St. Petersburg Polytechnic University Journal: Physics and Mathematics

RAR RUS 7-14 Peter the Great St. Petersburg Polytechnic University Vasil'ev Alexander vasiliev_ae@spbstu.ru Peter the Great St. Petersburg Polytechnic University Kozlovski Vitaly vkozlovski@phmf.spbstu.ru Bonch-Bruevich St. Petersburg State University of Telecommunications Kolgatin Sergey kolgatins@gmail.com Contribution of internal ionization processes in semiconductors to radiative losses of relativistic electrons The study presents analysis of mass radiative energy losses (RL) incurred by relativistic electrons in different materials commonly used in semiconductor electronics. We have specifically focused on accounting for the processes of 'internal' ionization, resulting in the production of electron-hole pairs in semiconductors and dielectrics. We have established that accounting for these processes is the only method offering consistent explanations on the values of mass RLs observed experimentally. The analysis performed should allow to make more detailed predictions for the performance of semiconductor devices in real conditions, particularly, in space. 10.18721/JPM.13301 621.38+539.1 relativistic electron ionization potential radiative energy losses silicon germanium graphene electron accelerator electron-hole pair https://physmath.spbstu.ru/article/2020.49.1/ 01_7-14_13(3)2020.pdf

RAR RUS 15-22 Amur State University Stukova Elena lenast@bk.ru Blagoveschensk State Pedagogical University Baryshnikov Sergey svbar2003@list.ru Phase transitions in composites based on diisopropylammonium chloride and lead titanate The paper presents the results of studies in the dielectric properties of (DIPAC)1–x/(PbTiO3)x composites with the x volume fraction of lead titanate in composite from 0.10 to 0.40. It has been shown that the addition of lead titanate to diisopropylammonium chloride leads to an increase in the dielectric constant and the appearance of additional phase transitions during heating and cooling. The appearance of a new phase transition was explained in the framework of the Landau – Ginzburg theory, taking into account the dipole-dipole interaction between the components. 10.18721/JPM.13302 537.226 ferroelectric composite phase transition dielectric constant lead titanate diisopropylammonium chloride https://physmath.spbstu.ru/article/2020.49.2/ 02_15-22_13(3)2020.pdf

RAR RUS 23-41 MBN Research Center at Frankfurt Innovation Center of Biotechnology Verkhovtsev Alexei verkhovtsev@mbnexplorer.com

Frankfurt am Main, Germany

MBN Research Center at Frankfurt Innovation Center of Biotechnology Korol Andrei korol@mbnexplorer.com

Frankfurt am Main, Germany

MBN Research Center at Frankfurt Innovation Center of Biotechnology Sushko Gennady sushko@mbnexplorer.com

Frankfurt am Main, Germany

Goethe University Frankfurt Schramm Stefan

Frankfurt am Main, Germany

7003387326 0000-0003-1602-6144 MBN Research Center at Frankfurt Innovation Center of Biotechnology Solov'yov Andrei solovyov@mbnresearch.com

3 Altenhöferallee, Frankfurt am Main, 60438, Germany

Generalized correction to embedded-atom potentials for simulation of equilibrium and nonequilibrium properties of metals A modification of an embedded-atom method (EAM)-type potential is proposed for a quantitative description of equilibrium and nonequilibrium properties of metal systems within the molecular dynamics framework. The modification generalizes the previously developed linear correction to EAM-type potentials [Sushko et al., J. Phys.: Condens. Matter 28 (2016) 145201] and asymptotically approaches zero at large interatomic distances. A general procedure for constructing this modification is outlined and its relation to the linear correction is elaborated. To benchmark this procedure, we examine the melting phase transition and several equilibrium properties of finite-size nanosystems made of silver, gold and titanium. The simulations performed with the modified potential predict higher bulk melting temperatures of the metals and agree better with experimental values as compared to the original EAM-type potential. Our results show that the modification works well for metals with both cubic and hexagonal lattice structures. The Gupta potential is chosen as an example but the modification proposed can also be applied to other potentials of the EAM type. 10.18721/JPM.13303 538.9, 544-971 molecular dynamics simulation many-body potential phase transition equilibrium properties metal nanoparticle https://physmath.spbstu.ru/article/2020.49.3/ 03_23-41_13(3)2020.pdf

RAR RUS 42-55 Voronezh State University of Engineering Technology Chernyshov Alexander chernyshovad@mail.ru Voronezh State University of Engineering Technology Sajko Dmitrij dmsajko@mail.ru Voronezh State Technical University Goryainov Vitalij gorvit77@mail.ru Voronezh State University of Engineering Technology Kuznetsov Sergei sfs134@mail.ru Voronezh State University of Engineering Technology Nikiforova Olga niki22@mail.ru The diffusion problem in a rectangular container with an internal source: exact solutions obtained by the fast expansion method The diffusion problem in a rectangular-shaped body with the Derichlet’s boundary conditions and an internal substance source depending on the rectangle points’ coordinates has been solved generally by the fast expansion method (FEM). The exact solution containing free parameters was obtained, and by changing them one could get many new exact solutions. Exact solutions to the problem with a constant internal source were shown as an example. From our analysis of the exact solutions it follows that the concentration and diffusion fluxes distributions should be symmetrical relative to the plane y = b/2, provided that the substance concentration in the corners of the rectangular area is equal to zero. An investigation into the difference in the diffusion fluxes along the coordinate axes showed that the constant internal source affected the difference in the nonsymmetrical fluxes, and the concentration of the substance in the area corners had no effect. 10.18721/JPM.13304 519.632 exact solution diffusion internal source rectangular shape fast expansion method https://physmath.spbstu.ru/article/2020.49.4/ 04_42-55_13(3)2020.pdf

RAR RUS 56-74 Peter the Great St. Petersburg Polytechnic University Zasimova Marina zasimova_ma@spbstu.ru Peter the Great St. Petersburg Polytechnic University Ivanov Nikolay ivanov_ng@spbstu.ru Technical University of Sofia Markov Detelin detmar@tu-sofia.bg

Bulgaria, Sofia

Numerical modeling of air distribution in a test room wit h 2D sidewall jet. I. Foundations for eddy resolving approach application based on periodical formulation The paper presents the methods and results of numerical modeling of turbulent airflow in a test room based on the vortex-resolving wall-modeled large eddy simulation approach. The room ventilation is provided by a plain air jet at Re = 5233. The jet is supplied from a slit placed at a side wall under the ceiling. The room geometry and airflow parameters correspond to the experimental benchmark test by Nielsen et al. (1978), but with the periodicity boundary conditions in the transverse direction. Calculations were carried out with the ANSYS Fluent software using fine grids consisting of up to 6x10^7 cells. The paper presents detailed analysis of parametric computations aimed at the evaluation of numerical simulation adequacy. In particular, the grid dependency study was performed and the Kolmogorov scale was estimated. 10.18721/JPM.13305 532.517 turbulent airflow plain jet large eddy simulation ventilation https://physmath.spbstu.ru/article/2020.49.5/ 05_56-74_13(3)2020.pdf

RAR RUS 75-92 Peter the Great St. Petersburg Polytechnic University Zasimova Marina zasimova_ma@spbstu.ru Peter the Great St. Petersburg Polytechnic University Ivanov Nikolay ivanov_ng@spbstu.ru Technical University of Sofia Markov Detelin detmar@tu-sofia.bg

Bulgaria, Sofia

Numerical modeling of air distribution in a test room with 2D sidewall jet. II. LES-computations for the room with finite width The paper presents the results of numerical modeling of turbulent airflow in a test room based on the vortex-resolving wall-modeled large eddy simulation approach. The room ventilation is provided by a plain air jet at Re = 5233. The jet is supplied from a slit placed at a side wall under the ceiling. The problem formulation reproduces the test experiment conditions (Nielsen et al., 1978, 1990) as completely as possible. Two configuration with various air supply slit width are considered. Calculations are carried out with the ANSYS Fluent software using the grid consisting of 48 million cells. The paper demonstrates that in the near-wall jet zone the computational results agree well with the experimental data, but visible disagreement is obtained in the recirculation flow region (occupied zone) with relatively low velocities. 10.18721/JPM.13306 532.517 turbulent airflow plain jet large eddy simulation ventilation https://physmath.spbstu.ru/article/2020.49.6/ 06_75-92_13(3)2020.pdf

RAR RUS 93-107 Samara National Research University Nikolaev Petr nikolaev.pn@ssau.ru An algorithm of the initial approximation formation in the ionospheric tomography problem with inter-satellite data registration In the paper, an original approach to the formationof the initial approximation in the ionospheric tomography problem with inter-satellite registration of total electron content is presented. The direct Radon transform of the electron density (ED)’s orbital profile is proposed to approximate using convolution of the function of latitudinal distribution of ED’s maximum in the profile with the kernel function. This approximation makes it possible to estimate the latitude distribution of the ED maximum from the total electron content measurements by the deconvolution procedure. An analytical expression of the convolution kernel was obtained. Based on the proposed approach, two variants of formation of the initial approximation which used different prior information, namely, on the solar activity index and on the height of the ionization maximum in the profile, were considered. An accuracy of the mentioned formation was analyzed by the results of statistical simulation, and it was compared with the previously known approach where both the height of the ionization maximum in the profile and ED at this height were known. 10.18721/JPM.13307 519.642; 550.388.2 satellite monitoring ionospheric tomography initial estimation statistical modeling https://physmath.spbstu.ru/article/2020.49.7/ 07_93-107_13(3)2020.pdf

RAR RUS 108-118 Peter the Great St. Petersburg Polytechnic University Chumakov Yuri chymakov@yahoo.com Peter the Great St. Petersburg Polytechnic University Khrapunov Evgenii hrapunov.evgenii@yandex.ru

195251, St. Petersburg, Polytechnicheskaya St, 29

Peter the Great St. Petersburg Polytechnic University Malykh Anastasiya anfatneva@yandex.ru The effect of large-scale disturbances on the laminar-turbulent transition in a free-convective layer on a vertical surface: an experimental study The results of an experimental study of a free convective boundary layer on a vertical heated surface are presented in this paper. Particular attention has been paid to investigation of the laminar-turbulent transition zone and determination of the zone boundaries. The main goal of the present work was to find the opportunity of the transition processes’ control by using various large-scale obstacles located in the region of the laminar section of the boundary layer. A vertical aluminum plate 90 cm wide and 4.95 m high served as a free-convection flow generator. Based on the obtained results, it is safe to state that there is a possibility of a significant reduction in the length of the transition zone through the use of large-scale obstacles. This way permits the beginning of the region with developed turbulent heat transfer to be moved nearer to the front edge of the surface. Thus, these obstacles can be considered as passive elements for controlling the heat transfer intensity. 10.18721/JPM.13308 532.5.013.13:532.526 natural convection laminar-turbulent transition heat transfer natural convective boundary layer experimental study https://physmath.spbstu.ru/article/2020.49.8/ 08_108-118_13(3)2020.pdf

RAR RUS 119-129 Peter the Great St. Petersburg Polytechnic University Sobolev Maxim m.e.sobolev@mail.ru Peter the Great St. Petersburg Polytechnic University Gorelik Aleksandr gorelik_a@mail.ru Peter the Great St. Petersburg Polytechnic University Vlasova Olga olvlasova@yandex.ru A novel physico-mathematical technique of analyzing the quantitative electroencephalograms: development and application The article presents a physical and mathematical model developed by the authors. The model allows analyzing the amplitude-frequency characteristic (AFC) of electroencephalograms (EEG) of a human brain. The proposed method of EEG processing, in contrast to the previously used one, is based on approximating the AFC by an equation that contains a set of coefficients. This method is convenient for comparing data obtained from different subjects and, as found, has diagnostic significance. Previously, only the frequency / amplitude ratio or its inverse was used for evaluations. The results achieved indicate the possibility of differentiating patients of various neuropsychic profiles according to the values of the parametric indicators obtained by approximating the EEG amplitude-frequency response. 10.18721/JPM.13309 53.023, 57.023, 57.087.1 quantitative EEG amplitude-frequency characteristic EEG mathematical analysis schizophrenia dementia https://physmath.spbstu.ru/article/2020.49.9/ 09_119-129_13(3)2020.pdf

RAR RUS 130-135 Peter the Great St. Petersburg Polytechnic University Gorobei Natalia n.gorobey@mail.ru Peter the Great St. Petersburg Polytechnic University Luk'yanenko Alexander alex.lukyan@rambler.ru The Ioffe Institute of the Russian Academy of Sciences Goltsev Alexander goltsev@ua.pt Symmetry transformation parameters as classical dynamic variables in the gauge theory A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and the condition is additionally imposed on the latter, which ensures the classical character of their dynamics in the quantum theory. As a result, additional dynamic variables and transverse physical degrees of freedom in the Hamiltonian become separated. The classical theory of the Yang–Mills field is considered. 10.18721/JPM.13310 530.12:517.988.38(075.8) gauge theory quantization symmetry transformation parameters Hamiltonian https://physmath.spbstu.ru/article/2020.49.10/ 10_130-135_13(3)2020.pdf

RAR RUS 136-155 57034855700 0000-0002-4088-4707 Peter the Great St. Petersburg Polytechnic University Antonov Valerii hmath@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Almazov National Medical Research Centre Semenyutin Vladimir lbcp@mail.ru Elizabethian Hospital Aliev Vulgar neurosurrgery2@eliz.ru Studies in the autoregulation of human cerebral circulation: models and methods The work contains a review of modern methods and tools used to study the regulation of human cerebral circulation. The first part discusses the basic concepts of the mathematical description of regulatory processes based on the biomedical signals analysis. The Fourier transform and transfer function, signal coherence, convolution of functions, correlation analysis, fractal analysis, wavelet transform, artificial neural networks, Hilbert – Huang transform are presented. The second part is devoted to the papers where these methods were used for medical examinations. Their analysis showed that there was a discussion of specialists regarding the choice between linear and nonlinear models of functioning the cerebral blood flow autoregulation system. It was concluded that there was currently no single approach to solving the problem, and there remains a need to continue the development of new methods and models and their implementation in medical practice. 10.18721/JPM.13311 57.087 mathematical model cerebral blood flow autoregulation biomedical signal https://physmath.spbstu.ru/article/2020.49.11/ 11_136-155_13(3)2020.pdf