Self-organized criticality: Difference between revisions
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'''Self-organized criticality (SOC)''' is one of a number of [[physics|physical]] mechanisms believed to underly the widespread occurrence of certain complex structures and patterns observed in nature, such as [[fractal]]s, [[power law]]s and [[1/f noise]]. Technically speaking, it refers to (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]]'' | 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]]''. These and related concepts have been enthusiastically applied across a diverse range of fields including not just physics but also [[biology|biological]] and [[social sciences|social]] topics. | ||
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. | 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. | ||
==Overview== | |||
==Examples of self-organized critical dynamics== | |||
===Theoretical models=== | |||
*[[Sandpile model|Bak-Tang-Wiesenfeld sandpile model]] | |||
*[[Forest fire model]]s | |||
*[[Olami-Feder-Christensen model]] | |||
*[[Bak-Sneppen model]] | |||
===Empirical observations=== | |||
== See also == | == See also == | ||
Revision as of 11:24, 9 February 2007
Self-organized criticality (SOC) is one of a number of physical mechanisms believed to underly the widespread occurrence of certain complex structures and patterns observed in nature, such as fractals, power laws and 1/f noise. Technically speaking, it refers to (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the 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. These and related concepts have been enthusiastically applied across a diverse range of fields including not just physics but also biological and social topics.
SOC is typically observed in slowly-driven non-equilibrium systems with extended 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.
Overview
Examples of self-organized critical dynamics
Theoretical models
- Bak-Tang-Wiesenfeld sandpile model
- Forest fire models
- Olami-Feder-Christensen model
- Bak-Sneppen model
Empirical observations
See also
References
- Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus. ISBN 0-387-94791-4.
- Bak, P. and Paczuski, M. (1995). "Complexity, contingency, and criticality". Proceedings of the National Academy of Sciences of the USA 92: 6689–6696.
- Bak, P. and Sneppen, K. (1993). "Punctuated equilibrium and criticality in a simple model of evolution". Physical Review Letters 71: 4083–4086. DOI:10.1103/PhysRevLett.71.4083. Research Blogging.
- Bak, P., Tang, C. and Wiesenfeld, K. (1987). "Self-organized criticality: an explanation of noise". Physical Review Letters 59: 381–384. DOI:10.1103/PhysRevLett.59.381. Research Blogging.
- Bak, P., Tang, C. and Wiesenfeld, K. (1988). "Self-organized criticality". Physical Review A 38: 364–374. DOI:10.1103/PhysRevA.38.364. Research Blogging.
- Buchanan, M. (2000). Ubiquity. London: Weidenfeld & Nicolson. ISBN 0-7538-1297-5.
- Jensen, H. J. (1998). Self-Organized Criticality. Cambridge: Cambridge University Press. ISBN 0-521-48371-9.
- Paczuski, M. (2005). "Networks as renormalized models for emergent behavior in physical systems". arXiv.org: physics/0502028.
- Turcotte, D. L. (1997). Fractals and Chaos in Geology and Geophysics. Cambridge: Cambridge University Press. ISBN 0-521-56733-5.
- Turcotte, D. L. (1999). "Self-organized criticality". Reports on Progress in Physics 62: 1377–1429. DOI:10.1088/0034-4885/62/10/201. Research Blogging.