Self-organized criticality
718855
223496283
2008-07-04T09:19:25Z
AnonyScientist
6036906
critical exponents
In [[physics]], '''self-organized criticality (SOC)''' is a property of (classes of) [[dynamical system]]s which have a [[critical point (physics)|critical point]] as an [[attractor]]. Their macroscopic behaviour thus displays the spatial and/or temporal [[scale invariance|scale-invariance]] characteristic of the [[critical point (physics)|critical point]] of a [[phase transition]], but without the need to tune control parameters to precise values.
The phenomenon was first identified by [[Per Bak]], [[Chao Tang]] and [[Kurt Wiesenfeld]] ("BTW") in a seminal paper published in 1987 in ''[[Physical Review Letters]]'', and is considered to be one of the mechanisms by which [[complexity]] arises in nature. Its concepts have been enthusiastically applied across fields as diverse as [[geophysics]], [[physical cosmology]], [[evolutionary biology]] and [[ecology]], [[economics]], [[quantum gravity]], [[sociology]], [[solar physics]], [[plasma physics]], [[neurobiology]] and others.
SOC is typically observed in slowly-driven [[non-equilibrium thermodynamics|non-equilibrium]] systems with extended [[degrees of freedom (physics and chemistry)|degrees of freedom]] and a high level of [[nonlinearity]]. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that ''guarantee'' a system will display SOC.
__TOC__
== Overview ==
Self-organized criticality is one of a number of important discoveries made in [[statistical physics]] and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of [[complexity]] in nature. For example, the study of [[cellular automata]], from the early discoveries of [[Stanislaw Ulam]] and [[John von Neumann]] through to [[John Horton Conway|John Conway]]'s [[Conway's Game of Life|Game of Life]] and the extensive work of [[Stephen Wolfram]], made it clear that complexity could be generated as an [[emergence|emergent]] feature of extended systems with simple local interactions. Over a similar period of time, [[Benoît Mandelbrot]]'s large body of work on [[fractals]] showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of [[phase transition]]s carried out in the 1960s and '70s showed how [[scale invariance|scale invariant]] phenomena such as [[fractals]] and [[power law]]s emerged at the [[critical point (physics)|critical point]] between phases.
[[Per Bak|Bak]], [[Chao Tang|Tang]] and [[Kurt Wiesenfeld|Wiesenfeld]]'s 1987 paper linked together these factors: a simple [[cellular automaton]] was shown to produce several characteristic features observed in natural complexity ([[fractal]] geometry, [[1/f noise]] and [[power law]]s) in a way that could be linked to [[critical point (physics)|critical-point phenomena]]. Crucially, however, the paper demonstrated that the complexity observed emerged in a robust manner that did not depend on finely-tuned details of the system: variable parameters in the model could be changed widely without affecting the emergence of critical behaviour (hence, ''self-organized'' criticality). Thus, the key result of BTW's paper was its discovery of a mechanism by which the emergence of complexity from simple local interactions could be ''spontaneous'' — and therefore plausible as a source of natural complexity — rather than something that was only possible in the lab (or lab computer) where it was possible to tune control parameters to precise values. The publication of this research sparked considerable interest from both theoreticians and experimentalists, and important papers on the subject are among the most cited papers in the scientific literature.
Due to BTW's metaphorical visualization of their model as a "[[Bak-Tang-Wiesenfeld sandpile|sandpile]]" on which new sand grains were being slowly sprinkled to cause "avalanches", much of the initial experimental work tended to focus on examining real avalanches in [[granular matter]], the most famous and extensive such study probably being the [[Oslo ricepile experiment]]. Other experiments include those carried out on magnetic-domain patterns, the [[Barkhausen effect]] and vortices in [[superconductors]]. Early theoretical work included the development of a variety of alternative SOC-generating dynamics distinct from the BTW model, attempts to prove model properties analytically (including calculating the [[critical exponent]]s), and examination of the necessary conditions for SOC to emerge. One of the important issues for the latter investigation was whether [[conservation of energy]] was required in the local dynamical exchanges of models: the answer in general is no, but with (minor) reservations, as some exchange dynamics (such as those of BTW) do require local conservation at least on average. In the long term, key theoretical issues yet to be resolved include the calculation of the possible [[universality class]]es of SOC behaviour and the question of whether it is possible to derive a general rule for determining if an arbitrary [[algorithm]] displays SOC.
Alongside these largely lab-based approaches, many other investigations have centred around large-scale natural or social systems that are known (or suspected) to display [[scale invariance|scale-invariant]] behaviour. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including: [[earthquakes]] (which, long before SOC was discovered, were known as a source of [[scale invariance|scale-invariant]] behaviour such as the [[Gutenberg-Richter law]] describing the statistical distribution of earthquake sizes, and the [[Omori law]] describing the frequency of aftershocks); [[solar flares]]; fluctuations in economic systems such as [[financial markets]] (references to SOC are common in [[econophysics]]); [[landscape formation]]; [[forest fires]]; [[landslides]]; [[epidemics]]; and [[biological evolution]] (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of [[punctuated equilibria|"punctuated equilibria"]] put forward by [[Niles Eldredge]] and [[Stephen Jay Gould]]). Worryingly, given the implications of a [[scale invariance|scale-free]] distribution of event sizes, some researchers have suggested that another phenomenon that should be considered an example of SOC is the occurrence of [[wars]]. These "applied" investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.
The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics.
== Examples of self-organized critical dynamics ==
In chronological order of development:
* [[Bak-Tang-Wiesenfeld sandpile]]
* [[Forest-fire models]]
* [[Olami-Feder-Christensen model]]
* [[Bak-Sneppen model]]
Scholars looking back into earlier literature have found a number of similar models:
* In geophysics, the [[Burridge-Knopoff model|Burridge-Knopoff]] spring-block model of earthquakes was the inspiration for the [[Olami-Feder-Christensen model]]
* Smalley, Turcotte and Solla (1985) and Katz (1986) used models quite close to BTW's sandpile and linked them to [[scale-invariance|scale-free]] phenomena of earthquakes
* [[Integrate-and-fire neuron]]s, when coupled in large numbers, can be shown to display SOC
== See also ==
* [[1/f noise]]
* [[Complex system]]s
* [[Fractal]]s
* [[Power law]]s
* [[Scale invariance]]
* [[Self-organization]]
* [[Critical exponents]]
==References ==
{{Unreferenced|date=April 2008}}
== Further reading ==
* {{cite book
| author = [[Per Bak|Bak, P.]]
| date = 1996
| title = How Nature Works: The Science of Self-Organized Criticality
| publisher = Copernicus
| location = New York
| id = ISBN 0-387-94791-4
}}
* {{cite journal
| author = [[Per Bak|Bak, P.]] and [[Maya Paczuski|Paczuski, M.]]
| date = 1995
| title = Complexity, contingency, and criticality
| journal = [[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the USA]]
| volume = 92
| pages = 6689–6696
| url = http://pnas.org/cgi/content/abstract/92/15/6689
| doi = 10.1073/pnas.92.15.6689
| pmid = 11607561
}}
* {{cite journal
| author = [[Per Bak|Bak, P.]] and [[Kim Sneppen|Sneppen, K.]]
| date = 1993
| title = Punctuated equilibrium and criticality in a simple model of evolution
| journal = [[Physical Review Letters]]
| volume = 71
| pages = 4083–4086
| doi = 10.1103/PhysRevLett.71.4083
}}
* {{cite journal
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| date = 1987
| title = Self-organized criticality: an explanation of <math>1/f</math> noise
| journal = [[Physical Review Letters]]
| volume = 59
| pages = 381–384
| doi = 10.1103/PhysRevLett.59.381
}}
* {{cite journal
| author = [[Per Bak|Bak, P.]], [[Chao Tang|Tang, C.]] and [[Kurt Wiesenfeld|Wiesenfeld, K.]]
| date = 1988
| title = Self-organized criticality
| journal = [[Physical Review A]]
| volume = 38
| pages = 364–374
| doi = 10.1103/PhysRevA.38.364
}}
* {{cite book
| author = [[Mark Buchanan|Buchanan, M.]]
| date = 2000
| title = Ubiquity
| publisher = Weidenfeld & Nicolson
| location = London
| id = ISBN 0-7538-1297-5
}}
* {{cite book
| author = [[Henrik Jeldtoft Jensen|Jensen, H. J.]]
| date = 1998
| title = Self-Organized Criticality
| publisher = [[Cambridge University Press]]
| location = Cambridge
| id = ISBN 0-521-48371-9
}}
* {{cite journal
| author = [[Maya Paczuski|Paczuski, M.]]
| date = 2005
| title = Networks as renormalized models for emergent behavior in physical systems
| journal = arXiv.org
| pages = physics/0502028
| url = http://arxiv.org/abs/physics/0502028
}}
* {{cite book
| author = [[Donald L. Turcotte|Turcotte, D. L.]]
| date = 1997
| title = Fractals and Chaos in Geology and Geophysics
| publisher = [[Cambridge University Press]]
| location = Cambridge
| id = ISBN 0-521-56733-5
}}
* {{cite journal
| author = [[Donald L. Turcotte|Turcotte, D. L.]]
| year = 1999
| title = Self-organized criticality
| journal = [[Reports on Progress in Physics]]
| volume = 62
| pages = 1377–1429
| doi = 10.1088/0034-4885/62/10/201
}}
* {{cite journal
| author = [[Md. Nurujjaman|A. N. Sekar Iyengar]]
| year = 2007
| title = Realization of {SOC} behavior in a dc glow discharge plasma
| journal = [[Physics Letters A]]
| volume = 360
| pages = 717–721
}}
*[http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=1&index1=20771 Self-organized criticality on arxiv.org]
[[Category:Critical phenomena]]
[[Category:Applied and interdisciplinary physics]]
[[Category:Chaos theory]]
[[Category:Self-organization]]
[[de:Selbstorganisierte Kritikalität]]
[[es:criticalidad autorganizada]]