Related papers: Efficient numerical methods for Anisotropic Diffus…
The bulk propagation speed of GeV-energy cosmic rays is limited by frequent scattering off hydromagnetic waves. Most galaxy evolution simulations that account for this confinement assume the gas is fully ionized and cosmic rays are…
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…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered.…
In weakly collisional, strongly magnetised plasmas such as the intracluster medium (ICM), hot accretion flows and the solar corona, the transport of heat and momentum occurs primarily along magnetic field lines. In this paper we present a…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
The arrival directions of TeV-PeV cosmic rays are remarkably uniform due to the isotropization of their directions by scattering on turbulent magnetic fields. Small anisotropies can exist in standard diffusion models, however, only on the…
A cosmological hydrodynamic code is described, which includes a routine to compute cosmic ray acceleration and transport in a simplified way. The routine was designed to follow explicitly diffusive acceleration at shocks, and second-order…
Cosmic ray propagation in the Milky Way and other galaxies is largely diffusive, with mean free path determined primarily by pitch angle scattering from hydromagnetic waves with wavelength of order the cosmic ray gyroradius. In the theory…
Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and $p/$He spectral…
The measurement of large scale anisotropies in cosmic ray arrival directions is generally performed through harmonic analyses of the right ascension distribution as a function of energy. These measurements are challenging due to the small…
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field, and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using…
The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrix have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them…
Non-thermal emission from relativistic Cosmic Ray (CR) electrons gives insight into the strength and morphology of intra-cluster magnetic fields, as well as providing powerful tracers of structure formation shocks. Emission caused by CR…
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…
The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense…
Constraining the behavior of cosmic ray data observed at Earth requires a precise understanding of how the cosmic rays propagate in the interstellar medium. The interstellar medium is not homogeneous; although turbulent magnetic fields…
We calculate cosmic ray transport with a collisional Boltzmann Transport Equation, including E-M forces. We apply the Crank-Nicholson Method to solve this equation. At each time step, the spatial distribution of cosmic rays is applied to…
In this letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are…