Related papers: Fractional diffusion of cosmic rays
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
The escape of cosmic rays from the Galaxy is expected to shape their spectrum inside the Galaxy. Yet, this phenomenon is very poorly understood and, in the absence of a physical description, it is usually modelled as free escape from a…
Propagation of cosmic rays (CRs) in turbulent and magnetized astrophysical media is a long-standing problem that requires both understanding of the properties of turbulent magnetic fields and their interaction with energetic particles. This…
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…
Recently a new transport theory of cosmic rays in magnetized space plasmas extending the quasilinear approximation to the particle orbit has been developed for the case of an axisymmetric incompressible magnetic turbulence. Here we…
An extensive program for the calculation of galactic cosmic-ray propagation has been developed. This is a continuation of the work described in Strong & Youssefi (1995). The main motivation for developing this code is the prediction of…
We have developed a model which aims to reproduce observational data of many kinds related to cosmic-ray (CR) origin and propagation: direct measurements of nuclei, antiprotons, electrons and positrons, gamma-rays, and synchrotron…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
The propagation length of high-energy photons through the Universe is limited by $e^+e^-$ pair production on the extragalactic background radiation. Previous studies reported discrepancies between predicted and observed attenuation,…
We survey the theory and experimental tests for the propagation of cosmic rays in the Galaxy up to energies of 10^15 eV. A guide to the previous reviews and essential literature is given, followed by an exposition of basic principles. The…
The nuclei fraction in cosmic rays (CR) far exceeds the fraction of other CR species, such as antiprotons, electrons, and positrons. Thus the majority of information obtained from CR studies is based on interpretation of isotopic abundances…
We study the solution of the diffusion equation for Ultra-High Energy Cosmic Rays in the general case of an expanding universe, comparing it with the well known Syrovatsky solution obtained in the more restrictive case of a static universe.…
A wave pulse (be it a gravitational wave or a light wave) undergoes anomalous dispersion in a vacuum in flat spacetimes with an even number of spatial dimensions even if all the frequencies move at the same speed. Such an anomalous…
We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
How and where cosmic rays are produced, and how they diffuse through various turbulent media, represent fundamental problems in astrophysics with far reaching implications, both in terms of our theoretical understanding of high-energy…
Multichannel Cosmic Ray (CR) spectra and the large scale CR anisotropy can hardly be made compatible in the framework of conventional isotropic and homogeneous propagation models. These models also have problems explaining the longitude…
The observation of the diffuse Galactic gamma ray flux is the most powerful tool to study cosmic rays in different regions of the Galaxy, because the energy and angular distributions of the photons encode information about the density and…
We present the results of a numerical simulation of propagation of cosmic rays with energy above $10^{15}$ eV in a complex magnetic field, made in general of a large scale component and a turbulent component. Several configurations are…