The work considers planar channeling of relativistic particles in a comoving frame of reference moving at a speed equal to the longitudinal component of the velocity of the channeled particle. In SSO, the motion of a particle during planar channeling will be one-dimensional, and for electrons and positrons with energies up to several GeV it will be non-relativistic, as in the hydrogen atom. potential from transverse coordinates. To determine the main characteristics of such a movement, it is proposed to use approximate Bohr-Sommerfeld quantization methods, which make it possible to make such a calculation analytically. The approximate method for calculating quantum states can be extended to consider transverse motion beyond the nonrelativistic approximation, even in a comoving frame. The energy distributions of permissible states of transverse finite motion are found for several variants of model potentials. It is shown that, despite the difference in the structure of energy levels, the average distances between energy levels are practically insensitive to the choice of model potential. The energies of the transverse motion levels are found for the case when the nonrelativistic approximation is not applicable even in the comoving reference frame.

Based on the effects of thermal conductivity and heating/radiation losses, the dispersion of acoustic waves in a rarefied high-temperature plasma is studied using the example of the plasma of the solar corona. For the radiation loss function, an analytical approximation is used, based on the values found using the CHIANTI code. It is shown that the appearance of quasi-periodic oscillations can be explained by the specific properties of dispersion associated with the presence of a minimum group velocity in the space of wave numbers. The wavelet spectrum of acoustic vibrations in this case has a structure called “a boomerang”. A procedure for calculating periods using the constructed boomerang curve is proposed. It is assumed that the initial plasma disturbance has the form of a localized pulse having high dispersion qualities due to its wide spectrum. This approach has grounds, it is known, for example, that various kinds of non-stationary processes in the solar corona are generated under the action of short-term pulses from convective cells. The spectrum of the time signal considered at some point of observation is continuous, and the periods are determined based on the local maxima available in the spectrum. In this sense, the concept of quasi-periodic oscillations differs from the traditional one, which refers to the presence of a finite or countable number of periods between which there is a certain relationship. Calculations are carried out on the example of high-temperature plasma of the solar corona, where quasi-periodic oscillations are observed everywhere and can serve as a tool for studying the physical properties of coronal plasma.

The work examines the movement of relativistic particles (electrons) along close-packed chains of atoms in single crystals (axial channeling). The motion of electrons is considered in the accompanying reference frame (CFR), which itself moves with a speed equal to the longitudinal axis of the channeling and the velocity component of the channeled particle. In SSO, the motion of an axially channeled particle is two-dimensional (flat), and for electrons with energies up to several GeV it will be non-relativistic, as in the hydrogen atom. The quantum characteristics of motion are determined by the energy of the particle (it plays the role of the mass of the electron in a two-dimensional “atom”), as well as by the parameters of the average potential of the atomic chain, which depend on the crystallographic direction and chemical composition of the crystal. Axial channeling can be considered as a unique model of a relativistic two-dimensional atom with controlled parameters. The work shows that the main characteristics of quantum states of transverse motion of particles during axial channeling are weakly sensitive to the functional dependence of the parameters of the average potential on transverse coordinates. To calculate such characteristics, it is convenient to use Bohr’s approximate quantization method, which allows one to obtain the result analytically. The modified Bohr quantization method can be used to calculate the characteristics of transverse motion, which even goes beyond the nonrelativistic approximation even in SSO. In this work, the energy spectra of permissible states of transverse orbital motion are calculated for several variants of model axially symmetric potentials. It is shown that, despite differences in structure, the average distances between energy levels are slightly insensitive to the choice of potential model. The level energies were found both for the case when a nonrelativistic approximation is applicable to describe the transverse motion in the SSO, and in a situation that goes beyond the nonrelativistic approximation.

The study of economic processes is based on the study of a large number of parameters. In this connection, in order to analyze the phenomena under study and solve prognostic problems, there is a need to use methods of multidimensional data analysis. The article examines the problem of identifying suspicious, from the point of view of financial solvency, credit institutions operating in the Russian market. This study is aimed at developing a methodology for multidimensional data analysis to identify suspicious credit institutions and predict the revocation of their licenses. To solve this problem, it is proposed to use hierarchical and iterative methods of cluster analysis, as well as the principal component method. Based on these methods, a methodology for forming a risk zone has been developed that makes it possible to predict the revocation of licenses from credit institutions. To determine the number of clusters, the Ward clustering method was used, as well as the elbow method, the silhouette method, and the Davis-Bouldin method. The combined use of cluster analysis methods and the principal component method made it possible to demonstrate the robustness of the proposed methodology. Data from Bank Reporting Form No. 101 were used in this study.

 The paper discusses the dynamics of aerosols as applied to the spread of airborne viral infections in conditions where the mutual movement of the objects under study should be taken into account. This feature should be most strongly manifested in urban environments, where various traffic flows are an integral part of the habitat of modern man. The movement of individual particles in two-dimensional geometry under the influence of gravity and friction, as well as an external electrostatic field, is considered. Within the framework of the developed model, the influence of initial conditions determined by the physiological processes of respiration and the state of the environment on the dynamics of the spread of exhaled aerosols is studied. An assessment was made of the distances over which aerosol particles can spread depending on the size and initial velocities of the particles. Larger particles have been shown to travel longer distances. While smaller particles are «frozen» into the environment and can only spread with air currents. When applied to the transmission of viral infections, this means completely different types of virus transportation depending on the size and type of dispersed phase. The results obtained were applied to the analysis of the characteristics of spread for viruses in metro.

This paper analyzes the analytical expressions available in the literature for calculating the coefficient of viscosity and thermal conductivity obtained from the Chapman-Enskog kinetic theory. A modification of the expressions is proposed taking into account the calculated value of the compressibility factor Z = PV/RT, obtained as a result of thermodynamic calculations using a theoretical model of the equation of state based on perturbation theory. To validate the modified expressions, the Green-Kubo model for modeling transport properties by the molecular dynamics method is considered. This model allows, within one calculation, to simultaneously calculate both the viscosity and thermal conductivity values, having previously performed the statization of the system in the NpT ensemble. Molecular dynamics and thermodynamic modeling of the transport properties of individual helium and hydrogen isotopes was carried out in the pressure range of 1–2000 atm and in the temperature range of 200–3000 K. The values of the viscosity and thermal conductivity coefficients were determined in the considered pressure and temperature range. It is shown that the use of modified analytical expressions for transfer coefficients makes it possible to calculate the viscosity and thermal conductivity of helium and hydrogen isotopes, taking into account the real pressure in the system in accordance with experimental data and the results of molecular dynamics modeling over a wide range of pressures and temperatures, including the supercritical region.

The paper shows the changes in the watt-ampere characteristics shape of LEDs made from various semiconductor structures AlGaInP, InGaN and GaP with variation of the electron injection into the active region of the LED changes. It is shown that the light output power is a criterion parameter of LEDs, the main lighting characteristic and a function of the applied forward current. For LEDs based on AlGaInP with multiple quantum wells of various types of installation, a significant decrease in the emission power is observed for yellow LEDs. For GaP-based devices, an inverse relationship is observed. It has been suggested that impurity centers manifest themselves as nonradiative recombination centers. It is described with high accuracy for all types of LEDs by a single power function. It has been established that the exponent a determines the LEDs operating mode and characterizes the light output power of an individual LED and the photodiode sensitivity used in measurements in a photometric sphere. It is different for various current ranges. It is assumed that LEDs behave differently in the specified current ranges in the presence of any external influences (operation, aging, long-term operation, radiation exposure).