2304-9782, 2618-8686, 2405-7223 13 1 2020 1-132

RAR RUS 7-13 Peter the Great St. Petersburg Polytechnic University Apushkinsky Evgeniy apushkinsky@hotmail.com Peter the Great St. Petersburg Polytechnic University Popov Boris popov@tuexph.stu.neva.ru Peter the Great St. Petersburg Polytechnic University Saveliev Vladimir saveliev@tuexph.stu.neva.ru Peter the Great St. Petersburg Polytechnic University Sobolevskiy Vladimir sobolevskiy@physic.spbstu.ru The anomalous g-factor value of paramagnetic iron centers in the topaz lattice with strong tetragonal distortion The theoretical and experimental results of analyzing the electron paramagnetic resonance (EPR) spectra of iron impurity paramagnetic centers in the topaz (aluminum fluorosilicate) lattice are presented. Characteristic defects of the system exhibiting some lines with abnormally large values of g-factor (4.33 and 2.66) in the EPR spectra have been found. The experimental results were discussed within the framework of a previously developed model describing a defect involving an impurity iron ion replacing the Al3+ or Si4+ ion. The "Fe3+– an oxygen vacancy" model is a special case of the complexes with strong tetragonal distortion. The g-factors were calculated taking into account the covalent nature of the bonds. 10.18721/JPM.13101 539.21÷539.219, 538.9 ÷ 538.915 spectrum center symmetry Hamiltonian g-factor topaz tetragonal distortion https://physmath.spbstu.ru/article/2020.47.1/ 1_7-13_12(1)2020.pdf

RAR RUS 14-25 0000-0002-3972-9259 Northern Water Problems Institute of Karelian Research Centre of RAS Smirnov Sergei sergeysmirnov92@mail.ru E-5484-2014 56020596900 Peter the Great St. Petersburg Polytechnic University Smirnov Evgeny aero@phmf.spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Direct numerical simulation of the turbulent Rayleigh – Bénard convection in a slightly tilted cylindrical container Results of direct numerical simulation of the turbulent convection in a bottom-heated cylindrical container have been presented. The height-to-diameter ratio was equal to 1.0. The calculations were performed for two media: mercury (Pr = 0.025) and water (Pr = 6.400) at Ra = 10^6 and 10^8 respectively. To suppress possible azimuthal movements of the global vortex (large-scale circulation) developing in the container, its axis was tilted a small angle with respect to the gravity vector. Structure of the time-averaged flow pattern symmetrical with respect to the central vertical plane was analyzed. Peculiarities of vortex structures developing in the corner zones were revealed. Representative profiles of the Reynolds stresses and components of the turbulent heat flux vector were obtained for the central vertical plane. 10.18721/JPM.13102 536.25 Rayleigh – Bénard convection tilted container turbulence direct numerical simulation large-scale circulation https://physmath.spbstu.ru/article/2020.47.2/ 2_14-25_13(1)2020.pdf

RAR RUS 26-41 Saint-Petersburg State University of Aerospace Instrumentation Pichugin Yuri yury-pichugin@mail.ru

Russia, 190000, St. Petersburg, Bolshaya Morskaya St., 61

A dynamic-stochastic approach to the construction and use of predictive models The paper considers two directions of development of the dynamic-stochastic approach to the construction and use of predictive models. The first direction is related to the uncertainty of the initial state of the simulated process, and the second ‒ to the stochastic nature of model parameter estimates. In the first case, we consider methods for calculating fast-growing perturbations (FGPs) of the initial state of atmospheric dynamics models and a method for using FGPs in optimizing observation systems based on information ordering. An example of determining the zones of dynamic instability of the Northern hemisphere is given. In the second case, a mathematical apparatus for generating perturbations of model parameters in accordance with their probability distribution is proposed. Based on the data of the USSR economic indices, a numerical example of perturbation of parameter estimates and integration of the Volterra model is given. 10.18721/JPM.13103 519.226.2-519.248 dynamic model fast-growing perturbation distribution of parameter estimates ensemble of forecasts economic index https://physmath.spbstu.ru/article/2020.47.3/ 3_26-41_13(1)2020.pdf

RAR RUS 42-53 0000-0003-0985-5964 Institute for Analytical Instrumentation of the RAS Berdnikov Alexander asberd@yandex.ru 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 Mutually homogeneous functions with finite-sized matrices This work continues our studies in the properties of the homogeneous Euler' s functions that can be used in the synthesis of electric and magnetic fields for electron and ion-optical systems to carry out spectrographic recording mode. A generalization of a functional general equation for homogeneous functions has been considered. This equation corresponds to linear functional relations with a minimal-sized matrix. A general solution of the obtained functional equation was found assuming of differentiability of the functions in question. The resulting systems of functions were termed mutually homogeneous functions by analogy with the homogeneous Euler's functions and the associated homogeneous Gel’fand’s functions. 10.18721/JPM.13104 517.51; 517.28; 517.983; 537.213, 537.8 functional equation associated homogeneous function mutually homogeneous functions spectrograph https://physmath.spbstu.ru/article/2020.47.4/ 4_42-53_13(1)2020.pdf

RAR RUS 54-65 Ryazan State University named for S.A.Yesenin Stepanov Vladimir vl.stepanov@365.rsu.edu.ru 0000-0003-3831-7882 Ryazan State University named for S.A.Yesenin Moos Evgueniy e.moos@rsu.edu.ru Ryazan State University named for S.A.Yesenin Shadrin Maxim m.shadrin@russia.ru Ryazan State University named for S.A. Esenin Savin Vladislav savin-vladislav@mail.ru

Ryazan, Russian Federation

Ryazan State University named for S.A.Yesenin Umnyashkin Andrew a.umniashkin@kvantron.com Ryazan State University named for S.A.Yesenin Umnyashkin Nicholas n.umniashkin@kvantron.com A triangulation sensor for measuring the displacements and high-precision monitoring of the production performance Using the method of laser triangulation as the base, a mobile high-precision sensor has been created for measuring displacements and monitoring of the geometric parameters of workpieces in production. Both the process of signal processing and the operation of the triangulation sensor were accelerated many times owing to the architecture of processes, which was based on a reduced set of commands using simple and effective instructions of the stm32f407vet6 microcontroller. The measurement procedure was carried out by searching for a laser spot, calculating the center of the spot using the center of mass method, converting the centroid into the metric and applying calibration tables. Sensor scan speed amounted to (3 – 5)∙103 s–1. 10.18721/JPM.13105 621.391:681.142 triangulation sensor microprocessor laser diode spot center interface control module https://physmath.spbstu.ru/article/2020.47.5/ 5_54-65_13(1)2020.pdf

RAR RUS 66-77 Peter the Great St. Petersburg Polytechnic University Chumakov Yuri chymakov@yahoo.com Peter the Great St. Petersburg Polytechnic University Aleksander Levchenya levchenya@yandex.ru Peter the Great St. Petersburg Polytechnic University Khrapunov Evgenii hrapunov.evgenii@yandex.ru

195251, St. Petersburg, Polytechnicheskaya St, 29

An experimental study of the flow in the area of influence of a cylinder immersed in the free convective boundary layer on a vertical surface New experimental data that quantitatively characterize fields of the mean velocity and temperature, the intensity of temperature and velocity pulsations, and also velocity-temperature correlations in the near zone of a circular cylinder placed on the vertical heated surface at the height corresponding to the fully turbulent flow regime have been presented. Systematic measurements in the middle vertical plane (the plane that contains the cylinder axis) were performed using constant temperature anemometer and resistance temperature detectors. The experimental data was compared with numerical simulation one obtained through solving the RANS equations. The overall data were in good agreement and indicated the cardinal restructuring of the flows both before the cylinder (where the horseshoe-shaped vortex formed) and behind the obstacle (in the near separated area and the recovery one of the natural convective near-wall layer). 10.18721/JPM.13106 532.526.4, 533.6.08 circular cylinder free-convective heat exchange hot wire anemometry area of influence https://physmath.spbstu.ru/article/2020.47.6/ 6_66-77_13(1)2020.pdf

RAR RUS 78-91 Peter the Great St. Petersburg Polytechnic University Dyubo Dmitry doobinator@rambler.ru Peter the Great St. Petersburg Polytechnic University Tsybin Oleg otsybin@rphf.spbstu.ru The contact ionization ion accelerator for the electrically powered spacecraft propulsion: a computer model Аn analytical electrodynamic algorithm has been developed in order to study physical processes and calculate mechanical forces in an ion accelerator. This algorithm is combined with computer simulation of the electromagnetic field and charged particles’ trajectories. Computer models of ion accelerators with surface or contact ionization in the injection region were considered as an example. Ultimately, the created theoretical apparatus makes it possible to evaluate the proposed engineering solutions and diagnostic parameters of electric spacecraft propulsions as well as to compare the applicability of various working agents inside. 10.18721/JPM.13107 621.455.4; 621.455.34 computer modeling ionization ion beam ion accelerator electrically powered spacecraft propulsion https://physmath.spbstu.ru/article/2020.47.7/ 7_78-91_13(1)2020.pdf

RAR RUS 92-105 Peter the Great St. Petersburg Polytechnic University Zimin Arseniy fz1min@yandex.ru Peter the Great St. Petersburg Polytechnic University Pashkevich Dmitrii pashkevich-ds@yandex.ru

St. Petersburg, Russian Federation

Peter the Great St. Petersburg Polytechnic University Maslova Anastasia anastasiiamaslova5@gmail.com Peter the Great St. Petersburg Polytechnic University Kapustin Valentin Valentin.Kapustin.2014@yandex.ru

St. Petersburg, Russian Federation

«New Chemical Products» Ltd. Alexeev Yury alexeev-588@yandex.ru

St. Petersburg, Russian Federation

The interaction processes of silicon tetrafluoride and hexafluorosilicates with hydrogen-containing and oxygenated substances: a thermodynamic analysis In the paper, the thermodynamic calculations have shown that at the temperatures above 1300 K, the main silicon-containing substance is silicon dioxide in the Si-F-H-O element system, and the main fluorine-containing one is hydrogen fluoride in the same system. The mentioned temperature was realized during the interaction reactions between silicon tetrafluoride, fluorosilicates and hydrogen-containing, oxygen-containing substances in the combustion mode. The high-temperature treatment of silicon tetrafluoride and fluorosilicates in the combustion mode can become the basis of industrial technology for hydrogen fluoride production. 10.18721/JPM.13108 536.7:536.1:544.341.2:661.487.1:519.6 silicon tetrafluoride hydrogen fluoride silicon dioxide thermodynamic equilibrium Gibbs energy https://physmath.spbstu.ru/article/2020.47.8/ 8_92-105_13(1)2020.pdf

RAR RUS 106-117 V.I. Vernadsky Crimean Federal University Starostenko Vladimir starostenkovv@cfuv.ru V.I. Vernadsky Crimean Federal University Mazinov Alim mazinovas@cfuv.ru V.I. Vernadsky Crimean Federal University Tyutyunik Andrey real-warez@mail.ru V.I. Vernadsky Crimean Federal University Fitaev Ibraim fitaev.i@cfuv.ru V.I. Vernadsky Crimean Federal University Gurchenko Vladimir gurchenko_v@mail.ru Nanostructed carbon and organic films: spectral microwave and optical characteristics Microwave and optical transmission and reflection spectra of thin films prepared by casting the aqueous and dichloromethane solutions of fullerene, as well as casting the chloroform solution of 4-methylphenylhydrazone N-isoamylisatin have been recorded in the 2.5 – 4.0, 8.2 – 12.0 GHz and 19 – 110, 330 – 740 THz ranges. The carbon samples precipitated from dichloromethane were established to be the most sensitive to the microwaves. There were 3.4 and 9.1 GHz absorption peaks in their spectrum. The 20 – 50 and 78 – 108 THz IR intervals were chosen for investigation as the most pronounced. The fullerene-containing films, having a linear optical spectrum, exhibited the maximal absorption factor. The organic samples, having a sharp increase of optical absorption in the 599.6 – 713.8 THz high-frequency region, exhibited an absorption edge of 3.05 eV. In this case the surface photomicrographs demonstrated a rather ramified relief with nontrivial 3D forms dependent on the solution nature, notably prominent for fullerene surfaces. 10.18721/JPM.13109 537.531, 621.371, 539.234 electromagnetic microwaves fullerene organic film optical range photomicrograph https://physmath.spbstu.ru/article/2020.47.9/ 9_106-117_13(1)2020.pdf

RAR RUS 118-126 57034855700 0000-0002-4088-4707 Peter the Great St. Petersburg Polytechnic University Antonov Valerii hmath@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Russian Research Center for Radiology and Surgical Technologies Bogomolov Oleg urologbogomolov@gmail.com

Russia, 197758, St. Petersburg, Pesochniy Settl., Leningradskaya St., 70

Emperor Alexander I St. Petersburg State Transport University Garbaruk Victor vigarb@mail.ru

Russia, 190031, St. Petersburg, Moskovsky Ave., 9

Petersburg State Transport University Fomenko Victor vfomenko1943@gmail.com A vector composed of medical parameters: determination of the distribution class In the paper, the authors present a method for determining the distribution class to which a selected random vector with medical parameters as components belongs. The method is based on the statistical significance test. The optimal selection problem for the significance level where the probability of the vector identification error is minimal has been solved. In order to tackle the problem, the authors used the prior information on belonging the vector components to the definite distribution class in which the statistical relationship between the medical parameters was taken into account. The developed mathematical model of patient condition should serve as support of decision-making on further treatment tactics. 10.18721/JPM.13110 519.816 mathematical simulation distribution class significance test power of test https://physmath.spbstu.ru/article/2020.47.10/ 10_118-126_13(1)2020.pdf

CHR RUS 127-129 Without author Alexander Epaminondovich Fotiadi (on the occasion of his 80th birthday) Alexander Epaminondovich Fotiadi (on the occasion of his 80th birthday) нет нет birthday https://physmath.spbstu.ru/article/2020.47.11/ 11_127-129_13(1)2020.pdf