Related papers: Do we observe L\'evy flights in cosmic rays?
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
Recent direct measurements of Galactic cosmic ray spectra by balloon/space-borne detectors reveal spectral hardenings of all major nucleus species at rigidities of a few hundred GV. The all-sky diffuse gamma-ray emissions measured by the…
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk…
A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the…
Various aspects of the connection between cloud cover (CC) and cosmic rays (CR) are analysed. We argue that the anticorrelation between the temporal behaviour of low (LCC) and middle (MCC) clouds evidences against causal connection between…
L\'{e}vy walk is a practical model and has wide applications in various fields. Here we focus on the effect of an external constant force on the L\'{e}vy walk with the exponent of the power-law distributed flight time $\alpha\in(0,2)$. We…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
The bulk of observed ultrahigh energy cosmic rays could be light or heavier elements, and originate from an either steady or transient population of sources. This leaves us with four general categories of sources. Energetic requirements set…
A shape of lateral distribution for charged particles in events with energy above 10^19eV is considered. Two methods were used for individual LDF parametrization. In the first approach, the index of power was determined for generalized…
Firm evidence for a radio emission counterpart of cosmic ray air showers is presented. By the use of an antenna array set up in coincidence with ground particle detectors, we find a collection of events for which both time and arrival…
While there is some level of consensus on a Galactic origin of cosmic rays up to the knee ($E_{k}\sim 3\times 10^{15}$ eV) and on an extragalactic origin of cosmic rays with energy above $\sim 10^{19}$ eV, the debate on the genesis of…
We provide our estimates of the intensity of the gamma-ray emission with an energy near 0.1 TeV generated in inrergalactic space in the interactions of cosmic rays with background emissions. We assume that the cosmic ray sources are…
Observations of cosmic rays have been improving at all energies, with higher statistics and reduced systematics. Fundamental questions remain regarding the origins of cosmic rays both within the Galaxy and in extragalactic sources, and new…
In this Letter we examine the arrival directions of the most energetic cosmic rays (E > 2 * 10^19 eV) detected by several air shower experiments. We find that data taken by different air shower arrays show positive correlations, indicating…
The gamma-ray sky >100 MeV is dominated by the diffuse emissions from interactions of cosmic rays with the interstellar gas and radiation fields of the Milky Way. Observations of these diffuse emissions provide a tool to study cosmic-ray…
Cosmic-ray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is two-fold turbulent mixing in that the particle…
We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the L\'evy-Lorentz gas, namely a 1-d model characterized by a fat polynomial tail of the distribution of…
The topological defect scenario of origin of the observed highest energy cosmic rays is reviewed. Under a variety of circumstances, topological defects formed in the early Universe can be sources of very massive particles in the Universe…
Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with…
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…