2304-9782, 2618-8686, 2405-7223 17 4 2024 1-177

RAR RUS 9-19 0009-0000-1236-0319 Lobachevsky State University of Nizhni Novgorod Chizhova Anastasia Lobachevsky State University of Nizhni Novgorod Nikolskaya Alena nikolskaya@nifti.unn.ru

Nizhni Novgorod, Russian Federation

0009-0009-4269-4585 Lobachevsky State University of Nizhni Novgorod Zaitseva Ekaterina 0000-0001-8850-2651 National Research Lobachevsky State University of Nizhni Novgorod Konakov Anton The electronic band structure of hexagonal silicon polytypes This work is devoted to calculations and an analysis of the electronic band structure (BS) for hexagonal (2H, 4H, 6H) and rhombohedral (9R, 15R, 21R) silicon polytypes using the empirical pseudopotential method (EPM). The calculation results for 3C, 2H and 4H have been in good agreement with experimental data. The data for 6H, 15R and 21R were obtained and analyzed for the first time. The BS for the 9R polytype calculated by EPM was almost identical to that obtained by the density functional theory method. This result indicates the possibility of using EPM for constructing BSs of various polytypes. The advantages of EPM over others were noted. The dependences of the widths of the direct and indirect energy gaps on the of crystal hexagonality degree were also studied. A partial “straightening” of the BS was established with increasing this degree of the objects. 10.18721/JPM.17401 538.915 silicon band structure pseudopotential method polytype hexagonality https://physmath.spbstu.ru/article/2024.77.1/ 01_9-19_17(4)2024.pdf

RAR RUS 20-33 Peter the Great St. Petersburg Polytechnic University Koyokin Vadim koiokin@mail.ru Peter the Great St. Petersburg Polytechnic University Bulovich Sergei bulovic@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

2D-statement simulation of thermogasdynamic processes in a rotary-blade engine with external heat supply To analyze the characteristics of a rotor-blade engine with external heat supply, a 2D model of this mechanism is considered. The simulation took into account the movement of the working chambers of the engine and the change in their shape. When the chamber came into contact with the gas distribution windows, either gas was transferred to the heat exchangers or the chamber was filled with gas. The formation and development of the jet flow structure in the mass transfer process of an engine – heat exchanger is investigated. The heat transfer process in the engine heat exchangers was modeled using the volumetric heat transfer coefficient, and their hydraulic resistance was also taken into account. The results of the study of heat and mass transfer processes in the engine were presented in the form of cyclograms and indicator diagrams. A comparison was made with the results obtained using the nodal value method. 10.18721/JPM.17402 621.412 rotary-blade engine with external heat supply simulation numerical integration УДК: 621.412 https://physmath.spbstu.ru/article/2024.77.2/ 02_20-33_17(4)2024.pdf

RAR RUS 34-47 Peter the Great St. Petersburg Polytechnic University Ris Vladimir vvris@spbstu.ru Peter the Great St. Petersburg Polytechnic University Galaev Sergey galaev@spbstu.ru Peter the Great St. Petersburg Polytechnic University Aleksander Levchenya levchenya@yandex.ru A spatially periodic flow and heat transfer in a rectangular channel with one ribbed wall The systematic data on the effect of ribbing on the parameters of a relative (in comparison with a smooth channel) increase in hydraulic resistance εp and heat transfer εq in the range of Reynolds numbers from 50 to 8∙106 has been obtained by numerical modeling of a developed spatially periodic flow and stabilized heat transfer of incompressible gas with a Prandtl number of 0.7 in a rectangular channel with one-sided internal ribbing. In the laminar regime, the εq value was found to be small and amounted about 10%, and εp value exceeding 2.5. In the turbulent regime, the εq value behaved nonmonotonic depending on the Reynolds number, the range of its variation was 1.5–2.6, while εp increased from 3.5 to 7.0. 10.18721/JPM.17403 532.542.4 ribbed channel periodic flow heat transfer enhancement RANS model LES-WALE model https://physmath.spbstu.ru/article/2024.77.3/ 03_34-47_17(4)2024.pdf

RAR RUS 48-56 0000-0003-2327-068X Mechanical Engineering Research Institute of the RAS Alifov Alishir a.alifov@yandex.ru Parametric and self-excited oscillations under nonlinear parametric action and lag in elasticity The interaction of parametric oscillations and self-oscillations under nonlinear parametric excitation and delay in elasticity is considered. To solve the differential equations of the system motion, the direct linearization method was used and equations for non-stationary and stationary modes of oscillations were derived. Using the Routh–Hurwitz criteria, stability conditions for stationary regimes were obtained. To find out the effect of nonlinear parametric excitation on the dynamics of mixed autoparametric oscillations, relevant calculations were carried out and a comparison was made of the results obtained in the presence and absence of delay. According to calculated data, in the presence of a delay, a change in amplitude values occurs, accompanied by a shift in the amplitude curves in the amplitude-frequency area, as well as their narrowing or broadening, compared to no lag. The presence of lag also affects the stability of oscillations. 10.18721/JPM.17404 534.16 self-oscillations parametric oscillations interaction nonlinearity delay elasticity method of direct linearization https://physmath.spbstu.ru/article/2024.77.4/ 04_48-56_17(4)2024.pdf

RAR RUS 57-67 Azerbaijan State Oil and Industry University Gamzaev Khanlar xan.h@rambler.ru Identification of the boundary regime in the process of water- oil displacement from the reservoir The water-oil displacement process (from a rectangular reservoir) has been considered, that is described by a nonlinear system of partial differential equations with respect to the reservoir pressure (RP) and displacing phase saturation (DPS). Within the framework of the proposed model, the task of identifying the regime at the output boundary of the reservoir according to the specified conditions at the input boundary was set. The difference approximation method was used to construct a difference analogue of the problem, implicit with respect to RP and explicit with respect to DPS. As a result, an explicit formula was obtained for determining the approximate RP value at the outlet boundary of the reservoir at a given time layer. Taking into account the calculated RP distribution in the reservoir, the DPS distribution in the time layer was determined using an explicit formula. Based on the proposed computational algorithm, numerical experiments were carried out for the model oil reservoir. 10.18721/JPM.17405 532.546: 519.63 flooding method two-phase flow displacing phase saturation boundary inverse problem decomposition https://physmath.spbstu.ru/article/2024.77.5/ 05_57-67_17(4)2024.pdf

REV RUS 68-87 0000-0002-4363-9352 Peter the Great St. Petersburg Polytechnic University Korablev Vadim korablev@spbstu.ru 0000-0003-0723-622X Peter the Great St. Petersburg Polytechnic University Rozhansky Vladimir 0000-0002-8165-0122 Peter the Great St. Petersburg Polytechnic University Sarygulov Askar dept.cfr@unecon.ru Physical and technical problems of fusion energy development: From fundamental research to the stage of industrial opening up This review article analyzes the physical and technical problems and judges the prospects for the development of fusion energy, taking into account both the results obtained by an international consortium of scientists within the framework of such projects as ITER and within the framework of individual national programs. Energy supply is one of the most complex challenges that mankind faces in the 21st century. In modern times, about 75 % of humanity's needs are provided by fossil energy carriers: oil, gas and coal. It is obvious now that renewable energy sources have their limit of use, primarily due to the instability of their energy production and the lack of technologies to create reserves in large volumes of energy produced by them. All this forces us to pay attention to such a source as the energy of controlled thermonuclear fusion. The article also analyzes new trends in the development of fusion energy based on consortia of scientists and the private sector, which set themselves the tasks of its accelerated commercialization and industrial opening up. 10.18721/JPM.17406 621.039 controlled thermonuclear fusion fundamental research industrial development https://physmath.spbstu.ru/article/2024.77.6/ 06_68-87_17(4)2024.pdf

RAR RUS 88-97 0000-0002-3640-677X Ioffe Institute Kaveev Andrey kaveev@mail.ioffe.ru

St. Petersburg, Russian Federation

0000-0001-5547-9387 Alferov University Fedorov Vladimir fedorov_vv@spbstu.ru 0009-0006-3064-4175 Alferov University Miniv Dmitriy Formation of diluted nitride InAs1–хNх core-shell nanowires on silicon Epitaxial arrays of the InAs1–хNх core-shell nanowires have been synthesized on Si (111) for the first time. The growth of the nanowires with a wurtzite-type crystal structure was demonstrated by a self-induced mechanism using the molecular beam epitaxy with plasma-assisted nitrogen activation. Using the transmission electron microscopy and X-ray diffraction analysis, a volume decrease in the wurtzite crystal unit cell with increasing nitrogen content was revealed. 10.18721/JPM.17407 539.231, 539.261 InAs1–хNх nanowire X-ray diffraction analysis self-induced growth mechanism https://physmath.spbstu.ru/article/2024.77.7/ 07_88-97_17(4)2024.pdf

RAR RUS 98-105 Peter the Great St. Petersburg Polytechnic University Vakulenko Aleksandr sasha705@mail.ru 0000-0002-4113-0405 Peter the Great St. Petersburg Polytechnic University Vanina Polina p.yu.vanina@gmail.com 0000-0002-2793-5717 Peter the Great St. Petersburg Polytechnic University Filimonov Alexey filimonov@rphf.spbstu.ru

St. Petersburg, Russian Federation

0000-0003-4867-1404 Ioffe Institute of the Russian Academy of Sciences Vakhrushev Sergey s.vakhrushev@mail.ioffe.ru Modernization of the methodology for obtaining phase transition temperatures using the piezoresponse force microscopy exemplified by study of a phase transition in the PZT single crystal A chopper amplification technique has been developed to correct zero drift when measuring the magnitude of the piezoelectric response using the PFM method under conditions of continuous temperature change. Employing this technique, the temperatures of the antiferroelectric – ferroelectric phase transition of a PZT 4% single crystal were obtained. A qualitative agreement with the results of measuring the saturation polarization obtained by the Sawyer – Tower method makes it possible to assert that the technical assumptions made are quite reasonable and the developed method is worthy of widespread use in such measurements. 10.18721/JPM.17408 538.956 ferroelectric lead zirconate titanate piezoresponse atomic force microscopy phase transition Sawyer – Tower method https://physmath.spbstu.ru/article/2024.77.8/ 08_98-105_17(4)2024.pdf

RAR RUS 106-113 Indira Mahavidyalaya, Kalamb Dist. Yavatmal Nemade Kailash krnemade@gmail.com 0000-0002-6896-4610 Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur, India Maheshwary Prashant prashantmaheshwary51@gmail.com

MH SH 236, Dist, near Shree Saraswati Temple, Malkapur, Kalamb, Maharashtra 445401, India

Vertical spin valve performance of NiFe/Co-PANI/NiFe system The organic materials are found to be potent candidates for spintronics applications. Here, we have presented a cobalt-loaded polyaniline (Co-PANI)-based spin valve with NiFe alloy as ferromagnetic contacts. The spin valve signal was observed at temperatures from 10 K to 300 K. The IV curve of the spin valve exhibited a linear relationship, which showed that Co-PANI behaved like metal in this valve. The highest value of the magnetoresistance (MR) was found to be 8.13% at 10 K, whereas it decreased to 3.32 % at 300 K. Similarly, the bias current effect showed that the highest value of MR was 3.46 % for 10 A, which reduced down to 0.93% for 40 A. 10.18721/JPM.17409 538.955-405 polymeric composites magnetic materials spin-valve organic spintronics https://physmath.spbstu.ru/article/2024.77.9/ 09_106-113_17(4)2024.pdf

RAR RUS 114-120 Institute for Analytical Instrumentation of the RAS Pomozov Timofey tim-kor@mail.ru Institute for Analytical Instrumentation of the RAS Muradymov Marat m.muradymov@gmail.com 0009-0003-8001-7469 Institute for Analytical Instrumentation of the RAS Tkach Egor egorka765@gmail.com 0000-0002-0547-987X Institute for Analytical Instrumentation RAS Yavor Mikhail mikhail.yavor@gmail.com The efficiency of a focusing system when ion current transporting to the differential pumping system of a mass spectrometer In this work, a charge particle beam transport in a corona discharge ion source with a thin diaphragm focusing system taking into account the gas-dynamic flow in the vicinity of the nozzle has been studied experimentally. The space of influence of the gas-dynamic flow on the ion transport in the vicinity of the nozzle was shown not to exceed two nozzle diameters. The results of comparing the efficiency of the ion beam transport in the ion source with using the focusing system and without it are presented. Using the focusing system allowed one to triple the current entering the collector and to raise the sum of currents entering the nozzle and collector by an order of magnitude. 10.18721/JPM.17410 621.384.8 ion source mass spectrometer differential pumping system focusing system ion transport https://physmath.spbstu.ru/article/2024.77.10/ 10_114-120_17(4)2024.pdf

RAR RUS 121-129 0000-0003-4292-0959 Peter the Great St. Petersburg Polytechnic University Golovitski Alexander alexandergolovitski@yahoo.com Ionic diffusion into the peripheral area of a glow discharge in the electronegative gases In the paper, the effect of negative ion diffusive penetration from the central space representing the ion-ion plasma on the electron-ion plasma located in the peripheral area of a positive column of a glow discharge in the strong electronegative gases has been studied. The said penetration was shown to be responsible for formation of an electron density profile being close to linear within the peripheral area and also for sufficient reduction of its transverse size. The explicit approximate analytic expressions for parameters of electron density profile were found. The results of a specially conducted computational experiment were compared with those obtained through the approximate solution, and their good agreement was established (the error did not exceed 13%). The research carried out is important for correct quantitative evaluations of ionization rate, electron temperature and a longitudinal field in a positive column of an electronegative glow discharge. 10.18721/JPM.17411 533.9.01 negative ions glow discharge plasma plasma stratification ionic diffusion https://physmath.spbstu.ru/article/2024.77.11/ 11_121-129_17(4)2024.pdf

RAR RUS 130-137 0009-0005-7144-4746 Peter the Great St. Petersburg Polytechnic University Muzyaev Evgeniy muzyaev.ev@edu.spbstu.ru 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru The Sivers asymmetry in deep inelastic charged lepton scattering on a transverse polarized proton target In the paper, it has been proposed a calculation algorithm that allows obtaining the value of the Sivers asymmetry in semi-inclusive deep inelastic scattering of charged leptons on a transversely polarized proton using the event generator PYTHIA8 and the StringSpinner plug-in. The calculation was performed in the kinematics of the COMPASS experiment: a muon with an energy of 160 GeV scatters on a stationary proton target. The proposed algorithm was shown to make it possible to estimate high accurately the Sivers asymmetry of the final hadron. 10.18721/JPM.17412 539.12 semi-inclusive deep inelastic scattering polarization Sivers asymmetry event generator https://physmath.spbstu.ru/article/2024.77.12/ 12_130-137_17(4)2024.pdf

RAR RUS 138-146 0009-0006-8542-4401 Peter the Great St. Petersburg Polytechnic University Shapaev Dmitry dima.shapaev@yandex.ru 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru The creation of direct photons during interactions of deuterium nuclei at energies of 13.5 GeV and 27.0 GeV In this study, the invariant spectra and nuclear modification factors of direct photons produced in deuteron collisions at energies sqrt{s_{NN}} = 13.5 and 27.0 GeV/nucleon, relevant to the NICA project have been obtained by calculation. In doing this, both nuclear modified parton distribution functions and parton distribution ones found for free nucleons were used. Our analysis indicated that the predicted spectra of direct photons as a function of the transverse momentum, as well as the nuclear modification factors in these interactions were scarcely affected by accounting for the nuclear parton distribution function. It also turned out that the nuclear modification factors for direct photons generated in deuteron collisions at the specified energies depended slightly on the transverse momentum within the range from 1 to 5 GeV, differed from unity, exhibiting values around 0.8. 10.18721/JPM.17413 539.122 direct photon nuclear modification factor SPD NICA parton distribution function https://physmath.spbstu.ru/article/2024.77.13/ 13_138-146_17(4)2024.pdf

RAR RUS 147-160 0009-0005-2924-9795 Peter the Great St. Petersburg Polytechnic University Frolov Maxim Peter the Great St. Petersburg Polytechnic University Savikovskii Artem savikovskij.av@edu.spbstu.ru Peter the Great St. Petersburg Polytechnic University Semenov Artem semenov.artem@googlemail.com An energy fracture criterion based on dissipative inequality A new approach to obtaining the energy criterion for the fracture of a thermoelastic body with a growing crack has been put forward. The criterion is based directly on the first and second laws of thermodynamics. An analysis was restricted by brittle quasi-static fracture processes in the weakly nonuniform temperature field (WNUTF). The Griffith conception of surface energy supplemented by the temperature dependence of this energy was used. No thermodynamic fluxes were shown to arise in the WNUTF, except for the rate of a growing crack. This result made it possible to extend the Griffith criterion to the nonisothermal case. The vectorial J-integral representing the energy flux vector at the crack tip was established to be the only fracture parameter for thermoelastic media with cracks. Different energy flux vector representation forms for cases of linear and nonlinear thermoelasticity were considered and discussed. 10.18721/JPM.17414 539.3,539.42 brittle fracture thermomechanical loading dissipative inequality energy fracture criterion https://physmath.spbstu.ru/article/2024.77.14/ 14_147-160_17(4)2024.pdf

RAR RUS 161-174 Peter the Great St. Petersburg Polytechnic University Petukhov Dmitrii d_a_petukhov@mail.ru 0000-0002-1022-0221 Peter the Great St. Petersburg Polytechnic University Frolov Maxim frolov_me@spbstu.ru

St. Petersburg, Russian Federation

A comparison of adaptive algorithms for solving plane problems in the linear elasticity theory using the zero- and first-order Raviart – Thomas elements Functional-type a posteriori error estimates are known for many problems of the elasticity theory. However, as followed from the work of S. I. Repin and A. V. Muzalevsky, the use of classical Finite Element Method (FEM) approximations for their implementation may lead to a growing overestimation of the absolute value of an error. Later, in the work of M. E. Frolov, it was shown that the use of approximations for mixed FEMs avoids a growing overestimation of the absolute error with mesh refinements. Further research in this direction was carried out by M. E. Frolov and M. A. Churilova using the simplest Raviart – Thomas and Arnold – Boffi – Falk approximations. In this paper, a comparative analysis is performed for zero-order and first-order Raviart – Thomas finite elements. It is shown for plane problems of linear elasticity that the use of the first-order Raviart – Thomas approximation significantly reduces an overestimation of the absolute error value. 10.18721/JPM.17415 519.63 finite element method reliable a posteriori error estimates Raviart – Thomas elements https://physmath.spbstu.ru/article/2024.77.15/ 15_161-174_17(4)2024.pdf