2304-9782, 2618-8686, 2405-7223 16 4 2023 1-226

RAR RUS 9-19 0009-0009-6273-1478 Ioffe Institute of RAS Ovezov Maksat 0000-0001-9626-7612 Ioffe Institute Ryabko Andrey

St. Petersburg, Russian Federation

0000-0001-5449-4446 Ioffe Institute Aleshin Andrey aleshin@transport.ioffe.ru

St. Petersburg, Russian Federation

0000-0001-6500-5492 St. Petersburg Electrotechnical University "LETI" Moshnikov Vyacheslav vamoshnikov@mail.ru 0000-0002-3469-5897 Alferov University Kondratev Valeriy kvm_96@mail.ru

St. Petersburg, Russian Federation

0000-0003-0195-8870 Maximov Alexander aimaximov@mail.ru Current – voltage characteristics of MaPbI3 perovskite films formed by the single-stage spin-coat method In the paper, the properties of MaPbI3 films made with or without a precipitant have been investigated. The samples had a planar geometry based on ceramic substrates with interdigitated gold electrodes and also based on glass substrates. The samples were irradiated with green light from an LED source, and a special setup was used to measure current–voltage (I–V) characteristics. The polycrystalline films exhibited high sensitivity (an increase in current by about 2 orders upon irradiation). The width of their optical band gap was the same regardless of the use of the precipitant but the maximum trap-filling voltages turned out to be very sensitive to such use. According to optical microscopy, the film microstructure was characterized by a growth of large long dendritic structures, i. e., the nucleation occurred in the solution mass during the films’ making. This growth mechanism may be convenient for the use of MaPbI3 films in photodetectors. 10.18721/JPM.16401 538.91 organometallic perovskite semiconducting polymer transport mechanism solar cell https://physmath.spbstu.ru/article/2023.70.1/ 01_9-19_16(3)2023.pdf

RAR RUS 20-29 0000-0002-9974-1073 Peter the Great St. Petersburg Polytechnic University Ganzha Alexander 0000-0003-1120-2102 Peter the Great St. Petersburg Polytechnic University Kniazeva Maria 0000-0002-2793-5717 Peter the Great St. Petersburg Polytechnic University Filimonov Alexey filimonov@rphf.spbstu.ru

St. Petersburg, Russian Federation

0000-0003-0474-3242 Peter the Great St. Petersburg Polytechnic University Burkovski Roman roman.burkovsky@gmail.com The polarizability anisotropy of oxygen atoms as a possible reason for the formation of antiferroelectricity in perovskites The paper analyzes the structural features of perovskite-like ABO3 type materials responsible for the formation of antiferroelectric phases. For this purpose, the descriptions of some single crystals have been compared using three models: the adapted Slater dipole model (I), the Cowley shell model (II) and the Born – Karman model supplemented with consideration dipole-dipole forces and parameterized basing on ab initio calculations by Ghosez (III). The parameters of model I were found at which qualitative agreement with the data on inelastic X-ray scattering obtained by experiments with lead hafnate was observed. An analysis of all the results led to the conclusion that model I and the Ghosez parameterization confirmed the hypothesis about the key role of the lateral component of the oxygen atoms’ polarizability over its axial component for the antiferroelectricity formation. However, model II data did not support this. 10.18721/JPM.16402 538.913 structural phase transition antiferroelectric shell model dipole-dipole interaction https://physmath.spbstu.ru/article/2023.70.2/ 02_20-29_16(3)2023.pdf

RAR RUS 30-41 0000-0003-1812-3714 Ioffe Institute Kontrosh Evgeniy kontrosh@mail.ioffe.ru

St. Petersburg, Russian Federation

0000-0003-4858-7544 Ioffe Institute Kalinovskii Vitaliy vitak.sopt@mail.ioffe.ru

St. Petersburg, Russian Federation

0000-0001-8893-7751 Ioffe Institute of RAS Klimko Grigory 0000-0003-2934-4176 Ioffe Institute of RAS Ber Boris boris.ber@mail.ioffe.ru Ioffe Institute Prudchenko Kseniia prudchenkokk@mail.ioffe.ru

St. Petersburg, Russian Federation

Ioffe Institute Tolkachev Ivan TolkachevIA@mail.ioffe.ru

St. Petersburg, Russian Federation

0000-0003-2173-1278 Ioffe Institute of RAS Kazantsev Dmitry Dukazantsev@mail.ioffe.ru Temperature characterization of GaAs/AlGaAs connecting tunnel diodes The current-voltage characteristics of two types of GaAs-(δSi)/i-(GaAs/Al0.2Ga 0.8As)/p++-Al0.2Ga0.8As-(δBe) tunnel diode (TD) structures grown at different temperatures and epitaxial layer thicknesses have been investigated in the temperature range 100–400 K. Temperature dependences of the main TD parameters were determined: the peak value of the tunnel current density (Jp), the valley current density (Jv) and the differential resistance (Rd). TD samples of structure A grown at 500 °C exhibited the highest values of the peak current density (Jp ≤ 220 A/cm2) with temperature stability of 93 % over the whole temperature range. TD samples of structure B grown at 450 °C showed lower values of the peak tunneling current density (Jp ≤ 150 A/cm2), with significantly linear temperature dependence. Our findings can be used in the design and development of monolithic multijunction photoconverters of powerful laser radiation. 10.18721/JPM.16403 621.315.592 current-voltage characteristics tunnel diode epitaxial layer differential resistance peak tunneling current https://physmath.spbstu.ru/article/2023.70.3/ 03_30-41_16(3)2023.pdf

RAR RUS 42-49 0009-0004-6988-9685 Peter the Great St. Petersburg Polytechnic University, Klevtsov Anton klevtsov_ai@spbstu.ru 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 0000-0003-4933-9534 Peter the Great St. Petersburg Polytechnic University Titov Andrey andrei.titov@rphf.spbstu.ru Peculiarities of structure damage accumulation under the implantation of ions of different masses into alpha-gallium oxide at low damage levels In the paper, the distributions of structure damage created in alpha-phase of gallium oxide by keV fluorine, phosphorus and xenon ion irradiation, have been obtained at room temperature. A noticeable effect of the average individual collision cascade density on the stable damage production efficiency at the surface was established. In contrast to many other semiconductors, an intermediate damage peak appeared in the alpha-Ga2O3 between the surface and bulk maxima. This intermediate peak visible in the RBS/C spectra at low damage levels was discovered for the first time. Characteristic peculiarities of the discovered maximum were investigated. 10.18721/JPM.16404 539.1.043 gallium oxide ion implantation radiation defect collision cascades Rutherford backscattering https://physmath.spbstu.ru/article/2023.70.4/ 04_42-49_16(3)2023.pdf

RAR RUS 50-62 0000-0001-9473-7430 Peter the Great St. Petersburg Polytechnic University Golubkov Valentin golubkovvd@gmail.com

St. Petersburg, Russian Federation

0000-0002-2775-9864 Peter the Great St. Petersburg Polytechnic University Garbaruk Andrei agarbaruk@mail.ru A comparison of two approaches to the global stability analysis using the example of the cylinder flow problem In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier–Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on. 10.18721/JPM.16405 532.5.013.4 global stability analysis Navier–Stokes equations Jacobian automatic differentiation https://physmath.spbstu.ru/article/2023.70.5/ 05_50-62_16(3)2023.pdf

RAR RUS 63-75 0000-0002-4700-6122 Peter the Great St. Petersburg Polytechnic University Timokhin Vladimir v.timokhin@spbstu.ru 0000-0002-8559-3209 Peter the Great St. Petersburg Polytechnic University Korobko Dmitriy korobko.dd@edu.spbstu.ru 0000-0002-1029-2049 Peter the Great St. Petersburg Polytechnic University Nurtdinova Linara nurtdinova.li@edu.spbstu.ru 0000-0002-1091-6405 Peter the Great St. Petersburg Polytechnic University Kapralov Vladimir 0000-0002-4572-4120 Peter the Great St. Petersburg Polytechnic University Sergeev Vladimir v.sergeev@spbstu.ru Simulation of a supersonic nozzle of a massive helium jet injector The paper describes the design and operating principle of a valve designed for testing the prototypes of key elements of a massive gas injection system: a seat and a supersonic nozzle. The calculation results for supersonic nozzle parameters close to optimal for the selected valve design have been presented. The simulation of gas flows through the seat and nozzle was carried out, the parameters of the formed jet at the injection system outlet in the nozzle near field were calculated. The choice of the "stepped" nozzle profile for the first tests was justified. An assessment was made of the requirements for the accuracy of manufacturing prototype nozzles. 10.18721/JPM.16406 533.17 numerical simulation magnetic confinement high-temperature plasma gas jets discharge shutdown https://physmath.spbstu.ru/article/2023.70.6/ 06_63-75_16(3)2023.pdf

RAR RUS 76-85 0000-0002-0969-0162 Alferov University of RAS Karaseov Kirill 0009-0003-1062-8360 Peter the Great St. Petersburg Polytechnic University Strizhkin Denis P-6861-2015 10041592700 https://orcid.org/0000-0003-2511-0188 Karaseov Platon platon.karaseov@spbstu.ru 0000-0003-4933-9534 Peter the Great St. Petersburg Polytechnic University Titov Andrey andrei.titov@rphf.spbstu.ru Size effects in molecular dynamics simulations of a fullerene ion impact on the silicon surface In the paper, the interaction of an accelerated C60 fullerene ion with silicon monocrystal surface has been studied using molecular dynamics simulation. The dependence of a resulting crater size and sputtering yield on the initial size of the target was obtained. We proposed that computational artifacts revealed in simulations appeared due to two main reasons: shock waves raised by impinging the C60 ion, came back through the periodic boundary increasing the temperature around the impact point; dissipation of the energy, brought to the surface by the fullerene molecule, between small amount of atoms in the small cell might also affect the simulated results. It was established that 11 × 11 nm is the least size of lateral crystal dimensions required for the valid results of the simulation of the 8 – 14 keV C60 ion impact. 10.18721/JPM.16407 539.21 molecular dynamics simulation С60 fullerene ion silicon size effect crystal sputtering https://physmath.spbstu.ru/article/2023.70.7/ 07_76-85_16(3)2023.pdf

RAR RUS 86-100 0000-0003-4608-7781 Shirshov Institute of Oceanology, RAS Gnevyshev Vladimir 0000-0003-4608-7781 St. Petersburg State University Belonenko Tatyana The Fourier analysis in inhomogeneous media In the paper, the definition and basic properties of the Fourier transform (FT) are discussed. It has been shown with specific examples that integral solutions of the model inhomogeneous equation, the nonstationary Cauchy problem on an inhomogeneous shear flow, and the boundary value problem on the transformation of internal waves in the vicinity of the focus in the inhomogeneous medium can be found by FT and using its properties. The constructed Fourier integrals refuted the widely held claim that the Fourier analysis is unusable for the study of inhomogeneous media. 10.18721/JPM.16408 532.5: 532.591: 532.592.2 Fourier analysis Laplace transform Cauchy problem waves inhomogeneous medium https://physmath.spbstu.ru/article/2023.70.8/ 08_86-100_16(3)2023.pdf

RAR RUS 101-117 Peter the Great St. Petersburg Polytechnic University Trofimovich Karina 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 An experimental apparatus for studying the characteristics of thermoelectric effect in nanostructures We present an experimental setup for the study of thermoelectric effect in point contacts between different materials and in nanostructures. Point contacts of controlled size are formed with the use of an atomic force microscope (AFM), thermopower dependences against the temperature drop and against the contact spot size determined from the force applied to the probe. Computer simulations of heat transport in the system were performed to evaluate influence of atmospheric air and of a liquid layer covering solid surfaces in the atmospheric conditions onto temperature distributions. This influence was found to be insubstantial, which makes it possible to conduct experiments on the atmosphere and not in high vacuum. 10.18721/JPM.16409 538.93, 536.241 thermoelectric effect point contact nanostructures atomic force microscope https://physmath.spbstu.ru/article/2023.70.9/ 09_101-117_16(3)2023.pdf

RAR RUS 118-133 0000-0002-6402-8112 Peter the Great St. Petersburg Polytechnic University Louksha Oleg louksha@rphf.spbstu.ru 0000-0002-3585-1169 Peter the Great St. Petersburg Polytechnic University Trofimov Pavel 0000-0003-4047-3956 Peter the Great St. Petersburg Polytechnic University Malkin Alexander alexmalkin47@gmail.com Enhancement of the 4-mm wavelength gyrotron efficiency by multistage energy recovery This study presents the results of a complex physical modeling of a moderate power gyrotron operating at the 4-mm wavelength range. The characteristics of electrodes and magnetic coils in a four-stage recovery collector were optimized taking into account the coordinate and velocity distributions of electrons. These distributions were obtained through a trajectory analysis in the electron optical system and calculation of electron-wave interaction in the gyrotron cavity. To reduce parasitic effects of the bundles of a toroidal solenoid used to create an azimuthal magnetic field in the collector region, a sectioned electron beam was employed. The study demonstrated that the gyrotron's total efficiency of approximately 79 % could be achieved, being close to the maximum efficiency value achievable with separation of electron fractions with different energies, provided that the current of electrons reflected from a collector should not exceed 1% of the total current of an electron beam. 10.18721/JPM.16410 621.385.6 microwave electronics gyrotron helical electron beam recuperation residual electron energy recovery https://physmath.spbstu.ru/article/2023.70.10/ 10_118-133_16(3)2023.pdf

RAR RUS 134-145 0000-0003-0985-5964 National Research Nuclear University MEPHI (Moscow Engineering Physics Institute) Sysoev Alexey aasysoyev@mephi.ru 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 0000-0003-3514-8577 Peter the Great St. Petersburg Polytechnic University Solovyev Konstantin k-solovyev@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

0000-0002-6162-9481 Peter the Great St. Petersburg Polytechnic University Krasnova Nadezhda n.k.krasnova@mail.ru Analytical study of operating modes of RF ion funnels in the gas dynamic interfaces of tandem triple-quadrupole mass-spectrometers The article considers analytical models of high-frequency electric fields which can be used effectively for fast, high-quality simulation of ion flow focusing and transport processes in the radio-frequency funnels. In particular, the use of such devices in the design of a tandem three-quadrupole mass spectrometer increases the amount of ions collected in the forevacuum region of the gas-dynamic interface of the electrospray ion source. The cases of funnels with two- and four-phase electrical voltages (options I and II), as well as with amplitude-modulated electrical voltages providing a pseudopotential mode with an Archimedean wave (III) have been analyzed. As a result, the most preferable design turned out to be option III. The use of such analytical models makes it possible to test effectively promising options and thereby significantly reduce costs for the preliminary selection of a principal scheme of a device with specified characteristics, including similar cases of other mass spectrometric designs. 10.18721/JPM.16411 537.534.7, 543.51 mass spectrometry gas dynamic interface radio-frequency trap tandem mass spectrometer triple-quadrupole mass-spectrometer https://physmath.spbstu.ru/article/2023.70.11/ 11_134-145_16(3)2023.pdf

RAR RUS 146-159 0000-0003-0376-4463 Institute for Problems of Mechanical Engineering RAS Frolova Ksenia fkp@ipme.ru 0000-0002-5173-3218 Institute for Problems in Mechanical Engineering RAS Vilchevskaya Elena vilchevskaya_en@spbstu.ru Comparison of approaches to accounting for imperfect contacts when determining the effective permeability of material The paper develops a complex approach to accounting for imperfect contacts (IC) when determining effective properties of various nature. The IC are assumed to be caused by various factors (microstructure features, process’s specifity and so on). To obtain macroscopic properties, we seek a solution of the homogenization problem for the material containing isolated ellipsoidal inhomogeneities when fields are discontinuous at the interphase boundaries. The paper considers, generalizes and compares two existing approaches to accounting for the IC, namely, an approach where IC is modeled by means of a field jump specified in terms of a ratio of field values on the outer and inner sides of the inhomogeneity boundary, and approach, which introduces inhomogeneity with a surface effect. To take into account IC, we have considered an equivalent inhomogeneity with ideal contacts at the boundary. Working the problem on determining the effective diffusional permeability of material provided an example. 10.18721/JPM.16412 539.21 effective properties imperfect contact equivalent inhomogeneity effective diffusional permeability homogenization problem https://physmath.spbstu.ru/article/2023.70.12/ 12_146-159_16(3)2023.pdf

RAR RUS 160-180 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 0000-0002-0238-2909 St. Petersburg State University Koshlan Tatiana Determining the size distribution function of irregularly shaped particles for human blood cells and finding their erythrocyte parameters (in vivo case) This article continues the authors’ research aimed at constructing and developing a mathematical model used both to determine the size distribution function of human blood cells in vivo, and to find blood parameters used in medical practice. At this stage of the work, the nonsphericity of blood particles was taken into account and the convergence of processes describing multiple scattering of laser radiation by blood was optimized through the use of the method of extended boundary conditions, which made it possible to increase the possibilities of using the T-matrix method. The mathematical model for the analysis of biological processes has received material embodiment in a new software package. Regularization parameters are determined automatically based on specified kernel errors and “measured” data using different criteria. It is shown that, using the developed model, it is possible to theoretically predict the number of erythrocytes of abnormal size in a biomaterial based on measuring the width of the found erythrocyte size distribution. 10.18721/JPM.16413 517.95+577.3+535.8+519.6 laser technologies Tikhonov regularization EBCM erythrocyte index unspherulated particle https://physmath.spbstu.ru/article/2023.70.13/ 13_160-180_16(3)2023.pdf

RAR RUS 181-188 0000-0002-8910-4775 Peter the Great St. Petersburg Polytechnic University Lobanov Andrey lobanov2.aa@edu.spbstu.ru 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru A generator of deep inelastic lepton-proton scattering based on the Generative-Adversarial Network (GAN) The paper considers the application of a Generative Adversarial Network (GAN) for the development of a generator of deep inelastic lepton-proton scattering. The difficulty of effective training of the generator based on GAN is noted. It is associated with the use of complex schemes of distributions of physical properties (energies, momentum components, etc.) of particles in the process of deeply inelastic lepton-proton scattering. It is shown that the GAN makes it possible to faithfully reproduce the distributions of lepton physical properties in the final state at different initial energies of the center of mass in the range between 20 and 100 GeV. 10.18721/JPM.16414 539.12 inclusive deep inelastic scattering neural network generative adversarial network lepton-proton scattering https://physmath.spbstu.ru/article/2023.70.14/ 14_181-188_16(3)2023.pdf

RAR RUS 189-197 0000-0002-8910-4775 Peter the Great St. Petersburg Polytechnic University Lobanov Andrey lobanov2.aa@edu.spbstu.ru 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru Simulation of semi-inclusive deep inelastic lepton scattering on a proton at energies of 20 – 100 GeV on the basis of the Generative-Adversarial Neural Network This paper continues a series of articles devoted to developing the capabilities of a deep inelastic lepton-proton scattering event generator based on the generative adversarial network (GAN). The investigation has focused on semi-inclusive reactions of deep inelastic scattering and, particularly, on hadron registration. The results confirmed that GAN could accurately generate distributions of physical properties of leptons and hadrons. It worked for different types of leptons and hadrons in the range of initial energies from 20 to 100 GeV in the center-of-mass system. The GAN demonstrated to preserve the inherent correlation between the characteristics of leptons and protons. 10.18721/JPM.16415 539.12 semi-inclusive deep inelastic scattering machine learning neural network generative-adversarial network https://physmath.spbstu.ru/article/2023.70.15/ 15_189-197_16(3)2023.pdf

RAR RUS 198-214 0000-0003-2083-8989 Peter the Great St. Petersburg Polytechnic University Temkina Valentina temkina_vs@spbstu.ru 0000-0001-5988-1429 Peter the Great St. Petersburg Polytechnic University Liokumovich Leonid leonid@spbstu.ru 0009-0007-4713-1293 Peter the Great St. Petersburg Polytechnic University Archelkov Arseniy arsarch11@gmail.com 0000-0001-7083-9184 Peter the Great St. Petersburg Polytechnic University Medvedev Andrei medvedev@spbstu.ru 0000-0002-1722-1964 Peter the Great St. Petersburg Polytechnic University Kozlov Artemy kozlov_as@spbstu.ru 0000-0002-6154-2538 Peter the Great St. Petersburg Polytechnic University Greshnevikov Konstantin Spun fibers and their description within the Jones formalism in analyzing the practical fiberoptic circuits In this paper, an analytical form for the Jones matrix of a real spun fiber has been obtained, taking into account a slight deviation of its properties from an idealized representation of this fiber by the rotation matrix. The derivation was made within the framework of the optical element model with phase anisotropy. The features of using the Jones matrix of a real spun fiber in analysis of practical fiber-optic circuits and modeling their signals were considered. The experiments with the spun fiber revealing the parameter deviations of the polarization modes of the real spun fiber from the idealized model and allowing estimation of this deviation level were performed. 10.18721/JPM.16416 535.5, 535-4, 535.012.2 Jones matrix formalism spun fiber phase anisotropy polarization state of light https://physmath.spbstu.ru/article/2023.70.16/ 16_198-214_16(3)2023.pdf

RAR RUS 215-223 0000-0003-3593-8253 Sidi Mohamed Ben Abdellah University Touail Youssef youssef9touail@gmail.com

Fès, Morocco

Sultan Moulay Slimane University Jaid Amine aminejaid1990@gmail.com

Beni-Mellal, Morocco

Chouaib Doukkali University El Moutawakil Driss d.elmoutawakil@gmail.com

El Jadida, Morocco

Fixed point theorems on orthogonal metric spaces via τ-distances In this paper, we prove two fixed point theorems in the setting of orthogonal complete metric spaces via τ-distances. Our theorems generalize and improve many known results in the literature (see, for example Refs. [6, theorem 4.2] and [3, theorem 3]). 10.18721/JPM.16417 515.1. fixed point orthogonal generalized E-weakly contractive maps orthogonal metric space Hausdorff topological spaces τ-distance https://physmath.spbstu.ru/article/2023.70.17/ 17_215-223_16(3)2023.pdf