St. Petersburg Polytechnic University Journal: Physics and Mathematics

RAR RUS 9-16 Herzen State Pedagogical University of Russia Guliakova Anna a.guliakova@gmail.com

St. Petersburg

Herzen State Pedagogical University of Russia Gorokhovatskiy Yuriy yurig@fromru.com Postdam University of Germany Frübing Peter frubing@uni-potsdam.de

Potsdam, Germany

Dielectric relaxation spectroscopy in the high-impact polystyrene/titanium-dioxide composite films The relaxation processes in high-impact polystyrene (HIPS) films filled with titanium dioxide (TiO2) of the rutile modification have been investigated by means of dielectric relaxation spectroscopy (DRS) supplemented by differential scanning calorimetry (DSC). Films with 2, 4, 6 and 8 vol.% TiO2 were compared to each other and to unfilled samples. Above the glass transition one relaxation became visible for unfilled HIPS. It could be identified as the α relaxation, related to the onset of micro-Brownian motions at the glass transition. The low-frequency (LF) process (which superimposed with α relaxation near Tg) was observed in all TiO2 containing films. The LF process for composite films was not uniform and showed Arrhenius behavior. At lower temperatures (up to about 130 °C) an activation energy of 1.1 eV was found, whereas in the limit of high temperatures, and particularly for higher TiO2 content the activation energy was 2.4 eV. 10.18721/JPM.12301 541.64: 678 dielectric spectroscopy high-impact polystyrene titanium-dioxide composite films https://physmath.spbstu.ru/article/2019.45.1/ 1_9-16_12(3)2019.pdf

RAR RUS 17-25 Peter the Great St. Petersburg Polytechnic University Bulovich Sergei bulovic@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

The system of multiphase flow equations in the equilibrium barotropic approximation: a numerical scheme In the paper, an economical integration scheme of a differential equation system has been proposed for the model of multiphase medium with a common pressure in liquids. The algorithm allows someone to consider various cases of multiphase medium flows with formation of any structure by the number of liquids under study and admits an asymptotic transition to a single-fluid model. The algebraic balance relation of the fluid volume fraction was stated through the form of a differential equation in pressure. The correctness of the Cauchy problem for an equation system was remade using repeated derivatives of the sought-for functions with respect to a spatial coordinate.The Riemann problem in the varying-area channel at various values of liquid pressure and its volume fraction on the different sides of a diaphragm in the three-fluid version was solved. 10.18721/JPM.12302 519.63:621.039 multi-fluid model numerical simulation correctness of Cauchy problem economical algorithm https://physmath.spbstu.ru/article/2019.45.2/ 2_17-25_12(3)2019.pdf

RAR RUS 26-44 0000-0003-0985-5964 Institute for Analytical Instrumentation of the RAS Berdnikov Alexander asberd@yandex.ru Institute for Analytical Instrumentation of the Russian Academy of Sciences Gall Lydia lngall@yandex.ru

Russia, 190103, St. Petersburg, 26 Rizhsky Ave.

Institute for Analytical Instrumentation of the Russian Academy of Sciences Gall Nikolai gall@ms.ioffe.ru

Russia, 190103, St. Petersburg, 26 Rizhsky Ave.

0000-0003-3514-8577 Peter the Great St. Petersburg Polytechnic University Solovyev Konstantin k-solovyev@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Basic Donkin's differential operators for homogeneous harmonic functions It has been shown that there are differential operators transforming the three-dimensional homogeneous harmonic functions into new three-dimensional ones. A characteristic feature of these operators is their reversibility: for any homogeneous harmonic function there is a homogeneous and harmonic prototype from which it can be obtained by applying the specified operator. The involved operators were called differential Donkin’s operators by the authors. The paper provides a complete list of fundamental first-order Donkin’s differential operators forming a linear basis of Thomson formulas for three-dimensional homogeneous harmonic functions. 10.18721/JPM.12303 517.51; 517.28; 517.983; 537.213, 537.8 electrostatic field magnetostatic field scalar potential homogeneous function harmonic function https://physmath.spbstu.ru/article/2019.45.3/ 3_26-44_12(3)2019.pdf

RAR RUS 45-62 0000-0003-0985-5964 Institute for Analytical Instrumentation of the RAS Berdnikov Alexander asberd@yandex.ru Institute for Analytical Instrumentation of the Russian Academy of Sciences Gall Lydia lngall@yandex.ru

Russia, 190103, St. Petersburg, 26 Rizhsky Ave.

Institute for Analytical Instrumentation of the Russian Academy of Sciences Gall Nikolai gall@ms.ioffe.ru

Russia, 190103, St. Petersburg, 26 Rizhsky Ave.

0000-0003-3514-8577 Peter the Great St. Petersburg Polytechnic University Solovyev Konstantin k-solovyev@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Donkin's differential operators for homogeneous harmonic functions The work continues the study of the Donkin’s operators for homogeneous harmonic functions. Previously, a basic list of such first-order operators for three-dimensional harmonic functions was obtained. The objective of this study is to prove that any linear combinations with constant coefficients made up of the Donkin’s basic operators are again Donkin’s operators. Since the reversibility property is fundamental for such operators, and since the reversibility of each of the linear differential operators taken separately does not automatically imply the reversibility of their linear combination, this statement is nontrivial and requires a strict proof. This proof has been given in this paper. 10.18721/JPM.12304 517.51; 517.28; 517.983; 537.213, 537.8 electrostatic field magnetostatic field scalar potential homogeneous function harmonic function https://physmath.spbstu.ru/article/2019.45.4/ 4_45-62_12(3)2019.pdf

RAR RUS 63-77 Submicron Heterostructures for Microelectronics Research and Engineering Center of the RAS Aladov Andrei

Russia, 194021, St.Petersburg, Polytechnicheskaya, 26

Herzen State Pedagogical University of Russia Berlov Dmitriy dberlov@yandex.ru

St. Petersburg

Submicron Heterostructures for Microelectronics Research and Engineering Center of the RAS Zakgeim Alexander zakgeim@mail.ioffe.ru

Russia, 194021, St.Petersburg, Polytechnicheskaya, 26

Submicron Heterostructures for Microelectronics Research and Engineering Center of the RAS Chernyakov Anton chernyakov.anton@yandex.ru

Russia, 194021, St.Petersburg, Polytechnicheskaya, 26

AAD-9657-2019 57197390995 Peter the Great St. Petersburg Polytechnic University Fotiadi Alexander fotiadi@rphf.spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Peter the Great St. Petersburg Polytechnic University Valjukhov Vladimir Valyukhov@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Hardware-software complex for characterization of a person’s functional status on exposure to light with the varied spectral color parameters The article deals with the main circuitry and software aspects of the creation a LED dynamically controlled system of high-quality lighting with the broad range of color temperatures Tc = 1700 – 10,000 K as a part of experimental installation of the hardware-software complex for impact on a person’s functional status. The findings of investigation on impacts of lighting with a different color temperature on a human body are given. These studies were based on changes in indicators of electrical activity of the brain, heart work, arterial blood pressure and other parameters. Processing of measurement data revealed efficiency and a nature of influence of light with different color temperatures on psychophysiological and functional status. 10.18721/JPM.12305 628.9, 612.822.3 LED RGB-color mixing dynamic light control light exposure functional status https://physmath.spbstu.ru/article/2019.45.5/ 5_63-77_12(3)2019.pdf

RAR RUS 78-91 Submicron Heterostructures for Microelectronics Research and Engineering Center of the RAS Aladov Andrei

Russia, 194021, St.Petersburg, Polytechnicheskaya, 26

Herzen State Pedagogical University of Russia Berlov Dmitriy dberlov@yandex.ru

St. Petersburg

Peter the Great St. Petersburg Polytechnic University Valjukhov Vladimir Valyukhov@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Peter the Great St. Petersburg Polytechnic University Vlasova Olga olvlasova@yandex.ru Submicron Heterostructures for Microelectronics Research and Engineering Center of the RAS Zakgeim Alexander zakgeim@mail.ioffe.ru

Russia, 194021, St.Petersburg, Polytechnicheskaya, 26

Herzen State Pedagogical University of Russia Panihina Anna scrimmyrim@gmail.com

St. Petersburg

AAD-9657-2019 57197390995 Peter the Great St. Petersburg Polytechnic University Fotiadi Alexander fotiadi@rphf.spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Experimental setup for studying the blue light effect on sense of time among persons with different type of vegetative regulation The effect of blue illumination (wavelength is about 460 nm) on human perception of short-time intervals of light, depending on a person’s predominance of activity of the sympathetic or parasympathetic parts of the autonomic nervous system has been studied using an experimental setup based on the LED dynamically controlled lighting system. The persons measured the duration of a minute before and after exposure to white (a control group) or monochromatic blue light. The effect of blue light was manifested in the predominance of excitability of the sympathetic part of the autonomic nervous system. The same persons showed a tendency to shorten the duration of the subjective minute after the light exposure. A similar effect of white light did not lead to significant changes in the same characteristics. The results of the study suggest that the individual effect of blue light on the function of time perception can be mediated through the regulation of the heart rate. 10.18721/JPM.12306 574.24, 628.938 light exposure sense of time LED blue light dynamically controlled light source https://physmath.spbstu.ru/article/2019.45.6/ 6_78-91_12(3)2019.pdf

RAR RUS 92-100 National Research Centre “Kurchatov Institute” Presniakova Natalia kolobylina@gmail.com

Moscow

National Research Centre “Kurchatov Institute”, Shubnikov Institute of Crystallography of Federal Scientific Research Centre “Crystallography and Photonics” of Russian Academy of Sciences Alexander Alexander a.vasiliev56@gmail.com

Moscow

National Research Centre “Kurchatov Institute” Yatsishina Ekaterina Yatsishina_EB@nrcki.ru

Moscow

Electron-microscopic methods in historical metallurgy: features of the use A methodological approach to integrated electron microscopic studies of metal objects of cultural heritage, developed in studying various exhibits from leading museums of Russia, has been presented. The application of the proposed approach allowed both historians and archaeologists to obtain in-depth, detailed information, which greatly supplemented the data currently available. 10.18721/JPM.12307 538.911+902/904 metal artifact transmission electron microscopy scanning electron microscopy complex research https://physmath.spbstu.ru/article/2019.45.7/ 7_92-100_12(3)2019.pdf

RAR RUS 101-109 0000-0003-4292-0959 Peter the Great St. Petersburg Polytechnic University Golovitski Alexander alexandergolovitski@yahoo.com Peter the Great St. Petersburg Polytechnic University Remiga Oksana remiga95@mail.ru

St. Petersburg

The electronegative glow discharge in the cylindrical and coaxial geometry: the comparison of optical radiation emission ability The transition from the traditional cylindrical discharge geometry to the coaxial one (where the discharge plasma is located in a gap between two coaxially placed cylindrical tubes) has been theoretically investigated for the positive column of an electronegative middle pressure glow discharge in the mixture of chlorine and inert gases. Here a new electron’s loss mechanism appears, i.e. the electron’s diffusional outgoing onto the inner wall. The discharge existence was proved to be only made possible by sufficient increasing of the ionization frequency and hence the electron temperature as well. The elevation of the electron temperature would cause a growth of the specific power of discharge ultraviolet radiation. The analytical expressions for estimating the electron temperature of the discharge plasma in the coaxial geometry were derived. 10.18721/JPM.12308 533.9.01 plasma radiation electronegative discharge electron temperature ionization frequency coaxial geometry https://physmath.spbstu.ru/article/2019.45.8/ 8_101-109_12(3)2019.pdf

RAR RUS 110-122 Dobrovolskaya Irina dobrov@hq.macro.ru 0000-0002-4823-0695 The S. M. Kirov Military Medical Academy of the Ministry of Defense of the Russian Federation Ivankova Elena ivelen@mail.ru Popryadukhin Pavel pavel-pn@mail.ru Yudin Vladimir yudin@hq.macro.ru Composite polymer matrices for tissue engineering and transplantology The article presents implementation of modern methods for producing one-, two-, and three-dimensional composite matrices for tissue engineering based on resorbable and non-resorbable polymers. Coagulation method for producing composite fibers based on chitosan and chitin nanofibrils, electrospinning method for composite nanofibers, lyophilization of chitosan solutions and their mixtures with nanoparticles to obtain three-dimensional porous matrices with increased stability of mechanical characteristics in aqueous media have been described. The results of the studies in the adhesion and kinetics of proliferation of stem and somatic cells of humans and animals on the developed matrices were given. In vivo experiments showed that materials in the form of fibers, films, tubular samples, and sponges could be used as implants for blood vessels and effective wound dressings. Moreover, the article contains the findings of an investigation into the kinetics of resorption of the involved materials in a living organism. 10.18721/JPM.12309 544.77.022.823 chitosan chitin nanofibrilla tissue engineering composite nanofiber composite sponge https://physmath.spbstu.ru/article/2019.45.9/ 9_110-122_12(3)2019.pdf

RAR RUS 123-130 Peter the Great St. Petersburg Polytechnic University Egorov Anatoliy egorov.a@spbstu.ru 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru Peter the Great St. Petersburg Polytechnic University Bakaev Victor v_bakaev@phmf.spbstu.ru

St. Petersburg

Peter the Great St. Petersburg Polytechnic University Nikittsina Inna nikitsinna@yandex.ru

St. Petersburg

An analysis of unfolding methods for measurement of hadron dijet production cross sections The comparison results of different methods of detector’s distortion elimination have been presented. The following methods were taken: bin-by-bin correction method, migration matrix inversion one, the one of maximal likelihood with Tikhonov regularisation (TUnfold), the one of singular value decomposition of the migration matrix (SVD), the one of D’Agostini iterations. The comparison of selected methods was performed through Monte Carlo simulation of hadron dijet production in proton-proton collisions at center-of-mass energy of 2.76 TeV and the simulation of а response of the CMS detector at Large Hadron Collider. The optimal scheme of unfolding was chosen for the measurement under study. Practical recommendations for building of unfolding procedure were given. 10.18721/JPM.12310 53.088.6 detector effect unfolding TUnfold SVD unfolding D'Agostini iterations https://physmath.spbstu.ru/article/2019.45.10/ 10_123-130_12(3)2019.pdf

RAR RUS 131-142 Peter the Great St. Petersburg Polytechnic University Berdnikov Alexander alexber@phmf.spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru Zharko Sergey zharkosergey94@gmail.com 0000-0002-3395-0454 Peter the Great St. Petersburg Polytechnic University Kotov Dmitry dmitriy.kotov@gmail.com Radzevich Pavel radzevichp@gmail.com Features of short-living neutral kaon production in copper-gold nuclei collisions at 200 GeV In this study, invariant transverse momentum spectra and nuclear modification factors of KS mesons produced in collisions of copper and gold nuclei (Cu + Au) at energy of 200 GeV have been measured. The research was carried out using the PHENIX spectrometer located at RHIC. The obtained KS meson nuclear modification factor values were compared with similar ones of η and π0 mesons along with hadronic jets measured under the same conditions. Moreover, the obtained values mentioned were compared with the corresponding data on KS mesons produced in binary collisions of gold and copper nuclei (Au + Au, Cu + Cu) at energy of 200 GeV as well. An analysis of the derived results pointed to the independence of the jet-quenching effect in the Cu + Au, Cu + Cu and Au + Au collisions at energy of 200 GeV from nuclear overlap form produced in these systems. 10.18721/JPM.12311 539.126.3 quark-gluon plasma jet-quenching nuclear modification factor ultrarelativistic heavy nuclei collisions https://physmath.spbstu.ru/article/2019.45.11/ 11_131-142_12(3)2019.pdf

RAR RUS 143-154 Peter the Great St. Petersburg Polytechnic University Berdnikov Alexander alexber@phmf.spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru Zharko Sergey zharkosergey94@gmail.com 0000-0002-3395-0454 Peter the Great St. Petersburg Polytechnic University Kotov Dmitry dmitriy.kotov@gmail.com Radzevich Pavel radzevichp@gmail.com Jet-quenching studies in ultrarelativistic copper-gold nuclei collisions using omega mesons In the paper, the measurement data on ω meson invariant transverse momentum spectra and nuclear modification factors in collisions of copper and gold nuclei (Cu + Au) at energy of 200 GeV have been presented. The studies were conducted with PHENIX spectrometer at RHIC. The obtained ω meson nuclear modification factors were equal (within the uncertainties) to ones derived for π0, η and KS mesons and for jets as well in the same collision system. The integrated ω-meson nuclear modification factors versus the numbers of nuclei taking part in the nuclei-nuclei interaction, were in agreement (within uncertainties) with the similar dependencies for Cu + Au, Au + Au and Cu + Cu collisions at energy of 200 GeV. The analysis of results suggested that the jet-quenching effect was independent (or weakly dependent) of the shape of a nuclear overlap region realized in these systems. 10.18721/JPM.12312 539.126.3 quark-gluon plasma jet-quenching effect nuclear modification factor omega meson https://physmath.spbstu.ru/article/2019.45.12/ 12_143-154_12(3)2019.pdf

RAR RUS 155-163 Peter the Great St. Petersburg Polytechnic University Larionov Nikolay larionov.nickolay@gmail.com Impact of dipole-dipole interaction on the cavity mode evolution in the model of few emitters laser In the paper, the simple model of а two-atom laser is theoretically studied. The both dipole-dipole coupled atoms are under conditions of incoherent pump, are placed into the Fabry – Perot cavity and interact with a single damping field mode. In the switched-off pump position, the effect of dipole-dipole interaction on evolution of the damping mode has been considered. This evolution was shown to be strongly dependent on an initial atomic superposition state of atoms. In the switched-on pump position, the ‘memory’ for the initial atomic state should collapse with time. 10.18721/JPM.12313 535.3 nanolaser single-atom laser dipole-dipole interaction near-field effect https://physmath.spbstu.ru/article/2019.45.13/ 13_155-163_12(3)2019.pdf

RAR RUS 164-176 Saint-Petersburg State University of Aerospace Instrumentation Pichugin Yuri yury-pichugin@mail.ru

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

The Shannon information quantity in the tasks associated with linear regression: usage pattern The article discusses the use of the Shannon information quantity (SIQ) in the tasks associated with linear regression. It has been shown that the SIQ contained in the response components with respect to stochastic parameters is expressed through the Fisher information matrix, is a convex functional on the set of response components, and is equivalent to the use of the D-criterion in the problems of planning the experiment at a sufficiently large scale of parameters. The SIQ relatively constant regression parameters were determined. An alternative formulation of the optimal experiment planning (OEP) problem was considered and its relation to the traditional formulation was analyzed. The problem of information ordering of data using regression on the basis of principal components was considered. Some algorithms taking into account the value of information in the presence of partial data gaps were proposed. 10.18721/JPM.12314 519.24 Shannon information quantity linear regression stochastic regression parameter https://physmath.spbstu.ru/article/2019.45.14/ 14_164-176_12(3)2019.pdf

RAR RUS 177-187 Peter the Great St. Petersburg Polytechnic University Modestov Victor modestov@compmechlab.com Strength of reinforced concrete structures under extreme mechanical impacts The article deals with feasibility studies of the strength of reinforced concrete structures under extreme mechanical impacts. The focus is on the interaction of the structure’s outer containment with a heavy aircraft. Modern physical models and methods of direct numerical simulation of processes are used with taking into account nonlinear behavior of materials. These approaches are verified on original model problems. The impact of a heavy transport aircraft on an undeformed reinforced concrete wall is determined. The thickness values of the outer containment of the reactor building are varied. The strength of structures with taking into account the pliability of soil bases on which reinforced concrete structures are located is also studied. 10.18721/JPM.12315 534 structural strength extreme mechanical impacts ferroconcrete finite element method https://physmath.spbstu.ru/article/2019.45.15/ 15_177-187_12(3)2019.pdf