2304-9782, 2618-8686, 2405-7223 St. Petersburg Polytechnic University Journal: Physics and Mathematics 12 2 2019 1-143
RAR RUS 7-22 0000-0002-6308-733X Peter the Great St. Petersburg Polytechnic University Kolesnik Elizaveta kolesnik_ev@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
 0000-0001-7608-7120 Peter the Great St. Petersburg Polytechnic University Smirnovsky Alexander smirta@mail.ru Numerical solution of a 3D problem on a supersonic viscous gas flow past a plate-cylindrical body junction at M 2.95 In the paper, results of numerical simulation of a shock-wave pattern and vortex structures forming in supersonic flow past an adjacent-to-plate elongate cylindrical body, which penetrates the developing flat-plate boundary layer, have been presented. The laminar flow regime at Mach number 2.95 was considered, Reynolds number was taken 4000. The solutions were obtained using two schemes for convective flux (HLL and AUSM). Comparison of the flow fields calculated with the mentioned schemes of the first and second orders of accuracy were conducted. Solution grid sensitivity issues were discussed. 10.18721/JPM.12201 519.6:533.6.011 high-speed flow viscous-inviscid interaction numerical simulation AUSM and HLL schemes https://physmath.spbstu.ru/article/2019.44.1/ 1_7-22_12(2)2019.pdf
RAR RUS 23-31 PJSC “Power Machines” Mannanov Emil Mannanov_ER@power-m.ru
St. Petersburg, Russian Federation
 St. Petersburg Electrotechnical University "LETI" Galunin Sergei galunin@mail.ru Nacke Bernhard nacke@etp.uni-hannover.de St. Petersburg Electrotechnical University "LETI" Kozulina Tatiana kozulina.tatiana@mail.ru Development of induction systems for disk heating The paper presents the experimental and numerical results obtained by the induction heating a steel disk. This study has been aimed at realizing the local uniform heating the disk at minimum temperature departure from 450°С. The system-of-interest included 3-turn inducers and a steel disk heated up. The computer-based investigation results were implemented at a laboratory mock-up. The temperature distribution over the disk material and its changes were recorded by a thermal imager. Simulation of electromagnetic and thermal processes occurring in heating a rotating disk-shaped work piece was carried out using ANSYS APDL base. A comparison between the obtained numerical data and experimental one showed a disagreement of about 5 %. It pointed to an adequacy of simulation carried out. A detailed analysis of the disagreement sources was made. 10.18721/JPM.12202 537.856 induction heating electrothermal task numerical simulation heat treatment heating with rotation https://physmath.spbstu.ru/article/2019.44.2/ 2_23-31_12(2)2019-(s).pdf
RAR RUS 32-48 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 Thomson formula for general harmonic functions The paper continues the investigation of electron and ion optical properties of electric and magnetic fields which can be represented in an analytical form. The target of this research is new recipes for generating analytical solutions of 3D Laplace equation, in particular, for generating 3D harmonic functions which are homogeneous in Euler terms. Linear algebraic expressions with first order partial derivatives which generalize the widely known Thomson formula (Kelvin transformation), are analyzed. The paper provides an exhaustive list of symmetric and homogeneous first order differentiating expressions that convert an arbitrary 3D harmonic function into some new 3D harmonic functions. The produced 3D expressions are generalized for the n-dimensional case. 10.18721/JPM.12203 517.51; 517.28; 517.983; 537.213, 537.8 electrostatic field magnetostatic field scalar potential Laplace’s equation Thomson formula https://physmath.spbstu.ru/article/2019.44.3/ 3_32-48_12(2)2019.pdf
RAR RUS 49-62 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 Thomson formula for homogeneous harmonic functions In the paper, it has been shown that the Thomson formula for three-dimensional harmonic homogeneous functions in Euler terms can be generalized using a linear algebraic form involving the first order partial derivatives of the initial function instead of pure algebraic linear expressions. An exhaustive list of the formed first order expressions converting arbitrary three-dimensional harmonic functions in Euler terms into new three-dimensional homogeneous harmonic functions was presented. 10.18721/JPM.12204 517.51; 517.28; 517.983; 537.213, 537.8 electrostatic field magnetostatic field scalar potential homogeneous function harmonic function https://physmath.spbstu.ru/article/2019.44.4/ 4_49-62_12(2)2019.pdf
RAR RUS 63-72 Peter the Great St. Petersburg Polytechnic University Petrichenko Mikhail fonpetrich@mail.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Peter the Great St. Petersburg Polytechnic University Kotov Evgeny ekotov.cfd@gmail.com
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 Numerical verification of weak solutions of the Crocco typical boundary problem using an implicit second order difference scheme To verify the solution of a typical Crocco boundary problem, a numerical experiment has been performed using an implicit second-order difference scheme. The computational experiment showed uniform convergence in the 0 ≤ х ≤ 1 interval for the numerical approximation of the solution to a weak solution with a small interval discrete sampling (of the order of N = 104 nodes). It was shown that a numerical solution approximated a weak solution of the typical Crocco limit problem, except for the right end of the integration interval. The solution of the Crocco boundary problem could be continued to the left of the point x = x0 while preserving the continuity and smoothness of the solution at this point. The point x = 1 represents the natural upper bound of the solution domain. 10.18721/JPM.12205 531 Crocco's typical boundary problem implicit difference scheme weak solution homotopy https://physmath.spbstu.ru/article/2019.44.5/ 5_63-72_12(2)2019.pdf
RAR RUS 73-87 Peter the Great St. Petersburg Polytechnic University Karseeva Elina elina.nep@gmail.com Peter the Great St. Petersburg Polytechnic University Velichko Elena velichko-spbstu@ya.ru Modification of laser correlation spectroscopy method for analyzing polydisperse nanoparticle suspensions The paper proposes a modification of the laser correlation spectroscopy method to improve the accuracy of determining the size of polydisperse nanoparticles in suspensions. The essence of the modification is to create an original scheme and an experimental data processing algorithm, which makes it possible to determine the size of highly polydisperse as well as nonspherical nanoparticles. A theory is given for calculating the size and shape of nanoparticles, as well as an algorithm for solving the inverse ill-posed problem of laser correlation spectroscopy. The approbation of the developed software and hardware complex is performed using model signals with different noise levels, as well as in the study of monodisperse and polydisperse suspensions of spherical and ellipsoidal particles with known sizes. 10.18721/JPM.12206 535.36, 535.4, 57.088 laser correlation spectroscopy nanoparticle dimension software and hardware complex https://physmath.spbstu.ru/article/2019.44.6/ 6_73-87_12(2)2019.pdf
RAR RUS 88-100 Peter the Great St. Petersburg Polytechnic University Pchitskaya Ekaterina katrincreative@yandex.ru Peter the Great St. Petersburg Polytechnic University Vlasova Olga olvlasova@yandex.ru Peter the Great St. Petersburg Polytechnic University Bolsunovskaya Marina bolsun_hht@mail.ru O-7971-2016 7006214225 0000-0001-7006-6951 UT Southwestern Med Ctr, Dept Physiol Bezprozvanny Ilya mnlabspb@gmail.com
Dallas, USA
 Analysis of dendritic spines morphology: from classical division to types toward alternative approaches This article provides a brief overview of the existing methods and approaches to analyzing the dendritic spines morphology playing an important role in the functioning of synaptic plasticity and memory formation mechanisms. Both various mathematical algorithms that classify spines according to their shape (thin, mushroom and stubby) and emerging alternative approaches have been considered. The reported scientific results point to uniform distribution of the main morphological parameters of dendritic spines; a number of authors cast some doubt on the often used division of spines into types and argue in favor of the existence of a shape continuum. Relying on this, a new approach to an analysis of dendritic spines morphology and to data presentation was advanced. It combines classification with the study of the distribution of dendritic spines by key morphological parameters. 10.18721/JPM.12207 577.35, 57.087, 57.087.2, 57.87.1 neuronal morphology mushroom spine thin spine stubby spine headed spine https://physmath.spbstu.ru/article/2019.44.7/ 7_88-100_12(2)2019.pdf
RAR RUS 101-110 Radzevich Pavel radzevichp@gmail.com Peter the Great St. Petersburg Polytechnic University Berdnikov Alexander alexber@phmf.spbstu.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru 0000-0002-3395-0454 Peter the Great St. Petersburg Polytechnic University Kotov Dmitry dmitriy.kotov@gmail.com Zharko Sergey zharkosergey94@gmail.com The measurement of eta meson nuclear modifiction factors in collisions of uranium nuclei Invariant spectra of η mesons production and nuclear modification factors of η и π0 mesons produced in binary collisions of uranium nuclei at energy of 192 GeV have been presented in the paper. This data was obtained using the PHENIX spectrometer of RHIC. These experimental results were analyzed and compared with similar data on binary collisions of gold nuclei at 200 GeV. The η и π0 mesons yields in central collisions of both uranium and gold nuclei (at energy values mentioned) were established to be suppressed equally. In the peripheral collisions, the nuclear modification factors of η и π0 mesons measured in the uranium nuclei collisions were suppressed more than those obtained in the gold ones. An analysis of a ratio of the η meson to π0 meson production spectra in the uranium nuclei collisions (at 192 GeV) revealed that the ratio was independent of the centrality class and the transverse momenta. 10.18721/JPM.12208 539.126.3 quark-gluon plasma eta meson jet-quenching effect nuclear modification factor https://physmath.spbstu.ru/article/2019.44.8/ 8_101-110_12(2)2019.pdf
RAR RUS 111-120 Radzevich Pavel radzevichp@gmail.com Peter the Great St. Petersburg Polytechnic University Berdnikov Alexander alexber@phmf.spbstu.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 0000-0003-0309-5917 Peter the Great St. Petersburg Polytechnic University Berdnikov Yaroslav berdnikov@spbstu.ru Zharko Sergey zharkosergey94@gmail.com 0000-0002-3395-0454 Peter the Great St. Petersburg Polytechnic University Kotov Dmitry dmitriy.kotov@gmail.com Suppression of the hadronic yields in the uranium nuclei collisions at the different quark’s composition of the produced particles This paper presents invariant spectra, nuclear modification factors and ratio of invariant spectra of light mesons, obtained in collisions of heavy uranium nuclei at 192 GeV. These values are studied with respect to transverse momenta, numbers of nucleon-nucleon collisions, numbers of participants and centrality. Light mesons production measurements are important in the study of heavy ion collisions, serving as hard probes of the quark gluon plasma (QGP). The research of light mesons in U + U collisions at 192 GeV allows discriminating the effects of hot matter depending on the geometric characteristics of the colliding heavy nuclei. The obtained results showed independence of the fragmentation of hard partons on the mass and composition of quarks and the absence of the influence of the geometric form of the colliding nuclei on the jet-quenching effect. 10.18721/JPM.12209 539.126.3 quark-gluon plasma light meson nuclear modification factor collision of heavy nuclei https://physmath.spbstu.ru/article/2019.44.9/ 9_111-120_12(2)2019.pdf
RAR RUS 121-129 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 Asymptotic effects in dijet production in proton-proton collisions at extremely high energies In the paper, the scope for the search of the Balitsky–Fadin–Kuraev–Lipatov (BFKL) evolution effects at future proton-proton colliders at center-of-mass energies of 14, 27 and 100 TeV has been analyzed for processes of dijets production with a large jet separation in rapidity at a dijet. Simulation of proton-proton collisions using Monte Carlo calculations performed with generator packages PYTHIA8 and HERWIG++ based on Dokshitzer–Gribov–Lipatov–Altarelli–Parisi evolution and with generator package HEJ+ARIADNE based on BFKL approach was carried out. The simulation observations pointed to a promise to reveal the BFKL effects experimentally under conditions established at future proton-proton colliders. 10.18721/JPM.12210 539.12 quantum chromodynamics BFKL approach dijet production; large rapidity https://physmath.spbstu.ru/article/2019.44.10/ 10_121-129_12(2)2019.pdf
RAR RUS 130-139 Peter the Great St. Petersburg Polytechnic University Tikhomirov Victor victikh@mail.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
 The exact solution of the problem on a crack emerging from the top of two dissimilar wedges A closed connection of two different isotropic wedges has been considered within the scope of the antiplane problem. A finite-length crack emerges from the top of this connection at an arbitrary angle to the symmetry axis of the structure. The exact solution of the problem was obtained through the problem’s reducing to the Wiener – Hopf scalar equation. The dependence of the stress intensity factor (SIF) at the crack tip on the structural parameters was studied. The effects of an increase and a decrease in SIF were compared with those known for the case of a homogeneous medium. It was shown that the stress asymptotics near the junction vertex could have one or two singular terms determining both strong and weak singularities at this singular point. 10.18721/JPM.12211 539.3 antiplane crack closed bimaterial wedge strong singularity weak singularity https://physmath.spbstu.ru/article/2019.44.11/ 11_130-139_12(2)2019.pdf