TITLE:
Nonlocal Models of Cosmic Ray Transport in the Galaxy
AUTHORS:
Vladimir V. Uchaikin
KEYWORDS:
Nonlocal Model, Anomalous Diffusion, Fractional Derivative, Fractal, Turbulence, Plasma, Cosmic Rays
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.2,
January
30,
2015
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.