The paper deals with the geometric properties of the zero curvature manifolds with affine connection having common geodesic lines with preservation of the affine (canonical) parameter with locally symmetric spaces of affine connectivity. This class of spaces is characterized by identities satisfied by the torsion tensor field and its covariant derivatives. Geodesic loops with homotheties of this class of affine connected manifolds are investigated.

The process of nonlinear ionization of a two-dimensional nanostructure with a long-range Coulomb potential by a superposition of constant and alternating electric fields is investigated. In the adiabatic approximation, the ionization probability of a two-dimensional atom is calculated taking the Coulomb correction into account. The dependence of the contribution of the Coulomb field to the ionization rate on the ratio of the strengths of constant and alternating electric fields in the process of multiphoton ionization of an atom is investigated. An analytical expression is obtained for the ionization probability of a two-dimensional atom by a constant electric field, taking the Coulomb correction into account.

The aim of the work is to carry out a computer simulation of the influence of the values of the pre-tilt angles and the anchoring energy of LC molecules in thin cells with different twist angles of the structure with antisymmetric boundary conditions on their optical and dynamic characteristics. It is shown that an increase in the values of the pretilt angles of the LC molecules on the orienting surfaces of the cells leads to a slight increase in the contrast ratio in the LC cells with spin angles of 0°, 90° and 270°, with a slight change in the total response time of such cells. In LC cells with a twist angle of the structure of 180°, an increase in the value of the pre-tilt angle leads to a decrease in the contrast ratio and a simultaneous increase in the total response time of such devices. At the same time, a decrease in the anchoring energy in thin LC cells with antisymmetric boundary conditions leads to an increase in the total response time of such modulators for all twist angles of the LC structure. However, for different twist angles of the LC structure, the contrast ratio with a decrease in the anchoring energy of LC molecules with substrates behaves in a different way. Thus, for structures with twist angles of 180° and 270°, the contrast ratio of thin LC cells decreases significantly with the anchoring energy, while for structures with twist angles of 0° and 90°, the contrast ratio increases slightly with decreasing the anchoring energy.

Based on the method described in our paper “Alternative calculation of covariant derivatives with an application to the problems of mechanics, physics and geometry”, we have calculated the result of the action of the Laplace operator on covariant and contravariant vector functions. The projections of the vectors B and C, defined as Bi = (∆A)i and Ci = (∆A)i, on the corresponding curvilinear orthonormal bases ei and ei are found. The general covariant expressions for the operators ∆A and graddivA that are valid in any curvilinear coordinate system are presented. As a reference material, the projections of the vector Ci = (∆A)i in a parabolic coordinate system are calculated. As an illustrative example, the problem of torsion of an elastically deformable vertically standing cylindrical body under the conditions of its uneven radial heating, provided that its lower end is rigidly fixed, is solved.

We report the development of a high-temperature installation for the synthesis of halide compounds to improve the capabilities of the method of horizontal directed crystallization (HDC) that makes it possible to expand the chemical classes of crystals grown. The main element of the facility is a graphite thermal unit, developed for growing fluorine-containing single crystals for the first time by the HDC method. To assess the installation operability and to identify the temperature features of the crystallization process, the research complex included mathematical modeling of the processes of hydrodynamics, heat and mass transfer inside the graphite thermal unit, as well as between it and the crystallization apparatus. Numerical calculations relied on Reynolds-averaged Navier-Stokes equations and a modified Stefan-Boltzmann law used for a not absolutely black body. The temperature ranges of thermal inertia, as well as the establishment of the thermodynamic equilibrium in the thermal unit of the growth facility up to temperatures above 1500 °C, were experimentally determined. Knowledge of the values of these temperature parameters is necessary to prevent spontaneous overheating of the melt during the growth of fluoride crystals.

The processes of stimulated emission and absorption of light by an electron on a cylindrical surface in an external field formed by a superposition of magnetic and electrostatic fields of the same direction are studied in the dipole approximation. The selection rules and the corresponding radiation frequencies are found. The total energy of stimulated emission and absorption is calculated.

We report some results of the analytical study of translational nonequilibrium in the shock wave that have been previously formulated in our systematic studies. Analytical models of high-speed translational nonequilibrium in binary gas mixtures are analyzed. The effect of high-speed overshoot in the shock wave with maximum compression is considered. It is shown that the maximum of this effect satisfies the principle of independence of the Mach number.