2304-9782, 2618-8686, 2405-7223 St. Petersburg Polytechnic University Journal: Physics and Mathematics 11 3 2018 1-146
RAR RUS 9-16 Voronezh State University of Forestry and Technologies named after G.F. Morozov Matveev Nikolay nmtv@vglta.vrn.ru
Russia, 394087, St. Voronezh, Timiryazev 8
 Based Electrical Technology, Industrial University of Ho Chi Minh City Hoai Thuong Nguyen nguyenthuongfee@iuh.edu.vn
12 Nguyen Van Bao, Ward 4, Go Vap, Ho Chi Minh, Vietnam
 Voronezh State University of Forestry and Technologies named after G.F. Morozov Kamalova Nina rc@icmail.ru
Russia, 394087, St., Voronezh, Timiryazev, 8
Voronezh State University of Forestry and Technologies named after G.F. Morozov Evsikova Nataliya natalyaevsikova@mail.ru
Russia, 394087, St., Voronezh, Timiryazev, 8
Voronezh State University of Forestry and Technologies named after G.F. Morozov Chernykh Alexander edu-ltu@vglta.vrn.ru
Russia, 394087, St., Voronezh, Timiryazev, 8
The wood in the inhomogeneous temperature field: Estimation of cellulose structure parameter fluctuations In the paper, the cellulose as a fiber-forming component of wood (natural composite) has been studied. The authors put forward a technique for estimating fluctuations of cellulose microstructure in the wood through monitoring the potential difference of the thermal polarization that arises in the samples placed into an inhomogeneous temperature field with a constant temperature gradient. Formalized simulation was used for an analysis of experimental results. The proposed technique made it possible to establish that the percent of the large-sized cellulose crystallites in the wood grew with increasing smoothly temperature gradient. Similar dynamics is not typical of linear crystalline polymers whose polarization decreases with growing temperature. The obtained effect can be assigned to the fact that natural wood exhibits heterogeneous structure. 10.18721/JPM.11301 53.082.63 microstructure crystallite composite cellulose macromolecule synthesized material https://physmath.spbstu.ru/article/2018.41.1/ 01_9-16_11(3)2018.pdf
RAR RUS 17-26 Zavoisky Physical-Technical Institute, FRC KazanSC of RAS Shaposhnikova Tatyana t_shap@kfti.knc.ru
Russia, 420029, Kazan, Sibirsky tract, 10/7
 Zavoisky Physical-Technical Institute, FRC KazanSC of RAS Mamin Rinat mamin@kfti.knc.ru
Russia, 420029, Kazan, Sibirsky tract, 10/7
 The phase separation phenomenological model: Manganite as an example In the paper, an effect of a second order phase transition has been considered in the context of the phenomenological model for a 2D charged system (2DCS) frustrated by the Coulomb interaction. The relationship between the order parameter and the charge was treated as a local temperature in the 2DCS. The existence of phase-separated states was shown to be a possibility in such a system. Various types of those states (strips, rings, etc.) were found by numerical calculations, and their parameters were determined. As the temperature is lowered, the 2DCS passes several phase transitions successively. Using the La(1–x)Sr(x)MnO3 manganite as an example it was shown that such a phenomenological model could be used to describe the phase separation close to a magnetic phase transition from a ferromagnetic state to a paramagnetic one when 0.10 < x < 0.15 and at the temperatures of 100 < T < 200 K. 10.18721/JPM.11302 538.9.53.01 second order phase transition phase separation manganite Coulomb interaction doping level https://physmath.spbstu.ru/article/2018.41.2/ 02_17-26_11(3)2018.pdf
RAR RUS 27-38 Peter the Great St. Petersburg Polytechnic University Petrichenko Mikhail fonpetrich@mail.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Zaborova Dariya zaborova-dasha@mail.ru Peter the Great St. Petersburg Polytechnic University Kotov Evgeny ekotov.cfd@gmail.com
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Musorina Tatiana flamingo-93@mail.ru Weak solutions of the Crocco boundary problems A procedure for designing an approximate solution of the Crocco boundary typical problem has been proposed in the paper. The procedure calls for the change of this initial problem by a nonlinear integral equation. The latter was solved by direct calculation of the integral using the mean-value theorem. . The averaging parameter was eliminated by integrating over the parameter in the (0, 1) interval. Widening the scope of the solution procedure was demonstrated and weak solutions were found. For the classical case, the weak solution was not too different from the Blasius exact one. The approximate value of the Blasius constant turned out to be 1/3 and differed from the exact one (0.33206) by 0.3 %. 10.18721/JPM.11303 517 Cauchy problem integral equation mean value theorem group of transformations solitary wave https://physmath.spbstu.ru/article/2018.41.3/ 03_27-38_11(3)2018.pdf
RAR RUS 39-51 Submicron Heterostructures for Microelectronics Research and Engineering Center of the RAS Aladov Andrei
Russia, 194021, St.Petersburg, Polytechnicheskaya, 26
 Jönköping University, School of Engineering Belov Ilia ilia.belov@ju.se.ru
Sweden St., Jönköping, Gjuterigatan, 5
 Peter the Great St. Petersburg Polytechnic University Valjukhov Vladimir Valyukhov@yandex.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 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
 A study of thermal regime in the high-power LED arrays Thermal resistance and temperature distribution for high-power AlGaInN LED chip-on-board arrays were measured by different methods and tools. The p–n junction temperature was determined through measuring a temperature-dependent forward voltage drop on the p–n junction, at a low measuring current after applying a high heating current. Furthermore, the infrared thermal imaging technique was employed to obtain the temperature map for the test object. A steady-state 3D computational model of the experimental setup was created including temperature-dependent power dissipation in the LED chips. Simulations of the heat transfer in the LED array were performed to further investigate temperature gradients observed in the measurements. Simulations revealed possible thermal deformation of the assembly as the reason for the hot spot formation. The bending of the assembly was confirmed by surface curvature measurements. 10.18721/JPM.11304 628.9 LED LED matrix thermal resistance infrared thermography thermal interface CFD model https://physmath.spbstu.ru/article/2018.41.4/ 04_39-51_11(3)2018.pdf
RAR RUS 52-64 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
 Generalization of the pseudopotential concept for radio-frequency quadrupole fields It is shown that the pseudopotential function, which describes the averaged motion of charged particles with accuracy up to quadratic terms for nonuniform radio-frequency fields, can be replaced by an infinite pseudopotential series for quadrupole radio-frequency electric fields. This replacement provides a more accurate description. It allows us to extend the parameter’s range of the radio-frequency field; in this range,радиоit makes possible to describe the motion of charged particles quantitatively and not just qualitatively. Unfortunately, even this extended concept of pseudopotential is not suitable enough for describing the motion of charged particles when approaching the region of the parametric resonance, where the motion of charged particles loses stability in the quadrupole radio-frequency fields. 10.18721/JPM.11305 537.534.7; 621.319.7 high-frequency electric field quadrupole mass filter secular oscillation pseudopotential https://physmath.spbstu.ru/article/2018.41.5/ 05_52-64_11(3)2018.pdf
RAR RUS 65-73 Peter the Great St. Petersburg Polytechnic University Larionova Dariya dlar@bk.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Larionova Mariya mlario@bk.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Mitrankov Yuriy mitrankovy@gmail.com
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Borisov Vladislav vl-borisof@yandex.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Solovev Vladimir hydraca39@gmail.com
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Berdnikov Alexander alexber@phmf.spbstu.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Cumulative protons production during the carbon nucleus fragmentation on the beryllium target The collision of carbon nuclei with beryllium targets has been simulated in the framework of the Liège Intranuclear Cascade model at the carbon nuclei initial kinetic energies of 0.60, 0.95, 2.00 GeV / nucleon. Proton production invariant cross-sections at the nuclei collision angle of 3.5 degrees were obtained. It was shown that the dependence of experimental invariant cross-sections on the cumulative variable x in the range 0.9 < x < 2.4 could be interpret on the basis of taking into account the Fermi motion of nucleons in nuclei, multiple scattering processes, and the formation of delta resonance. The calculation results were compared with experimental data and findings of investigation where data was analyzed in the context of the quark cluster model. 10.18721/JPM.11306 539.126.3 cumulative particle delta resonance Liège Intranuclear Cascade model beryllium target https://physmath.spbstu.ru/article/2018.41.6/ 06_65-73_11(3)2018.pdf
RAR RUS 74-89 Saint-Petersburg State University of Aerospace Instrumentation Pichugin Yuri yury-pichugin@mail.ru
Russia, 190000, St. Petersburg, Bolshaya Morskaya St., 61
 Notes on using the principal components in the mathematical simulation The paper discusses the issues related to the use of principal components analysis (PCA) in mathematical simulation. The paper significantly expands the range of the solved problems using PCA. In particular, the solutions of the following three tasks are given: (i) structural similarity and homogeneity estimation for random Gaussian vectors; (ii) recovery of missing data; (iii) the forecast of non-stationary time series based on the caterpillar method, which is a generalization of PCA for non-stationary time series. To solve the problems, to restore missing data and to predict the data, the author offers an unbiased estimation of the variance of the error of the regression on the PCs base for the cases of large and small samples. All the main statements are formulated in the form of theorems proved by the author. 10.18721/JPM.11307 519.24 principal component variance of the regression error small sample volume https://physmath.spbstu.ru/article/2018.41.7/ 07_74-89_11(3)2018.pdf
RAR RUS 90-98 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 Blagoveshchenskaya Ekaterina kblag2002@yahoo.com
Russia, 190031, St. Petersburg, Moskovsky Ave., 9
 Russian Research Center for Radiology and Surgical Technologies Bogomolov Oleg urologbogomolov@gmail.com
Russia, 197758, St. Petersburg, Pesochniy Settl., Leningradskaya St., 70
 Emperor Alexander I St. Petersburg State Transport University Garbaruk Victor vigarb@mail.ru
Russia, 190031, St. Petersburg, Moskovsky Ave., 9
 Russian Research Center for Radiology and Surgical Technologies Yakovleva Julia vmkaf@pgups.ru
Russia, 197758, St. Petersburg, Pesochniy Settl., Leningradskaya St., 70
 The exponential model of cell growth: a simulation error Mathematical modeling of pathological changes in the body is the means of obtaining information for making decisions about the method of treatment. Numerous studies have shown that the exponential model describes the tumor cells growth, and the time of antigen doubling determines the aggression of cancer cells growth. The present work investigates inaccuracies in determining the antigen doubling time as a function of measurement errors. The study showed that the decision on the method of treatment could be changed by taking into account errors in the prognosis of patient’s condition. For patient’s stratification in groups of high, medium and low risks, various threshold values corresponding to the antigen level are proposed. The results are presented in the form of a table and graphs. 10.18721/JPM.11308 519.8/616-006 mathematical modeling pathological changes antigen simulation error https://physmath.spbstu.ru/article/2018.41.8/ 08_90-98_11(3)2018.pdf
RAR RUS 99-107 Peter the Great St. Petersburg Polytechnic University Tikhomirov Victor victikh@mail.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Sharp V-notch fracture criteria under antiplane deformation The criteria for brittle fracture of a sharp V-notch when it is loaded with antiplane concentrated forces have been considered: a criterion for the maximum average stress, a criterion for the average energy density of deformation, and an approach based on the joint use of the force and energy criteria. Failure loads estimates on the basis of the exact solutions and using asymptotics of stresses near the V-notch tip were found. A comparative analysis of the failure loads obtained through those criteria was carried out. For the asymmetric loading, the initial angle of the crack propagation from the V-notch tip was determined. In the calculation of this angle, the application of the stress asymptotics was shown to result in significant errors and to require the consideration of regular terms in the stress representations. 10.18721/JPM.11309 539.3 antiplane deformation sharp V-notch fracture criterion average stress deformation energy https://physmath.spbstu.ru/article/2018.41.9/ 09_99-107_11(3)2018.pdf
RAR RUS 108-121 Kutateladze Institute of Thermal Physics Mullyadzhanov Rustam rustammul@gmail.com
Russia, 630090, Novosibirsk, Acad. Lavrentiev Ave., 1
 Kutateladze Institute of Thermal Physics Yavorsky Nikolay nick@itp.nsc.ru
Russia, 630090, Novosibirsk, Acad. Lavrentiev Ave., 1
 The far field of a submerged laminar jet: Linear hydrodynamic stability A linear stability problem for a submerged Landau – Squire jet has been considered. It was shown that in the space, the intrinsic perturbation amplitude varied as a power function of the spherical radius R, read from the motion source. It was established that the increment in the sinusoidal disturbance became more than that for axisymmetric one for Re _D > 31. The linear stability theory was applied to the value of the laminar-turbulent transition coordinate as a function of the Reynolds number. A model criterion for a laminar-turbulent transition in the far jet region was proposed. For the first time, this made it possible to obtain a good agreement between the theoretical results and experimental data for Re_D < 2000. 10.18721/JPM.11310 532.5.013.4 laminar jet Landau solution hydrodynamic stability far field https://physmath.spbstu.ru/article/2018.41.10/ 10_108-121_11(3)2018.pdf
RAR RUS 122-132 Peter the Great St. Petersburg Polytechnic University Avdeev Evgeniy avdeev-evgeni@yandex.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Pletnev Alexander AAPletnev@yandex.rii
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Bulovich Sergei bulovic@yandex.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Three-fluid formulation and a numerical method for solving the stationary problem of thermal hydraulics of a two-phase annular dispersed flow The article presents a one-dimensional three-fluid model for solving the stationary flow problem on a two-phase steam-water annular dispersed stream in a vertical heated channel, based on nine balance equations with an equal phase pressure assumed. The validation of the marching algorithm of the described stationary problem has been carried out by comparison with the published experimental data relating to a two-phase flow in a circular pipe under adiabatic conditions for pressures of 3 – 9 MPa, total flow rates of 500 – 3000 kg /(m^2∙s) and internal diameters of 10 and 20 mm. The total pressure differences in the channel were calculated. Good qualitative agreement with experimental data was obtained. Small quantitative disagreements were found. They were shown to be reduced by the refinement of the closing relations. 10.18721/JPM.11311 536.7; 532.5; 519.6 two-phase steam-water flow three-fluid model numerical solution https://physmath.spbstu.ru/article/2018.41.11/ 11_122-132_11(3)2018.pdf
RAR RUS 133-142 0000-0003-2770-2304 Sonora University, Department of Investigation for Physics, Hermosillo, Mexico Lipovka Anton nila_lip@mail.ru
83000, Mexico, Calle Rosales e Boulevard Luis, Encinas s/n Colonia Centro, Hernosillo
 Lipovka Neonila nila_lip@mail.ru Radio emission of stars in the Monoceros constellation In the present paper, the optical identifications of the bright stars from the Monoceros constellation with strong radio sources have been suggested. The Monoceros constellation is projected on the bright region of the Milky Way, where the densities of the stars and gas are rather high. 17 stars brighter than 11m are located within the one square degree plate under investigation. All these stars were identified with radio sources from NVSS survey of NRAO observatory. Considerable radio refraction was revealed in the interstellar medium. It was found that twelve stars among seventeen ones exhibited radio emission characterized by non-thermal spectrum. 10.18721/JPM.11312 528.2 coordinates system optical identification of radio objects interstellar space https://physmath.spbstu.ru/article/2018.41.12/ 12_133-142_11(3)2018.pdf