Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series最新文献

{"title":"Optical and electrophysical properties of nitride TiAlSiN and carbonitride TiAlSiCN coatings: influence of reactive magnetron deposition regimes","authors":"S. Konstantinov, F. F. Komarov, I. V. Chizhov, V. A. Zaikov","doi":"10.29235/1561-2430-2024-60-2-162-176","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-162-176","url":null,"abstract":"The development of thin-film thermal control coatings for small spacecraft is relevant. Coatings based on titanium nitride are capable of functioning in unfavorable conditions of near and deep space, due to their high resistance to the irradiation by high-energy particles. Using the reactive magnetron sputtering method, the nanostructured TiAlSiN and TiAlSiCN coatings were formed on the substrates of silicon oxide (SiO2), glass-ceramic CT-1 and single-crystalline silicon (Si(100)). A study of the electrophysical and optical properties of the formed coatings was carried out. The deposited coatings demonstrate a good reflectivity in the infrared range of spectrum (700–2000 nm), what is important for reducing the overheating of the spacecraft (SC) under the influence of the direct sunlight. In the visible range of spectrum (400–700 nm), a low level of total Rtotal reflection is observed. This is promising for satellites designed to observe the Earth’s surface. The values of solar absorption coefficients αs, emissivity coefficients ε0, ratios αs/ε0, as well as the equilibrium temperature Tр for the samples under study were obtained. The values of resistivity ρ and surface resistance R□, electron concentration N and electron mobility μ were determined. It has been discovered that TiAlSiN, TiAlSiCN films are electrically conductive: ρTiAlSiN = (92÷4260) ∙ 10–7 Ω ∙ m, ρTiAlSiCN = (51÷2360) ∙ 10–7 Ω ∙ m. It has been found that adding carbon to the coating composition reduces the resistance. The obtained nanostructured coatings of TiAlSiN nitride and TiAlSiCN carbonitride can be used as temperature control coatings for small spacecrafts.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"17 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141659569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypersingular integro-differential equation with quadratic functions in coefficients","authors":"A. P. Shilin","doi":"10.29235/1561-2430-2024-60-2-117-131","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-117-131","url":null,"abstract":"A new linear integro-differential equation of order n ≥ 3, given on a closed curve located in the complex plane, is investigated. Integrals in the equation are understood in the sense of the finite part according to Hadamard. A characteristic feature of the equation is the presence of quadratic functions of a special kind in its coefficients. The equation is reduced first to the boundary value problem of linear conjugation for analytical functions. In the case of its solvability, two linear differential equations should be further solved in the domains of the complex plane with some additional conditions for the solution. All conditions for the solvability of the original equation are explicitly specified. When they are executed, the desired solution is constructed in a closed form. An example is given.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"22 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141663681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classical solution to mixed problems from the theory of longitudinal impact on an elastic semi-infinite rod in the case of separation of the impacting body after the collision","authors":"V. Korzyuk, J. Rudzko","doi":"10.29235/1561-2430-2024-60-2-95-105","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-95-105","url":null,"abstract":"In this work, we consider two coupled initial-boundary value problems, which, based on the Saint-Venant theory, model the longitudinal impact phenomena in a semi-infinite rod. The mathematical formulation of the problem is two mixed problems for the one-dimensional wave equation with conjugation conditions. The Cauchy conditions are specified on the spatial half-line. The initial condition for the partial derivative with respect to the time variable has a discontinuity of the first kind at one point. The boundary condition, which includes the unknown function and its first- and second-order partial derivatives, is specified on the time half-line. The solution is constructed by the method of characteristics in an explicit analytical form. The uniqueness of the solution is proved, and the conditions under which a piecewise-smooth solution exists are established. The classical solution to a mixed problem with matching conditions is considered.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diffraction of displaced Gaussian light beams on ultrasound in paratellurite crystals","authors":"Г. В. Кулак, П. И. Ропот, О. В. Шакин, Gennadii V. Kulak, Peter I. Ropot, O. Shakin, © Кулак","doi":"10.29235/1561-2430-2024-60-2-146-152","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-146-152","url":null,"abstract":"The Bragg diffraction of displaced Gaussian light beams on a slow shear ultrasonic wave in paratellurite crystals, in which the beam energy is efficiently transferred from the zero diffraction order to the first, is investigated. It is established that circularly polarized light beams should be used to optimize the energy exchange of diffracted light beams in the considered geometry of acousto-optic interaction. It is shown that the diffracted beams have the form of displaced Gaussian beams, the spatial structure of which is determined by the displacement parameter of the incident beam and the ultrasound power.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141665327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Low-frequency capacitor with hopping electrical conductivity of the working substance (on the example of a-Si:H)","authors":"N. Poklonski, I. I. Anikeev, S. A. Vyrko","doi":"10.29235/1561-2430-2024-60-2-153-161","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-153-161","url":null,"abstract":"We propose a structural and electrical schemes of a capacitor based on a 3 μm thick a-Si:H (amorphous hydrogenated silicon) layer separated from the metal plates by 0.3 μm thick dielectric layers of SiO2 (silicon dioxide). We consider room temperatures (T ≈ 300 K) when in the absence of illumination for a-Si:H the hopping mechanism of electron migration via point defects of the structure prevails. For such a capacitor, the dependencies of the capacitance on the frequency of the measuring signal ω/2π in the range from 0.1 to 300 Hz are calculated for the a-Si:H layer with stationary hopping electrical conductivity σdc ≈ 1 ∙ 10−10 (Ohm ∙ cm)−1. It is assumed that there is no end-to-end electron transfer between the a-Si:H layer, dielectric layers and capacitor plates in the small-signal mode of capacitance measurement. It is shown that the real part of the capacitance of the capacitor decreases with increasing angular frequency ω, and the imaginary part is negative and depends non-monotonically on ω. The decrease in the real part of the device capacitance to the geometric capacitance of the series-connected oxide layers and the a-Si:H layer with increasing ω is due to a decrease in the electrical resistance of the capacitor. As a result, with increasing ω, the imaginary part of the capacitance is shunted by the hopping electrical conductivity of the capacitor. The phase shift for a sinusoidal electrical signal supplied to the capacitor is determined depending on the frequency ω/2π in the range of 0.1–300 Hz for the values of electrical conductivities of the hydrogenated amorphous silicon layer σdc ≈ 1 ∙ 10−11, 1 ∙ 10−10, and 1 ∙ 10−9 (Ohm ∙ cm)−1 at the temperature 300 K. With an increase in the electrical conductivity σdc of the a-Si:H layer, the minimum absolute value of the phase shift angle (≈65°) shifts to the high- frequency region (from 1 to 100 Hz). The proposed low-frequency capacitor can find application in electrical circuits for detecting low-frequency electrical signals for the purposes of biomedicine.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"96 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141663977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Massless spin 2 field in 50-component approach: exact solutions with cylindrical symmetry, eliminating the guage degrees of freedom","authors":"Alina V. Ivashkevich, V. Red’kov, A. M. Ishkhanyan, А. В. Ивашкевич, В. М. Редьков, А. М. Ишханян","doi":"10.29235/1561-2430-2024-60-2-132-145","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-132-145","url":null,"abstract":"We begin with some known results of the 50-component theory for a spin-2 field described in cylindrical coordinates. This theory is based on the use of a 2nd-rank symmetric tensor and a 3rd-rank tensor symmetric in two indices. In the massive case, this theory describes a spin-2 particle with an anomalous magnetic moment. According to the Fedorov – Gronskiy method, which is based on projective operators, all 50 functions involved in the description of the spin-2 field for the case of the free particle can be expressed in terms of only 7 different functions constructed from Bessel functions. This leads to a homogeneous system of linear algebraic equations for 50 numerical parameters. We have found 6 independent solutions to these equations. Additionally, we have obtained explicit expressions for 4 guage solutions defined in accordance with the Pauli – Fierz approach. These solutions are exact and correspond to non-physical states that do not affect observable quantities, such as the energy-momentum tensor. Finally, we have constructed two classes of solutions that represent physically observable states.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"102 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141666443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Markov fracture models of inhomogeneous media and design of layered structures synthesized by additive technology","authors":"M. Zhuravkov, Yu. Zamzhitskaya-Chigareva","doi":"10.29235/1561-2430-2024-60-2-106-116","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-2-106-116","url":null,"abstract":"We consider the problem of studying the fracture of a composite macrolayer synthesized by additive technology on a solid substrate, to which the boundary of the lower microlayer is rigidly bonded. The materials of the microlayers are homogeneous and isotropic. The thicknesses of microlayers and the total thickness of the macrolayer are the control parameters of synthesis. The physical and mechanical characteristics of the microlayers and their combination in the macrolayer are also controlling parameters. The layer is fractured by a crack, which may appear in the top layer (or any other layer) and move toward the substrate or free surface, perpendicular to the boundaries of the microlayers. The crack can stop at the boundaries between the layers (then it is treated as a separate state) or pass through the boundaries without stopping. Based on the theory of Markov chains, the average lifetime of a stratified layer synthesized on a substrate using additive technology and the variance of the number of cycles (lifetime) characterizing the quality of the synthesized structure are calculated. On the basis of the materials available for the synthesis of the layered coating, the problems of optimal design of the composite body with maximum average resource, minimum resource dispersion, maximum specific strength for given geometric and physical-mathematical constraints on the composite parameters are solved. To find optimal solutions, dynamic programming algorithms are used, implemented on circuits (graphs) of sequential selection of a combination of layer materials according to their synergistic properties.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"106 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141666099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Formation of multibeam dynamic gradient interference light fields with refractive optical elements","authors":"A. Ryzhevich, I. V. Balykin, T. A. Zheleznyakova, N. S. Kazak","doi":"10.29235/1561-2430-2024-60-1-72-88","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-72-88","url":null,"abstract":"This paper presents methods for the formation and properties of light fields that controllably vary in time and space, obtained as a result of the interference of three or four coherent light beams using refractive optical elements. The formation of three-beam and four-beam interference fields is carried out using trihedral and tetrahedral glass pyramids respectively. The possibility of the interference field displacement in the transverse plane is ensured by devices for controlled phase changes of at least two of the interfering beams. The directions of propagation of these beams do not lie in the same plane with the optical axis of the original beam incident on the pyramid. In threeand four-beam dynamic interference fields the peak intensity values are higher than in the original laser beams and two-beam interference fields, so it is advisable to use them for processing flat objects with laser radiation, moving the interference maxima along the surface of the object. With a pairwise azimuthal displacement of the propagation directions of four interfering beams around the longitudinal axis, a dynamic interference field is formed, the periodically structured maxima of which cyclically smoothly change their shape from cells to band and back. At different speeds of pairs of directions the interference structure of the maxima rotates around the longitudinal axis. Therefore, this field can be used for therapeutic effects on biological tissues and for mixing microparticles in suspensions and emulsions. Since the local maxima of the intensity of all these interference fields have dimensions of the order of several micrometers while exceeding in value the maximum intensity of the initial light beam, these fields in the cross section are gradient and therefore can be used not only for laser exposure, but also for moving ensembles of microparticles including for sorting and changing concentration.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"1159 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140748936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Implementation of asynchronous mode in a linear periodic system with the nontrivial lower left block of averaging of the coefficient matrix","authors":"A. Demenchuk","doi":"10.29235/1561-2430-2024-60-1-7-14","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-7-14","url":null,"abstract":"A linear control system with a periodic matrix of coefficients and program control is considered. The matrix under control is constant, rectangular (the number of columns does not exceed the number of rows) and its rank is not maximum, i. e. less than the number of columns. It is assumed that the control is periodic, and the module of its frequencies, i. e. the smallest additive group of real numbers, including all Fourier exponents of this control, is contained in the frequency module of the coefficient matrix. The following task is posed: to construct such a control from an admissible set that switches the system to asynchronous mode, i. e. the system must have periodic solutions such that the intersection of the frequency moduli of the solution and the coefficient matrix is trivial. The problem posed is called the problem of synthesis of asynchronous mode. The solution to the formulated problem significantly depends on the structure of the average value of the coefficient matrix. In particular, its solution is known for systems with zero average. In addition, solvability conditions were obtained in the case when the matrix under control has zero rows, the averaging of the coefficient matrix is reduced to the form with upper left diagonal block and with zero remaining blocks. In this paper we consider a more general case with a nontrivial left lower block. Assuming an incomplete column rank of the matrix function composed from the rows of oscillation path of the coefficient matrix, we construct the control explicitly. This control switches the system to asynchronous mode.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"27 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140753210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the symmetry algebra of a one-dimensional quantum-mechanical oscillator on a hyperbola","authors":"A. N. Lavrenov, I. Lavrenov","doi":"10.29235/1561-2430-2024-60-1-34-42","DOIUrl":"https://doi.org/10.29235/1561-2430-2024-60-1-34-42","url":null,"abstract":"The quantum-mechanical problem of a harmonic oscillator on a hyperbola as a one-dimensional space of constant negative curvature is considered in this article. A generalization to the singular oscillator model in the context of one-dimensional Cayley – Klein geometries is given by the factorization method. The energy spectrum and wave functions of stationary states are found having the curvature of space as a parameter. For the energy levels of the singular oscillator, the effect of non-zero curvature is clearly manifested through a positive or negative term, depending on the sign of the curvature, which is quadratic in the level number. The results obtained are consistent with those previously published. The dynamical symmetry of the problem is shown explicitly as a quadratic Hahn algebra QH(3) or its isomorphic Higgs algebra.","PeriodicalId":516297,"journal":{"name":"Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series","volume":"472 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140750770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}