2304-9782, 2618-8686, 2405-7223 16 1 2023 1-165

RAR RUS 7-15 Herzen State Pedagogical University of Russia Lapatin Nikolay NICOLJAPAT@mail.ru Herzen State Pedagogical University of Russia Castro Arata Rene recastro@mail.ru 0000-0001-9604-4769 Herzen State Pedagogical University of Russia Karulina Elena karulina@mail.ru Dielectric spectroscopy of perfluorosulfonic membranes in proton- and terbium-substituted forms The present study was aimed to reveal the mechanisms of electrical conductivity of the perfluorosulfonic membrane (MF-4SK) in the proton-substituted form and an effect of Tb ions modified this matrix on these mechanisms. The frequency dependences of the complex permittivity at a temperature of 293 K and the temperature dependences of it at a frequency of 1 kHz for samples of the both forms have been measured. An increase in the permittivity ε´ value with decreasing frequency and increasing temperature was brought out. The maxima of the dielectric loss factor were obtained for the layers of the studied systems at different temperatures. The obtained experimental data allowed us to assume that there were distributions over relaxation times for relaxation oscillators. A transition from classical to quantum mechanical charge transfer was discovered and interpreted for the original and modified membranes. 10.18721/JPM.16101 53.08, 538.9 perfluorosulfonic membrane dielectric spectroscopy proton terbium temperature dependence and frequency one https://physmath.spbstu.ru/article/2023.62.1/ 01_7-15_16(1)2023.pdf

RAR RUS 16-23 Peter the Great St. Petersburg Polytechnic University Vakulenko Aleksandr sasha705@mail.ru 0000-0003-4867-1404 Ioffe Institute of the Russian Academy of Sciences Vakhrushev Sergey s.vakhrushev@mail.ioffe.ru Ioffe Institute, RAS Koroleva Ekaterina e.yu.koroleva@mail.ioffe.ru NRC "Kurchatov Institute" - Central Research Institute KM "Prometheus" Vasilyeva Evgenia mail@crism.ru The permittivity – thickness relationship of a PMN (111) single crystal In this work, the permittivity measurements of lead magnoniobate PMN (111) single crystals with thicknesses of 400 µm, 25 µm and 10 µm have been carried out at a frequency of 0.1 Hz. The samples in the form of plane-parallel plates were prepared by hand grinding and then their sides were coated with 80 nm Cr-Au electrodes. The topography of the sample surfaces was controlled by AFM. The temperature dependences of the complex permittivity were obtained in the range from 150 to 350 K. The changes in the temperature dependences of ε with varying the thickness of the single crystals were analyzed. The peak on the temperature curve of ε' was shown to shift to a higher temperature with a decrease in the sample’s thickness, and its width increasing significantly. A phenomenological expression was proposed to describe the permittivity ‒ thickness relationship of a single crystal. 10.18721/JPM.16102 538.956 ferroelectric relaxor lead magnoniobate permittivity temperature dependence single-crystal thickness https://physmath.spbstu.ru/article/2023.62.2/ 02_16-23_16(1)2023.pdf

RAR RUS 24-32 Peter the Great St. Petersburg Polytechnic University Alexandrov Sergey salexandrov@spbstu.ru Peter the Great St. Petersburg Polytechnic University Khattab Yossef yossef.physics@gmail.com Nanosized vertical nanosheets made of molybdenum disulphide: Electrical and optoelectronic properties In the paper, the results of the studies in the electrical and optoelectronic properties of vertical sheets made of MoS2 have been presented for the first time. These objects are characterized by a high surface area, exposed edges, reasonable carrier mobility values and high light absorptance. Samples with an average size of about 150 nm were grown by the one-stage metal-organic chemical vapor deposition (MOCVD) technique. Vertically oriented MoS2 sheets were investigated using the scanning electron and X-ray photoelectron microscopy, the X-ray diffraction and Raman spectroscopy. I-V characteristics of the samples were obtained as well. Optoelectronic properties of the samles were studied using an argon laser (operates at a wavelength of 513 nm) with a mechanical light modulator. An analysis of the obtained results allows us to state that the studied V-MoS2 sheets should be considered as a very promising material for optoelectronics needs. 10.18721/JPM.16103 544.778.4:546.775 chemical vapor deposition molybdenum disulphide vertical nanosheet optoelectronic and electrical properties https://physmath.spbstu.ru/article/2023.62.3/ 03_24-32_16(1)2023.pdf

RAR RUS 33-50 Institute for Nuclear Problems of Belarusian State University Haurylavets Viktor bycel@tut.by

Minsk, Belarus

MBN Research Center at Frankfurt Innovation Center of Biotechnology Korol Andrei korol@mbnexplorer.com

Frankfurt am Main, Germany

MBN Research Center at Frankfurt Innovation Center of Biotechnology Sushko Gennady sushko@mbnexplorer.com

Frankfurt am Main, Germany

M-5766-2013 57192222016 0000-0002-3584-4583 Peter the Great St. Petersburg Polytechnic University Ivanov Vadim ivanov_vk@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

7003387326 0000-0003-1602-6144 MBN Research Center at Frankfurt Innovation Center of Biotechnology Solov'yov Andrei solovyov@mbnresearch.com

3 Altenhöferallee, Frankfurt am Main, 60438, Germany

Radiation of high-energy electrons when channeling in the bent silicon and germanium monocrystals In the paper, the simulation results on propagation of high-energy charged particles in the bent crystalline (Si and Ge) media have been presented within the atomistic approach. The calculation results were compared with literary experimental data obtained by measuring the output angular distribution of 855 MeV electrons with their very low initial divergence. Moreover, the literary experimental data on output radiation spectra for short bent Si and Ge crystals with different bending radii were taken into account. A good agreement between all the results was found. 10.18721/JPM.16104 538.911; 539.1.03 ultrarelativistic electron bent monocrystal silicon germanium channeling radiation when electrons channeling https://physmath.spbstu.ru/article/2023.62.4/ 04_33-50_16(1)2023.pdf

RAR RUS 51-64 Admiral Makarov State University of Maritime and Inland Shipping Sukhoterin Mikhail mvs1948@list.ru Peter the Great St. Petersburg Polytechnic University Lalin Vladimir Lalin_vv@spbstu.ru St. Petersburg State University of Architecture and Civil Engineering Kondratjeva Lidia N. Lidia condratjevaln@yandex.ru Admiral Makarov State University of Maritime and Inland Shipping Baryshnikov Sergey rector@spbuwc.ru Admiral Makarov State University of Maritime and Inland Shipping Voytko Irina voytkoiv@gumrf.ru Free vibrations of a rectangular plate with clamped opposite edges (a CFCF-plate) The paper proposes an iterative method for finding the natural frequencies of symmetric oscillations for a rectangular CFCF plate using two hyperbolic-trigonometric series in two coordinates. In this case, a resolving homogeneous infinite system of linear equations which contains the desired natural frequency as a parameter has been obtained. Instead of deriving and solving the frequency equation, it was proposed to use the sequential search for the desired frequency values (the "shooting method") in combination with the method of successive approximations. Numerical results were found for the first three symmetric eigenforms. The influence of the number of series terms and the number of iterations on the accuracy of the results was investigated. The obtained results were compared with those of other authors and the published experimental data. 10.18721/JPM.16105 539.312: 004.942 rectangular CFCF-plate oscillations natural frequency hyperbolic-trigonometric series iterative process https://physmath.spbstu.ru/article/2023.62.5/ 05_51-64_16(1)2023.pdf

RAR RUS 65-81 Government College for Girls, Department of Mathematics Kaur Iqbal bawahanda@gmail.com

Palwal, Kurukshetra, Haryana, India

Kurukshetra University, University Institute of Engineering & Technology, Department of Computer Science & Engineering Singh Kulvinder ksingh2015@kuk.ac.in

Kurukshetra, Haryana, India-136119

The two-temperature effect on a semiconducting thermoelastic solid cylinder based on the modified Moore – Gibson – Thompson heat transfer This study introduces a new modified Moore – Gibson – Thompson Photo-Thermal (MGTPT) theory with two temperatures for semiconductor material. The photo-thermoelastic effects has been investigated in an infinitely constrained semiconducting solid cylinder subjected to variable heat flux in the form of exponential laser pulse. The Laplace transforms were used for the solution of the mathematical model in the transformed domain. The numerical inversion was applied to obtain the displacement components, the conductive temperature, the carrier density, and the thermal stresses in the physical domain. The impact of different theories of thermoelasticity with two temperatures on the displacement, temperature, thermal stresses and carrier density were represented graphically and discussed using Matlab software. 10.18721/JPM.16106 536.251 semiconducting media two temperature effect modified Moore – Gibson – Thompson heat transfer https://physmath.spbstu.ru/article/2023.62.6/

RAR RUS 82-96 “B. E. Vedeneev VNIIG”, JSC Andrianova Elena elena-andrianova@bk.ru “B. E. Vedeneev VNIIG”, JSC Novitskii Dmitrii ndv63@yandex.ru “B. E. Vedeneev VNIIG”, JSC Onischuk Valeriy valery.onischuk@gmail.com Theoretical justification of natural frequency identification in the FDD (Frequency Domain Decomposition) method This paper is the first to provide a justification for the main criterion of the Frequency Domain Decomposition (FDD) algorithm based on the singular value decomposition of a spectral measured signals’ density. The algorithm is used for monitoring the structures such as buildings, bridges, dams, to determine experimentally their state (under operating conditions) without application of vibroexciters. The criterion is used to search for natural frequencies. The justification included the double-ended estimate for the first singular value of the spectral density matrix, the estimate making it possible to prove strictly the criterion's applicability under some fulfilled conditions. 10.18721/JPM.16107 51-74 frequency domain decomposition damping coefficient spectral density matrix natural mode shape and frequency https://physmath.spbstu.ru/article/2023.62.7/ 07_82-96_16(1)2023.pdf

RAR RUS 97-110 0000-0003-4292-0959 Peter the Great St. Petersburg Polytechnic University Golovitski Alexander alexandergolovitski@yahoo.com 0000-0002-1434-5056 Pskov State University Kontsevaya Vera nkoncevoi@mail.ru 0000-0002-4610-7394 Peter the Great St. Petersburg Polytechnic University Kulikov Kirill kulikov.kirill.g@gmail.com An electrodynamic model for determining the distribution function of particles by size for blood cells in vivo This paper is devoted to construction of a mathematical model for determining the distribution function of blood cells by size. After considering the problem of light scattering on a spheroidizied particle with a multilayer structure and arbitrary oriented in space, the reflection coefficient of a plane wave from the biostructure model with a smoothly irregular structure has been found. This approach made it possible to construct a model of the said structure with several layers. Based upon the reflection of a Gaussian beam from this structure the distribution function of blood cells by size was obtained. Some methods such as the T-matrices apparatus, the Huygens – Fresnel transform, the Tikhonov's regularization were involved. The mathematical model proposed for the first time allowed theoretical calculation of the size distribution functions of spheroidizied particles simulating blood cells for the case in vivo. 10.18721/JPM.16108 517.95+577.3+535.8+519.6 laser technology Tikhonov's regularization method T-matrices method Huygens – Fresnel transform https://physmath.spbstu.ru/article/2023.62.8/ 08_97-110_16(1)2023.pdf

RAR RUS 111-124 Samara University, Department of Physics Abraha Ataklti Gebreyohanes atklt.physics@gmail.com

Samara, Ethiopia

Adama Science and Technology University Belay Abebe Gemta abebebelay96@gmail.com

Adama, Ethiopia

Binding of caffeine with nicotinamide: A study by means of fluorescence quenching and UV-Vis spectroscopic techniques In this work, the binding of caffeine (CAF) with nicotinamide (NIC) has been investigated by means of fluorescence quenching and UV-Vis spectroscopic techniques. The results showed that CAF could effectively quench the intrinsic fluorescence of NIC due to a static quenching mechanism rather than a dynamic one. The key parameters of the process: the quenching constant and the bimolecular quenching rate one, the number of binding sites (n ≈ 1), as well as the thermodynamic properties of NIC with CAF were calculated. The binding constants were 6.500 and 5.577 kL/mole at 295 and 303 K respectively. The thermodynamic parameter values determined using the Van’t Hoff’s equation (ΔH = –14.220 kJ/mole, ΔS = 22.764 J/(mole∙K)) indicated that the binding process was continuous and electrostatic forces had a major role in the reaction of CAF with NIC molecules. Similarly, the UV-Vis absorption spectra of the interaction were studied and used to confirm the fluorescence quenching mechanism of the molecules. 10.18721/JPM.16109 539.19/535.372 fluorescence quenching binding constant nicotinamide caffeine https://physmath.spbstu.ru/article/2023.62.9/ 09_111-124_16(1)2023.pdf

RAR RUS 125-131 Peter the Great St. Petersburg Polytechnic University Matvienko Aleksandra N. matvienko_an@spbstu.ru The ways to form midi-fullerens structure exemplified by С22, С24 and С26 isomers In this paper, the possible ways of forming the midi-fullerene isomers, namely C22, C24 and C26, have been systematized. Three simplest mechanisms for their synthesizing are known. They are the fusion of carbon cupolas having the same symmetry; the fusion of fullerenes having compatible symmetry; embedding carbon dimers into initial fullerenes. The structures with minimal energy were formed through the use of the third mechanism retaining the topological three-fold symmetry. The symmetry order of studied fullerenes changed from the third to the sixth. The geometric modeling carried out in conjunction with the analysis of structures’ formation energies gives researchers a clear idea of the structure of the resulting fullerenes. 10.18721/JPM.16110 54.022 isomer periodic system fusion reaction growth fullerene energy https://physmath.spbstu.ru/article/2023.62.10/ 10_125-131_16(1)2023.pdf

RAR RUS 132-139 Usmanov Anton R. Usmanov ysman2d@gmail.com Peter the Great St. Petersburg Polytechnic University Modestov Victor modestov@compmechlab.com Method of specifying the centrifugal loads of shafts in calculation of the rotor unbalance behavior In the paper, a calculation method for specifying the centrifugal loads (SCLM) of free turbine rotors (turbine shaft unbalance method) has been put forward. The traditional method does not take this effect into account whereas the unbalance can lead to significant rotor deflections when approaching the critical frequencies. The SCLM in the solution of the problem within the elasticity theory in beam approximation using the finite element method (FEM) and the eigenfunction expansion method was exemplified by a three shaft system. The loads caused by thickness variation, radial runout of outside surfaces and the one of mounting surfaces were considered. An experiment consisting of vibration tests of a gas turbine engine was carried out. The test task showed that taking the shaft unbalance into account gave results being closer to the experimental ones. 10.18721/JPM.16111 629.7.036 unbalance shaft deflection centrifugal load thickness variation radial runout tolerance https://physmath.spbstu.ru/article/2023.62.11/ 11_132-139_16(1)2023.pdf

RAR RUS 140-151 National Research Moscow State University of Civil Engineering Razakova Rio-Rita chernova_riorita@mail.ru Semenov Institute of Chemical Physics, Russian Academy of Sciences Turusov Robert rob-turusov@yandex.ru Thermoelastic parameters of layered composites The paper presents calculations of thermoelastic parameters of layered composite structure (substrate + adhesive) using the contact layer method. The corresponding mathematical model (taking into account the presence of a contact layer) has been used to study properties of a layered rod subjected to heating. Temperature dependences of Young's modulus, CLTE and thermal stresses for layered, built-up and polymeric specimens were obtained and analyzed. A comparison of the calculation data on the effective properties of objects under investigation obtained by the classical formulae and by the contact layer method was made. The importance of taking into account the contact layer presence and its parameters in the study of thermoelastic characteristics of layered structures was proved. 10.18721/JPM.16112 531 / 534 layered composite adhesive mechanics contact layer method Young’s modulus CLTE https://physmath.spbstu.ru/article/2023.62.12/ 12_140-151_16(1)2023.pdf

RAR RUS 152-162 Peter the Great St. Petersburg Polytechnic University Shevchenko Sergei shevchenko.sergei.a@yandex.ru Peter the Great St. Petersburg Polytechnic University Melnikov Boris melnikovboris@mail.ru Using the theory of design of experiment and the sensitivity analysis method in simulation of a gyroscope resonator The paper proposes a little-distributed approach to a priori estimation of object characteristics. The mathematical model of the Coriolis vibratory gyroscope resonator which is being developed to determine the splitting of its eigenfrequency, has been chosen as an object. The frequency splitting is caused by the presence of imperfections of the resonator due to the manufacturing process. The theory of design of experiment and the sensitivity analysis method were used to estimate the model characteristics. The model is based on the determining relations of the theory of thin elastic tensile shells and on the Hamilton's variational principle. It was shown that the application of the taken methods allowed us to reveal the model parameters making the minimum contribution to the values of the output parameters and to simplify the model by their excluding. 10.18721/JPM.16113 531.383 Coriolis vibratory gyroscope sensitivity analysis Sobol index design of experiment https://physmath.spbstu.ru/article/2023.62.13/ 13_152-162_16(1)2023.pdf