Self-Organized Criticality

Jensen, Henrik Jeldtoft

doi:10.1017/cbo9780511622717

Cited by 1,136 publications

(695 citation statements)

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“…Bak (1996) gave a nontechnical discussion of the elementary ideas. A pedagogical synthesis of the literature through the mid-1990s was given by Jensen (1998).…”

Section: Sandpile Dynamicsmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

260

397

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A pedagogical review of the historical development and current status (as of early 2000) of systematic statistical theories of plasma turbulence is undertaken. Emphasis is on conceptual foundations and methodology, not practical applications. Particular attention is paid to equations and formalism appropriate to strongly magnetized, fully ionized plasmas. Extensive reference to the literature on neutral-fluid turbulence is made, but the unique properties and problems of plasmas are emphasized throughout. Discussions are given of quasilinear theory, weak-turbulence theory, resonance-broadening theory, and the clump algorithm. Those are developed independently, then shown to be special cases of the direct-interaction approximation (DIA), which provides a central focus for the article. Various methods of renormalized perturbation theory are described, then unified with the aid of the generating-functional formalism of Martin, Siggia, and Rose. A general expression for the renormalized dielectric function is deduced and discussed in detail. Modern approaches such as decimation and PDF methods are described. Derivations of DIA-based Markovian closures are discussed. The eddy-damped quasinormal Markovian closure is shown to be nonrealizable in the presence of waves, and a new realizable Markovian closure is presented. The test-field model and a realizable modification thereof are also summarized. Numerical solutions of various closures for some plasmaphysics paradigms are reviewed. The variational approach to bounds on transport is developed. Miscellaneous topics include Onsager symmetries for turbulence, the interpretation of entropy balances for both kinetic and fluid descriptions, self-organized criticality, statistical interactions between disparate scales, and the roles of both mean and random shear. Appendices are provided on Fourier transform conventions, dimensional and scaling analysis, the derivations of nonlinear gyrokinetic and gyrofluid equations, stochasticity criteria for quasilinear theory, formal aspects of resonance-broadening theory, Novikov's theorem, the treatment of weak inhomogeneity, the derivation of the Vlasov weak-turbulence wave kinetic equation from a fully renormalized description, some features of a code for solving the direct-interaction approximation and related Markovian closures, the details of the solution of the EDQNM closure for a solvable three-wave model, and the notation used in the article.

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“…Bak (1996) gave a nontechnical discussion of the elementary ideas. A pedagogical synthesis of the literature through the mid-1990s was given by Jensen (1998).…”

Section: Sandpile Dynamicsmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

260

397

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“…4) that the cracked rock is a critical system [6,35,67]. Systems verging on criticality maintain dynamic interactive processes that evolve locally until they reach criticality, when all members influence all other members [67][68][69]. Equilibrium thermo-dynamics is the classical critical system, and enthusiasts argue that almost all complex systems in nature are critical systems [70].…”

Section: Critical Systems Of Stress-aligned Fluid-saturated Cracksmentioning

confidence: 99%

A review of shear-wave splitting in the compliant crack-critical anisotropic Earth

Crampin¹,

Peacock²

2005

Wave Motion

162

111

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“…It is coherent in the sense that once it is established, at the largest scales the overall average shape of the sandpile does not change much, even though it displays complicated and unpredictable behavior at the smaller scales when driven. It is repetitive and robust in the sense that it is the state to which the system converges regardless of the initial condition and of any tuning of parameters, except that the driving force is asymptotically small (Jensen, 1998;Hwa et al, 1992). Similar models have been used to describe plasma dynamics (Lu and Hamilton, 1991;Carreras et al, 1996;Chapman et al, 1998;Takalo et al, 1999a,b;Vassiliadis et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

The magnetosphere as a complex system

Valdivia

Rogan

Muñoz

et al. 2005

Advances in Space Research

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The magnetosphere is a complex system, with multi-scale spatio-temporal behavior. Self-organization is a possible solution to two seemingly contradicting observations: (a) the repeatable and coherent substorm phenomena, and, (b) the underlying selfsimilar turbulent behavior in the plasma sheet. Such states, are seen to emerge naturally in a plasma physics model with sporadic dissipation, through spatio-temporal chaos.

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Self-Organized Criticality

Cited by 1,136 publications

References 0 publications

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Fundamental statistical descriptions of plasma turbulence in magnetic fields

A review of shear-wave splitting in the compliant crack-critical anisotropic Earth

The magnetosphere as a complex system

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