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UFN, 2004, Volume 174, Number 8, Pages 809–852 (Mi ufn78)  

This article is cited in 171 scientific papers (total in 171 papers)


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

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 $\mathcal C\approx 1.327…$, 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.


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English version:
Physics–Uspekhi, 2004, 47:8, 749–788

Bibliographic databases:

PACS: 05.40.-a, 05.45.Df, 05.65.+b, 94.30.-d
Received: July 4, 2003
Revised: March 30, 2004

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
\by L.~M.~Zelenyi, A.~V.~Milovanov
\paper Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics
\jour UFN
\yr 2004
\vol 174
\issue 8
\pages 809--852
\jour Phys. Usp.
\yr 2004
\vol 47
\issue 8
\pages 749--788

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