THEORETICAL STUDYING SPECTRAL CHARACTERISTICS OF Zn-LIKE IONS ON THE BASIS OF RELATIVISTIC MANY-BODY PERTURBATION THEORY

A theoretical study of the spectroscopic characteristics of Zn-like multiply charged ions is carried out within the framework of the relativistic many-body perturbation theory. The optimized Dirac-Kohn-Shem approximation was chosen as the zero approximation of the relativistic perturbation theory. Optimization has been fulfilled by means of introduction of the parameters to the Kohn-Sham exchange and correlation potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian.

Computational Model for Radial Plain Bearing with Non-Circular Bearing Surface Profile and Fusible Coating on Shaft Surface

The paper presents a study based upon: a Newtonian fluid flow equation (“thin layer”), a continuity equation, and an equation of the molten-profile radius for a shaft coated with a fusible metal alloy; considering a mechanical energy dissipation rate formula, the authors produced an asymptotic and accurate automodel solution for the zero approximation (melting ignored) and first approximation (adjusted for melting) of a radial plain bearing featuring a fusible metal coating and a bearing profile adapted to the specific friction parameters. The paper further presents analytical dependencies describing the molten surface radius, velocity and pressure fields for zero and first approximation. Besides, it determines the key operating parameters of the frictional couple, the bearing capacity, and the friction. It also shows how the parameters arising from the melting of the surface affect the bearing capacity and friction where the bearing surface profile is adapted to the specific conditions of friction.

Buckling of the cylindrical shell joint with annular plates under external pressure

By means of an asymptotic method the buckling under the uniform external pressure of the thin cylindrical shell supported by identical annular plates is analyzed. Boundary conditions on an internal parallel of the shell joined to a thin plate are obtained. At the edges of the shell the free support conditions are introduced. We seek the approximate solutions of the eigenvalue problem as a sum of slowly varying functions and edge effect integrals. On a parallel, where the plate joint with the shell, the main boundary conditions for the formulation of an eigenvalue problem of zero approximation are obtained. This problem describes also vibrations of a simply supported beam stiffened by springs. Its solution we seek as linear combinations of Krylov’s functions. It is shown, that in zero approximation it is possible to replace a narrow plate with a circular beam. At increase in width of a plate stiffness of the corresponding spring tend to a constant. It occurs because of localization plate deformations near to the internal edge of a plate. As an example the dimensionless critical pressure for the case when the shell is supported by one plate is found. The replacement of a narrow plate with a circular beam does not lead to appreciable change of the critical pressure, however for a wide plate the beam model gives the overestimated value of critical pressure.

Determination of regional earthquake parameters from surface wave records

We consider in this paper the possibility of the source models construction for two regional earthquakes: in Akaba (June 27, 2015, Mw=5.5) and in the Dead Sea region (July 4, 2018, Mw=4.8) by surface wave records analysis. Fundamental Love and Rayleigh modes recorded by seismic networks IRIS, GEOSCOPE, and GEOFON were used for this purpose. At the first stage, at zero approximation we describe the source by moment tensor, considering the instantaneous point shear dislocation (double-couple) at a given depth. Four equivalent solutions were obtained from the amplitude spectra of surface waves. For an unambiguous choice of a solution, additional data were used, such as the signs of the first P-wave arrivals (for the Aqaba earthquake) or phase spectra (for an earthquake in the Dead Sea) were calculated for each of the four solutions. Based on the minimum values of the constructed joint residuals, a unique solution was chosen for each event. Then, considering the source flat, the following integral parameters were obtained: the duration of the process in the source, the lengths of the major and minor axes of the source, the average instant centroid velocity, the angle between the major axis of the source and the axis of the strike, the angle between the direction of motion of the instant centroid and the axis of the strike. The quality of the obtained solutions is estimated using the normalized residual function. This function characterizes the difference between the theoretical amplitude spectra and the observed ones. In the case of the earth-quake in the Dead Sea, the resolution of this function for some parameters was so small that it was not possible to obtain a solution. Also, for the earthquakes under consideration, the ambiguity associated with a significant excess of the surface wavelengths over the depth of the shallow source was analyzed

Asymptotic method for constructing a model of adiabatic guided modes of smoothly irregular integrated optical waveguides

The paper considers a class of smoothly irregular integrated optical multilayer waveguides, whose properties determine the characteristic features of guided propagation of monochromatic polarized light. An asymptotic approach to the description of such electromagnetic radiation is proposed, in which the solutions of Maxwells equations are expressed in terms of the solutions of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field in the zero approximation. The gradient of the phase front of the adiabatic guided mode satisfies the eikonal equation with respect to the effective refractive index of the waveguide for the given mode.The multilayer structure of waveguides allows one more stage of reducing the model to a homogeneous system of linear algebraic equations, the nontrivial solvability condition of which specifies the relationship between the gradient of the radiation phase front and the gradients of interfaces between thin homogeneous layers.In the final part of the work, eigenvalue and eigenvector problems (differential and algebraic), describing adiabatic guided modes are formulated. The formulation of the problem of describing the single-mode propagation of adiabatic guided modes is also given, emphasizing the adiabatic nature of the described approximate solution of Maxwells equations.

MATHEMATICAL MODEL FOR DETERMINING THE INTERNAL ELECTROMAGNETIC FIELD IN A SMALL FISH (WHITEBAIT)

The work is devoted to the development of a mathematical model that allows one to determine the electromagnetic fields of the microwave range inside sturgeon whitebait in order to stimulate their development. Our chosen method of calculating the mathematical model of internal electromagnetic fields in fish whitebait is planned to be used in the future for the experiment. This will increase the viability of whitebait as well as further healthy growth of sturgeon small fish and the selection of the best individuals for further artificial reproduction. A literature analysis of the influence of electromagnetic radiation on aquatic organisms and living organisms has been carried out. The effect of electromagnetic radiation on sturgeon whitebait in the first two weeks of their development is considered. In this case, the problems are solved using integro-differential equations in the case of quasi-statistics. A distinctive feature of this method is that it automatically satisfies the boundary conditions on the surface of the element. The solution of the problem of determining the electromagnetic fields inside the fish fry will be carried out taking into account its small size in comparison with the length of the falling electromagnetic radiation. In our case, as the larva grows, its size increases and the zero approximation give a rather crude result. Suggested expressions for zero, first, second, etc. approximations. Its allow take into account the growth of whitebait and the change in the ratio between their size and the incident wavelength. At the same time, it should be noted the high accuracy of this method, since already in the zero approximation its error did not exceed 15% in comparison with experimental studies of the scattering of electromagnetic fields on metal objects of ellipsoidal shape.

Spiral structure of the liquid particles trajectories near free surface of the vortex

Экспериментально и аналитически исследованы характеристики вихревого течения со свободной поверхностью, образующегося в результате вращения активаторного диска, расположенного на дне цилиндрического контейнера, заполненного водой. Получены аналитические выражения, показывающие, что траектории жидких частиц вблизи поверхности вихря представляют собой трехмерные спирали, по которым происходит течение от периферии к центу вихря. Показано, что рассчитанные и визуализированные траектории жидких частиц хорошо согласуются между собой и относятся к классу пространственных логарифмических спиралей. The work is aimed to compare results of analytical and experimental modeling of vortex fluid flow. The compound flow of liquid (water) occurs in a vertical cylindrical container without upper endwall under the action of the disk rotating at the bottom endwall. The two main components of the emerging flow are the toroidal vortex and the vortex with vertical axis. The equations are written in the cylindrical coordinate system dictated by the geometry of the problem. On the basis of the existing analytical expression, which describes the free surface form of the compound vortex in the zero approximation, an approach is developed to describe the trajectories of individual “liquid particles”. The obtained result allows to explore the velocity field structure near the free surface. The obtained expressions indicate that the velocity field near free surface becomes more pronounced in the tangent direction. This result is confirmed in the experimental studies of the compound vortex flow. The analytical forms of liquid particle trajectories near and on the free surface of the compound vortex are obtained. The general particle movement is from the container sidewall along the free surface to its center and further down the spiral-helical line. The images of the visualized particles trajectories both on the free surface (logarithmic spiral) and in the liquid depth are obtained in experiments and testify in favor of the implemented approach to the construction of analytical solution of the liquid particle motion for the vortex flow of the mentioned type. The correspondence of the calculated free surface forms obtained with the help of analytical expressions and those observed in the experiments with different parameters of the vortex flow shows that the developed approach to the problem can be based on a simplified description.

Рентгеновские лазеры в потоках кластеров и в наноструктурированных мишенях

The paper presents a brief review of recent works concerning the modeling of X-ray lasers in cluster flows and in nanostructured targets. Calculations of the atomic characteristics are based on relativistic perturbation theory with a model potential of zero approximation. Two new results are discussed: (1) it is shown that a subpicosecond X-ray laser with λ = 41.8 nm formed in a xenon cluster flow can serve as an alternative to a free-electron laser and (2) in heavy Ni-like ions ( Z ≥ 60), the ionization of ions and recombination of electrons are balanced at electronic temperatures ≥1500 eV; thus, the state of a Ni-like ion is quasi-steady-state. The inversions of many transition levels of an X-ray laser are also quasi-steady-state. The possibility of experimental observation of X-ray lasers based on 3 p ^54 d ^104 p [ J = 0] – 3 p ^63 d ^94 p [ J = 1] intrashell transitions in Gd^36+ with wavelengths in the water window region is discussed.

Simulation of the flow of a two-layer liquid film on a cylindrical surface

The problem of a stationary joint flow of a two-layer liquid film and gas along the outer (or inner) surface of a circular cylinder of radius r0 is considered. It is assumed that the films are insoluble in one another, and there are no chemical reactions. The axis of the body is located vertically, and the films flow down from its top. The film is affected by gravity, as well as a gas stream directed upwards or downwards. A cylindrical coordinate system (r, θ, z) is introduced: the z coordinate is measured along the axis of the cylinder, r and θ are the polar coordinates in a plane perpendicular to the axis of the body. To describe the flow of a liquid film, a viscous incompressible fluid model is used, which is based on the equations of continuity and Navier-Stokes. The following boundary conditions are set on the interface surfaces: on the solid surface - draw off “sticking”, on the “liquid-liquid” and “liquid-gas” interfacial surfaces - the conditions of equilibrium of forces and continuity of speeds. To simplify these differential equations, the method of a small parameter, for which the relative thickness of the films is selected, is applied. Solutions of simplified equations (in a zero approximation) are obtained in analytical form. Functional dependences are obtained for calculating the optimal effect of the gas flow on the "working" film. In accordance with the described method, calculations of the flow of a two-layer film on the outer and inner surfaces of the circular cylinder are performed in cases where the gas stream is directed upwards, downwards , and also when the gas flow is absent. An increase in the relative thicknesses of the films δ1 and δ2 (with decreasing radius of the cylinder r0) leads to an increase in deviations from the case of a plane surface that corresponds to the limiting case δ1 = δ2 = 0. The results of calculations of the flow of a two-layer liquid film on the surface of a circular cylinder are presented. The analysis of the influence of physical parameters on the speed profiles is carried out. The results of calculations for determining the optimal effect of gas flow on a liquid film are presented, when the profile of the speed of the "working" film is the most uniform