Related papers: Fractional diffusion of cosmic rays

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…

The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a…

Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal…

Diffuse $\gamma$-ray emission is a key probe of cosmic rays (CRs) distribution within the Galaxy. However, the discrepancies between observations and theoretical model expectations highlight the need for refined uncertainty estimates. In…

Supernova remnants have long been considered as a promising candidate for sources of Galactic cosmic rays. However, modelling cosmic-ray transport around these sources is complicated by the fact that the overdensity of cosmic rays close to…

In this effort we exactly solve the fractional diffusion-advection equation for solar cosmic-ray transport proposed in \cite{LE2014} and give its {\it general solution} in terms of hypergeometric distributions. Also, we regain all the…

In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals.…

Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…

The spatial distribution of cosmic ray (CR) particles in the interstellar medium (ISM) is of major importance in radio astronomy, where its knowledge is essential for the interpretation of observations, and in theoretical astrophysics,…

The search for the origin of cosmic rays is as active as ever, mainly driven by new insights provided by recent pieces of observation. Much effort is being channelled in putting the so called supernova paradigm for the origin of galactic…

Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…

In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale self-affine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory…

The supernova paradigm for the origin of galactic cosmic rays has been deeply affected by the development of the non-linear theory of particle acceleration at shock waves. Here we discuss the implications of applying such theory to the…

We develop a theory to account for the cosmic ray spectrum between 1 GeV and 10^4 GeV following the earlier papers of this series. We use the basic concept that the cosmic ray particles are accelerated in a supernova shock that travels…

Continuum gamma-ray emission produced by interactions of cosmic rays with interstellar matter and radiation fields is a probe of non-thermal particle populations in galaxies. After decades of continuous improvements in experimental…

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…

Using the methods of computer modeling this scientific paper studies the special features of diffusion of the particles subjected to the external periodic force in the crystal lattice. The particle motion is described by a Langevin…

We study the large-scale distribution of the arrival directions of the highest energy cosmic rays observed by various experiments. Despite clearly insufficient statistics, we find a deficit of cosmic rays at energies higher than 10^{20} eV…

We introduce a novel diffusion model for the propagation of cosmic rays (CRs) that incorporates an anisotropic diffusion tensor of a general form within a realistically modeled large-scale Galactic magnetic field. The parameters of the…

Cosmic rays are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads to the excitation of both resonant and non-resonant streaming instabilities. The self-generated…