Related papers: Do we observe L\'evy flights in cosmic rays?
When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and…
Ultra-high energy cosmic ray protons accelerated in astrophysical objects produce secondary electromagnetic cascades during propagation in the cosmic microwave and infrared backgrounds. We show that such cascades can contribute between ~1%…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
Two models of anomalous diffusion of cosmic ray in the leaky-box approximation are compared: one of them is based on the decoupled time-space L\'evy flights and the other on fractional walks with a finite free motion velocity. Distributions…
In the new precision era for cosmic ray astrophysics, theoretical predictions cannot content themselves with average trends, but need to correctly take into account intrinsic uncertainties. The space-time discreteness of the cosmic ray…
The lateral distribution function (LDF) for coherent electromagnetic radiation from air showers initiated by ultra-high-energy cosmic rays is calculated using a macroscopic description. A new expression is derived to calculate the coherent…
Ultra-high energy cosmic rays are mostly charged particles and they are therefore deflected by magnetic fields on their path from their sources to Earth. An interesting phenomenon arising from these deflections is the appearance of multiple…
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…
The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian. However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to…
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…
Propagation of ultra-high energy photons in the galactic and intergalactic space gives rise to cascades comprising thousands of photons. Using Monte Carlo simulations, we investigate the development of such cascades in the solar…
We study the statistics of encounters of L\'evy flights by introducing the concept of vicious L\'evy flights - distinct groups of walkers performing independent L\'evy flights with the process terminating upon the first encounter between…
We study L\'{e}vy-like and truncated L\'{e}vy-like flights with step probability distribution of the form $r^{-1+\nu}$ for negative, positive, and zero $\nu$, focusing on the appearance of fractal geometry characteristics in the generated…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
The galactic diffuse $\gamma$-ray emission, as seen by Fermi Large Area Telescope (LAT), shows a sharp peak in the region around 4 kpc from the Galactic center, which can be interpreted either as due to an enhanced density of cosmic-ray…
Cosmic-ray (CR) sources temporarily enhance the relativistic particle density in their vicinity over the background distribution accumulated from the Galaxy-wide past injection activity and propagation. If individual sources are close…
Temporal broadening of pulsar signals results from electron density fluctuations in the interstellar medium that cause the radiation to travel along paths of different lengths. The Gaussian theory of fluctuations predicts that the pulse…
Recent multifrequency observations contribute to derive a comprehensive picture of the origin and evolution of relativistic particles in galaxy clusters. In this review I briefly discuss theoretical aspects and open problems of this…
We employed the method of virial expansion in order to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We found that the…
We calculate the flux of ultra high energy photons from individual ordinary (i.e. non-superconducting) cosmic strings and compare the results with the sensitivity of current and proposed TeV and EeV telescopes. Our calculations give only…