Inverse problem for the equation of ultrahigh energy cosmic ray transport

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.     

Solving the inverse transport problem in intergalactic space and determining the energy spectrum and composition of extragalactic sources of ultrahigh-energy particles

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.     

Maximum energy of cosmic rays accelerated in supernova remnants

Amplification of the magnetic field in young supernova remnants leads to the corresponding increase in the maximum energy of particles approximately to the knee energy 3 × 10¹⁵ eV at the end of the free expansion stage. The knee in the spectrum of cosmic rays is due to the transition of the supernova remnant from the free expansion stage to the Sedov stage. The knee energy is calculated for different types of supernovae. The maximum energy of accelerated particles teaches Z × 10¹⁷ eV for the observed remnant expansion velocities.     

Nonlinear propagation of cosmic rays in the galaxy

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.     

Determining the elastic equilibrium of a cylindrical shell by Vekua’s theory based on the classical elasticity theory and the theory of binary mixtures

Using the approach based on separation of variables, an analytic solution of the class of boundary value problems of the shallow cylindrical shell theory is constructed by Vekua’s method. The cylindrical shell is assumed to be rectangular in the plan. Conditions of a free support or sliding fixation are given on the sides of the rectangle; the load on the shell being arbitrary. The solution of boundary value problems is constructed using both a classical elastic medium and the theory of binary mixtures. Analysis of the constructed solutions is carried out.     

Some non-classical thermoelasticity problems for a rectangular parallelepiped

Meccanica - In the Cartesian system of coordinates, thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. On the lateral faces of a parallelepiped either...     

Induced scattering and two-photon absorption of Alfvén waves with arbitrary propagation angles

An equation for the spectral energy density of collisionless Alfvén waves, propagating at arbitrary angles to the average magnetic field, is derived on the basis of the theory of weak turbulence. The main nonlinear processes for the case studied are induced scattering and two-photon absorption of Alfvén waves by thermal ions. An equation is derived for thermal particles which describes particle diffusion, accompanying these processes, in momentum space. The results are qualitatively different from previous results obtained by other authors for Alfvén waves propagating along the average magnetic field.     

Cosmic ray spectrum produced by galactic supernova remnants

Cosmic ray acceleration by supernova shocks is considered. A new numerical code is used to describe the cosmic ray acceleration and shock wave evolution. The magnetohydrodynamic turbulence generation in the shock precursor by streaming instability of accelerated particles is taken into account. The cosmic ray spectrum produced by supernova explosion in uniform interstellar medium is simulated.     

Spectrum of galactic cosmic rays accelerated in supernova remnants

The spectra of protons, nuclei, and electrons accelerated by shocks in supernova remnants of different types were determined. The calculations were made using a numerical code that allows us to model spherical shock evolution and particle acceleration with allowance for the back reaction of accelerating particles on a hydrodynamic flow. The effect of Alfvenic particle drift in the amplified magnetic field in the regions upstream and downstream of the shock was taken into consideration. The maximum energy of accelerated particles is as high as ∼5 × 10¹⁸ eV for iron nuclei in Type IIb supernova remnants. The calculated spectrum and composition of cosmic rays in the interstellar medium are in good agreement with observations.