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Nonlocal Models of Cosmic Ray Transport in the Galaxy

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http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53678#.VM8xcSzQrzE

Author(s) 
Vladimir V. Uchaikin

Affiliation(s)
Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk, Russia.

ABSTRACT
Studying the cosmic ray transport in the Galaxy, we deal with two interacting substances: charged particles and interstellar magnetic field. Two coupled local equations describe this complicated system, but elimination of one of them (say, the magnetic field equation) transforms remaining one (the cosmic rays equation) into the nonlocal form. The most popular nonlocal operators in the cosmic ray physics are integro-differential operators of fractional order. This report contains review of recent works in this direction, including original results of the author. In the last section, some specific problems are discussed: fractional operators with soft truncation of their kernels, nonlocal properties of fractional Laplacian, and a true form of the fractional material derivative.

KEYWORDS
Nonlocal Model, Anomalous Diffusion, Fractional Derivative, Fractal, Turbulence, Plasma, Cosmic Rays

Cite this paper
Uchaikin, V. (2015) Nonlocal Models of Cosmic Ray Transport in the Galaxy. Journal of Applied Mathematics and Physics, 3, 187-200. doi: 10.4236/jamp.2015.32029.

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