Aim: To show that under the Schwarzschild horizon, the solution for the geodetic line allows for a root feature when the radius of the body reaches a critical value Within the framework of the space-time Schwarzschild metric, the solution of the equations of geodesic lines in the spherically symmetric case is investigated, taking into account external (non-gravitational) forces. Methodology. The research method is based on the analysis of the solution of the geodetic equation when taking into account external non-gravitational fields. Results. As a result of the calculations, it is shown that under the Schwarzschild horizon, the solution allows for a root feature. Research implications. The result obtained in the article suggests that when the test bodies move in strong gravitational fields, a root feature appears in the metric, the physical nature of which is not gravitational and its origin is due to other physical fields.

Aim. We consider the rheological behavior of a rigid-chain polymer solution, which forms a lyotropic nematic crystal at high concentrations. Methodology. An approximation of the experimental data of the non-Newtonian flow is carried out on separate intervals of the shear rate. Results. We present the equations of the structural rheological model that relate rheological properties to the structure of the polymer solution. Research implications. Equations are proposed that can approximate the experimental data on separate intervals of the shear rate corresponding to a certain structural state of the polymer solution.

Aim. We study the relationship of the structure and properties of materials with their ability to transfer heat in various ways. Methodology. The theory and the results of practical measurements of thermal conductivity components of a randomly scattering structure are compared using two experimental methods and the modification of the radiation properties of samples. Results. The method for measuring the thickness of radiative-conductive relaxation and temperature jump in the medium near the radiation screen, as well as the radiant and conductive components and the total thermal conductivity of the medium, is described. The type of dependence is determined, and the components of thermal conductivity are measured in a wide range of thicknesses during compression of a fibrous canvas, including conductive contributions due to the movement of heat through the air and through the fibers. The change in the radiation contribution to the thermal conductivity due to the metallization of the fiber surface is estimated. Research implications. It is confirmed that different methods for measuring the contributions of the thermal conductivity components of materials give the same result. The conditions of the minimum of the structure thermal conductivity depending on its density are determined. The effect of the metallization of fibers on the thermal conductivity components of the structure is demonstrated.

Aim. For a blunt body of revolution with a power generatrix and spherical bluntness, we calculate the heat flux at a critical point. Methodology. By solving the variational problem, we determine the degree of minimum resistance and the bluntness radius in the generatrix of the body as functions of the elongation in a wide range of Reynolds numbers. Results. For a blunt body of revolution with a power generatrix and spherical bluntness, the drag force and heat flux at the critical point in a hypersonic rarefied gas flow are calculated based on several local models. Research implications. The results obtained in this work are more important for the optimization of the body and the creation of aircrafts in the aerospace industry.

Aim. We study the influence of kinetic and quantum wave properties of degenerate electron plasma on the S-wave interaction with metal half-space. Methodology. The dependence of the energy absorption coefficient of S-waves by metal half-space on the radiation frequency not exceeding the plasma frequency is studied and analyzed using theoretical formulae that take into account the transverse dielectric permittivity of the plasma of conduction electrons. Results. It is shown that at the usual values of the collision frequency of conduction electrons, the results for quantum electron plasma differ from the results for classical electron plasma and for classical electron gas. In the case of small values of the collision frequency of electrons, the results for quantum and classical electron plasmas almost coincide at the frequencies less than the plasma frequency, and differ at frequencies near this frequency. Research implications. The obtained results can be used in the theoretical study of interaction of radiation with metals, as well as in the development of optical devices using metal radiation detectors.

Aim. Features of propagation of shock compression waves in samples of compressed nickel nanoparticles have been studied for the first time by laser interferometry under uniaxial loading conditions at relatively low pressures of 1.7 and 4.1 GPa. Methodology. Shock wave profiles of a compressed nickel nanopowder loaded by a one-dimensional shock compression wave are measured by a laser interferometry method. Results. Shock wave profiles and points of the shock Hugoniot of the material are obtained. The Hugoniot elastic limit is determined to be 0.48 GPa. Research implications. It is found that shock wave profiles of pressed nickel nanoparticles have a complex multi-stage structure in which the precursor wave is clearly distinguished. It is shown that the compression wave profile can be described by multiple reflection of the precursor wave from a sample surface and an oncoming plastic shock wave. It is established that in the range of studied pressures, the sample thickness and the loading regime determine the process of shock compression. It is demonstrated that the difference between the states of matter behind the plastic shock wave front before the first precursor reflection and after the last reflection is significant.

Aim of study: investigation the ergodicity of a dynamical system for a set equations of amplitudes Tollmien-Schlichting waves, with the help of approximation stochastic behavior of turbulent pulsations, and comparison the pulsation characteristics of a developed turbulent boundary layer in terms of the waveguide model with experiment at zero pressure gradient. Methodology. The paper uses machine analytics and a complex of MATHEMATICA application programs. A number of results are obtained on the basis of dynamical systems theory. Results. The convergence of time averages and phase averages is shown. In addition, a good convergence of the theoretical results due to the coherent component with the experimental results has been demonstrated. Research implication.The applicability of the waveguide model for studying the statistics of flow velocity pulsations in the turbulent boundary layer for an incompressible fluid at zero pressure gradient is shown.

Aim. The paper reviews modern theoretical and experimental studies by various authors in the field of the physics of dipole bosonic and fermionic quantum ultracold gases. Methodology. The procedures and methods for studying the two-dimensional and three-dimensional interaction of dipoles are briefly compared and analyzed. Results. We analyze the scattering of polar molecules depending on the parameters of their interaction: the energies of the dipoles, their mutual arrangement, the influence of external fields, and the parameters of the short-range interaction. Research implications. The urgency of developing a theoretical description of planar systems of diatomic polar molecules is demonstrated.

Aim of the work is to develop a physical and mathematical model that combines the kinetic and hydrodynamic description of the flow, and to increase its computational efficiency. Methodology. An analytical research method was used in the work. To study the properties of the resulting model, the method of a numerical experiment was used. Results. The calculation results show that the combined kinetic-hydrodynamic model (KHM) makes it possible to physically adequately describe the processes occurring in the transition region of the gas medium flow. There are no discontinuities in the derivatives of the gas parameters in the region where the model components are stitched together. The KHM model allows setting boundary conditions on absorbing surfaces. The values of such an integral characteristic as cx(α), calculated by the KGM, are in satisfactory agreement with the results of calculations by the model kinetic equation. Research implications. When calculating relatively dense gases (Kn = 0,01), the model allows to reduce the memory consumption of the computing device by about three orders of magnitude and the processor time by two orders of magnitude compared to the model kinetic equation. The developed model can be used in a wide range of Knudsen numbers.