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.

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 inverse problem of cosmic ray transport of ultra-high energy cosmic rays is considered. The analysis of Auger data on energy spectrum, energy dependence of mean logarithm of atomic mass number and its variance allows definite conclusions on the shape of the source spectrum in the frameworks of the inverse problem approach. The discussion on regularization procedure for considered ill-posed problem is presented.

The propagation of ultrahigh-energy nuclei in an expanding Universe filled with background electromagnetic radiation is considered. A numerical method for solving the inverse problem for the equation of cosmic-ray transport is developed that allows the spectrum of sources to be determined from the cosmic-ray spectrum observed near the Earth. The spectra of injected protons and nuclei in extragalactic sources are found by assuming that they are functions of the magnetic rigidity of particles. The data from observations obtained in the Auger experiment are used.

The energy spectra of extragalactic sources of cosmic rays are calculated by solving an inverse problem of the transport of cosmic rays with energies of 10 18 –10 21 eV in a Universe filled with background electromagnetic radiation. Calculations are performed using cosmic-ray spectra measured on Earth in Auger experiments. It is assumed that protons and iron nuclei dominate in the composition of a source.

The propagation of ultrahigh energy nuclei in an expanding universe filled with background electromagnetic radiation is considered. A numerical method for solving the inverse problem for the equation of cosmic ray transport is developed. The method allows us to determine a source spectrum from the cosmic ray spectrum observed near Earth. The spectra of injected protons and nuclei of iron were found in extragalactic sources under the assumption that these types of particles predominate in the composition of the sources. The method of calculation is illustrated using observational data obtained in the Auger and Telescope Array experiments.

The worldwide neutron monitor network is a unique tool for obtaining with high accuracy the information on density variations, energy spectrum and anisotropy of comic rays at the Earth, outside its atmosphere and magnetosphere. These hourly averaged parameters were obtained over the whole period of cosmic ray monitoring by the ground level neutron monitor network (from 1957 till present) and are collected within the MySQL database. The Internet-project has developed for free access and supplying of cosmic ray density and anisotropy data in different formats.

Propagation of cosmic rays in the interstellar medium after their emergence from sources—supernova remnants—may be accompanied by the development of flow instability which forms high magnetohydrodynamic turbulence and leads to nonlinear cosmic ray diffusion. A self-similar solution to the nonlinear diffusion equations is found and it is shown that the noted mechanism leads to an effective diffusion coefficient of cosmic rays, which coincides with the empirical value.

The possible astrophysical origin of cosmic ray events above the GZK cutoff is discussed. The flux of particles accelerated in the bursts of Galactic sources and scattered back by random intergalactic magnetic fields is calculated.

eV and dominates at higher energies. Indications are that cosmic ray spectrum above 5×10 19 eV does not fall down as rapidly as it is expected at the uniform distribution of extragalactic sources. In the present work we show that in principle the tail of extremely energetic particles beyond the GZK cut off might be produced by the Galactic Gamma Ray Burst events or other types of exploding sources in the Galaxy if the accelerated particles are efficiently scattered back by random extragalactic magnetic field. The bursts in the Galaxy are rare and not directly seen at the present time that allows an understanding of high observed isotropy of cosmic rays.

Diffusive shock acceleration of energetic particles in a system of numerous stellar wind termination shocks and stellar-wind/supernova blast wave shocks is considered. We derive equations for the particle distribution function on momentum that describes collective particle acceleration. The form of the steady-state spectrum of accelerated particles depends on the global pattern of the interstellar gas flow. These results are discussed within a context of cosmic ray acceleration in star associations and in connection with a problem of cosmic ray reacceleration in the galactic disk.