Related papers: Fractional diffusion of cosmic rays
The enigma of cosmic ray origin and propagation stands as a key question in particle astrophysics. The precise spatial and spectral measurements of diffuse Galactic gamma-ray emission provide new avenues for unraveling this mystery. Based…
A new conceptual approach for examining the origin of cosmic rays is developed by considering the characteristics of particle trajectory distributions in four-dimensional Euclidean space-time. Transformation of an isotropic distribution…
Cosmic ray propagation in the Milky Way and other galaxies is largely diffusive, with mean free path determined primarily by pitch angle scattering from hydromagnetic waves with wavelength of order the cosmic ray gyroradius. In the theory…
The arrival directions of Galactic cosmic rays exhibit anisotropies up to the level of one per-mille over various angular scales. Recent observations of TeV-PeV cosmic rays show that the dipole anisotropy has a strong energy dependence with…
This paper is devoted to the anomalous diffusion limit of kinetic equations with a fractional Fokker-Planck collision operator in a spatially bounded domain. We consider two boundary conditions at the kinetic scale: absorption and specular…
Nowadays, the calculation of the Galactic Cosmic Rays diffusion coefficient with direct microscopic numerical simulations is a widespread approach. In this work, we investigated the numerical limits for such calculations and demonstrated…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
The propagation of $\gamma$ rays over very large distances provides new insights on the intergalactic medium and on fundamental physics. On their path to the Earth, $\gamma$ rays can annihilate with diffuse infrared or optical photons of…
Cosmic ray anisotropy has been observed in a wide energy range and at different angular scales by a variety of experiments over the past decade. However, no comprehensive or satisfactory explanation has been put forth to date. The arrival…
Using a so-called hemispherical model we derive a general transport equation for cosmic ray and thermal particles scattered in pitch angle by magnetic inhomogeneities in a moving collisionless plasma. The weak scattering through 90 degrees…
The theory of diffusive particle acceleration explains the spectral properties of the cosmic rays below energies of approx. 10^6 GeV as produced at strong shocks in supernova remnants (SNR's). To supply the observed flux of cosmic rays, a…
Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
We present two observations related to theapplication of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE.…
The distribution of arrival directions of cosmic rays is remarkably isotropic, which is a consequence of their repeated scattering in magnetic fields. Yet, high-statistics observatories like IceCube and HAWC have revealed the presence of…
Recent advances on gamma-ray observations from SuperNova Remnants and Molecular Clouds offer the possibility to study in detail the properties of the propagation of escaping Cosmic Rays (CR). However, a complete theory for CR transport…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
We explore the impact of diffusive cosmic rays (CRs) on the evolution of the interstellar medium (ISM) under varying assumptions of supernova explosion environment. In practice, we systematically vary the relative fractions of supernovae…
We use a diffusion galactic model to analyze the end of the Galactic cosmic ray spectrum and its mixing with the extragalactic cosmic ray flux. We analyze the transition between Galactic and extragalactic components using two different…