Related papers: Do we observe L\'evy flights in cosmic rays?
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The…
It is known from some time that to explain some apparently {\it exotic events} observed in cosmic ray experiments, a deeply penetrating component in cosmic rays is needed, which, in turn, leads frequently to the nonexponential distributions…
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 investigate the possibility that ultra high energy cosmic rays (E > 10^19 eV) are related to the distribution of matter on large scales. The large scale structure (LSS) data stems from the recent IRAS PSCz redshift survey. We present…
Recently, anomalous superdiffusion of ultra cold 87Rb atoms in an optical lattice has been observed along with a fat-tailed, L\'evy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical…
The multiple scattering of photons in a hot, resonant, atomic vapor is investigated and shown to exhibit a L\'evy Flight-like behavior. Monte Carlo simulations give insights into the frequency redistribution process that originates the long…
We report the studies of emission from a novel random amplifying medium that we term a ``Levy Laser'' due to the non-Gaussian statistical nature of its emission over the ensemble of random realizations. It is observed that the amplification…
Cosmic rays with energies above $10^{19}$ eV, observed in 1999-2004 by the High Resolution Fly's Eye (HiRes) experiment in the stereoscopic mode, were found to correlate with directions to distant BL Lac type objects (BL Lacs), suggesting…
Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However,…
A number of seemingly {\it exotic} phenomena seen in the highest cosmic-ray experiments are briefly discussed. We argue that they indicate existence of non-statistical fluctuations and strong correlations in the fragmentation region of…
It is presumed that the observed cosmic rays up to about $3\times 10^{18}$ eV are of Galactic origin, the particles being the ones which are found in the composition of the stellar winds of stars that explode as supernova into the…
We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a L\'evy flight random walk. For such system, the step-length distribution can be modeled as…
We study symmetric L\'evy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the L\'evy process. Incorporating the boundary…
The cosmic rays spectrum has been shown to extend well beyond 10^20 eV. With nearly 20 events observed in the last 40 years, it is now established that particles with energies near or above 10^21 eV. No nearby astrophysical object has been…
Rayleigh-Levy flights have played a significant role in cosmology as simplified models for understanding how matter distributes itself under gravitational influence. These models also exhibit numerous remarkable properties that enable the…
We present theoretical and experimental results of L\'evy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between…
The particle lateral distribution function (LDF) of air showers at a given altitude is sensitive to the mass composition and primary energy of cosmic rays. Studies of the LDF are difficult to perform due to experimental effects such as…
Cosmic rays (CRs) generate diffuse emission while interacting with the Galactic magnetic field (B-field), the interstellar gas and the radiation field. This diffuse emission extends from radio, microwaves, through X-rays, to high-energy…