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We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker-Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of magneto-hydrodynamic (MHD) equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming well as adiabatic compression and several radiative loss mechanisms. We discuss applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.
We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-$Lstar$ starburst, and $Lstar$ gala
This work has the main objective to provide a detailed investigation of cosmic ray propagation in magnetohydrodynamic turbulent fields generated by forcing the fluid velocity field at large scales. It provides a derivation of the particle mean free p
We propose a machine learning method to investigate the propagation of cosmic rays, based on the precisely measured spectra of primary and secondary nuclei Li, Be, B, C, and O by AMS-02, ACE, and Voyager-1. We train two Convolutional Neural Network m
The High Altitude Water Cherenkov (HAWC) telescope recently observed extended emission around the Geminga and PSR~B0656+14 pulsar wind nebulae (PWNe). These observations have been used to estimate cosmic-ray (CR) diffusion coefficients near the PWNe
Information on cosmic-ray (CR) composition comes from direct CR measurements while their distribution in the Galaxy is evaluated from observations of their associated diffuse emission in the range from radio to gamma rays. Even though the main intera