Related papers: Diffusive shock acceleration: non-classical model …
We study the dynamics of a tracer particle subject to a constant driving force $E$ in a one-dimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer grows…
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…
The theory of particle acceleration at shock fronts is briefly reviewed, with special emphasis on the production of the particles responsible for the nonthermal emission from blazars. The flat radio/IR spectra of these sources cannot be…
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…
We explore the physics of shock evolution and particle acceleration in non-relativistic collisionless shocks using multidimensional hybrid simulations. We analyze a wide range of physical parameters relevant to the acceleration of cosmic…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Diffusive shock acceleration is invoked to explain non-thermal particle acceleration in Supernova Remnants, Active Galactic Nuclei (AGN) Jets, Gamma ray Bursts (GRBs) and various large scale cosmic structures. The importance of achieving…
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
The momentum distribution of particles accelerated at strong non-relativistic shocks may be influenced by the spatial distribution of the flow speed around the shock. This phenomenon becomes evident in the cosmic-ray modified shock, where…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
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.…
A recent model of Ariel et al. [1] for explaining the observation of L\'evy walks in swarming bacteria suggests that self-propelled, elongated particles in a periodic array of regular vortices perform a super-diffusion that is consistent…
Propagation of energetic particles across the mean field direction in turbulent magnetic fields is often described as spatial diffusion. Recently, it has been suggested that initially the particles propagate systematically along meandering…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…
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…
Electron acceleration to non-thermal, ultra-relativistic energies (~ 10-100 TeV) is revealed by radio and X-ray observations of shocks in young supernova remnants (SNRs). The diffusive shock acceleration (DSA) mechanism is usually invoked…
The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have…
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,…
Motivated by cosmic ray (CR) re-acceleration at a potential Galactic Wind Termination Shock (GWTS), we present a numerical model for time-dependent Diffusive Shock Acceleration (DSA). We use the stochastic differential equation solver…