Related papers: Do we observe L\'evy flights in cosmic rays?
Cosmic rays with energies above $10^{18}$ eV are currently of considerable interest in astrophysics and are to be further studied in a number of projects which are either currently under construction or the subject of well-developed…
We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…
Probing the anomalous nanoscale intermixing using molecular dynamics (MD) simulations in Pt/Ti bilayer we reveal the superdiffusive nature of interfacial atomic transport. It is shown that the Pt atoms undergo anomalous atomic transport…
Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…
After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of…
Several independent pieces of information have recently hinted at a prominent role of cosmic rays in controlling their own transport, within and around the sources as well as throughout their propagation on Galactic scales and even possibly…
The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300 \AA\ - 1700 \AA) is deduced to originate only partially in the dust-scattered radiation of FUV-emitting stars: the source of a substantial fraction of the FUV…
We study the deflection of ultra high energy cosmic ray protons in different models of the regular galactic magnetic field. Such particles have gyroradii well in excess of 1 kpc and their propagation in the galaxy reflects only the large…
Our purpose is to evaluate the rate of the maximum energy and the acceleration rate that cosmic rays acquire in the non-relativistic diffusive shock acceleration as it could apply during their lifetime in various astrophysical sites, where…
A numerical and analytical study of the role of exponentially truncated L\'evy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov…
The problem of the origin of cosmic rays in the shocks produced by supernova explosions at energies below the so called 'knee' (at ~3*10$^6$ GeV) in the energy spectrum is addressed, with special attention to the propagation of the…
Concurrent observations of Lyman continuum (LyC) and Lyman-alpha (Lya) emission escaping from star-forming systems at low redshift are essential to understanding the physics of reionization at high redshift (z >~ 6). Some have suggested…
Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the…
Recent results by space borne experiments took cosmic ray data to a precision level. These new results are able to challenge the conventional scenario for cosmic ray acceleration and propagation in the Milky Way. In these contributions,…
A substantial increase of the mean logarithmic mass $<\ln A>$ of galactic cosmic rays {\em vs} energy has been observed . We study three effects that could explain this trend i) different source spectra for protons and heavy nuclei ii) a…
L\'{e}vy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of external potentials almost at anytime and anywhere. In…
The existence of cosmic ray particles up to the ultra-high energy limit (> 10^20 eV) is now beyond any doubt. The detection of cosmic particles with such energies imposes a challenge for the comprehension of their sources and nature. On one…
L\'evy flights and L\'evy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities are discontinuity versus continuity of their trajectories and…
An analysis of arrival directions of extensive air showers generated by cosmic rays in the PeV energy range and registered with the EAS MSU and EAS-1000 Prototype arrays reveals a considerable number of regions of excessive flux of cosmic…
The origin of the highest-energy cosmic rays remains a mystery. The lack of a high energy cutoff in the cosmic ray spectrum together with an apparently isotropic distribution of arrival directions have strongly constrained most models…