Volume 193, Nº 3 (2023)

Mathematical modeling of the propagation of charged particles in the interstellar medium is a key aspect of the physics of cosmic rays. Improvements in measuring systems and enhancement of statistics via the results of extraterrestrial astronomy stimulate regular revisions of the computational models. Most of the currently used approaches are based on the local model of normal diffusion, which is attracting growing criticism. Reservations about this model arise because, first, it is in conflict with the relativistic principle of maximum speed and, second, it ignores specific spatial correlations in the properties of the turbulent interstellar medium. In this regard, in a previous review article by the first author (Physics–Uspekhi 56 1074 (2013)), some arguments were adduced in favor of a nonlocal model of cosmic ray transport based on fractional differential operators. In this review, we continue expounding on the physical and mathematical properties of the fractional differential theory, with more attention focused on the procedure for incorporating the features of the interstellar medium into nonlocal operators. New results obtained in the framework of this approach are presented, compared, and discussed.

A brief overview of the key methods for analyzing the structure of three-dimensional (3D) matter is given by using as an example melts of simple model systems like Lennard-Jones, Yukawa, and inverse power law. The behavior of simple structural measures characterizing matter near the melting line is considered in fine detail, and their advantages and disadvantages are discussed. Some indicators that characterize liquid near the melt line are proposed, and their universality and applicability for determining structure of melts of real liquids are discussed. Finally, the structural properties of two-dimensional (2D) liquids are compared with 3D ones. For 2D systems, simple universal criteria of melting are proposed, and their universality is shown using as an example a Yukawa system.

The paper presents the results of a study of the magnetic field dependences of the Hall and Nernst–Ettingshausen coefficients in a wide temperature range of 10–370 K in a thin ferromagnetic CoPt film formed on a semi-insulating gallium arsenide substrate by electron beam evaporation in a vacuum. The presence of the dominant contribution of the anomalous component of the effects in the entire investigated temperature range is shown. The experimentally obtained temperature dependences of the amplitude of the effects are presented, and they are compared with the theoretical model.