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Uspekhi Fizicheskikh Nauk, 2004, Volume 174, Number 8, Pages 809–852
DOI: https://doi.org/10.3367/UFNr.0174.200408a.0809
(Mi ufn78)
 

This article is cited in 244 scientific papers (total in 244 papers)

REVIEWS OF TOPICAL PROBLEMS

Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics

L. M. Zelenyi, A. V. Milovanov

Space Research Institute, Russian Academy of Sciences
References:
Abstract: The goal of this review is to outline some unconventional ideas behind new paradigms in the modern theory of turbulence. Application of nonstandard, topological methods to describe the structural properties of the turbulent state is considered and the transition to kinetic equations in fractional derivatives for describing the microscopic behavior of a medium is examined. Central to the discussion is the concept of the percolation constant $\mathcal C\approx 1.327\dots$, a universal parameter describing the topology of nonequilibrium (quasi)stationary states in complex nonlinear dynamical systems allowing self-organized critical behavior. Much attention is given to the formation of power-law energy density spectra in turbulent media. A number of topical problems in modern cosmic electrodynamics, including the self-consistent fractal model of a turbulent current sheet, substorm dynamics, and the formation and dynamical evolution of large-scale magnetic fields in the solar photosphere and interplanetary space, are also discussed.
Received: July 4, 2003
Revised: March 30, 2004
English version:
Physics–Uspekhi, 2004, Volume 47, Issue 8, Pages 749–788
DOI: https://doi.org/10.1070/PU2004v047n08ABEH001705
Bibliographic databases:
Document Type: Article
PACS: 05.40.-a, 05.45.Df, 05.65.+b, 94.30.-d
Language: Russian
Citation: L. M. Zelenyi, A. V. Milovanov, “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics”, UFN, 174:8 (2004), 809–852; Phys. Usp., 47:8 (2004), 749–788
Citation in format AMSBIB
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\by L.~M.~Zelenyi, A.~V.~Milovanov
\paper Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics
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\vol 174
\issue 8
\pages 809--852
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\crossref{https://doi.org/10.3367/UFNr.0174.200408a.0809}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004PhyU...47R...1Z}
\transl
\jour Phys. Usp.
\yr 2004
\vol 47
\issue 8
\pages 749--788
\crossref{https://doi.org/10.1070/PU2004v047n08ABEH001705}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000225645400001}
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  • https://www.mathnet.ru/eng/ufn/v174/i8/p809
  • This publication is cited in the following 244 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Успехи физических наук Physics-Uspekhi
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