2304-9782, 2618-8686, 2405-7223
St. Petersburg Polytechnic University Journal. Physics and Mathematics
14
1
2021
1-192
RAR
RUS
8-20
Lebedeva
Olga
Volgograd State University
lebedeva_os@volsu.ru
Lebedev
Nikolay
Volgograd State University
nikolay.lebedev@volsu.ru
Lyapkosova
Irina
Volgograd State Agricultural University
lyapkosova_irina@mail.ru
Elastic conductivity of germanene “arm-chair” nanoribbons with donor impurities
In the article, results of theoretical calculations of the piezoresistance characteristics of impurity germanene nanoribbons (NR) of the “arm-chair” type with donor defects with various concentrations uniformly distributed in the crystal lattice of the nanomaterial have been presented and analyzed. Arsenic atoms were used as donor impurities. Investigations of the NR’s band structure were carried out in the frameworks of the Hubbard’s and Anderson’s models. The computation of the main characteristic of the piezoresistance effect, i.e., the longitudinal component of the elastic conductivity tensor was carried out using the Green's function method within the framework of the same theoretical models. An analysis of the dependence of this characteristic on the tensile and compressive strains, the concentration of impurities and the nanoribbon width were carried out.
10.18721/JPM.14101
538.915+975; 544.22.022.343; 544.225.22+25
band structure
stress-strain state
piezoresistance effect
elastic conductivity tensor
https://physmath.spbstu.ru/article/2021.51.1/
01_8-20_14(1)2021.pdf
RAR
RUS
21-31
Zelikman
Mark
Peter the Great St. Petersburg Polytechnic University
marzelik@mail.ru
Current configurations in the long Josephson contact in an external magnetic field
Current configurations in a periodically modulated long Josephson contact located in an external magnetic field are considered for values of the pinning parameter I greater than and less than the critical one (Iс). It is shown that, if I > Iс, the maximum value of the non-quenching current is determined by the contact length and does not depend on the value of the external magnetic field. In the case I < Iс, the critical current is determined by the value of the magnetic field at which the vortices begin to fill the entire length of the contact, and does not depend on the length of the contact. At the same time, with the growth of the external magnetic field, the critical value of the current decreases.
10.18721/JPM.14102
538.945
long Josephson contact
magnetic field
undimmed current
vortices
https://physmath.spbstu.ru/article/2021.51.2/
02_21-31_14(1)2021.pdf
RAR
RUS
32-57
Semenov
Artem
Peter the Great St. Petersburg Polytechnic University
semenov.artem@googlemail.com
A microstructural model of ferroelectrоelastic material with taking into account the defects’ evolution
For the description of the hysteresis behavior of ferroelectrics/ferroelastics under multiaxial combined electrical and/or mechanical loading, a thermodynamically consistent microstructural model of a ferroelectroelastic material is proposed taking into account the presence and evolution of polar point defects. The model also takes into account multiphase composition, anisotropy of properties, domain structure, and dissipative motion of domain walls. The linear theory of the charged point defects evolution is proposed based on the free energy of defects in the quadratic form of the polarization vector and strain tensor of defects. The dependence of the hysteresis loop shift (due internal field bias) on parameters of the free energy of defects is shown. Comparison of computation results with experimental curves of dielectric, mechanical, and electromechanical hysteresis for polycrystalline piezoelectric PZT PIC-151, BaTiO3, single-crystal PMN-PZT and KTS doped with acceptor additives, showed a good agreement.
10.18721/JPM.14103
539.3, 537.226.4
polycrystalline piezoceramics
point defect
constitutive equation
hysteresis
finite element homogenization
https://physmath.spbstu.ru/article/2021.51.3/
03_32-57_14(1)2021.pdf
RAR
RUS
58-71
Sadin
Dmitriy
Military Space Academy named after A.F. Mozhaysky
sadin@yandex.ru
Golikov
Igor
Military Space Academy named after A.F. Mozhaysky
igira55@yandex.ru
Shirokova
Elena
Military Space Academy named after A.F. Mozhaysky
shirokelen-78@mail.ru
Testing of the hybrid large-particle method using two-dimensional Riemann problems
The full potential of the hybrid large-particle method using the known and new Riemann problems in two-dimensional domains has been studied. The method includes a space-time second-order approximation for smooth solutions. Using the artificial viscosity nonlinear correction and the convective fluxes hybridization maintained monotonicity of solutions. Centrally symmetrical problems with a complex shock-wave structure and with the development of instability on the contact boundary were studied in details. The test calculations demonstrated high resolution, low dissipation, and stability of the method.
10.18721/JPM.14104
519.6:533.6.011
hybrid large-particle method
two-dimensional Riemann problems
high resolution
https://physmath.spbstu.ru/article/2021.51.4/
04_58-71_14(1)2021.pdf
RAR
RUS
72-84
Gataulin
Yakov
Peter the Great St. Petersburg Polytechnic University
yakov_gataulin@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
A flow in the blood vessel with a one-side stenosis: numerical study of the structure and local turbulization
In the paper, the LES results of a flow by using a model of the blood vessel with a one-side 70% stenosis, at a Reynolds number of 1803, have been presented. The Germano – Lilly model was applied to subgrid viscosity evaluation. A jet-like zone and a recirculation one were found to stand out just behind the stenosis, and a pair of secondary-flow vortices forms being within each of them. Instabilities of the mixing layer initiated the flow turbulence with formation of vortex structures of different scales at the boundary between the reverse flow zone and the jet. These structures filled the whole cross-section of the vessel about the flow attachment point. Turbulent shear stresses were significant in magnitude only at a flow section of about four-caliber length. Further downstream, the flow relaminarised.
10.18721/JPM.14105
532.542.4
blood flow
stenosis
turbulence
numerical simulation
large eddy simulation
https://physmath.spbstu.ru/article/2021.51.5/
05_72-84_14(1)2021.pdf
RAR
RUS
85-99
Baranov
Maksim
Peter the Great St. Petersburg Polytechnic University
baranovma1993@gmail.com
Tsybin
Oleg
Peter the Great St. Petersburg Polytechnic University
otsybin@rphf.spbstu.ru
Velichko
Elena
Peter the Great St. Petersburg Polytechnic University
velichko-spbstu@ya.ru
Structured biomolecular films for microelectronics
In order to develop the technology for dehydration of biomolecular films with specified parameters under electrostatic field (EF), the structures of dehydrated films obtained from aqueous solutions of albumin molecules and deposited on the solid glass substrates in the EF have been studied, dehydration conditions being varied. The resulting structures were examined under microscope (with recording the micrographs) in the light passing through the films and in the one reflected from the substrates. An analysis of the micrographs made it possible to reveal characteristic inhomogeneity arising in the films and recognize their main types. The optimal regions of parameters in which the film production modes were predominantly realized were found. For the first time, a "bubble" model for interpretation of the spatially inhomogeneous structure of dehydrated biomolecular films was put forward. In the model, the processes conditioned by dissolved gases in the initial solutions were taken into account.
10.18721/JPM.14106
53.093, 53.096, 57.031, 57.033, 57.038
self-organized structure
biomolecular film
microelectronics
biological molecule
electrochemistry
biosensor
https://physmath.spbstu.ru/article/2021.51.6/
06_85-99_14(1)2021.pdf
RAR
RUS
100-110
Anikonov
Dmitriy
Sobolev Institute of Mathematics
anik@math.nsc.ru
Konovalova
Dina
Sobolev Institute of Mathematics
dsk@math.nsc.ru
Duhamel-type integral for the initial boundary value problem
The paper considers the initial boundary value problem for the wave equation for the case of three spatial variables. The definition of a generalized solution has been introduced and the theorem of unique existence has been proved. A new formula was proposed, being an analog of the well-known Duhamel integral. The most part of the paper is devoted to the analysis of differential properties of the solution. In particular, the possibility of breaking the second partial time derivative on a certain hyperplane was indicated, and its break value was given. This property allowed us to set the inverse problem of determining the coefficient of the equation and propose an algorithm for solving it under the condition of non-zero internal action on a 2D subset. In this case, the known data were considered to be the values of a fixed oscillating point’s position at every moment of time. applying the results obtained for a smaller number of variables. For physical interpretation, the case of two spatial variables is the most obvious as a study of the process of transverse vibrations of semi-bounded surfaces of the membrane type. Here is a list of some publications by other authors that are close to the topic of our work.
10.18721/JPM.14107
517.946
wave equation
Duhamel integral
inverse problem
descent method
Cauchy problem
https://physmath.spbstu.ru/article/2021.51.7/
07_100-110_14(1)2021.pdf
RAR
RUS
111-127
Bizyaev
Ivan
Peter the Great St. Petersburg Polytechnic University
ivanbiziaev@yandex.com
0000-0002-2519-2577
Gabdullin
Pavel
Peter the Great St. Petersburg Polytechnic University
gabdullin_pg@spbstu.ru
Gnuchev
Nikolay
Peter the Great St. Petersburg Polytechnic University
nmg@rphf.spbstu.ru
0000-0002-3321-7797
Arkhipov
Alexander
Peter the Great St. Petersburg Polytechnic University
arkhipov@rphf.spbstu.ru
Low-field electron emission from thin films of metals
The paper presents an experimental study of the low-threshold field electron emission from thin films of metals (Mo, W, Zr, Ni and Ti) deposited on silicon substrates by magnetron sputtering. Several samples of such films having effective thickness in the range 6–10 nm were capable of room-temperature electron emission in electric field with macroscopic intensity as low as a few kV/mm. Optimized thermofield treatment procedure further improved their emission properties reducing the threshold field by several times. AFM study revealed a correlation between film’s emission properties and their surface topography. At the same time, no equally pronounced correlation of the emissivity with other characteristics of coatings (including the sort of the metal and the silicon substrate conductivity type) was detected. Results of the study witness in favor of two-temperature (or hot-electron) emission mechanism for the investigated coatings.
10.18721/JPM.14108
537.533.2, 598.9
field emission
thin films
atomic force microscopy
hot-electron emission
https://physmath.spbstu.ru/article/2021.51.8/
08_111-127_14(1)2021.pdf
RAR
RUS
128-137
0000-0003-4292-0959
Golovitski
Alexander
Peter the Great St. Petersburg Polytechnic University
alexandergolovitski@yahoo.com
Korenyugin
Dmitriy
Peter the Great St. Petersburg Polytechnic University
polarisdk@mail.ru
Moderate and low pressure glow discharge in the gap between two eccentric tubes
The positive column of a low and moderate pressure glow discharge located between two dielectric cylindrical walls with noncoincident parallel axes has been considered, the discharge current being aligned along the axes. The electron temperature of such discharge plasma was shown to be higher than the one of traditional cylindrical geometry when the outer plasma radii being equal; but the spatial distribution of plasma density in the discharge cross-section can acquire the strong inhomogeneity in the azimuthal direction.
10.18721/JPM.14109
533.9.01
glow discharge
positive column
eccentric geometry
electron temperature
https://physmath.spbstu.ru/article/2021.51.9/
09_128-137_14(1)2021.pdf
RAR
RUS
138-146
Tiba
Ali
Peter the Great St. Petersburg Polytechnic University
alitiba1991@gmail.com
Egorov
Anatoliy
Peter the Great St. Petersburg Polytechnic University
egorov.a@spbstu.ru
0000-0003-0309-5917
Berdnikov
Yaroslav
Peter the Great St. Petersburg Polytechnic University
berdnikov@spbstu.ru
Lomasov
Vladimir
Peter the Great St. Petersburg Polytechnic University
lomasov_vn@spbstu.ru
Сopper-64 isotope production through the cyclotron proton irradiation of the natural-nickel target
A design procedure and numerical simulation of a production process for Cu-64 isotope by the 64Ni (p, n)64Cu nuclear reaction have been developed. The required radionuclide applicable in the nuclear medicine is produced through irradiating a cyclotron target of natural nickel with a proton beam. The process conditions were dictated by the capabilities of the cyclotron; an initial kinetic energy of 17 MeV (at a current of 10 µA) was fed into computation. As a result, dependencies of the Cu-64 isotope production on the target thickness and on the irradiation time were obtained. The target depth of proton penetration was investigated, and it was established where the peak radionuclide concentration was produced. An analysis of the obtained data made possible the finding of the optimal thickness of the nickel target being of 0.54 mm.
10.18721/JPM.14110
539.1.03
copper-64
natural nickel
yield calculation
target thickness
proton beam
https://physmath.spbstu.ru/article/2021.51.10/
10_138-146_14(1)2021.pdf
RAR
RUS
147-154
Gorobei
Natalia
Peter the Great St. Petersburg Polytechnic University
n.gorobey@mail.ru
Luk'yanenko
Alexander
Peter the Great St. Petersburg Polytechnic University
alex.lukyan@rambler.ru
Goltsev
Alexander
The Ioffe Institute of the Russian Academy of Sciences
goltsev@ua.pt
The proper mass of the universe
A modification of the covariant theory based on the concept of the proper mass (mass distribution) of the system is proposed. The proper mass is a special dynamic quantity that forms a fundamental frame of reference for measuring proper time and spatial shifts without violating the theory’s covariance. A simple model of an ingomogeneous system (universe, string) with two proper time parameters, whose constraint algebra is isomorphic to SL2, is considered.
10.18721/JPM.14111
530.12:517.988.38(075.8)
universe
time
mass
covariance
reference frame
algebra of constraints
https://physmath.spbstu.ru/article/2021.51.11/
11_147-154_14(1)2021.pdf
RAR
RUS
155-163
57034855700
0000-0002-4088-4707
Antonov
Valerii
Peter the Great St. Petersburg Polytechnic University
hmath@spbstu.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
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
Making a collective expert decision based on the Neumann – Pearson algorithm
In the article, the possibility of processing voting results in the case of a team of experts with different efficiency in assessing the situation has been considered. The experts were expected to decide whether or not a patient suffering from a specific disease. The most intelligent combination of the individual expert’s votes into a collective council’s decision was required. Our algorithm was based on the Neumann – Pearson principle of minimizing the type 2 error probability at the fixed type 1 error probability. The team of experts with different qualifications was shown to be able to draw a correct conclusion with a high probability.
10.18721/JPM.14112
519.254
team of experts
assessment efficiency
Neumann and Pearson method
https://physmath.spbstu.ru/article/2021.51.12/
12_155-163_14(1)2021.pdf
RAR
RUS
164-176
Timofeev
Sergey
Baikal State University
timofeevsv12@gmail.com
Baenkhaeva
Ayuna
Baikal State University
ayunab2000@mail.ru
Mathematical modeling of information confrontation
The article continues our studies in the previously constructed mathematical model of dissemination of new information in the society. The model is a system of four ordinary differential equations with quadratic nonlinearity in the right parts. Two fundamental domains have been taken in the parameter space of the model and they may be of interest in application. In some sense, these domains provide two diametrically opposite and essentially different scenarios of new information dissemination. In every case, the global properties of the phase pattern of the constructed dynamic system were investigated using qualitative methods of the theory of differential equations. Both conceptual and geometric interpretations of the obtained results were given.
10.18721/JPM.14113
517.938:070
differential equation
stationary solution of system
invariant set
asymptotic stability
https://physmath.spbstu.ru/article/2021.51.13/
13_164-176_14(1)2021.pdf
RAR
RUS
177-189
0000-0003-0376-4463
Frolova
Ksenia
Institute for Problems of Mechanical Engineering RAS
fkp@ipme.ru
Cross-property connections between Young's modulus and diffusion coefficient of two-phase composite
The paper interrelates changes in the effective elastic and diffusion properties of a two-phase composite using microstructural parameters. It is suggested that there are some inhomogeneities identical in shape in the material. The development of the cross-property connections in the explicit tensor form has been presented. The segregation effect, being a constant jump in concentration of particles of the solute flux at the matrix/inhomogeneity interface, was taken into account. It is a good practice to apply the derived cross-property relations to finding some effective properties of material using others when the material’s microstructure is unknown. The obtained expressions were put to the test for isotropic material with pores; the approximate correlations were compared with exact ones found for the specific microstructure.
10.18721/JPM.14114
539.3
effective Young’s modulus
effective diffusion coefficient
cross-property connection
segregation effect
https://physmath.spbstu.ru/article/2021.51.14/
14_177-189_14(1)2021.pdf