2304-9782, 2618-8686, 2405-7223 14 1 2021 1-192

RAR RUS 8-20 Volgograd State University Lebedeva Olga lebedeva_os@volsu.ru Volgograd State University Lebedev Nikolay nikolay.lebedev@volsu.ru Volgograd State Agricultural University Lyapkosova Irina 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 Peter the Great St. Petersburg Polytechnic University Zelikman Mark 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 Peter the Great St. Petersburg Polytechnic University Semenov Artem 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 Military Space Academy named after A.F. Mozhaysky Sadin Dmitriy sadin@yandex.ru Military Space Academy named after A.F. Mozhaysky Golikov Igor igira55@yandex.ru Military Space Academy named after A.F. Mozhaysky Shirokova Elena 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 Peter the Great St. Petersburg Polytechnic University Gataulin Yakov yakov_gataulin@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

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 Peter the Great St. Petersburg Polytechnic University Baranov Maksim baranovma1993@gmail.com Peter the Great St. Petersburg Polytechnic University Tsybin Oleg otsybin@rphf.spbstu.ru Peter the Great St. Petersburg Polytechnic University Velichko Elena 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 Sobolev Institute of Mathematics Anikonov Dmitriy anik@math.nsc.ru Sobolev Institute of Mathematics Konovalova Dina 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 Peter the Great St. Petersburg Polytechnic University Bizyaev Ivan ivanbiziaev@yandex.com 0000-0002-2519-2577 Peter the Great St. Petersburg Polytechnic University Gabdullin Pavel gabdullin_pg@spbstu.ru Peter the Great St. Petersburg Polytechnic University Gnuchev Nikolay nmg@rphf.spbstu.ru 0000-0002-3321-7797 Peter the Great St. Petersburg Polytechnic University Arkhipov Alexander 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 Peter the Great St. Petersburg Polytechnic University Golovitski Alexander alexandergolovitski@yahoo.com Peter the Great St. Petersburg Polytechnic University Korenyugin Dmitriy 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 Peter the Great St. Petersburg Polytechnic University Tiba Ali alitiba1991@gmail.com 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 Lomasov Vladimir 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 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 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 Peter the Great St. Petersburg Polytechnic University Antonov Valerii hmath@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

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 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 Baikal State University Timofeev Sergey timofeevsv12@gmail.com Baikal State University Baenkhaeva Ayuna 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 Institute for Problems of Mechanical Engineering RAS Frolova Ksenia 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