2304-9782, 2618-8686, 2405-7223
St. Petersburg Polytechnic University Journal. Physics and Mathematics
13
1
2020
1-132
RAR
RUS
7-13
Saveliev
Vladimir
Peter the Great St. Petersburg Polytechnic University
saveliev@tuexph.stu.neva.ru
Sobolevskiy
Vladimir
Peter the Great St. Petersburg Polytechnic University
sobolevskiy@physic.spbstu.ru
Apushkinsky
Evgeniy
Peter the Great St. Petersburg Polytechnic University
apushkinsky@hotmail.com
Popov
Boris
Peter the Great St. Petersburg Polytechnic University
popov@tuexph.stu.neva.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
Smirnov
Sergei
Peter the Great St. Petersburg Polytechnic University
sergeysmirnov92@mail.ru
E-5484-2014
56020596900
Smirnov
Evgeny
Peter the Great St. Petersburg Polytechnic University
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
Pichugin
Yuri
Saint-Petersburg State University of Aerospace Instrumentation
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
0000-0002-6162-9481
Krasnova
Nadezhda
Peter the Great St. Petersburg Polytechnic University
n.k.krasnova@mail.ru
0000-0003-0985-5964
Berdnikov
Alexander
Institute for Analytical Instrumentation of the RAS
asberd@yandex.ru
0000-0003-3514-8577
Solovyev
Konstantin
Peter the Great St. Petersburg Polytechnic University
k-solovyev@mail.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
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
Shadrin
Maxim
Ryazan State University named for S.A.Yesenin
m.shadrin@russia.ru
Savin
Vladislav
Ryazan State University named for S.A. Esenin
savin-vladislav@mail.ru
Ryazan, Russian Federation
Umnyashkin
Andrew
Ryazan State University named for S.A.Yesenin
a.umniashkin@kvantron.com
Umnyashkin
Nicholas
Ryazan State University named for S.A.Yesenin
n.umniashkin@kvantron.com
Stepanov
Vladimir
Ryazan State University named for S.A.Yesenin
vl.stepanov@365.rsu.edu.ru
0000-0003-3831-7882
Moos
Evgueniy
Ryazan State University named for S.A.Yesenin
e.moos@rsu.edu.ru
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
Khrapunov
Evgenii
Peter the Great St. Petersburg Polytechnic University
hrapunov.evgenii@yandex.ru
195251, St. Petersburg, Polytechnicheskaya St, 29
Chumakov
Yuri
Peter the Great St. Petersburg Polytechnic University
chymakov@yahoo.com
Aleksander
Levchenya
Peter the Great St. Petersburg Polytechnic University
levchenya@yandex.ru
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
Dyubo
Dmitry
Peter the Great St. Petersburg Polytechnic University
doobinator@rambler.ru
Tsybin
Oleg
Peter the Great St. Petersburg Polytechnic University
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
Maslova
Anastasia
Peter the Great St. Petersburg Polytechnic University
anastasiiamaslova5@gmail.com
Kapustin
Valentin
Peter the Great St. Petersburg Polytechnic University
Valentin.Kapustin.2014@yandex.ru
St. Petersburg, Russian Federation
Alexeev
Yury
«New Chemical Products» Ltd.
alexeev-588@yandex.ru
St. Petersburg, Russian Federation
Zimin
Arseniy
Peter the Great St. Petersburg Polytechnic University
fz1min@yandex.ru
Pashkevich
Dmitrii
Peter the Great St. Petersburg Polytechnic University
pashkevich-ds@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
Tyutyunik
Andrey
V.I. Vernadsky Crimean Federal University
real-warez@mail.ru
Fitaev
Ibraim
V.I. Vernadsky Crimean Federal University
fitaev.i@cfuv.ru
Gurchenko
Vladimir
V.I. Vernadsky Crimean Federal University
gurchenko_v@mail.ru
Starostenko
Vladimir
V.I. Vernadsky Crimean Federal University
starostenkovv@cfuv.ru
Mazinov
Alim
V.I. Vernadsky Crimean Federal University
mazinovas@cfuv.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
Garbaruk
Victor
Emperor Alexander I St. Petersburg State Transport University
vigarb@mail.ru
Russia, 190031, St. Petersburg, Moskovsky Ave., 9
Fomenko
Victor
Petersburg State Transport University
vfomenko1943@gmail.com
57034855700
0000-0002-4088-4707
Antonov
Valerii
Peter the Great St. Petersburg Polytechnic University
hmath@spbstu.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
Bogomolov
Oleg
Russian Research Center for Radiology and Surgical Technologies
urologbogomolov@gmail.com
Russia, 197758, St. Petersburg, Pesochniy Settl., Leningradskaya St., 70
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