It is shown that the acceleration of particles by a powerful relativistic jet associated with the activity of a supermassive black hole in the Galactic center several million years ago may explain the observed cosmic ray spectrum at energies higher than $10^{15}$ eV. The accelerated particles are efficiently confined in the extended magnetized gas halo created by the supernova and central black hole activity just after the Galaxy formation. We found that both the heavy and light chemical composition of ultra-high energy cosmic rays can be consistent with observations.

It is shown that the relativistic jets associated with the growth and past activity of the supermassive black hole in the Andromeda galaxy could be the main source of cosmic rays with energies above $10^{15}$ eV. Most of the cosmic ray energy is related to a bow shock of the jet that produces multi-PeV cosmic rays with light composition. The highest energy cosmic rays with heavy composition are produced in the jet itself. The spectra of energetic particles produced in Andromeda galaxy and propagated to the Earth are calculated and compared with observations.

Acceleration of cosmic rays in astrophysical jets is investigated. Particles are accelerated at the outer bow shock and by shear flows in the jet cocoon. Applications for the origin and chemical composition of ultra-high-energy cosmic rays are discussed.

The propagation of ultrahigh-energy cosmic rays from nearby sources is studied. It is shown that the spectrum, chemical composition, and anisotropy observed at energies above 5 × 1018 eV can be explained within the model of one nearby galaxy (M87) if the source is strongly enriched with heavy nuclei.

We consider diffusive shock acceleration in supernova remnants throughout their evolution including a radiative stage. It is found that a more efficient acceleration and fast exit of particles at the radiative stage results in the hardening of the source cosmic ray proton and electron spectra at energies $\sim 100-500$ GeV. The effect is stronger for cosmic ray electrons.

The transport equation for cosmic rays in the Galaxy is solved simultaneously with equation for energy density of magnetohydrodynamic turbulence. The obtained spectra of cosmic ray nuclei with energies 105 to 1011 eV are consistent with observational data, including the peak in the ratio of secondary to primary nuclei fluxes at around 1 GeV/nucleon.

A study is performed of the acceleration of cosmic rays by shock waves propagating in bubbles of hot rarefied gas created by the stellar wind of supernova progenitors. Spectra of accelerated particles produced in type Ib/c supernova remnants are determined.

A study is performed of the effect the cosmological evolution and spatial distribution of sources have on solving the inverse problem of determining the spectra of ultrahigh energy cosmic ray sources. The solution allows for the propagation and energy losses of protons and nuclei in the expanding Universe. It is established that active galactic nuclei are the most probable sources of ultrahigh energy cosmic rays.

The heliospheric modulation potential of galactic cosmic rays (CRs) is reconstructed for the era of neutron monitoring. It is based on using a modern model of the interstellar spectrum of galactic CRs and the spectrum of CR density variations. The spectrum of CR variations is obtained via global spectrographic processing of continuous monitoring data from the world network of detectors and is calibrated using data from direct measurements of the particle spectrum on the PAMELA magnetic spectrometer in base year 2009.

The inverse problem of cosmic ray transport of ultra-high energy cosmic rays is considered. The source spectrum and composition are derived based on the Auger data on energy spectrum, energy dependence of mean logarithm of atomic mass number and its variance. The regularization procedure for considered ill-posed problem and the statistical analysis of experimental data are employed.

We investigate acceleration of cosmic rays by shocks and accretion flows in galaxy clusters. Numerical results for spectra of accelerated particles and nonthermal emission are presented. It is shown that the acceleration of protons and nuclei in the nearby galaxy cluster Virgo can explain the observed spectra of ultra high energy cosmic rays.

The inverse problem of cosmic ray transport of ultra-high energy cosmic rays is considered. The source spectrum and composition are derived based on the recent Auger data on energy spectrum, energy dependence of mean logarithm of atomic mass number and its variance. The dependence of results on the extrapolation of observable spectrum beyond energies 10(20) eV is investigated.

The monthly rigidity spectrum of cosmic ray (CR) variations in the 19-24 cycles of solar activity was obtained by the global survey method using the data of continuous ground and near-Earth monitoring of CRs, exempted from atmospheric and local effects.The changes of the spectrum, first obtained for such a long period, made it possible to reveal the features of large-scale effects in CR modulation, the presence of 22-year and 11-year CR variations in the spectrum, and confirm an abnormal spectrum change in the 70s. The paper assumes a rigidity spectrum of CRs, given in a three-parameter form. Analysis of the obtained long-term CR variations for particles with rigidity 10 GV shows that the amplitude of the 22-year wave in the CR intensity increases from cycle to cycle and reaches its maximum value at the minimum of 23/24th solar activity cycle. Softening of the spectrum at the cycle minima has been revealed for the negative polarity of the solar magnetic field (qA<0). The reasons for the abnormally high CR density at the minimum of the 24th cycle and the spectrum features in the 70s are discussed. The spectrum of long-term CR variations in the 19-24 solar activity cycles, determined from the experimental data, makes it possible to verify some conclusions of the theory of heliospheric CR modulation concerning the role of the magnetic drift of particles in cycles with the different polarity of the solar magnetic field. In particular, we propose the explanation for the observed R−2 spectrum of the variations in the minima of the negative solar activity cycles, related with the scattering of particles in the vicinity of the neutral current sheet.

Cosmic ray acceleration by astrophysical shocks in supernova remnants is briefly reviewed. Results of numerical modeling taking into account magnetic field amplification by streaming instability and shock modification are presented. Nonthermal emission produced by accelerated particles in young and old supernova remnants is compared with available data of radio, X-ray, and gamma-ray astronomy. We also discuss a possibility of particle acceleration to PeV energies at supernova shocks propagating in the interstellar bubbles created by stellar winds of supernova progenitors.

A nonlinear model of cosmic-ray acceleration at the shock fronts in the supernova remnants W28, W44, and IC433 is investigated. The hydrodynamic evolution of a supernova remnant, including the shock modification by the pressure of accelerated particles and the streaming instability of particles upstream of the shock propagating in a partially ionized interstellar gas, is modeled. The electromagnetic radiation generated by accelerated particles is calculated and compared with observations in a wide range of photon energies.

Cosmic ray acceleration by astrophysical shocks in supernova remnants is briefly reviewed. Results of numerical modeling taking into account the magnetic field amplification by streaming instability and the shock modification are presented. Nonthermal emission produced by accelerated particles in old supernova remnants is compared with available data of modern radio, X-ray and gamma-ray astronomies. It is also shown that high-energy neutrinos produced in young supernova remnants of Type IIn extragalactic supernova can explain the recent IceCube detection of astrophysical neutrinos.

We consider the diffusive shock acceleration in interstellar bubbles created by powerful stellar winds of supernova progenitors. Under the moderate stellar wind magnetization the bubbles are filled by the strongly magnetized low density gas. It is shown that the maximum energy of particles accelerated in this environment can exceed the ”knee” energy in the observable cosmic ray spectrum.