Том 64, № 4 (2019)

The structural transformation of solid hydrogen under compression along the isotherm of 100 K in the region of transition into the conductive state was studied within the density functional theory. The pressure, the pair correlation function of protons, the density of electron states, and the electrical conductivity were calculated within a range of hydrogen densities from 1.14 to 2.11 g/cm³. The transition of the monoclinic structure of molecular solid hydrogen into the orthorhombic Cmca structure with 12 hydrogen atoms in a unit cell was revealed. In this case, the electrical conductivity was observed to grow, though hydrogen remained molecular. Hydrogen molecules decomposed under compression to the density of 1.563 g/cm³. A unit cell, the thus-formed quasi-tetrahedron, was built of five protons with a distance of 0.92 Å from the central proton to the four others.

The combined numerical and physical modeling of a glow discharge between plane disk electrodes in molecular nitrogen is performed at pressures р = 3 and 5 Torr. The satisfactory description of experimental data by the drift-diffusion model is shown. The simultaneous analysis of experimental and calculated data has permitted identification of the normal burning regime of a glow discharge. However, the essential effect of model parameters such as the secondary electron emission coefficient and the first Townsend coefficient on the calculated voltage–current characteristic has been demonstrated in this case.

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

Within the framework of a one-temperature model of thermoelasticity, an analysis of the effect of electron localization processes on the thermoelastic response of conductors under pulsed-laser action is conducted. It is shown that electron localization can lead to considerable tightening of the deformation processes in conductors as compared with processes that develop in accordance with a typical thermoelastic mechanism.

A decaying 2D homogeneous and isotropic turbulent flow is considered in the self-similar limit, which is achieved with large values of the Reynolds number formed using the time and kinetic energy of the flow if the initial value of the averaged enstrophy tends to infinity with the viscosity tending to zero. In this case, the enstrophy-dissipation rate has a nonzero finite limit. The correlation function of the vorticity field and the enstrophy spectral density in the inertial range of distances and wave numbers, where these functions are free from the effect of viscosity and large-scale flow parameters, is investigated. It turns out that the inertial range exists in the decaying 2D self-similar turbulence in physical space but is absent in the space of wavenumbers. This means that the turbulent vortices of the appropriate size do not contribute to the spectral density, and the well-known law of the first degree is not satisfied. At large wave numbers, the spectral density of enstrophy behaves nonmonotonically—it first decreases faster than the law of the minus first degree and, then, in the dissipation region, it has a growth segment and a second peak. In this case, the enstrophy flow along the spectrum on the left boundary of the dissipation region is only a fraction of the enstrophy-dissipation rate.

The problem of a heating source acting on a certain part of a beam surface and moving along it with given speed \({v}\) is solved. It is shown that the most significant role in formation of the beam deflection under loading by a compression force is played by concentrated moments occurring at the moving boundary of the heating source. It is noted that for a source speed less than some critical value, the beam deflection is essentially nonmonotonic. In this case, the largest beam bending deflection occurs when the source speed reaches a value corresponding to the Euler critical force.

The formulation of problems on the equilibrium of a nonlinearly elastic solid with continuously distributed dislocations is proposed for the case of superposition of large strains. The numerical results showing the effect of distributed dislocations on the stress‒strain state of the beam are presented.