a system has well defined “identity,” while SOC assumes response as a global invariant which has only universal properties. Unlike the deterministic chaos, the boundedness is free to explain the sensitivity to initial conditions independently from the mathematical object that generates them. Alongside, it turns out that the traditional approach to the deterministic chaos has its ample understanding under the concept of boundedness.

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.

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