St Petersburg Polytechnic University Journal-Physics and Mathematics最新文献

The paper presents the results of the numerical and physical experiments, aimed at assessing the influence of pulsed force of electromagnetic field on the melt motion and the fluid velocities. The experiment was performed on the eutectic alloy Galinstan in the cylindrical volume, where an ultrasonic Doppler velocimeter was employed for velocity measurements under conditions of pulsed and steady EM field application. A numerical simulation of the melt flow, forced by the steady EM force, involved a 2D axisymmetric model. The k-ε turbulence model was used to obtain the information about the melt velocities. The verification of the numerical model was carried out for the steady case. The effects of pulsed and steadily applied Lorentz force were compared using the physical experiment. An intensity of the velocity pulsations in Galinstan for the pulsed frequencies in the range from 0.05 to 1 Hz considerably exceeded the values measured in the permanently stirred melt. For higher values of pulsed frequencies (from 1 to 10 Hz) the effect decreases and only slightly differs from the influence of the permanently applied Lorentz force.

The paper considers the method suggested by Papkovich for rectangular plates and its application for a cantilever plate bending under a uniform load. The required function of the bendings is chosen in the form of a sum of the corresponding beam function and a biharmonic function, which is a series in terms of unorthogonal eigenfunctions of the problem. The eigenfunctions satisfy the homogenous boundary conditions on the longitudinal edges (the clamped and the opposite ones). It is suggested to find series coefficients from the condition of the minimum residuals effect on the corresponding displacements of the transverse edges. It leads to an infinite system of linear algebraic equations for the required coefficients in the complex form. The coefficients of homogenous solutions were found for the cases in which the approximating series contained sequentially 2, 3,...,7 terms. The eigenvalues, the bendings of the edge opposite to the clamped edge, and the bending moments in the clamped section were calculated. Convergence of the reduction method and stability of the computational process were analyzed.

In this paper, the charge-balance, the energy-balance and the moment equations and Poisson's equation have been used to describe the charging process for a dust particle in the undisturbed plasma taking into account the emission variety (secondary electron, electron-ion, thermal-field electron and photoelectron types) in the intermediate regime of ion motion. Such an approach was associated with the fact that the dust-particle charge specified by the parameters of the above-mentioned plasma depends heavily on electron emission from the particle surface. Collisions between ions and atoms as well as ionization also essentially affect the formation of the ion flux onto the surface of dust particles. The computational procedure we propose has allowed solving the chosen set of equations for an arbitrary relationship between the ion mean free path, the particle radius and the Debye length. The electron emission was shown to decrease the absolute value of the dust-particle charge. Moreover, the collisions with atoms lead to the ion flux deceleration onto the particle surface whereas the depth of the disturbance space of plasma increased with decreasing the ionization frequency.

The charge relaxation processes in the films based on polyimide and polytetrafluoroethylene (the latter serves as a coating) have been studied. The coating effect on the charge relaxation processes in the films under high humidity conditions was revealed. The obtained experimental data was analyzed in the context of the present-day knowledge of the charge relaxation mechanism. The complex spectra of the thermally stimulated depolarization currents (TSDC) were resolved into individual components described by the first-order kinetics equations using computer simulation. The TSDC activation energies were calculated and interpreted in terms of the mechanism of release of charge carriers. It was shown that the polytetrafluoroethylene coats on film surfaces lead to an essential increase in the electret state stability at elevated temperature and high humidity.

Axonometric projections together with corresponding graphs for fullerenes are constructed in the range from 24 to 48. The growth of fullerenes is studied on the basis of the mechanism, according to which a carbon dimer embeds in a hexagon of an initial fullerene. This leads to stretching and breaking the covalent bonds which are parallel to arising tensile forces. In this case, instead of the hexagon adjoining two pentagons, one obtains two adjacent pentagons adjoining two hexagons. As a result, there arises a new atomic configuration and there is mass increase of two carbon atoms. We considered direct descendants of fullerene C₂₄; namely, C_2n, where n = 13–24.

Polar optical phonons in quaternary nitride-based superlattices have been investigated in the framework of the dielectric continuum model. In the considered systems, the superlattice period consisted of two main GaN and AlN layers and two interstitial Al_0.5Ga_0.5 N layers. Such a structure simulates binary superlattices with diffuse interfaces. The presence of the finite thickness interface layers was shown to give rise to appearance of several low-intensity additional phonon modes active in Raman scattering; frequency splitting of such modes is sensitive to relative thickness of intermediate layers. The fundamental Raman-intense polar phonon modes were also stated to be independent on the interface thickness, and these modes were very sensitive to the main layer thicknesses.

This study tested the effect of intravenous injections of CyPPA [the activator of small conductance calcium-activated potassium channels of types 2 and 3 (SK2/SK3)] on the firing frequency of cerebellar Purkinje cells of laboratory male mice at the age of 6 months via the method of extracellular in vivo recordings from Purkinje cells. This method revealed that 1 mM CyPPA tail vein injections lead to progressive reduction of Purkinje cells firing frequency. Thus, simple spike's firing frequency decreases by 16% in one hour after injection, by 49% in two hours after injection, and by 61% in three hours. The obtained results confirmed the hypothesis about the important role of SK channels in the maintenance of Purkinje cells spontaneous activity in vivo. Since deterioration of biophysical and physiological functions is observed in many cerebellar ataxias, SK channels can serve as a potential target for the treatment of such disorders.

This article focuses on solving the disjunctive problem. Various methods of constructing disjunctive cuts (DC) from the logical limitations on linear inequalities have been presented. A general principle of DC and a principle allowing to strengthen these cuts were established. By virtue of the stated principles, solving the problems of optimization with a great number of limitations can be simplified. Two theorems were formulated and proved. Four examples illustrated various theoretical statements.

The suggested principles and the procedures based on them provide the theoretical background to the elaboration of algorithms intended for software implementation in solving practical problems.

An exact solution of the antiplane problem for a semi-infinite interface crack in a piecewise-homogeneous wedge under a self-balanced load on its sides has been obtained. Three types of boundary conditions on the wedge sides were examined: the both sides being stress-free; both sides being clamped, and one side being stress-free with the second one clamped. As a result of using the Wiener–Hopf method, the solution was represented in quadratures. Green's functions were obtained for stress intensity factors; in the case of a geometrically symmetrical wedge structure simple formulae were found for these functions. The stress singularity in the apex of the wedge was studied. In contrast to the homogeneous wedge structure the asymptotic of the stresses near the apex was established to have sometimes two singular terms for some values of the composite parameters.

In this article, the problem of the number of spikes (level crossings) of the stationary narrowband Gaussian process has been considered. The process was specified by an exponentially-cosine autocorrelation function. The problem had been solved earlier by Rice in terms of the joint probabilities’ density of the process and its derivative with respect to time, but in our article we obtained the solution using the functional of probabilities’ density (the functional was obtained by Amiantov), as well as an expansion of the canonical stochastic process. In this article, the optimal canonical expansion of a narrowband stochastic process based on the work of Filimonov and Denisov was also considered to solve the problem. The application of all these resources allowed obtaining an exact analytical solution of the problem on spikes of stationary narrowband Gaussian process. The obtained formulae could be used to solve, for example, some problems about the residual resource of some radiotechnical products, about the breaking sea waves and others.