Vol 61, No 12 (2019)

A geometrical model of a massive spinning particle, whose quantization corresponds to the unitary irreducible representation of the Poincaré group, is considered. It is shown that the class of gauge-equivalent trajectories of the particle forms a cylindrical surface in d = 4 Minkowski space. Basing ourselves on the fact that the trajectories of the particle are cylindrical lines, we have obtained the equations of motion of the particle on a world sheet along timelike and isotropic trajectories.

The mean values of the potential \( \left\langle \hat{\varPi}\right\rangle \) and kinetic \( \left\langle \hat{\mathrm{T}}\right\rangle \) energy of an electron in a hydrogenlike atom are found. It is found by direct calculation that \( \left\langle \hat{\varPi}\right\rangle =2E \) and \( \left\langle \hat{\mathrm{T}}\right\rangle =\mid E\mid \) for arbitrary states with set of quantum numbers {n,l,m} . Such relations for the ground state {n = 1, l = m = 0} are well known and are a particular case of this general result. Thus, this work can have methodological value as a helpful supplement to the traditional university course in quantum mechanics. Moreover, on the scientific plane, it is possible to apply these results to a calculation of the energy of a two-electron atom by the variational method in spaces with number of dimensions D = 3,2, and 1.

Estimators of the reliability function characteristics of a non-restorable element using auxiliary information on the time to failure distribution law under conditions of nonparametric prior uncertainty are suggested. Optimal mean square error estimators and adaptive optimal estimators are constructed, and their limiting distributions are found. Illustrative examples are presented.

The paper studies the instability of the plastic flow and fracture of metal-intermetallic laminated composites using a three-dimensional multi-scale model of the dislocation kinetics and mechanics of the elastoplastic medium under the dynamic high-temperature compression. The suggested theoretical stress-strain curves represent the behavior of laminated composites at different deformation temperatures and layer arrangements. It is shown that the inclusion of soft plastic metallic layers into the intermetallic matrix stabilizes the plastic flow of laminated composites, significantly increases the plasticity and time to fracture and decreases the deformation resistance. The layer arrangement has no great effect on the stability of plastic deformation.

This work is dedicated to a study of the influence of the duration of an electrical discharge on the size of the melting zone formed at a cathode of VT20 titanium alloy. It is found that the melting zone possesses radial symmetry and is surrounded by a ring-shaped zone, whose surface is exposed to electrical erosion. The dependence of the radii of the melting region and the erosion zone, and of the volume of melted metal on the duration of the discharge pulse is determined in the interval from 0.05 ms to 1 ms. A mathematical model is proposed, allowing us to calculate the temperature distribution in a metal plate at different times during the discharge. The parameters of a nonstationary surface heat source arising in the region of the electrical discharge are found from the condition of coincidence of the position of the boundary of the solid–melt phase transition observed in experiments and determined by solving the heat transfer equation.

The paper presents research results of the deformation-induced surface topography of Ni₃Fe alloy single crystals oriented toward the multiple shear bands at uniaxial compression. It is shown that in prismatic single crystals with a regular base configuration, macrobands of the localized shear strain over the octahedral planes propagate in their unconfined shear bands. During the deformation process, the single crystal with a complicated configuration fractures into two hyperfragments with a regular shape such that macrobands of the localized shear strain appear in their unconfined shear bands.

Experimental data on electric signal transmission through tissues of the vestibular organ of a guinea pig are presented. Stimulating electrodes are implanted in three ampullae of semicircular canals to which an alternating voltage of 170 mV is applied. The receiving electrode is implanted in the termination of vestibular nerves. The impedance of the vestibular organ tissues has been measured depending on the stimulating signal frequency. It is shown that the amplitude phase characteristics of the resulting signal at the termination of the vestibular nerves depend on the position of the stimulating electrodes and on the stimulating signal frequency. The presence of conductive disturbance currents and their influence on the resulting signal waveforms are established. A method for eliminating the influence of the conductive disturbance currents by means of application of additional electric pulses with a certain phase shift to the stimulating electrodes is suggested.

Within the framework of Hubbard’s model using an approximation of static fluctuations, the energy spectrum of the π-electron subsystem of an icosahedral C₈₀ fullerene isomer is obtained. Based on the energy spectrum, an optical absorption spectrum of metal-nitride complexes M₃N@C₈₀ (M = Gd, Tm, Dy) is simulated. It is quite consistent with the respective experimental spectrum.

The ν₂ + ν₁₀ (B_u) hybrid band of the trans-C₂H₂D₂ molecule in the region 2100–2300 cm^–1 is studied for the first time. The spectrum has been analyzed using the method of combination differences. Based on the obtained experimental data, about 900 \( \left({J}^{\mathrm{max}}=20\;\mathrm{and}\ {K}_a^{\mathrm{max}}=9\right) \) energy levels are assigned.

The results of studies of the characteristics of contacts with Schottky barriers on a pseudomorphic AlGaAs/InGaAs heterostructure are presented. The Ti-based Schottky diodes were created by a standard pHEMT technology. It is shown that the parameters of the fabricated contacts with Schottky barriers are close to the characteristics of ideal contacts based on aluminum or molybdenum created in the process of molecular beam epitaxy. It is also shown that as compared to the diodes based on AlGaAs homostructures, the measured Schottky barrier height is smaller and the ideality factor is higher in diodes created on pseudomorphic heterostructures. Along with the well-known methods for determining the Schottky-barrier height, we tested a technique based on the measurement of the threshold voltage in diodes with a two-dimensional electron gas.

With the help of the evolution operator method, we have established unitary connection between quadratic systems, namely between a free particle with variable mass M(t) , a particle with variable mass M(t) in a variable homogeneous field, and a harmonic oscillator with variable mass M(t) and frequency ω(t) , on which a variable force F(t) acts. Knowledge of the unitary connection allowed us to express easily in general form the propagators, invariants, wave functions, and other functions of a linear potential and a harmonic oscillator in terms of the corresponding quantities for a free particle. We have analyzed the linear and quadratic invariants in detail. Results known in the literature follow as particular cases from the general results obtained here.

The paper presents a mathematical model for processing of physics experimental data in the form of a non-Markovian infinite-server multi-resource queuing system with Markov modulated Poisson process arrivals and arbitrary service time. It is proved that the joint steady-state probability distribution of the total volume of the occupied resource of each type converges to a multidimensional Gaussian distribution under the asymptotic condition of the growing intensity of the arrival process. The parameters of this asymptotic distribution are derived.

The paper proposes a mathematical model of thermal explosion in mechanically activated Nb–2Si powder blend. A study of the dynamics of mechanical activation synthesis of the Nb–Si system shows that preliminary activation of the initial powder components intensifies the formation of NbSi₂ phase. Thermokinetic and thermophysical constants are obtained for the mechanochemical synthesis using the experimental data and the inverse problem method.

Line profiles of the krypton spectra emitted by the plasma of current sheets are simulated. Current sheets are formed under the impact of magnetic fields with singular X-lines. The spectral line profiles are calculated by the method of the energy matrix diagonalization of an atom in an electric field. The dependence of the behavior of the line profiles on the parameters of an alternating electric field arising inside the plasma of current sheets and the dependence of these profiles on the plasma temperature are investigated. The criteria which allow one to reveal spectral lines serving as the indicators of the appearance of anomalous electric fields inside current sheets are suggested.

Based on acoustic remote measurements of vertical profiles of three wind velocity components in a 200-meter boundary layer of the atmosphere, values of the kinetic energy of the atmosphere and its components: kinetic energy of ordered motion E_MKE (with average wind velocity) and turbulent kinetic energy E_TKE are estimated. An analysis of their vertical profiles has demonstrated that at altitudes up to ~25–50 m, the turbulent kinetic energy values and their spreads are very small and sharply increase with altitude. The maximum E_TKE values are observed at midnight, as well as the maximum E_MKE values. In the morning, the contribution of the kinetic energy of the ordered motion in the lower 100-meter layer of the atmosphere exceeds that of the turbulent motion, which can be caused by the presence of a wind shear in the corresponding wind velocity profiles. The vertical E_MKE profile increases in the morning, reaches maximum values by noon, and then decreases by midnight. The diurnal variations of the kinetic energy are characterized by the presence of several minima and maxima whose values and times of occurrence depend on the meteorological conditions during sounding session, the presence and characteristics of cloudiness, and the solar radiation intensity.

Numerical analysis of the micromagnetic model was used to reveal the ‘resonance’ feature of relaxation processes in nanocrystalline thin magnetic films. This feature manifests itself in the form of sharp broadening of the ferromagnetic resonance (FMR) line at a certain frequency f₁ depending on magnetic characteristics of the film, and is observed only in films the thickness of which exceeds some threshold value d_min. Sharp broadening of the FMR line is accompanied by significant shift of the resonance field, whereas the shift value changes the sign at frequency ~ f₁. It was shown analytically that the nature of observed effects is associated with the two-magnon process of spin waves scattering on quasi-periodic magnetic microstructure – magnetization ‘ripple’. Obtained expressions for the threshold value of film thickness d_min and frequency of maximum broadening of FMR line f₁ agree well with the results of numerical computation of micromagnetic model.