相关论文: Fractional diffusion of cosmic rays
One of the unsolved problems in cosmic ray (CR) physics is the small radial gradient of the gamma-ray intensity compared to the inferred CR source distribution in the Galactic disk. In diffusive CR propagation models the most natural…
We consider the propagation of cosmic rays in turbulent magnetic fields. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulations, in which the turbulence is injected on large scale and cascades to small…
We consider the problem of the cosmic ray spectrum formation assuming that cosmic rays are produced by Galactic sources. The anomalous diffusion equation proposed in our recent papers is used to describe cosmic ray propagation in the…
We calculate the energy spectra and mass composition of cosmic rays in energy region 1 - 10^8 GeV/particle under the assumption that cosmic rays propagation in the Galaxy is described by anomalous diffusion equation. Our results and…
We obtain the angular distribution of the cosmic rays reaching an observer from an individual source and after propagation through a turbulent magnetic field, for different ratios between the source distance and the diffusion length. We…
The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the…
The propagation of cosmic rays can be described as a diffusive motion in most galactic environments. High-energy gamma-rays measured by Fermi have allowed inference of a gradient in the cosmic-ray density and spectral energy behavior in 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…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
We present an analytic solution to diffusion equation for high energy cosmic rays in the expanding universe. The particles are assumed to be ultra-relativistic and they can have energy losses arbitrarily dependent on energy and time. The…
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…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
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…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…