相关论文: New Solution of Diffusion-Advection Equation for C…
In this effort we exactly solve the fractional diffusion-advection equation for solar cosmic-ray transport proposed in \cite{LE2014} and give its {\it general solution} in terms of hypergeometric distributions. Also, we regain all the…
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…
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…
We study the solution of the diffusion equation for Ultra-High Energy Cosmic Rays in the general case of an expanding universe, comparing it with the well known Syrovatsky solution obtained in the more restrictive case of a static universe.…
Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $\tilde B/\langle B\rangle \sim 1$ is present on top of the mean field gradient,…
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…
A theory of cosmic-ray transport in multi-phase diffusive media is developed, with the specific application to cases in which the cosmic-ray diffusion coefficient has large spatial fluctuations that may be inherently multi-scale. We…
We show the necessity for a new approach towards comprehensive and consistent simulations of the propagation of galactic cosmic rays. Our developments are optimised for addressing the spatially 3-dimensional inhomogeneous diffusion problem…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term.…
We consider the astrophysical implications of the diffusion equation solution for Ultra-High Energy Cosmic Rays (UHECR) in the expanding universe, obtained in paper I (V.Berezinsky & A.Gazizov, ApJ 643 (2006) 8). The UHECR spectra are…
We consider the propagation of galactic cosmic rays in the fractal interstellar medium. Steady state solution of the fractional diffusion equation, describing cosmic ray propagation, is found. We show that the exponent of the steady state…
We present a numerical algorithm for the incorporation of the active cosmic ray transport, into the ZEUS-3D magnetohydrodynamical code. The cosmic ray transport is described by the diffusion-advection equation. The applied form of the…
Super-bubbles are shells in the interstellar medium produced by the simultaneous explosions of many supernova remnants. The solutions of the mathematical diffusion and of the Fourier expansion in 1D, 2D and 3D were deduced in order to…
We model the transport of cosmic ray nuclei in the Galaxy by means of a new numerical code. Differently from previous numerical models we account for a generic spatial distribution of the diffusion coefficient. We found that in the case of…
Cosmic ray transport on galactic scales depends on the detailed properties of the magnetized, multiphase interstellar medium (ISM). In this work, we post-process a high-resolution TIGRESS magnetohydrodynamic simulation modeling a local…
Conventional cosmic-ray propagation models usually assume an isotropic diffusion coefficient to account for the random deflection of cosmic rays by the turbulent interstellar magnetic field. Such a picture is very successful in explaining…
We present results obtained from our newly developed Galactic cosmic-ray transport code PICARD, that solves the cosmic-ray transport equation. This code allows for the computation of cosmic-ray spectra and the resulting gamma-ray emission.…
The origin of the ultrahigh energy cosmic ray remains being a mystery. However, a considerable progress has been made in the past few years due to the good quality data recorded by current cosmic ray observatories. One of the recent…
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…