Related papers: Efficient numerical methods for Anisotropic Diffus…
Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. But a well-known defect of diffusive approximation whereby some of the particles propagate unrealistically fast has directed…
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for substantial revisions in the picture of cosmic ray transport. In this paper we use recently obtained scaling laws for MHD modes to calculate the scattering…
We describe and discuss the properties of three numerical methods for solving the diffusion equation for the transport of the chemical species and of the angular momentum in stellar interiors. We study through numerical experiments both…
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…
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,…
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…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
In astrophysics, the search for sources of the highest-energy cosmic rays continues. For further progress, not only ever better observatories but also ever more realistic numerical simulations are needed. We compare different approaches for…
Context: An analytical solution of the generalized diffusive and convective transport equation is derived to explain the transport of cosmic ray protons within elliptical galaxies. Aims: Cosmic ray transport within elliptical galaxies is an…
We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic…
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…
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
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…
This paper presents an introduction to the astrophysics of cosmic rays and diffuse gamma rays and discusses some of the puzzles that have emerged recently due to more precise data and improved propagation models: the excesses in Galactic…
There is a growing set of observational data demonstrating that cosmic rays exhibit small-scale anisotropies (5-30 deg) with amplitude deviations lying between 0.01-0.1 percent that of the average cosmic ray flux. A broad range of models…
We argue that the diffusion of cosmic rays in the Galactic magnetic field has to be strongly anisotropic. As a result, the number of CR sources contributing to the local CR flux is reduced by a factor $\sim 200$. The CR density is therefore…
We constrain the energy at which the transition from Galactic to extragalactic cosmic rays occurs by computing the anisotropy at Earth of cosmic rays emitted by Galactic sources. Since the diffusion approximation starts to loose its…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic-ray transport. The transition from a…
Context. The diffusive shock acceleration mechanism has been widely accepted as the acceleration mechanism for galactic cosmic rays. While self-consistent hybrid simulations have shown how power-law spectra are produced, detailed…