2304-9782, 2618-8686, 2405-7223 18 3 2025 1-168

RAR RUS 9-19 0000-0003-4867-1404 Ioffe Institute of the Russian Academy of Sciences Vakhrushev Sergey s.vakhrushev@mail.ioffe.ru 0009-0009-9951-758X Peter the Great St. Petersburg Polytechnic University Reimers Serafim 0000-0003-0225-0487 Ioffe Institute of RAS Bronwald Iurii yuramel@gmail.com Critical scattering of synchrotron radiation in the lead zirconate-titanate (PZT2.4) using the Last model for the soft mode In this work, an experimental and theoretical studies of critical scattering for the PbZr0.976Ti 0.024O3 (PZT2.4) compound in the vicinity of the Brillouin zone center have been carried out taking into account the mode coupling. The scattering measurements were carried out at the European Synchrotron Radiation Facility (ESRF). One-dimensional profiles of the scattering intensity dependence on the wave vector were obtained using specially developed programs. The Last model was used for the optical soft mode in the Brillouin zone center. The frequencies and polarization vectors of the renormalized modes were determined by quantitative analysis of the scattering profile for the soft direction [1 0 1]. Good agreement between the calculated results of the model and the experimental data was achieved. The polarization vector’s change of the lowest transverse acoustic mode was traced as a function of the reduced wave vector. 10.18721/JPM.18301 538.913 ferroelectric antiferroelectric phase transition lattice dynamics critical scattering https://physmath.spbstu.ru/article/2025.81.1/ 01_9-19_18(3)2025.pdf

RAR RUS 20-29 0000-0003-2327-068X Mechanical Engineering Research Institute of the RAS Alifov Alishir a.alifov@yandex.ru The influence of nonlinear parametric excitation on the interaction of forced, parametric and self-oscillations In order to reveal the effect of nonlinear (cubic) parametric excitation (NPE) on the interaction of forced, parametric, and self-oscillation with a limited-power energy source, a widely used computed model of a self-oscillating system receiving energy from such a source was used. Solutions of nonlinear differential equations of the model were constructed using the direct linearization method (DLM), which is distinguished from the known ones by its simplicity its simplicity and low time costs. The friction force characteristic causing self-oscillations was linearized by DLM. Equations for the amplitude, oscillation phase and the velocity of the energy source in nonstationary and stationary motion cases were derived. Using the Routh – Hurwitz criteria, the stability of stationary movements was considered. The influence of NPE on the interaction of forced, parametric and self-oscillations was investigated by calculations. The latter showed NPE to change the shape of the amplitude curves inherent in linear action and to have a significant impact on the motion stability. 10.18721/JPM.18302 534.16 interaction forced oscillations parametric oscillations self-oscillations nonlinearity direct linearization method https://physmath.spbstu.ru/article/2025.81.2/ 02_20-29_18(3)2025.pdf

RAR RUS 30-48 0000-0002-9235-8549 Institute for Analytical Instrumentation, RAS Bulyanitsa Anton antbulyan@yandex.ru 0000-0003-0985-5964 Institute for Analytical Instrumentation of the RAS Berdnikov Alexander asberd@yandex.ru Institute for Analytical Instrumentation RAS Evstrapov Anatoly an_evs@mail.ru

St. Petersburg, Russian Federation

An optimized Lanczos Tau-method The paper puts forward an effective algorithm for producing approximate polynomial solutions for linear ordinary differential equations (LODEs) and sets of LODEs with polynomial coefficients and polynomial right-hand side functions. The algorithm is an upgraded version of the Lanczos Tau-method and provides the optimal deviation of the approximate solution from the exact one according to the minimax norm for a given interval. With minor modification, the algorithm allows one to find approximate expressions for the derivatives of the exact solutions with sufficiently greater accuracy than the derivatives of the approximate solutions are capable of providing that. 10.18721/JPM.18303 517.926.4 minimax norm Chebyshev polynomial optimal approximation linear ordinary differential equation Tau-method https://physmath.spbstu.ru/article/2025.81.3/ 03_30-48_18(3)2025.pdf

RAR RUS 49-59 0000-0002-1750-1536 Samara National Research University Telegin Aleksey 0009-0003-2601-4144 Samara National Research University Kalaev Mikhail A detector of micrometeoroids and space debris particles based on a film inductance coil In the paper, a model of a detector of high-speed microparticles (micrometeoroids and space debris) is proposed, made in the form of a round spiral film inductance coil. The design of the gauge ensures the creation of frequency resonance that occurs when the metal strip of the coil is broken. The obtained results of a laboratory and computer simulations of the detector showed that the film coil is suitable for recording high-speed microparticles larger than 100 μm on a spacecraft such as CubeSаt. The fracture point of the inductance coil can be found by analyzing the shift of the resonant frequency of the amplitude-frequency characteristic. In this case, the reliable determination of the point becomes possible if the number of the broken turn is greater than 5. 10.18721/JPM.18304 621.384.62 micrometeoroid space debris inductance coil crater spacecraft laboratory simulation https://physmath.spbstu.ru/article/2025.81.4/ 04_49-59_18(3)2025.pdf

RAR RUS 60-67 0009-0000-5368-6788 Peter the Great St. Petersburg Polytechnic University Arseniy A. 0000-0002-6707-6216 Ioffe Institute of RAS Pleshakov Ivan 0000-0001-6052-8251 Ioffe Institute of RAS Kuzmin Yuri 0009-0004-2565-8834 Institute for Analytical Instrumentation of RAS Fofanov Yakov A dual-beam method for studying the inhomogeneity induced by laser radiation in a magnetic fluid In the paper, a new method of experimental study based on the induction of a so-called thermal lens (TL) by the focused high-level laser radiation has been put forward for magnetic fluids. This TL is a region with a spatially changing refractive index, which occurs due to the redistribution of the nanoparticle concentration in the material and the thermal expansion of the carrier fluid. This region was illuminated by the low-level light emission of an auxiliary laser. The optical response of the medium was recorded as diffraction patterns formed from each of these two beams. The shape of the diffraction pattern in the auxiliary beam was shown to depend on the angle at which it was directed to the TL. The diffraction spot sizes were found to depend on the strength of the applied external magnetic field. 10.18721/JPM.18305 544.032.65 magnetic fluid laser radiation thermal lens light-induced inhomogeneity diffraction pattern https://physmath.spbstu.ru/article/2025.81.5/ 05_60-67_18(3)2025.pdf

RAR RUS 68-81 0000-0003-1528-669X Peter the Great St. Petersburg Polytechnic University Tonkov Dmitry 0009-0004-3109-2830 Peter the Great St. Petersburg Polytechnic University Kobylyatskaya Mariya 0009-0008-2967-8487 Peter the Great St. Petersburg Polytechnic University Vasilyeva Ekaterina Peter the Great St. Petersburg Polytechnic University Gasumyants Vitaly vgas@rphf.spbstu.ru 0000-0001-9623-4001 Peter the Great St. Petersburg Polytechnic University Tolochko Oleg ol_tol@hotmail.com Electrical and mechanical properties of flexible polymer composite materials with various carbon fillers We studied the conductive and mechanical properties of polymer composites based on styrene butadiene rubber as a matrix and three different carbon fillers, namely graphite, graphene and carbon nanotubes. Based on the analysis of the resistivity dependences on the concentrations of various fillers, the values of percolation thresholds were determined. The sensitivity of the resistivity of all synthesized composites to the degree of their uniaxial stretching was investigated. The maximum values of the gauge factor were observed in composites with graphene filler. It was also found that in composites with carbon nanotubes as a filler, the deformations arising under applied stresses have an elastic character. After removing the tensile stresses, these composites completely relaxed to their initial size. Contrary to this, in composites with graphite and graphene, even minimal stresses caused the appearance of plastic deformations, and their complete relaxation did not occur after stress was removed. 10.18721/JPM.18306 537.9 polymer composite styrene-butadiene rubber carbon resistivity percolation threshold gauge factor deformation https://physmath.spbstu.ru/article/2025.81.6/ 06_68-81_18(3)2025.pdf

RAR RUS 82-90 Peter the Great St. Petersburg Polytechnic University Larionova Dariya dlar@bk.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru 0000-0002-3395-0454 Peter the Great St. Petersburg Polytechnic University Kotov Dmitry dmitriy.kotov@gmail.com An analysis of the features of charged hadron production in collisions of bismuth nuclei at an energy of 9.2 GeV using the Blast-Wave model The paper presents charged hadron invariant spectra obtained in Bi+Bi collisions at an energy of 9.2 GeV on the basis of simulation performed using the UrQMD hybrid generator and the MPDroot package. The spectra were analyzed in the framework of statistical and Blast-Wave models, resulting in the values of temperatures and baryonic chemical potentials corresponding to the stages of kinetic and chemical freeze-out in Bi+Bi collisions. The results were discussed in the context of the phase diagram of nuclear matter. 10.18721/JPM.18307 539.125.4, 539.126.3 quark-gluon plasma charged hadrons MPD NICA phase diagram nuclear matter https://physmath.spbstu.ru/article/2025.81.7/ 07_82-90_18(3)2025.pdf

RAR RUS 91-97 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 Direct photon asymmetries in the longitudinally polarized proton-proton collisions at energies from 9 to 27 GeV This paper presents the development of the Generative Adversarial Network (GAN) model to study the properties of direct photons produced in proton-proton collisions. The study aims to extend the capabilities of our model (developed previously) by introducing the initial collision energy parameter √sNN in the range from 9 to 27 GeV. The model has been trained on the data generated using PYTHIA8 and tested both at training energies and at intermediate energy values. Special attention was paid to the ability of the model to preserve kinematic dependencies and to reproduce the double longitudinal spin asymmetry ALL. The results proved the possibility of using the GAN to interpolate the characteristics of direct photons in terms of collision energy. 10.18721/JPM.18308 539.12 asymmetries direct photons neural network generative-adversarial network https://physmath.spbstu.ru/article/2025.81.8/ 08_91-97_18(3)2025.pdf

RAR RUS 98-106 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 A comparative analysis of hadron creation in deuteron-deuteron interactions at energies of 13.5 GeV and 27.0 GeV This paper presents the results of nuclear modification factors for hadrons in deuteron-deuteron collisions at energies of √(s_NN)=13.5 GeV and √(s_NN)=27.0 GeV. We have applied the widely-used nuclear-modified parton distribution functions and parton distribution functions for free nucleons to determine nuclear modification factors (NMFs) of J/ψ, D± and π0 mesons. The obtained results showed the NMFs values of J/ψ and π0 ones to remain close to unity over the entire transverse momentum range from 0.5 to 4.5 GeV/c. The NMFs values of D± ones decreased sharply with increasing the transverse momentum at √(s_NN)=13.5 GeV, but they remained close to unity at √(s_NN)=27.0 GeV. 10.18721/JPM.18309 539.126 nuclear modification factor SPD NICA parton distribution function hadron https://physmath.spbstu.ru/article/2025.81.9/ 09_98-106_18(3)2025.pdf

RAR RUS 107-126 Nantong University, Ocean University of China Akintsov Nikolai akintsov777@mail.ru

People’s Republic of China

Kuban State University Nevecheria Artem artiom1989@mail.ru 0000-0001-7499-0578 Institute of High Current Electronics, Siberian Branch of RAS Kozhevnikov Vasily Vasily.Y.Kozhevnikov@ieee.org 0000-0003-1378-576X Moscow State University of Technology and Management (The First Cossack University) Kopytov Gennadiy rektorat@mgutm.ru 0000-0003-3536-0092 Dalian University of Technology Cao Tun caotun1806@dlut.edu.cn

2 Linggong Road, Dalian City, 116024, People’s Republic of China

Integrals of motion of a relativistic particle in 1 + 1 dimensions with coupled parameters The eigenfunctions and eigenvalues of the integrals of motion γ and θ have been studied. An invariant form of motion was obtained for the derivatives of γ and θ, with respect to the proper time and velocity of a relativistic particle (RP). The integrals γ and θ were shown to be mutually expressible. Inverse values 1/E and 1/P were introduced for the energy and momentum of a free RP. A one-to-one correspondence of the RP energy and momentum was obtained. The properties of the γ integral expressed in terms of 1/E and 1/P were determined as a functional dependence γ = γ(1/E, 1/P). Forms of the motion equations depending on the γ and θ integrals were obtained using Lagrangian and Hamiltonian formalism. Based on the latter, a generalized integral of motion describing all types of motions in 1+1 dimensions was derived. Mutually expressive differential forms of RP motion were introduced. 10.18721/JPM.18310 530.121 integral of motion special relativity Lagrangian and Hamiltonian formalisms https://physmath.spbstu.ru/article/2025.81.10/ 10_107-126_18(3)2025.pdf

RAR RUS 127-140 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 Active control of bending vibrations of Timoshenko beams using state observers When describing bending vibrations of elastic beams, the transition from the Bernoulli – Euler model to the Timoshenko model leads to a complication in the dynamic behavior of the beam and to the emergence of new dynamic effects and a new spectrum of vibration modes. The aim of this study is to test control approaches developed for Bernoulli – Euler beams, for thicker beams described by the Timoshenko model, and to study the influence of beam thickness on the efficiency of such approaches. For this purpose, the problem of active damping of forced bending vibrations of simply supported metal beams has been studied numerically using control systems with state observers, where point forces or moments serve as control inputs. It was shown that the proposed approach remained effective for the vibration control problem of Timoshenko beams at lower modes over a wide thickness range of the considered beams. 10.18721/JPM.18311 531.391+681.5 Bernoulli – Euler beam Timoshenko beam active vibration control state observer https://physmath.spbstu.ru/article/2025.81.11/ 11_127-140_18(3)2025.pdf

RAR RUS 141-155 0000-0003-0376-4463 Institute for Problems of Mechanical Engineering RAS Frolova Ksenia fkp@ipme.ru Institute for Problems in Mechanical Engineering of the RAS Bessonov Nikolay nickbessonov1@gmail.com.ru 0000-0002-5173-3218 Institute for Problems in Mechanical Engineering RAS Vilchevskaya Elena vilchevskaya_en@spbstu.ru A solution to the problem of elasticity caused by mass transport in the presence of imperfect contacts at the internal interfaces of a two-phase material The paper studies the influence of imperfect contacts (IC) at the phase interfaces of a micro-heterogeneous material on the macroscopic transport of impurity and the stress-strain state caused by its accumulation. Two types of IC are considered: segregation, which involves the accumulation of impurity that disrupts the continuity of concentration, and the formation of bypass paths for accelerated diffusion, which disrupts the continuity of the normal component of the flux. Modeling the coupled processes of mass transport and changes in the stress-strain state of the medium consists of two stages. In the first stage, the effective diffusion permeability of the material is determined using micromechanical methods. In the second stage, the macroscopic elasticity problem caused by mass transport is solved. The analysis is carried out using the example of a long cylinder, which is a two-phase material at the micro-level, consisting of a matrix and less permeable prolate spheroidal inhomogeneities with an arbitrary distribution of orientations. 10.18721/JPM.18312 539.21 diffusion elasticity due to mass transport effective properties imperfect contact phase interface two-phase material https://physmath.spbstu.ru/article/2025.81.12/ 12_141-155_18(3)2025.pdf

RAR RUS 156-165 0000-0001-9438-5711 Institute for Problems of Mechanical Engineering of RAS Sizikov Valentin Self-synchronization stability of vibration exciters of a two-mass apparatus for processing granular materials The article studies stability conditions for self-synchronization of vibration exciters in antiphase oscillation regime of working tools of an apparatus for granular materials processing. The apparatus operating regime provides grinding, attrition and mixing processing of material grains combined with a transportation process. The condition of stable antiphase rotation regime of vibration exciters’ rotors has been found with implementation of integral criterion of stability of synchronous motions. The condition of stable self-synchronization rotation regime of vibrational exciters’ rotors was found with the usage of integral criterion of stability of synchronous movements. The obtained relationships allow one to choose parameters of apparatus construction and to specify vibrational working tool’s operating regimes that perform effective implementation of process of granular material treatment. 10.18721/JPM.18313 534.1 two-mass apparatus working tools walls self-synchronization of vibrators integral criterion of synchronization stability granular materials https://physmath.spbstu.ru/article/2025.81.13/ 13_156-165_18(3)2025.pdf