Vol 61, No 3 (2018)

A complete solution of the problem of squaring the Dirac equation with arbitrary external electromagnetic field is expounded.

Using the Monte Carlo method, the influence of the complexes of antiphase boundaries (APBs) (a pair of shear APBs and a pair of thermal APBs) on the low-stability, pre-transitional states of BCC-alloys is considered by the example of a conventional copper alloy CuZn and an intermetallic compound NiAl. It is shown that in the region of low-stability structural-phase states the energy of formation of a complex of thermal APBs is higher than that of shear APBs. The contribution of APBs into disordering is appreciable up to the structural-phase transition temperature. The most significant factor in terms of the long-range order is the formation of the defect itself; the differences in the APB type or the plane of their occurrence do not so much affect the longrange order behavior with the temperature variation. The type of APBs however appreciably affects the structural-energy characteristics of the system at the temperatures below the phase transformation temperature. Logically, a system with structural defects is less ordered than a defect-free system. The presence of a defect favors the onset of disordering at lower temperatures: it starts at lower temperatures in the case of thermal APBs (TAPBs) compared to shear APBs (TAPBs). In a BCC-system with a complex of TAPBs the first signs of disordering invariably appear near the phase boundary in the neighborhood of large atoms (Zn–Zn in the CuZn alloy or Al–Al in the NiAl intermetallide). In the alloy with a complex of shear APBs the distortion of ordering at low temperatures is observed in the regions where the boundaries cross. The presence of antiphase boundaries affects the alloy stability under heating. It is shown that disordering is accompanied by smearing of the boundaries and their faceting. It follows from a comparative analysis of the peculiarities of disordering in the BCC-system under study (classical alloy CuZn and intermetallide NiAl) under conditions of higher temperatures in the region of low-stability, pre-transitional states that the order – disorder phase transition in the CuZn alloy takes place as a result of disordering of the system, while in the intermetallide NiAl the change of long-range order results from the structural-phase transition.

Analytical expressions were produced for the space charge sheath thickness and ion current to the sheath in collisional mode in cylindrical geometry. Comparison was performed with numerical solution to Poisson’s equation without dividing into the sheath and the plasma. Approximating formulas were provided for a wide range of pressures.

The optical absorption and cathodoluminescence spectra of nine diamond specimens are investigated at the temperatures 295 K and 82–295 K, respectively. By the presence of an N3a electron-vibrational system with a phonon-free line at 2.68 eV, six of them are identified as natural diamonds. By the presence of the electron-vibrational system at 2.56 eV and a structureless band at 2.54 eV, associated with nickel in the optical absorption and luminescence spectra, two specimens are identified as synthetic diamonds grown at high pressures and temperatures. By the presence of exciton luminescence at 5.271 eV and the absence of any spectral, impurity-related peculiarities, one of the specimens is identified as a synthetic diamond grown by the chemical vapor deposition. Based on the data obtained, a procedure is proposed for identifying natural and synthetic diamonds and determining a model scheme of the radiation-thermal treatment of the specimens.

The data on the electrical, structural, and magnetic properties of the iron doped gallium arsenide obtained by various methods are systematized. The conditions for obtaining structures with magnetic properties are considered.

The paper presents high-resolution electron microscopy investigations of the structure and morphology of cadmium selenide nanocrystals and nanoplatelets, and nanoplatelets having cadmium selenide core/crown nanostructure. These nanocrystals and nanoplatelets are obtained by the colloid technology and are deposited onto carbon substrates using the Langmuir–Blodgett method. It is shown that two-dimensional structures of nanocrystals and nanoplatelets can be formed on carbon substrates. The quantity specifications of these structures are determined in this paper.

An error in calculating the tropospheric delay of satellite navigation signals is estimated for different atmospheric phenomena. As atmospheric phenomena, different precipitation types (hydrometeors) and electrical phenomena (thunderstorms and summer lightning) are considered. The tropospheric delay is calculated for the Saastamoinen and Hopfield models with the vertical profiles of the atmospheric meteorological parameters obtained by aerological sounding. The error of the given methods is determined by a comparison of the calculated and true values of the zenith tropospheric delays. The influence of the atmospheric phenomena on the error value is analyzed.

General expressions for the dependence of the Fermi energy, pressure, and total energy of a degenerate neutron gas in a magnetic field on the magnitude of the field and the neutron concentration with allowance for the anomalous magnetic moment of the neutron have been obtained in implicit form, and the dependence of these quantities on the field is presented in graphical form for the neutron concentration C = 10³⁸ cm^–3, which is typical for neutron stars. Analytical estimates of the pressure have been made for the magnitude of the fields possible in neutron stars ~10¹⁷–10¹⁹ G and this neutron concentration ~10³⁸ cm^–3, including when the neutron gas is close to its saturated state with preferred orientation of the anomalous magnetic moment of all the neutrons in alignment with the field. It is found that even such fields ~10¹⁷ G have practically no effect on the pressure in comparison with the case when the field is absent, an effect being possible only for В ~ 10¹⁸–10¹⁹ G. The analytical dependence on the neutron concentration of the corresponding field B_S at which the neutron gas transitions to the saturated state has been found in explicit form. It is established that for B > B_S the indicated characteristics of the neutron gas, and likewise its state, no longer change.

A second-quantization treatment of the solution of the equation of classical mechanics is carried out. It is shown that all of the information about the multiparticle process of creation of a pair of scalar particles by a nonstationary potential barrier is contained in the solutions of Newton’s one-particle equation. The corresponding solution does not depend on Planck’s constant. It is shown that for any spatial quantum problem there exists a temporal classical analog. The obtained results can be used in quantum geometrodynamics.

A method for determining the effective surface area of a spent satellite depending on its spatial orientation is suggested on the example of the GLONASS spacecraft (SC). To determine the effective area, a point-set model is considered. The satellite is represented as a set of points uniformly distributed over the SC surface. Then longitude and latitude angles are varied in the system of coordinates rigidly affixed to the SC, and the point set is projected onto the image plane. The contour of the projected set is determined, and its area is calculated. As a result, an approximate dependence of the effective satellite area on two orientation angles is obtained.

Plasma characteristics in the gap at lowered pressure in the presence of primary electrons are analyzed for the hydrodynamic model in the cold ion approximation. It is demonstrated that at a certain critical ionization level, the plasma state changes abruptly. The potential drop in the plasma can be not only more, but also less than ln(2)kTe/e, and hence the velocity of ions exiting from the plasma can be more or less than the Bohm velocity. For low ionization intensity and formation of the plasma with a high fraction of primary electrons, the velocity of secondary electron exiting from the plasma becomes equal to their thermal velocity, and their distribution differs significantly from the Boltzmann distribution.

To calculate the energy and equilibrium density of electron-hole pairs in SiO₂/Si/SiO₂ quantum wells (QWs), nonlinear Schrödinger equations for electrons and holes were numerically solved. Calculations were carried out for (100) and (111) silicon surfaces and various values of the QW width. It is shown that the binding energy of electron-hole pairs in a quasi-two-dimensional electron-hole liquid (EHL) is much higher than the binding energy in a three-dimensional EHL. The results of calculations are compared with the experimental results for a wide range of QW widths.

The paper focuses on modeling carbon nanotubes/nanofibers in polymer nanocomposites representing coil macromolecules. It is shown that models used for the description of coil macromolecules in solutions can be also used to describe the structure of the annular formations of nanoscale modifying additions.

Rotational operators of the SO(3) group and corresponding irreducible rotational operators of the T_d point group up to the 8^th rank are determined for molecules of spherical top type based on the formalism of irreducible tensorial operators.

A shift of higher harmonic peak in the spectrum of synchrotron radiation with increasing energy of a radiating particle is investigated by a numerical method. Calculations were carried out for ν^(max) ≤ 100 and all polarization components.

The paper describes the problem of finding the likelihood ratio for specific problem of stochastic system recognition in continuous time to member functions within continuous-discrete time, which depend not only on current, but also on arbitrary numbers of previous non-observable process values.