St. Petersburg Polytechnic University Journal: Physics and Mathematics

RAR RUS 9-17 Abrosimov Alexander MANOWAR89@mail.ru Agarev Vladimir agarev_v_n@mail.ru Numerical simulation of the resonance-tunnel structure based on the Schottky barrier and a GaAs/AlGaAs heterojunction The resonance tunneling diode has been widely studied because of its importance in the field of nanoelectronic technology and its potential applications in very high speed/functionality devices and circuits. Even though much progress has been made in this regard, the most popular structure of these diods consists of barriers created by heterojunctions only. In this paper, we present numerical simulation results for a two-barrier resonance-tunnel structure consisting of the Schottky barrier and a GaAs/AlGaAs heterojunction. We considered its potential application to the resonance-tunnel diodes working at room temperature. The configuration of this structure was optimized using numerical simulation methods. A current voltage characteristic was simulated by the example of the optimized structure, and the influence of the thermal current on the obtained dependence was analyzed. Citation: A.S. Abrosimov, V.N. Agarev, Numerical simulation of the resonance-tunnel structure based on the Schottky barrier and a GaAs/AlGaAs heterojunction, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 9 – 17. DOI: 10.18721/JPM.11101 10.18721/JPM.11101 538.935 numerical simulation resonance-tunnel structure Schottky barrier heterojunction https://physmath.spbstu.ru/article/2018.39.1/ 01_9_18_1_11_2018.pdf

RAR RUS 18-25 Ryazan State University named for S.A.Yesenin Tregulov Vadim trww@yandex.ru Ryazan State University named for S.A.Yesenin Stepanov Vladimir vl.stepanov@365.rsu.edu.ru Melnik Nikolay melnik@lebedev.ru Properties of the semiconductor structure with a p–n-junction created in a porous silicon film under laser radiation The possibility of formation of a p–n-junction in a film of porous silicon by means of pulse laser radiation have been shown. Methods of Raman spectroscopy and photoluminescence spectroscopy were used to investigate features of transformation of a microstructure of a film of porous silicon under the influence of laser radiation. It was established that influence of a single laser impulse lasting 18 ns with the wavelength of 355 nanometers and energy of an impulse in the range of 85 – 200 mJ lead to disappearance of an amorphized phase and an increase in the sizes of crystallites in a film of porous silicon. In the paper it was shown that the p–n-junction was formed under the influence of laser radiation inside the largest silicon crystallites of a porous silicon film. To study the features of the electrophysical characteristics of the obtained semiconductor structure, methods for measuring the current-voltage and the capacitance-voltage characteristics were used. The obtained p–n-junction was sharp. The mechanisms of current flow had a complex character and were mainly determined by the processes of generation and recombination of carriers in the space-charge region of the p–n-junction involving the energy levels of the traps. Citation: V.V. Tregulov, V.A. Stepanov, N.N. Melnik, Properties of the semiconductor structure with a p–n-junction created in a porous silicon film under laser radiation, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 18 – 25. DOI: 10.18721/JPM.11102 10.18721/JPM.11102 538.91 porous silicon film p–n-junction laser radiation Raman scattering photoluminescence https://physmath.spbstu.ru/article/2018.39.2/ 02_18_25_1_11_2018.pdf

RAR RUS 26-33 Platko Anastasiya stewnstewn@gmail.com Herzen State Pedagogical University of Russia Sotova Yulia juliasotova1992@mail.ru Herzen State Pedagogical University of Russia Gorokhovatskiy Yuriy yurig@fromru.com 0000-0001-9604-4769 Herzen State Pedagogical University of Russia Karulina Elena karulina@mail.ru 0000-0001-5647-1854 Kazan National Research Technological University Galikhanov Mansour Electret effect in biodecomposed polylactide films filled with nanoscale magnesia In the paper, the results of studies in the charge relaxation mechanism in polylactide films with nanoscale hydrophilic filler (magnesia) have been obtained using thermally stimulated depolarization current (TSDC) and thermally stimulated surface-potential decay (TSSPD) methods. The loading of the hydrophilic filler (magnesia) was shown to result in the polymer conductance reduction, i.e., in the improvement of the electret properties of the composite. The optimal content of magnesia (4%) responsible for the highest electret state stability in polylactide films was determined. The values of the effective frequency factor and the activation energy of the deep traps for the injected charge being inherent to the polymer matrix were estimated by regularization technique. The obtained results demonstrate the capability of making active (long time retaining the organoleptic properties of the products) and biodegradable (solving the problem of recycling) packaging materials based on composite polylactide films with magnesia as a filler. Citation: A.P. Platko, Yu.I. Sotova, Yu.A. Gorokhovatskiy, E.A. Karulina, M.F. Galikhanov, Electret effect in biodecomposed polylactide films filled with nanoscale magnesia, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 11(1) (2018) 26 – 33. DOI: 10.18721/JPM.11103 10.18721/JPM.11103 537.9 polylactide hydrophilous filler biodecomposed film electret state charge-dipole complex https://physmath.spbstu.ru/article/2018.39.3/ 03_26_33_1_11_2018.pdf

RAR RUS 34-43 Zhukov Nikolay nzhukov@herzen.spb.ru Marchenko Alla al7140@rambler.ru Shakhovich Kirill shakhovichkirill@gmail.com Mössbauer emission spectra of stannum daughter isotopes measured under condition of a dynamic radioactive equilibrium of tellurium parent isotopes and antimonium daughter ones The information on a valence and a coordination states of the 119mSn daughter atoms formed in the cationic and anionic lattice sites of the crystalline lead telluride PbTe and the glassy arsenic telluride As2Te3 from the 119Sb and 119mTe parent isotopes has been obtained using the emission Mössbauer spectroscopy with the 119mTe parent isotopes being in a dynamic radioactive equilibrium with the 119Sb daughter ones. It was found by calculation and experimentally that the proportion of various valent and coordinate states of tin atoms in the crystal and the glass depended on the preparation moment of Mössbauer sources. Moreover, the displacement of a part of the 119Sb daughter atoms from lattice sites of the 119mTe parent isotopes as a result of a radioactive decay was established when bringing into agreement with experimental data. Citation: N.N. Zhukov, A.V. Marchenko, K.B. Shakhovich, Mössbauer emission spectra of stannum daughter isotopes measured under condition of a dynamic radioactive equilibrium of tellurium parent isotopes and antimonium daughter ones, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 11(1) (2018) 34 – 43. DOI: 10.18721/JPM.11104 10.18721/JPM.11104 539.16.08 dynamic radioactive equilibrium Mössbauer emission spectroscopy isotope telluride lead arsenic https://physmath.spbstu.ru/article/2018.39.4/ 04_34_43_1_11_2018.pdf

RAR RUS 44-54 Klinkov Victor klinkovvictor@yandex.ru Spectral and luminescent properties of doped fluoroaluminate glasses promising for optical temperature sensors Spectral and luminescent properties of Er3+-doped fluoroaluminate glasses have been studied and presented in the paper. The subject of inquiry was 98MgCaSrBaYAl2F14-2Ва(РО3)2 glass, the ErF3 concentrations were of 0.1 – 1.0 mol. %. The optical absorption spectra were analyzed in the range from 190 to 1700 nm, and the nature of absorption bands was explained on a basis of the Er3+ ion energy diagram. The upconversion spectra were measured at 77 and 300 K in the 500 – 700 nm range upon 975 nm laser excitation. The temperature dependences of FIR were calculated using the experimental data in a range of (77 – 300) K. Among the samples under investigation the 0.1% ErF3 one possessed the greatest response to temperature changes in the range of (77 – 300) K. The studied material was proved to be a candidate for realizing the optical temperature sensors. Citation: V.A. Klinkov, Spectral and luminescent properties of doped fluoroaluminate glasses promising for optical temperature sensors, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 11 (1) (2018) 44 – 54. DOI: 10.18721/JPM.11105 10.18721/JPM.11105 535.33, 681.586.36 optical temperature sensor rare-earth ion absorption spectrum luminescenc fluoroaluminate glass https://physmath.spbstu.ru/article/2018.39.5/ 05_44_54_1_11_2018.pdf

RAR RUS 55-65 Isaenko Iliya a906nn@gmail.com Makhnov Andrey a_makhnov@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

Schmidt Alexander alexander.schmidt@mail.ioffe.ru Simulation of high-speed cavitating flows in channels Cavitation is a process of vapour and gas bubbles formation in a liquid flow. It occurs when a flow pressure drops below a certain level depending on liquid’s physical properties and its temperature. One of the important factors of cavitation is the presence of unsolved microscopic bubbles filled with gas and/or vapour in real liquids. These bubbles, or nucleation sites, evolve under pressure drops that are sufficient for evaporation of surrounding liquid. A model of cavitating flows based on Euler – Lagrange description of multiphase medium has been developed. It took into account heterogeneous nature of cavitation bubbles formation. The Rayleigh – Plesset equation along with interphase mass and energy transfer equations were used to simulate bubbles evolution. The developed model provides qualitatively accurate prediction of cavity shape and its borders position in comparison with the experimental data. Citation: I.I. Isaenko, A.V. Makhnov, E.M. Smirnov, A.A. Schmidt, Simulation of high-speed cavitating flows in channels, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 55 – 65. DOI: 10.18721/JPM.11106 10.18721/JPM.11106 532.528 high-speed flow cavitation Rayleigh–Plesset equation multiphase medium https://physmath.spbstu.ru/article/2018.39.6/ 06_55_65_1_11_2018.pdf

RAR RUS 66-72 Chulyaeva Elena Ognev Boris develop@moctkom.ru Kuznetsov Sergey ksn@moctkom.ru The concept of building a wireless optical communication network between surface ships The problem of organization of a wireless optical multi-node network (MANET) between surface ships has been considered. This type of connection can be an alternative to the classical radio message. The advantages of optical communication are faster data transmission, high security and immunity to interference. The goal of the work is creation of computer model of such communication network, a choice of an algorithm of the organization of logical network infrastructure and determination of the main technical requirements to optical communication terminals. The software “The emulator of a wireless optical network” was developed for simulation of the network of the moving surface ships. For the organization of a communication network the well-known algorithms of discrete mathematics (such as the Kruskal algorithm) were used. The simulation of the network was carried out; technical requirements to optical communication terminals as an element of the specified network were formulated. Citation: E.G. Chulyaeva, S.N. Kuznetsov, B.I. Ognev, The concept of building a wireless optical communication network between surface ships, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 66 – 72. DOI: 10.18721/JPM.11107 10.18721/JPM.11107 621.373.826 wireless optical communication free space optics optical communication terminal MANET https://physmath.spbstu.ru/article/2018.39.7/ 07_66_72_1_11_2018.pdf

RAR RUS 73-85 Peter the Great St. Petersburg Polytechnic University Chumakov Yuri chymakov@yahoo.com Peter the Great St. Petersburg Polytechnic University Aleksander Levchenya levchenya@yandex.ru Malah Hamid hamid.malah@gmail.com The vortex structure formation around a circular cylinder placed on a vertical heated plate The interaction process analysis and results of numerical simulation of a free-convection boundary layer developing around a circular cylinder placed on a vertical heated plate are presented. The cylinder axis is directed normally to the plate. The numerical model is based on the Navier–Stokes and the energy balance equations. The assumed system of equations is solved using the Boussinesq approximation. It is shown that the presence of a three-dimensional obstacle (cylinder) on the plate results in the formation of a complex vortex structure both upstream and downstream of the cylinder. In particular, a horseshoe vortex formed upstream of it is similar to vortex formation that has been observed in forced convection heat transfer by many researchers. In this paper, the tentative results of the study of the complex three-dimensional vortical structure in conditions of free convection and its influence on the heat transfer are presented. Citation:Yu.S. Chumakov, A.M. Levchenya, H. Malah, The vortex structure formation around a circular cylinder placed on a vertical heated plate, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 73 – 85. DOI: 10.18721/JPM.11108 10.18721/JPM.11108 532.526 numerical modeling natural convection heat transfer vortex structure horseshoe vortex system heat transfer coefficient https://physmath.spbstu.ru/article/2018.39.8/ 08_73_85_1_11_2018.pdf

RAR RUS 86-101 0000-0003-0041-9971 Peter the Great St. Petersburg Polytechnic University Bykov Nikolay nbykov2006@yandex.ru On simulation of cluster formation process under water vapor spherical expansion into vacuum The calculation of a water vapor outflow into vacuum has been performed using the direct simulation Monte Carlo with taking into account a condensation process. Two cluster-formation models were employed for simulation. The former is based on a kinetic approach, the latter is based on conclusions drawn from the modified classical nucleation theory. The analysis of physical adequacy of models and features of their program implementation was carried out. The simulation of spherical vapor expansion from an evaporating surface was performed over a range of Knudsen numbers corresponding to transient and near-continual flow regimes. The influence of a condensation process on gasdynamic flow parameters was analyzed. The effect of freezing of cluster mole-fractions when receding from the evaporating source was demonstrated. Citation: N.Yu. Bykov, On simulation of cluster formation process under water vapor spherical expansion into vacuum, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 86 – 101. DOI: 10.18721/JPM.11109 10.18721/JPM.11109 541.11 direct simulation Monte Carlo condensation water cluster transient flow regime https://physmath.spbstu.ru/article/2018.39.9/ 09_86_101_1_11_2018.pdf

RAR RUS 102-111 Mamontov Alexander snowchek@mail.ru Petrakov Anatoliy petrakov@syktsu.ru Zimin Sergey zimin@uniyar.ac.ru Porosity and surface morphology of lead selenide – tin selenide layers on silicon substrates: X-ray diffraction studies In the paper, the surface porosity and morphology of Pb0.97Sn0.03Se films on silicon substrates subjected to anodic electrochemical etching in the Tompkins-Johnson’s electrolyte at a current density of 1 mA/cm2 have been studied using X-ray reflectometry. To reduce the difference in lattice parameters of a growing film, buffer CaF2 layer (about 2 nm thick) and buffer PbSe one (about 400 nm thick) were used. The averaged thickness of re-precipitated near-surface selenium layer was determined to be 45 nm. The X-ray experimental results showed qualitative agreement with electron-microscopical data. It was established by high-resolution X-ray diffraction methods that macroporous structure with transverse and longitudinal porous projections of sizes 47 and 82 nm (relatively) was forming in electrochemical etching. The angle of porous tilt with the surface normal was found to be 34.5 degrees. The applicability of high-resolution X-ray methods to nondestructive investigation of porous structure was shown. Citation: A.I. Mamontov, A.P. Petrakov, S.P. Zimin, Porosity and surface morphology of lead sele-nide – tin selenide layers on silicon substrates: X-ray diffraction studies, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 102 – 111. DOI: 10.18721/JPM.11110 10.18721/JPM.11110 537.874.4 + 538.971 + 538.975 anodizing porosity total external reflection method electrochemical etching lead-tin selenide https://physmath.spbstu.ru/article/2018.39.10/ 10_102_111_1_11_2018.pdf

RAR RUS 112-121 Khripunov Albert xelmie@mail.macro.ru Stepanova Tamara t_stepanova2005@mail.ru Saprykina Nataliya saprykina@hq.macro.ru Astapenko Ella imc@hq.macro.ru Romanov Dmitriy ichsran@isc.nw.ru Tkachenko Albina albina.tkachenko@mail.ru E-4237-2014 12784708700 0000-0001-9050-4453 Peter the Great St. Petersburg Polytechnic University Kapralova Victoria kapralova2006@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Morphology of dried nanogel films of bacterial cellulose impregnated with the silver nitrate solution A comparative study of dried nanogel films of the Gluconacetobacter xylinus cellulose (GXC) in native and disintegrated forms treated with AgNO3 solution has been carried out by means of SEM and XRD. The supermolecular structure of samples studied was shown to be 3D network of nanostrips formed with oriented macrofibrils in which amorphous and crystalline regions alternate. XRD patterns of the GXC dry films, pre-treated with AgNO3 aqueous solution, demonstrate both residual AgNO3 and reduced Ag0, the latter positioned in longwise direction of morphologic structure elements. The XRD and SEM studies of dried GXC films disintegrated in 1 % AgNO3 aqueous solution showed the presence of reduced Ag0 in the form of nanoparticles 10 – 50 nm in diameter located in the free volume of the GXC 3D network nearby structural elements. Citation: A.K. Khripunov, T.P. Stepanova, N.N. Saprykina, E.P. Astapenko, D.P. Romanov, A.A. Tkachenko, V.M. Kapralova, Morphology of dried nanogel films of bacterial cellulose impregnated with the silver nitrate solution, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 11(1) (2018) 112 – 121. DOI: 10.18721/JPM.11111 10.18721/JPM.11111 577.114 nanogel film bacterial cellulose SEM XRD https://physmath.spbstu.ru/article/2018.39.11/ 11_112_121_1_11_2018.pdf

RAR RUS 122-137 Basalaev Artyom artem.basalaev@cern.ch Naryshkin Yuriy yury.naryshkin@cern.ch Dark matter searches at the Large Hadron Collider One of the promising lines of investigation at the Large Hadron Collider (LHC) is a search for dark matter particles. Despite a large body of evidence for dark matter existence, its nature remains unknown. The leading hypothesis is that dark matter consists of weakly interacting massive particles. Collider searches for such particles are most sensitive in the case of spin-dependent interactions, and for the low masses of dark matter particles in the case of spin-independent interactions. The strategies of dark matter searches at the LHC are described, and upper limits on dark matter-nucleon cross-sections based on the experimental data collected in 2015 and 2016 by the ATLAS and CMS collaborations are presented in comparison with the results of other experiments. In conclusion, the perspectives of further searches of dark matter at the LHC are discussed. Citation: A.E. Basalaev, Yu.G. Naryshkin, Dark matter searches at the Large Hadron Collider, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 122 – 137. DOI: 10.18721/JPM.11112 10.18721/JPM.11112 539.12 dark matter LHC ATLAS CMS WIMP dark matter associative production mono-X https://physmath.spbstu.ru/article/2018.39.12/ 12_122_137_1_11_2018.pdf

RAR RUS 138-146 7006360562 Peter the Great St. Petersburg Polytechnic University Cherepanov Andrey hsapst@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Elecromagnetic wave propagation in the three-layer ferrite-dielectric structure A problem of wave propagation in a rectangular waveguide containing a three-layer ferrite-dielectric-ferrite (FDF) structure has been considered in the paper. The calculation of a free-space FDF structure usually runs into difficulties. The proposed approach has been made it possible to obtain a rigorous solution for the waveguide modes for which there is no dependence of electromagnetic fields on a coordinate directed along a magnetizing magnetic field. It is the main mode of the FDF structure that governs principal properties of a phased array. The obtained relationships were shown to describe the modes’ behavior for a free-space FDF waveguide. The dependences of the mode propagation constants on the magnetizing magnetic field were calculated, electromagnetic field structures of the main and the higher modes were found. The optimal structure parameters were determined. They are optimal when the controllability of the FDF structure by a constant magnetic field is maximal. Citation: A.S. Cherepanov, Elecromagnetic wave propagation in the three-layer ferrite-dielectric structure, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 11 (1) (2018) 138 – 146. DOI: 10.18721/JPM.11113 10.18721/JPM.11113 537.86, 621.396.67 ferrite waveguide antenna dielectric structure magnetizing magnetic field https://physmath.spbstu.ru/article/2018.39.13/ 13_138_146_1_11_2018.pdf

RAR RUS 147-156 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 Quantization of the energy density in a closed universe The energy of a closed universe is represented as a difference of two positive definite quantities, one of which includes the energy of matter and the energy of gravitational waves on the expanding universe background. The second quantity relates to the universe expansion and is called the energy of space. The whole energy of the universe equals zero provided the classical gravitational constraints are taken into account. In quantum theory a principle of the energy density of the matter minimum is formulated in the condition that the quantum gravitational constraints are also fulfilled in average. The states of the universe which satisfy the conditional minimal principle have different degree of the physical degrees of freedom excitation and, according to the gravitational constraints, corresponding excitation of space. The state of minimal excitation is proposed to be taken as the Beginning of the universe, and all the set of solutions, correspondingly, as admitted physical states of the universe at different moments of a cosmic time. Citation: N.N. Gorobey, A.S. Lukyanenko, Quantization of the energy density in a closed universe, St. Petersburg Polytechnical State University Journal. PhysicsandMathematics. 11 (1) (2018) 147–156. DOI: 10.18721/JPM.11114 10.18721/JPM.11114 530.12:517.988.38(075.8) energy time expanding universe gravitational constant quantum state reference frame https://physmath.spbstu.ru/article/2018.39.14/ 14_147_156_1_11_2018.pdf

RAR RUS 157-166 Institute for Problems of Mechanical Engineering of RAS Belyaev Alexander 13augen@mail.ru Shurpatov Anatoliy a.shurpatov@gmail.com Ma Chin-Chin ccma@ntu.edu.tw Determining the contact force of an axial collision of an elastic rod with a rigid impactor The problem of axial impact of a rigid body on elastic rod is considered. The Semi-Analytical Method (SEM) and Finite Element Method (FEM) are applied to handle the problem. The SEM of solving the problem implies the quasi-static Hertz theory and numerical integration of obtained differential equations. The number of necessary degrees of freedom of the FEM solution is determined and numerical simulation is carried out. The time of contact interaction and dependence of the contact force on the contact time are calculated. The longitudinal wave propagation in the rod is investigated. The obtained results are compared with the data from natural experiments. An inverse dependence between impacting mass and the accuracy of both methods is discussed. The results of comparison confirm the appropriateness of both methods for solving the problem. Citation: A.K. Belyaev, A.O. Shurpatov, Ch.-Ch. Ma, Determining the contact force of an axial collision of an elastic rod with a rigid impactor, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 11 (1) (2018) 157 – 166. DOI: 10.18721/JPM.11115 10.18721/JPM.11115 539.3 axial collision contact force finite element method https://physmath.spbstu.ru/article/2018.39.15/ 15_157_166_1_11_2018.pdf