2304-9782, 2618-8686, 2405-7223 16 3 2023 1-191

RAR RUS 9-18 Moscow State University of Technology and Management Smirnov Mikhail m_u_smirnov@mail.ru Lipetsk State Pedagogical University named after P. P. Semenov-Tyan-Shansky Filippov Vladimir wwfilippow@mail.ru Moscow State University of Technology and Management Ziyautdinov Vladimir zevslipetsk@yandex.ru Bogonosov Konstantin k.bogonosov@mgutm.ru Phenomenological approach to the description of phase transitions in solids A general model approach to the problem of describing the competition and coexistence of different phases of a condensed state is considered on the basis of Landau's theory of second-order phase transitions. We show that the multicomponent order parameter leads to a more complex pattern of phase transitions and the appearance of regions in the phase diagram in which different spatially ordered states can compete or coexist. The solution of the necessary equations of the Ginzburg-Landau theory was carried out by the variational method. The model considered in this paper is applicable to the analysis of phase transitions in solids with different electrical properties (transitions to the superconducting state, metal-dielectric and metal-semiconductor transformations) and magnetic states (paramagnet-ferromagnet, paramagnet-antiferromagnet). The proposed approach makes it possible to numerically simulate the free energy of a solid near the phase transition points. The necessary conditions and limits of applicability of the analyzed computational model are indicated. 10.18721/JPM.16301 538.9 second-order phase transition order parameter phenomenological approach competition and coexistence of phases https://physmath.spbstu.ru/article/2023.67.1/ 01_9-18_16(3)2023.pdf

RAR RUS 19-28 Amur State University Sakhnenko Anna anna_izbickaya@mail.ru Blagoveshchensk State Pedagogical University Milinskiy Alexey a.milinskiy@mail.ru Blagoveschensk State Pedagogical University Baryshnikov Sergey svbar2003@list.ru Amur State University Stukova Elena lenast@bk.ru Blagoveshchensk State Pedagogical University Egorova Irina bgpu.chim.egorova@mail.ru Dielectric and thermal properties of nanocomposites based on diisopropylammonium iodide and alumina nanoparticles In the paper, nanocomposites based on diisopropylammonium iodide (DIPAI.) and Al2O3 nanoparticles (sized 100 nm) have been synthesized with varying a volume fraction of the latter (0.05, 0.10, 0.20). Temperature dependences of the permittivity and a signal of differential thermal analysis of the samples (in the range of 300 – 400 K) were studied in heating and cooling modes. Their infrared spectra were recorded at room temperature as well. An analysis of the measured temperature dependences indicated a change in the sequence of phase transitions in nanocomposites compared with the pure DIPAI. The totality of the results obtained allowed us to conclude that a change in hydrogen bonds with the participation of amino groups manifested itself in the nanocomposite structure took place. This can lead to the appearance of a ferroelectric state in the DIPAI. 10.18721/JPM.16302 537.226 ferroelectric permittivity nanocomposite phase transition DIPAI alumina https://physmath.spbstu.ru/article/2023.67.2/ 02_19-28_16(3)2023.pdf

RAR RUS 29-38 Peter the Great St. Petersburg Polytechnic University Kharin Nikita kharin.nikita66@gmail.com

St. Petersburg, Russian Federation

Peter the Great St. Petersburg Polytechnic University Panevin Vadim pvyu@rphf.spbstu.ru Peter the Great St. Petersburg Polytechnic University Petruk Anton wotgustik@yandex.ru Peter the Great St. Petersburg Polytechnic University Vinnichenko Maxim mvin@spbstu.ru 0000-0002-0048-7512 Peter the Great St. Petersburg Polytechnic University Norvatov Ilya norv2@mail.ru

St. Petersburg, Russian Federation

0000-0001-5547-9387 Alferov University Fedorov Vladimir fedorov_vv@spbstu.ru Influence of stimulated interband emission on terahertz photoluminescence in n-type gallium arsenide layers In the paper, a possibility of increasing the terahertz (THz) radiation intensity under optical interband pumping in the epitaxial GaAs layer doped with shallow donors has been studied. An increase in the intensity of THz radiation was achieved by implementation of conditions for stimulated interband radiation in the near-IR range, which depopulated intensively the donor ground state. The photoluminescence spectra of the samples were measured by Fourier spectrometer. Photoluminescence spectra were recorded in the near-IR and THz ranges in the sub- and post-threshold working conditions of radiation generation in the near-IR range. In the THz spectra, a change in behavior of the dependence of the radiation intensity on pumping was observed. The change was due to a decrease in the radiative lifetime of electrons at the impurity level. 10.18721/JPM.16303 538.958 photoluminescence terahertz radiation impurity transition epitaxial layer bulk semiconductor stimulated emission https://physmath.spbstu.ru/article/2023.67.3/ 03_29-38_16(3)2023.pdf

RAR RUS 39-48 0000-0003-2327-068X Mechanical Engineering Research Institute of the RAS Alifov Alishir a.alifov@yandex.ru The interaction of mixed forced, parametric and self-excited oscillations at limited excitation and delays On the basis of a dynamic model of a frictional self-oscillating system, the influence of delays in elasticity and friction causing self-oscillations on mixed forced, parametric and self-oscillations during the interaction of an oscillating system with an energy source has been considered. The solution of nonlinear differential equations of motion of an oscillatory system and an energy source was constructed using the method of direct linearization. The latter differs from the known methods for the analysis of nonlinear systems by many advantages, including ease of use. Based on the Routh – Hurwitz criteria, the stability conditions for the analysis of stationary motions were obtained. Calculations were carried out to obtain information on the influence of delays on the oscillation modes. This influence was established to be very significant. The stability of stationary oscillations depends both on the characteristics of the energy source and on the magnitude of the delay; a weak or very weak stability appears. 10.18721/JPM.16304 534.16 limited excitation oscillations delay Routh – Hurwitz criteria direct linearization https://physmath.spbstu.ru/article/2023.67.4/ 04_39-48_16(3)2023.pdf

RAR RUS 49-58 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

Simulation of thermophysical processes in a rotor-blade engine with external heat supply by nodal analysis The well-known algorithm of mathematical modeling in nodal values has been used to analyze the operation of a rotary-blade engine with external heat supply. The calculation procedure allows obtaining the required combination of exchange processes between the introduced elements using the formation of a graph in the form of a connection matrix when the switching of nodes depends on time. The values of thermodynamic functions found as a result of calculation by a known algorithm were compared with their values taken from indicator diagram characteristics. The influence of the finite rate of heat and mass transfer processes on the pressure and temperature values within a repetitive cyclic process was demonstrated. 10.18721/JPM.16305 621.412 rotary-blade engine nodal analysis method cyclic process numerical simulation https://physmath.spbstu.ru/article/2023.67.5/ 05_49-58_16(3)2023.pdf

RAR RUS 59-72 Peter the Great St. Petersburg Polytechnic University Baranov Maksim baranovma1993@gmail.com Peter the Great St. Petersburg Polytechnic University Karseeva Elina elina.nep@gmail.com Peter the Great St. Petersburg Polytechnic University Tsybin Oleg otsybin@rphf.spbstu.ru Supercomputer dynamical models of glycine, tryptophan and diphenyl-L-alanine in the electrical fields of terahertz and infrared spectral ranges In the paper, a method for analyzing molecular oscillations of the glycine, tryptophan and difenilalanine amino acids in the electric fields of the THz/IR frequency ranges has been implemented with Fourier-frequency spectrum calculation of the integral dipole moment amplitude-time realizations obtained by supercomputer modeling. The achieved results inhibited new possibilities of applying this method, supplemented the understanding of the dynamic properties of biomolecules. The method and the data obtained can be recommended in the development of nanobiotechnologies, bioelectronics, and hetero hybrid microelectronic devices with embedded biomolecular components. 10.18721/JPM.16306 53.093, 53.096, 57.031, 57.033, 57.038 molecular dynamics simulation amino acid biomolecular electronics glycine tryptophan diphenylalanine https://physmath.spbstu.ru/article/2023.67.6/ 06_59-72_16(3)2023.pdf

RAR RUS 73-86 St. Petersburg State University Grishchenko Alexei gai-gr@yandex.ru St. Petersburg State University Ignatovich Igor i.ignatovich@spbu.ru St. Petersburg State University Petrosian Ovanes o.petrosyan@spbu.ru Optimization of the microstructure of composite materials taking into account the constraints on their properties In the paper, an approach to optimizing the microstructure of composite materials under given restrictions on its properties has been put forward. The approach is based on the application of conditional optimization methods. The effective elastic properties were determined using the finite element homogenization procedure. As an example, the fiber-reinforced composite with ball-shaped inclusions was optimized taking into account the limitations on its thermal conductivity and elastic modulus at macro level using artificial intellect methods. 10.18721/JPM.16307 539.3, 678.01 composite material homogenization finite element method сonditional optimization artificial intellect method https://physmath.spbstu.ru/article/2023.67.7/ 07_73-86_16(3)2023.pdf

RAR RUS 87-94 Ioffe Institute Lebedev Alexander shura.lebe@mail.ioffe.ru

St. Petersburg, Russian Federation

Ioffe Institute of RAS Davydov Sergey Sergei_Davydov@mail.ru A theoretical study of macromolecule interaction with the quasi-free-standing and epitaxial graphene formed on the silicon carbide polytypes A two-level model of an organic macromolecule has been put forward in order to analyze theoretically the interaction of dangling molecular orbitals of the organic macromolecule with quasi-free-standing and epitaxial graphene. The model initially contains a completely filled (HOMO) and empty (LOMO) levels. Within the framework of the standard adsorption approach, the interaction of these levels with quasi-free and epitaxial graphene was considered. Silicon carbide polytypes were considered as substrates. Our estimates showed that the maximum transition of electrons from dangling bonds to epitaxial graphene took place for the 3C-SiC substrate. 10.18721/JPM.16308 536.12 two-level macromolecule model single-layer graphene semiconductor substrate https://physmath.spbstu.ru/article/2023.67.8/ 08_87-94_16(3)2023.pdf

RAR RUS 95-114 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 Peter the Great St. Petersburg Polytechnic University Buchilko Igor igor.buchilko@gmail.com 0000-0001-7083-9184 Peter the Great St. Petersburg Polytechnic University Medvedev Andrei medvedev@spbstu.ru 0000-0001-5216-6588 Peter the Great St. Petersburg Polytechnic University Petrov Aleksandr petrov.av1@spbstu.ru Description of polarization-maintaining fibers in analyzing the practical fiber-optic circuits using the Jones formalism In this paper, analytical forms of the Jones matrix of a polarization-maintaining (PM) optical fiber have been obtained, taking into account a slight deviation of the real fiber of this type from its ideal representation by the linear phase plate model. The derivation was made within the framework of the polarization element model with phase anisotropy. The features of using different variants of matrices in simulation were considered. The results could be used to describe practical fiber-optic circuits with PM fibers, simulate their signal, and analyze the effect of polarization mismatches in the circuits’ work. The experiments revealing deviations of the parameters of the polarization modes of real PM fibers from the idealized model and allowing estimation of the level of this deviation were performed. 10.18721/JPM.16309 535.5, 535-4, 535.012.2 Jones formalism polarization-maintaining fiber phase anisotropy polarization state of light https://physmath.spbstu.ru/article/2023.67.9/ 09_95-114_16(3)2023.pdf

RAR RUS 115-130 Department of Physics, Tri-Chandra Multiple College, Tribhuvan University Khadka Chandra chandrabahadur9988@gmail.com

Kathmandu, Nepal

Derivation of the Lorentz transformation for determination of space contraction The paper demonstrates the incompleteness of the relativistic space contraction formula for space-time coordinates transformation between inertial frames of reference in the existing normally acknowledged version of the theory of special relativity. The reason is the lack of a formula expressing the space contraction in terms of the cosines of the direction of an object’s movement. Thus a modified version of the special relativity theory has been presented through a natural extension of the Lorentz transformation to three dimensions of space. The new transformations are based on the same mathematical operation as the Lorentz transformation, and provide mathematical information similar to that of a single-axis movement. An expression for the new transformation between inertial frames, when there was simultaneous relative motion in three directions, was introduced. The presence of relative motion in three directions between a parallelepiped and an observer (were introduced) made it possible to obtain the formulas of the directions of the ends of the parallelepiped. In fact, the Lorentz transformation was interpreted, revealing transformation of space-time coordinates in three dimensions. This offers ample scope for finding the space contraction within moving frame of reference. 10.18721/JPM.16310 510.10 frame of reference Lorentz transformation special relativity space contraction https://physmath.spbstu.ru/article/2023.67.10/ 10_115-130_16(3)2023.pdf

RAR RUS 131-149 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 Computation of fracture parameters for cracks in materials with cubic symmetry in the plane strain state In the paper, an oblique rectilinear central crack opening in an uniaxially tensile plane with a mixed mode of fracture (combination of normal separation and longitudinal shear modes) in two types of anisotropic materials (orthotropic one and one with cubic symmetry) has been studied. Stress intensity coefficient values for different crack orientations were calculated using expressions derived from the Lekhnitskii formalism and extrapolated methods for displacements and stresses. The results of verification of the used approach based on comparison of the finite element calculation with analytical one were presented (the difference was less than 0.75 %). A comparative analysis of the stress intensity and crack opening coefficients for three types of symmetry of elastic properties: isotropic material, material with cubic symmetry and orthotropic material was carried out. 10.18721/JPM.16311 539.3, 539.42 linear fracture mechanics anisotropic material Lekhnitskii formalism stress intensity factor https://physmath.spbstu.ru/article/2023.67.11/ 11_131-149_16(3)2023.pdf

RAR RUS 150-159 Peter the Great St. Petersburg Polytechnic University Tikhomirov Victor victikh@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

An antiplane crack emerging from the top of a composite functional gradient wedge In the paper, the problem on an interface longitudinal shear crack located between two functionally graded wedge-shaped regions and emerging from their common vertex has been considered. The shear modules of the materials are quadratic functions of the polar angle. This kind of functional inhomogeneity made it possible to express all the components of the elastic field through a single harmonic function. Using the Mellin integral transform, the problem was reduced to the Wiener – Hopf scalar equation, for which an exact solution was obtained. The influence of gradients of elastic properties of materials and geometric parameters of the structure on the stress intensity factor was studied. 10.18721/JPM.16312 539.3 functionally graded wedge interface crack of longitudinal shear stress intensity factor https://physmath.spbstu.ru/article/2023.67.12/ 12_150-159_16(3)2023.pdf

RAR RUS 160-176 Institute for Problems of Mechanical Engineering, RAS Fedotov Aleksandr alvafed@yandex.ru

St. Petersburg, Russian Federation

Institute for Problems of Mechanical Engineering of RAS Belyaev Alexander 13augen@mail.ru Institute for Problems in Mechanical Engineering of the RAS Polyanskiy Vladimir vapol@mail.ru Numerical study of the efficiency of modal filter method and observer method for implementation of modal control of vibrations of elastic systems The article compares the efficiency of two methods for implementing modal control for active vibration suppression of distributed elastic systems. The former is the modal filter method, which implies a linear transformation of measured and control signals; the latter is the method of modal observers, which uses the object model to reconstruct the state vector from the measurement signals. For this purpose, the problem of suppression of forced bending vibrations of a thin metal beam at several lower resonance frequencies has been solved numerically for two different objects. The simulation results showed an undeniable advantage of the observer method over the modal filter one. The inherent effects of signal transmission in the control loop, occurring in real systems but usually neglected in numerical studies were analyzed. It was established that these phenomena had a significant impact on the efficiency of the synthesized control systems. Therefore, they must be taken into account in numerical simulations. 10.18721/JPM.16313 531.391+681.5 active vibration suppression modal control modal filters observers elastic systems https://physmath.spbstu.ru/article/2023.67.13/ 13_160-176_16(3)2023.pdf

RAR RUS 177-188 LLC "Evolution Marine Digital" Afanasov Evgeny zhenya.afanasov@yandex.ru State Marine Technical University Kadyrov Sergey skadyrov@gmail.com State Marine Technical University Pevzner Vitaliy vpevzner@mail.ru The Stokes problem for an elliptic contour The paper considers the problem on small harmonic oscillations of an elliptical contour immersed in the incompressible viscous fluid. Analytical and asymptotic methods for solving this problem have been proposed. The results obtained in the numerical implementation of the analytical method and the results of asymptotic solutions were compared. The possibilities of describing the solution in almost the entire range of values of the dimensionless viscosity parameter by joint application of the proposed methods were shown. 10.18721/JPM.16314 532.5.032 Stokes problem viscous incompressible fluid solid body vibrations elliptical cylinder https://physmath.spbstu.ru/article/2023.67.14/ 14_177-188_16(3)2023.pdf