2304-9782, 2618-8686, 2405-7223 17 2 2024 1-176

RAR RUS 8-20 0000-0003-1442-4886 Peter the Great St. Petersburg Polytechnic University Babich Elena 0000-0002-6308-733X Peter the Great St. Petersburg Polytechnic University Kolesnik Elizaveta kolesnik_ev@mail.ru The testing of some extra accuracy schemes on the problem of the shock wave – vortex interaction In the paper, the calculation results of the shock wave – isoentropic vortex interaction have been presented. A complex nonstationary shock wave pattern was analyzed. The influence of the scheme for approximating the convective flows on the solution accuracy was shown to be weak. The results of calculations conducted using some extra accuracy schemes are presented: the data obtained by the second-order TVD scheme and the fifth-order WENO one being compared. The most accurate reconstruction of the vortex structure after its interaction with the shock wave was found to be achieved in the calculations when taking the WENO scheme. 10.18721/JPM.17201 519.6:533.6.011 shock wave interaction isoentropic vortex numerical simulation finite volume method extra accuracy scheme https://physmath.spbstu.ru/article/2024.73.1/ 01_8-20_17(2)2024.pdf

RAR RUS 21-32 “B. E. Vedeneev VNIIG”, JSC Andrianova Elena elena-andrianova@bk.ru An algorithm for finding the damping coefficients based on vibration surveys using the frequency domain decomposition (FDD) method The article presents an algorithm and a theoretical justification for the method of finding the damping coefficients on the base of vibration surveys using the frequency domain decomposition (FDD) method. This method is used for monitoring the structures such as buildings, bridges, dams, to determine experimentally their state (under operating conditions) without application of vibroexciters. 10.18721/JPM.17202 51-74 frequency domain decomposition damping coefficient spectral density matrix natural mode shape and frequency https://physmath.spbstu.ru/article/2024.73.2/ 02_21-32_17(2)2024.pdf

RAR RUS 33-38 Peter the Great St. Petersburg Polytechnic University Matvienko Aleksandra N. matvienko_an@spbstu.ru The ways to form fullerens structure exemplified by С28 and С30 isomers The systematization of possible ways to form C28 and C30 fullerene isomers has been completed in this work. An additional confirmation was obtained that fullerenes created by incorporating dimers into the initial structure had a minimum energy. Two other methods for the formation of new fullerenes were also considered, namely, the connection of two domes with the same symmetry and that of fullerenes with compatible symmetry. The symmetry order of the studied fullerenes varied from the second to the seventh ones. A collaboration analysis of the formation energy values and geometric simulation results allowed us to draw conclusions about the structural changes in the resulting fullerenes. 10.18721/JPM.17203 54.022 dimer isomer symmetry fulleren energy https://physmath.spbstu.ru/article/2024.73.3/ 03_33-38_17(2)2024.pdf

RAR RUS 39-60 0000-0003-0985-5964 Institute for Analytical Instrumentation of the RAS Berdnikov Alexander asberd@yandex.ru 0000-0002-9235-8549 Institute for Analytical Instrumentation, RAS Bulyanitsa Anton antbulyan@yandex.ru 0000-0003-3514-8577 Peter the Great St. Petersburg Polytechnic University Solovyev Konstantin k-solovyev@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

On associated homogeneous Gelfand functions The paper proposes refined definitions for associated homogeneous functions (AHFs) of real variables, which are of great practical importance for a wide range of problems. I. M. Gelfand and Z. Ya. Shapiro were the first in 1955 to introduce AHFs into scientific use. However, the possibilities of using these functions in various applications have not been exhausted to this day. The proposed definitions inherit the basic idea of the original paper to define chains of new functions using the recurrent linear functional relations, where some homogeneous Euler function is the starting point. This makes it possible to apply the corresponding results not only for differentiable and continuous functions, but also for discontinuous functions, including discontinuous ones at all points. The possibility of constructing a detailed consistent theory of AHFs of real variables, defined by a chain of linear recurrent functional relations of a general form, is shown. The basic theorems are formulated and proven. Further ways of generalizing the functions under consideration are discussed. 10.18721/JPM.17204 517.982.42 associated homogeneous Gelfand functions homogeneous Euler function recurrent linear functional relations https://physmath.spbstu.ru/article/2024.73.4/ 04_39-60_17(2)2024.pdf

RAR RUS 61-70 Peter the Great St. Petersburg Polytechnic University Usychenko Victor usychenko@rphf.spbstu.ru 0000-0003-1519-0460 Peter the Great St. Petersburg Polytechnic University Chernova Anastasiya A microwave method for measuring the low-frequency noise of transistors In the article, we have proposed to use microwave-fluctuation meters resistant to external intense electromagnetic noise in order to measure the low-frequency (LF) noise of microwave transistors working under these conditions. The transistor located on the board is excited by a low-noise microwave generator, the oscillation amplitude of which, being modulated by the LF noise of the transistor, is measured by a microwave spectrum analyzer. The proposed method was tested on GaN/AlGaN heterotransistors, in whose channels the electron density was formed by spontaneous and piezoelectric polarization. In addition to experimental testing, a theoretical justification for the method is presented. We obtained conditions in which the normalized spectra of oscillation amplitude fluctuations were similar to the normalized LF noise of the transistor current. 10.18721/JPM.17205 621.391.822, 621.391.823 low frequency noise microwave transistor fluctuations of microwave oscillations GaN/AlGaN heterostructure https://physmath.spbstu.ru/article/2024.73.5/ 05_61-70_17(2)2024.pdf

RAR RUS 71-79 Al-Wataniya Private University Nassif Alaa alaa.nassif@wpu.edu.sy

Al-Wataniya Private University, International Hama‒Homs‎ Highway, Hama, XQ92+PMC, Syria

University Homs Sahyouni Walid wsahyouni@homs-univ.edu.sy

Homs University, Homs, PP75+5VC, Syria

University Homs Zeidan Ola ozedan@homs-univ.edu.sy

Homs, PP75+5VC, Syria

Discussion of plasma focus parameters and gain/loss energy ‎processes for a designed plasma focus device In this research, a design for a dense plasma focus device has been developed, the plasma-focus parameters and the processes of gain/loss energy have been studied using the Lee code. The outcome was compared with that for UNU ICTP/PFF dense plasma focus device. The obtained results gave a good agreement between the data on the two devices, they also showed an increase in the linear emission process and thus an increase in the X-ray yield of the designed device compared to UNU ICTP/PFF one. 10.18721/JPM.17206 533.9.07 dense plasma focus,‎‏ Lee code,‎‎ line emission https://physmath.spbstu.ru/article/2024.73.6/ 06_71-79_17(2)2024.pdf

RAR RUS 80-93 Peter the Great St. Petersburg Polytechnic University Bizyaev Ivan ivanbiziaev@yandex.com P-6861-2015 10041592700 https://orcid.org/0000-0003-2511-0188 Karaseov Platon platon.karaseov@spbstu.ru 0000-0003-1770-1877 Peter the Great St. Petersburg Polytechnic University Karabeshkin Konstantin 0000-0002-2519-2577 Peter the Great St. Petersburg Polytechnic University Gabdullin Pavel gabdullin_pg@spbstu.ru 0000-0002-3321-7797 Peter the Great St. Petersburg Polytechnic University Arkhipov Alexander arkhipov@rphf.spbstu.ru Transformation of the structure of thin metal films upon activation of their ability to low-voltage electron emission This work continues the studies of low-threshold field electron emission from thin (6 – 10 nm) films of refractory metals (Mo or Zr) deposited on flat Si substrates. Now, we have investigated the changes in the films’ morphology induced by thermo- and electroforming procedures and by the extraction of emission current. In SEM images of the samples taken after emission experiments, we observed the signs of solid-state dewetting (agglomeration) of the films, presumably caused by ion bombardment. This hypothesis was verified by SRIM simulations of the effect of ions on Mo-film/Si-substrate structure, as well as by an experiment at a HVEE-500 ion implanter. 10.18721/JPM.17207 537.533.2, 538.975, 539.1.06 thin films low-field electron emission film dewetting ion bombardment https://physmath.spbstu.ru/article/2024.73.7/ 07_80-93_17(2)2024.pdf

RAR RUS 94-119 0000-0003-0985-5964 Institute for Analytical Instrumentation of the RAS Berdnikov Alexander asberd@yandex.ru 0000-0002-0873-8849 Institute for Analytical Instrumentation of the Russian Academy of Sciences Masyukevich Sergey Institute for Analytical Instrumentation of the RAS Pomozov Timofey tim-kor@mail.ru 0009-0002-1506-0631 Institute for Analytical Instrumentation, RAS Hasin Yuri 0000-0003-3514-8577 Peter the Great St. Petersburg Polytechnic University Solovyev Konstantin k-solovyev@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Analytical electric potentials for simulation of the multipole radiofrequency ion funnels with nonlinear profiles The article considers analytical expressions for electric field potentials that correspond to radio frequency funnels with quadratic, cubic and biquadratic profiles. The funnel electrodes are a sequence of diaphragms with a circular or multipole structure and apertures of variable size. The latter varies along the transport channel according to the desired law. The resulting expressions can be useful for fast, high-quality simulation of radiofrequency devices designed to convey ion beams with simultaneous focusing. 10.18721/JPM.17208 537.21, 517.958 Laplace equation periodic electrodes analytical electric field ion guide ion funnel https://physmath.spbstu.ru/article/2024.73.8/ 08_94-119_17(2)2024.pdf

RAR RUS 120-133 0000-0001-5547-9387 Alferov University Fedorov Vladimir fedorov_vv@spbstu.ru 0000-0001-7521-3754 Alferov University, RAS Fedina Sergey fedina.serg@yandex.ru 0000-0002-3640-677X Ioffe Institute Kaveev Andrey kaveev@mail.ioffe.ru

St. Petersburg, Russian Federation

0000-0002-1571-209X ITMO University Kirilenko Demid demid.kirilenko@mail.ioffe.ru

St. Petersburg, Russian Federation

Ioffe Institute, RAS Faleev Nikolai nfaleev@mail.ioffe.ru 0000-0001-9792-045X Peter the Great St. Petersburg Polytechnic University Mukhin Ivan muhin_is@spbstu.ru The formation of single-domain gallium phosphide buffer layers on a silicon substrate without the use of migration enhanced epitaxy technique In the paper, the influence of growth factors and silicon surface condition on the epitaxial formation of single-domain GaP buffer layers on Si (001) has been studied. A novel two-stage growth technique for the epitaxial building-up of this structure has been put forward and developed. In contrast to using the migration enhanced epitaxy technique, the proposed technology allows one to separate the nucleation and growth stages, to control the doping profile of the GaP buffer layers. The latter is important for further functional applications. The main factors determining the orientation of GaP crystalline lattice when it nucleates on the Si vicinal surface were found. The structural perfection of the grown buffer layers at both stages was proved through careful control by TEM, RHEED, AFM, and HRXRD. These findings have important implications for further functional applications. 10.18721/JPM.17209 539.23 heterostructure molecular beam epitaxy buffer layer gallium phosphide silicon substrate https://physmath.spbstu.ru/article/2024.73.9/ 09_120-133_17(2)2024.pdf

RAR RUS 134-140 Peter the Great St. Petersburg Polytechnic University Tretyakov Artem tretartem@gmail.com E-4237-2014 12784708700 0000-0001-9050-4453 Peter the Great St. Petersburg Polytechnic University Kapralova Victoria kapralova2006@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Peter the Great St. Petersburg Polytechnic University Loboda Vera vera_loboda@mail.ru 0000-0001-7579-7577 Institute of Macromolecular Compounds Sapurina Irina sapurina@mail.ru Peter the Great St. Petersburg Polytechnic University Sudar Nikolai sudar53@mail.ru Effect of doping agent evaporation on thermoelectric properties of carbon nanotube–polyaniline composite The paper presents the results of experimental study of the influence of the doping agent (acid) nature on the conductivity, Seebeck coefficient, and thermoelectric power factor of composite material based on multilayer carbon nanotubes coated with polyaniline. Polyaniline was deposited on carbon nanotube surfaces by heterophase synthesis (in-situ polymerization), by oxidative polymerization of aniline in the presence of nanotubes dispersed in the reaction medium. Hydrochloric, camphorsulfonic and dodecylbenzenesulfonic acids were used as doping agents. The effect of temperature on the conductivity, Seebeck coefficient and thermoelectric power factor of the investigated composite materials has been studied in the range from 300 to 410 K. Comparison of the influence of the acid volatility on the changes in these parameters in the heating-cooling cycle allowed us to conclude that the decrease in conductivity and increase in the Seebeck coefficient when heating composites doped with different acids is caused by the acid removal from the samples. 10.18721/JPM.17210 53.06 thermoelectrics conducting polymers carbon nanotubes conductivity Seebeck coefficient https://physmath.spbstu.ru/article/2024.73.10/ 10_134-140_17(2)2024.pdf

RAR RUS 141-149 0009-0000-5779-9966 Ioffe Institute of RAS Semenov Sergey The temperature effect on impulse dielectric strength of polymer films In the paper, the experimental data on the temperature effect on the breakdown strength of polypropylene, polycarbonate and poly(ethylene terephthalate) films 2.0–2.5 μm thick have been obtained over a temperature range from 293 to 363 K. When the film samples were heated, the breakdown electric field strength was found to decrease slightly but to reveal a significant scatter of values. It was shown that the experimental results on the pulsed electrical breakdown of the polymer films could be described basing the notion of the ionization mechanism of the polymer breakdown, not related to the development of an impact ionization of the polymer molecules. 10.18721/JPM.17211 53.043 impulse dielectric strength temperature polypropylene polycarbonate poly(ethylene terephthalate) https://physmath.spbstu.ru/article/2024.73.11/ 11_141-149_17(2)2024.pdf

RAR RUS 150-159 0000-0003-2770-2304 Sonora University, Department of Investigation for Physics, Hermosillo, Mexico Lipovka Anton nila_lip@mail.ru

83000, Mexico, Calle Rosales e Boulevard Luis, Encinas s/n Colonia Centro, Hernosillo

0000-0002-1655-9242 Southern Adventist University, School of Engineering and Physics Andrianarijaona Vola avola@southern.edu

PO Box 370, Collegedale, TN 37315-0370, USA

0000-0003-4348-7923 Southern Adventist University, School of Engineering and Physics Davis Colton coltondavis@southern.edu

PO Box 370, Collegedale, TN 37315-0370, USA

Derivation of the Klein – Gordon – Fock equation from first principles In this paper, the Klein – Gordon – Fock equation is derived from the first principles. There is no need to postulate the existence of wave functions or to axiomatically introduce values of equation coefficients within the framework of the applied approach. The equation was derived on an adiabatically variable manifold, locally described by the FRW metric with complete electrodynamics constructed on it. Here the transverse electromagnetic field (TEMF) is quantized due to the adiabatic change in the metric tensor and the Planck constant acts as an adiabatic invariant of the TEMF. Moreover, the wave functions appear in the equations in a natural way, being eigenfunctions of the Sturm – Liouville problem. These are the functions in which the TEMF function is expanded. To summarize, the proposed approach makes obvious the physical meaning both of the equation itself and of quantum mechanics in general. 10.18721/JPM.17212 530.145.85 Klein – Gordon – Fock equation Schrödinger equation Sturm – Liouville problem quantization of electromagnetic field https://physmath.spbstu.ru/article/2024.73.12/ 12_150-159_17(2)2024.pdf

RAR RUS 160-173 Department of Physics, Tri-Chandra Multiple College, Tribhuvan University Khadka Chandra chandrabahadur9988@gmail.com

Kathmandu, Nepal

Formulation of the Lorentz transformation equations in the three dimensions of space The Lorentz transformation of space and time between two inertial frames of reference is one of the pillars of the special theory of relativity. Until now, the Lorentz transformation equations have been considered on the base of one-dimensional motion between the inertial frames. The goal of this article is to extend the ordinary one-dimensional Lorentz transformation to motion along X-, Y-, and Z-directions, i.e., to achieve a space-time coordinate transformation in the three-dimensional (3D) space. We particularly discovered the modified Lorentz transformation equations along 3 directions, and this helped us to analyze the space contraction phenomena of a cuboid due to the relative motion between the inertial frames in the 3D space. As a final point, this study concluded that all length, breadth and height of a cuboid appeared to be shortened to the observer if there is the relative motion between the cuboid and an observer in the 3D space. 10.18721/JPM.17213 510.10 frame of reference Lorentz transformation space contraction special relativity theory https://physmath.spbstu.ru/article/2024.73.13/ 13_160-173_17(2)2024.pdf