Scientific Notes of

Taurida National V.I. Vernadsky University

Taurida National V.I. Vernadsky University

Series

Physical and Mathematical Sciences

**Vol. 23 (62), No. 1. P. I. 2010****Physics and Mathematics Sciences.**

**Roshchupkin S.N., Petrash A.N., Lelyakov A.P.**

The Exact Solution Describing Movement of a Null-String in Majumdar-Papapetrou Space-Time

*In this article we have received exact solution of motion equations null-string in static metric Majumdar - apapetrou which describes system consisting of n black holes.*

**Lelyakov A.P.**

Boundary Conditions for the Gravitational Field Produced by a Closed Null-String, of Constant Radius

*In this article we have received the boundary conditions for metric functions describing a gravitational field closed null-string of constant radius which goes along an axis z and at each moment of time completely lays in a plane orthogonal this axis.*

**Fridman Yu.A., Klevets Ph.N., Voytenko A.P.**

The Influence of the Magnetoelastic Interaction on Phase States of U_{2}Co_{15}Si_{2} Alloy Film

*The paper deals with the model of magnetic and magnetoelastic properties of U _{2}Co_{15}Si_{2} alloy ferromagnetic film. The present model takes into account the influence of the magnetic dipole and magnetoelastic interactions. Within the frameworks of the model proposed the temperature driven phase transitions are investigated. It is shown that the "easy-axis" and the "easy-plane" phases realize in the system under consideration. Thus, the phase transition between them is of the first kind and occurs through the intermediate – spatially inhomogeneous – state domains). The temperatures of the "easy-axis" phase and the "easy-plane" phase stability are derived.*

**Fadeyeva T.A., Rubass A.F., Volyar A.V.**

Quadrefringence of the Vortex Beams in Birefringent Crystals

*We have found the asymmetric splitting of a high-order circularly polarized vortex-beam in a uniaxial crystal. The l-order vortex-beam splits into the same one and the beam with the 1-1 vortices at the beam axis while one optical vortex is shifted along the direction perpendicular to the inclination plane of the beam. Such a vortex displacement causes the transverse shift of the partial beam. We consider this effect both in terms of the conservation law of the angular momentum flux and on the base of the solutions to the paraxial wave equation. We revealed that the transverse shift of the crystal traveling beam depends on neither a magnitude nor a sign of the vortex topological charge being defined only by a handedness of the initial circular polarization and a sign of the inclination angle of the beam.*

**Dzedolik I.V., Lapayeva S.N., Vershitsky V.I., Markova L.S.**

Control of Optical Vortex Phase by External Electric Field in the Dielectric Resonator

*The possibility of an optical vortex phase control by the variation of external electric field in the dielectric Fabry-Perot resonator is shown theoretically and experimentally. In the Mach-Zehnder interferometer where the crystal gallium phosphide in the form of rectangular prism in the objective shoulder is placed, the interference pattern is obtained in the form of a spiral rotating around its own axis if the intensity of external electric field is changing. The number of turns of the spiral depends on the intensity of the external electric field. Considered phenomenon can be used for designing of the physical quantity data sensors and the optical devices applied in the optical transmission lines.*

**Alexeyev C.N., Lapin B.P., Yavorsky M.A.**

The Higher Order Optical Vortices and Topological Phase in Coiled Anisotropic Elliptic Fibers

*An analytical solution has been obtained for vectorial wave equation for coiled anisotropic elliptic fibers by using the perturbation theory with degeneracy. It has been showed that for the azimuthal numbers l >1 in the case of strong anisotropy the mode's structure is presented by linear polarized optical vortices. The propagation constants are calculated and the topological phase is computed for linear polarized optical vortex.*

**Basiladze G.D., Berzhansky V.N., Dolgov A.I., Milyukova E.T.**

Transformation of the Fiber Cores under Conditions of Weak and Strong Fusing of Optical Coupler

*Biconical tapers of single-mode-fiber couplers made by the fused biconical-taper method under different technological conditions out of two fibers with different concentration GeO _{2} in cores were experimentally investigated. It was determined that due to the different concentration of germanium asymmetrical change of dimensions of cores along fiber tapers depends on technological condition of coupler fusing.*

**Yevstafyev O., Preobrazhensky V.L., Perno P., Berzhansky V.N.**

Explosive Dynamics of Three-Phonon Instability in Magneto-Elastic System FeBO_{3}

*A theoretical model of supercritical oscillation dynamics in magnetoelastic materials is suggested. This model takes into account strong magneto-elastic nonlinearity outside the anharmonic approximation. With a help of original method the supercritical dynamics of FeBO _{3} is researched and the effect of explosive three-boson instability is discovered. The discovered effect is explained with the help of suggested theoretical model.*

**Ryabushkin D.S., Neroda E.S.**

Two-Pulse Echo in Dynamic Molecules of Water

*The dynamics of forming of NMR echo in two-spin systems with dipole-dipole interaction is theoretically investigated. For the decision of the task the stochastic equation of Liouville was used. The investigated system was considered to be able to occupy two equilibrium positions in a lattice and accomplish random «jumping» between them. It is demonstrated that for pulse series 90°y–τ–β°x a signal forms that is a mixture of free induction decay (FID) and solid-echo and each summand has a weighting coefficient depending on the angle of rotation. In the case of the series 90°y–τ–β°y it is observed only FID, i.e. in-phase echo doesn't form.*

**Ponomarenko V.I., Popov V.V.**

Lattice of Thin Magnetic Wires in Rectangular Waveguide

*An analytical solution is given for the scattering problem from two magnetic microwires placed in rectangular waveguide and followed with a short. Using known numerical solution of scattering by an inductive nonmagnetic metal-cylinder, in the case of thin wires new numerical algorithm is proposed for solving the scattering problem for a lattice with an arbitrary number of magnetic wires.*

**Suchikova J.A, Kidalov V.V., Sukach G.A.**

Investigation of a Chemical Compound of a Porous Surface n-InP (111)

*Porous InP / layers have been produced by electrochemical anodic etching. Surface morphology of the porous films of InP were examined by scanning electron microscopy (SEM). The chemical composition of the porous films of InP was determined from Energy Despersive Analysis of X-rays (EDAX). On the surface of porous InP oxygen and fluorine have been found out.*

**Chuklov V.A., Yagupov S.V., Strugatsky M.B., Postivey N.S.**

Thermal Fluctuations on the Stage of Iron Borate FeBO_{3} Crystallization

*In the work the way of determination of spectral density of thermal fluctuations in the field of Iron Borate crystallisation, based on connection of spectral density with correlation function is offered. Observed thermal fluctuations are identified as flikker-noise that testifies to the fluctuation nature of the physical process*

**Yagupov S.V., Strugatsky M.B., Postivey N.S., Kostulin S.S.**

Application of Differential-Thermal Analysis for Research of Solution-in-Melt Crystallization

*The method of differential thermal analysis is applied for determination of crystallization zones of Iron Borates monocrystals, synthesized from solution in melt in the system Fe _{2}O_{3} – B_{2}O_{3} – PbO – PbF_{2}. To that purpose, the sensitive DTA device is developed and made. The results of DTA are confirmed a probe method.*

**Yevdokimov S.V., Yatsenko А.А., Yatsenko А.V.**

Simple Amplifier for Pyroelectric Measurements

*Precision differential electrometric amplifier is described, which have sufficient preferences in comparing to specialized manufactured devices in the case of exploiting of reference resistors with resistance less than 2 GOhm. Sensitivity of this device is limited by the noise of the reference resistors, and the device can be used for the measurements of the slowly changed currents with accuracy up to 1 fA. *

**Stadnyk I.P., Filippov D.M.**

Optimization of Parameters of a Linear Induction Motor with a Smooth Stator of the Maximum Condition of the Start-up Traction

*With the developed methodology, based on the method of integral equations, numerical calculations traction linear induction motor with a smooth stator mode brakes. Optimization of parameters of a linear induction motor with a smooth stator from the condition of the maximum start-up traction.*

**Lyashko D.A., Lyashko S.D.**

Use of Crosscorrelational Method for Determination of Fundamental Parameters of Stars

*The algorithm of determination of fundamental parameters of stars is described, such as an effective temperature, logarithm of acceleration of gravity, speed of rotation and projection of rate of own movement on the ray of sight. In basis of method the method of кросс-корреляции of the looked after spectrums is fixed with the base of these synthetic spectrums, wrap-round all of range of spectral classes. The described method allows to estimate the fundamental parameters of star and, in future, utillize them as the first approaching for more exact analysis. It is also possible to define belongings of group of the probed stars to the dissipated star accumulation.*

**Shaposhnikov A.N., Berzhansky V.N., Prokopov A.R., Karavainikov A.V., Milyukova E.T., Golub V.O.**

Crystallization of RIBS-Iron Garnet Films

*The crystallization processes of RIBS-sputtering iron-garnet films of composition Bi _{2,8}Y_{0,2}Fe_{5}O_{12}, Bi_{2,5}Gd_{0,5}Fe_{3,8}Al_{1,2}O_{12}, Bi_{1,5}Gd_{1,5}Fe_{4,5}Al_{0,5}O_{12} and Bi_{1,0}Y_{0,5}Gd_{1,5}Fe_{4,2}Al_{0,8}O_{12} on the GGG, glass ceramics substrates and SiO2 films are investigated. Film crystallization was carried out by annealing in a vacuum as well as in air at atmospheric pressure. It is shown the possibility to crystallize the films with high Bi content on SiO_{2} films across the film with a low Bi content as sublayer to form the one-dimensional magnetophotonic crystals.*

**Vishnevskii V.G., Nedviga A.S., Nesteruk A.G., Berzhansky V.N., Dudarenko I.V.**

Thermomagnetic Recording Information in Epitaxial Ferrites-Garnets, and its Use in Phonoscopic Examination

*The results of experiments in estimations of space resolution and sensitivity of magneto-optic visualization information from magnetic records with use of thermo-magnetic printing method are presented. Borders of changes and causes of limits of these parameters are founded. Using concrete examples possibilities and advantages of the thermo-magnetic printing in the signalogram analysis for criminal law examination (phonoscopy) are shown.*