2304-9782, 2618-8686, 2405-7223 10 3 2017

RAR RUS 9-17 Ilinskiy Alexander ilinskiy@mail.ioffe.ru Peter the Great St. Petersburg Polytechnic University Pashkevich Marina marpash@yandex.ru Shadrin Evgeniy shadr.solid@mail.ioffe.ru Stage-by-stage modeling of the mechanism of semiconductor – metal phase transition in vanadium dioxide The algorithm of stage-by-stage qualitative modeling of the mechanism of a semiconductor – metal phase transition in vanadium dioxide has been proposed. The basis for the model is a statement that the transition is complex in character and consists of the anhysteretic, purely electronic Моtt transition occurring over a wide temperature range, and the temperature-abrupt structural Peierls transition having a thermal hysteresis. The initial stage of the model is based on the solution of a quantum-mechanical problem of an electronic spectrum of a linear vanadium-ion’s chain. The model is completed by consideration of correlation effects and a martensitic character of the structural transition through taking consecutively account of results obtained by X-ray, spectroscopic, impedansmetric and magnetoresonance metods. Citation: A.V. Il’inskiy, M.E. Pashkevich, E.B. Shadrin, Stage-by-stage modeling of the mechanism of semiconductor – metal phase transition in vanadium dioxide, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 9–17. DOI: 10.18721/JPM.10301 10.18721/JPM.10301 537.226.33 phase transition correlation energy Migdal distribution Моtt transition Peierls transition https://physmath.spbstu.ru/article/2017.37.1/ 01_9_17_10_3_2017.pdf

RAR RUS 18-25 Alekseeva Olga blackhole2010@yandex.ru Ioffe Physical Technical Institute of the Russian Academy of Sciences Naberezhnov Alexander alex.nabereznov@mail.ioffe.ru Amur State University Stukova Elena lenast@bk.ru Simkin Valeriy simkin@nf.jinr.ru Stabilization of the nop ferroelectric phase in the potasium nitrate – barium titanate ferroelectric composites The study of temperature evolution of KNO3 (NOP) structure in ferroelectric (1 – x)KNO3 + (x)BaTiO3 composites with BaTiO3 concentrations х = 0.25, 0.50 and 0.53 has been carried out on cooling with the use of neutron diffraction technique. It was shown that, on cooling, the phase transition temperature (Tc) from the high-temperature paraelectric phase into the ferroelectric one did not depend on barium titanate concentration and coincided practically with Tc for the pure NOP. Moreover, it was found that the admixture of BaTiO3 enlarged essentially the temperature range of NOP ferroelectric phase stability in the composites with BaTiO3 concentrations x = 0.25 and 0.50. The suppression of the ferroelectric phase was observed for the composite with x = 0.53. Citation: O.A. Alekseeva, A.A. Naberezhnov, E.V. Stukova, V.G. Simkin, Stabilization of the NOP ferroelectric phase in the potasium nitrate – barium titanate ferroelectric composites, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 18–25. DOI: 10.18721/JPM.10302 10.18721/JPM.10302 538.9 ferroelectric composite ferroelectric phase transition neutron diffraction https://physmath.spbstu.ru/article/2017.37.2/ 02_18_25_10_3_2017.pdf

RAR RUS 26-37 Ryakhovskiy Aleksey alexey.i.ryakhovskiy@mail.ioffe.ru 57034855700 0000-0002-4088-4707 Peter the Great St. Petersburg Polytechnic University Antonov Valerii hmath@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Peter the Great St. Petersburg Polytechnic University Kalinin Nikolay nvkalinin@rambler.ru The eos choice effect on the simulated results obtained for an underwater electrical explosion of conductors In the paper, the effect of the choice of equations of state (EOSs) depicting the states of metal plasma and water on the simulated results obtained for an underwater electrical explosion of conductors has been analyzed. In order to compare various EOSs, a one-dimensional, cylindrically symmetrical, magnetohydrodynamic model of an underwater wire explosion was employed. The simulated results were compared with the experimental data on both micro- and nanosecond explosions of aluminum and copper wires. The right choice of EOSs and the model of transportation coefficients allowed us to improve the agreement between the experimental and simulated data and to replicate the thermodynamic evolution of the system more closely. The made comparison revealed the most appropriate EOSs for application to simulation of an electrical explosion. Citation: A.I. Ryakhovskiy, V.I. Antonov, N.V. Kalinin, The EOS choice effect on the simulated results obtained for an underwater electrical explosion of conductors, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 26–37. DOI: 10.18721/JPM.10303 10.18721/JPM.10303 004.942 magnetohydrodynamics electrical explosion of conductors metal plasma equation of state https://physmath.spbstu.ru/article/2017.37.3/ 03_26_37_10_3_2017.pdf

RAR RUS 38-51 Kislitcina Irina irina_kislitsyna@mail.ru Peter the Great St. Petersburg Polytechnic University Malykhina Galina g_f_malychina@mail.ru Simulation of on-the-fly measuring system of a descent module under uncertainty of the lunar-surface composition The measurement method for determination of the motion parameters of the module de-orbiting upon the lunar surface has been suggested. The surface-scattered gammas emitted by a radioactive source are detected using four receptors under uncertainty of the lunar-soil’s elemental composition. The radar-tracking system’s exist in the module allows adaptation of the gamma-ray altimeter to the lunar-soil composition. A mathematical model of the measuring system has been put forward, and dependences of the gammas’ flux level on the module altitude and the angle of the slanted surface were obtained. The model makes possible analyzing the relative position of the radioactive source and the receptors and the composition effect of the substrate. The measurement algorithm uses a recursive neural network, which is proposed to train in advance and adapt during the module landing. Citation: I.A. Kislitsyna, G.F. Malykhina, Simulation of on-the-fly measuring system of a descent module under uncertainty of the lunar-surface composition, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 38–51. DOI: 10.18721/JPM.10304 10.18721/JPM.10304 681.51:621:391 descent module scattered gamma radiation adaptation lunar-soil composition https://physmath.spbstu.ru/article/2017.37.4/ 04_38_51_10_3_2017.pdf

RAR RUS 52-63 Pozhilov Aleksey aapozhilov@mail.ru Peter the Great St. Petersburg Polytechnic University Zaytsev Dmitry zaitsev-aero@yandex.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 simulation of heat and mass transfer in a 3D model of a loop heat pipe evaporator The article presents results of 3D numerical simulation of flow and conjugate heat and mass transfer in a model of the TacSat-4 satellite loop heat pipe evaporator. Mathematical model includes the Reynolds averaged Navier-Stokes equations describing a flow in the liquid and vapor regions, Darcy’s law for filtration modeling in the wicks and the energy equation with accurate coupling of connected sub-domains including effects of evaporation on interfaces between the porous and vapor regions. According to the simulation results, the evaporation localizes mainly at the vapor groove corners near the evaporator body. The vapor grooves operate under essentially different conditions, as a result, the flow rates differ several times. Significant thickening of the evaporator body yields only weak reduction in a level of the grooves’ flow rate non-uniformity. Citation: A.A. Pozhilov, D.K. Zaitsev, E.M. Smirnov, A.A. Smirnovsky, Numerical simulation of heat and mass transfer in a 3D model of a loop heat pipe evaporator, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 52–63. DOI: 10.18721/JPM.10305 10.18721/JPM.10305 536.246 numerical simulation conjugate heat and mass transfer loop heat pipe evaporator https://physmath.spbstu.ru/article/2017.37.5/ 05_52_63_10_3_2017.pdf

RAR RUS 64-74 Jaiswal Shailesh Sawala Niraj nssawala@gmail.com Koparkar Kishor Nagpure Pankaj Bhatkar Vinod Omanwar Shreeniwas Omanwar@rediffmail.com Visible quantum cutting in green emitting BaF2: Gd3+, Tb3+ phosphors: an approach towards mercury-free lamps Visible quantum cutting (QC) via down-conversion (DC) has been observed in the green emitting BaF2 co-doped with Gd3+, Tb3+ phosphors synthesized by wet chemical method. Powder X-ray diffraction (XRD) analysis showed structural purity of the synthesized phosphors. The excitation (PLE) and PL spectra in the vacuum ultraviolet (VUV) or UV region were measured with the help of 4B8-VUV spectroscopy experimental station of the Beijing Synchrotron Radiation Facility (BSRF). In the QC process, one VUV-UV photon absorbed cuts into more than one visible photons emitted by Tb3+ through cross relaxation (CR) and direct energy transfer (DET) between Tb3+ and Tb3+ or Tb3+ and Gd3+, depending on the excitation wavelength. From the emission spectra monitored at different wavelength excitation, the two-step energy transfer process was investigated, and theoretically calculated quantum efficiency observed was found to be 148 % and 177 % at the excitation wavelength of 174 nm and 219 nm respectively. Citation: S.R. Jaiswal, N.S. Sawala, K.A. Koparkar, P.A. Nagpure, V.B. Bhatkar, S.K. Omanwar, Visible quantum cutting in green emitting BaF2 : Gd3+, Tb3+ phosphors: an approach towards mercury-free lamps, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 64–74. DOI: 10.18721/JPM.10306 10.18721/JPM.10306 537.226.33 quantum cutting inorganic phosphor cross relaxation energy transfer quantum efficiency https://physmath.spbstu.ru/article/2017.37.6/ 06_64_74_10_3_2017.pdf

SCO RUS 75-83 Peter the Great St. Petersburg Polytechnic University Larionov Nikolay larionov.nickolay@gmail.com Formation of the angular dependence of intensity of the light scattered on the optically dense atomic ensemble Теоретически исследуется рассеяние пробного излучения на оптически плотном холодном атомном ансамбле. Для описания многократного рассеяния света атомами ансамбля используется квантово-электродинамический подход, основанный на диаграммной технике Константинова – Переля – Келдыша. С помощью этого подхода, для случая неподвижных двухуровневых атомов (переход Jg = 0 → Je = 1) выводится явное аналитическое выражение для сечения n-кратного некогерентного рассеяния. Численный анализ полученного выражения, проведенный методом Монте-Карло, позволил проследить роль различных порядков рассеяния в формировании угловой зависимости интенсивности рассеянного света. Citation: N.V. Larionov, Formation of the angular dependence of intensity of the light scattered on the optically dense atomic ensemble, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (2) (2017) 75–83. DOI: 10.18721/JPM.10307 10.18721/JPM.10307 535.3 cold atomic ensemble Konstantinov – Perel – Keldysh diagram technique incoherent scattering https://physmath.spbstu.ru/article/2017.37.7/ 07_75_83_10_3_2017.pdf

RAR RUS 84-94 Sobolev Institute of Mathematics Anikonov Dmitriy anik@math.nsc.ru Kipriyanov Yaroslav yaroslav.kipriyanov@gmail.com Sobolev Institute of Mathematics Konovalova Dina dsk@math.nsc.ru An inverse problem for the equation of membrane's vibration A mathematical model for membrane’s vibration process is used in this paper. The model is based on seeking a solution of the second-order hyperbolic differential equation. A new inverse problem is set and investigated in two versions. In the first version the known data are as follows: the coefficient defining a phase velocity, starting data of the Cauchy problem, the Cauchy problem solution on the two given planes, derivatives of the solution along the vector being normal to these planes. The challenge has been in localizing the support of the right-hand side of the equation for vibrations. The algorithm permitting to find the bounded domain containing the unknown support was designed. In the second version the algorithm refers to the case where the coefficient defining a phase velocity is unknown but an interval of its possible values is known. A series of runs was performed to illustrate the proposed model. Citation: D.S. Anikonov, Ya.A. Kipriyanov, D.S. Konovalova, An inverse problem for the equation of membrane’s vibration, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 84–94. DOI: 10.18721/JPM.10308 10.18721/JPM.10308 517.958 simulation the equation of membrane's vibration integral geometry inverse problem https://physmath.spbstu.ru/article/2017.37.8/ 08_84_94_10_3_2017.pdf

RAR RUS 95-99 Smirnov Pavel s.paul@mail.ru Shirokov Ivan summertouch@mail.ru Shevlyakov Georgy Georgy.Shevlyakov@phmf.spbstu.ru High-efficiency and robust M-estimates of the scale parameter on the Q-estimate basis     The highly efficient and robust Q-estimate of the scale parameter proposed by Rousseeuw and Croux (1993) and commonly employed has been approximated using computationally fast Huber M-estimates. The suggested M-estimates were shown to be robust and highly efficient for an arbitary underlying data distribution due to right choosing the approximation parameters. The following indicators of the efficiency and robustness of M-estimates of scale were computed: their asymptotic variances, influence functions and breakdown points. A special attention was given to the particular cases of the Gaussian and Cauchy distributions. It is noteworthy that for the Cauchy distribution, the suggested robust estimate of scale coincides with the maximal likelihood estimate. Finally, the computation time of these highly-efficient and robust estimates of scale is 3-4 times less than for the corresponding Q-estimates. Citation: P.O. Smirnov, I.S. Shirokov, G.L. Shevlyakov, Highly-efficient and robust M-estimates of the scale parameter on the Q-estimate basis, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 95–99. DOI: 10.18721/JPM.10309 10.18721/JPM.10309 519.233.2 M-estimate Q-estimate robustness scale parameter Gaussian distribution Cauchy distribution https://physmath.spbstu.ru/article/2017.37.9/ 09_95_99_10_3_2017.9.pdf

RAR RUS 100-115 Parand Kourosh k_parand@sbu.ac.ir Delkhosh Mehdi Operational matrices to solve nonlinear Riccati differential equations of an arbitrary order In this paper, an effective numerical method to achieve the numerical solution of nonlinear Riccati differential equations of an arbitrary (integer and fractional) order has been developed. For this purpose, the fractional order of the Chebyshev functions (FCFs) based on the classical Chebyshev polynomials of the first kind have been introduced, that can be used to obtain the solution of these equations. Also, the operational matrices of fractional derivative and product for the FCFs have been constructed. The obtained results illustrated demonstrate that the suggested approaches are applicable and valid. Key words: fractional order of the Chebyshev functions; operational matrix; Riccati differential equations; Galerkin method; differential equation of arbitrary order. Citation: K. Parand, M. Delkhosh, Operational matrices to solve nonlinear Riccati differential equations of an arbitrary order, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 100–115. DOI: 10.18721/JPM.10310 10.18721/JPM.10310 517.923 fractional order of the Chebyshev functions operational matrix Riccati differential equations Galerkin method differential equation of arbitrary order https://physmath.spbstu.ru/article/2017.37.10/ 10_100_115_10_3_2017.pdf

RAR RUS 116-122 Seregin Sergey Seregin-komshome@yandex.ru The splitting features of a frequency spectrum of a gyroscope based on elastic waves in solids: an isolated imperfect ring as an example The calculation results on dynamic characteristics of a geometrically imperfect ring turning out of shape in its plane have been exemplified by a simpler computational model for a ring resonator of a gyroscope based on elastic waves in solids. The specific malconformations were shown to be responsible for a splitting of the flexural frequency spectrum of such rings. In so doing the spectral mismatch may appear in cases different from the ideas of modern theory. The splitting of the flexural frequency spectrum was established to occur not only in the cases when the number of formative waves being equal to that of malconformation waves of the ring (as it is commonly believed at present) but in the cases when the number of formative waves being two, three, four and so on times more than that of malconformation waves. Citation:S.V. Seregin, The splitting features of a frequency spectrum of a gyroscope based on elastic waves in solids: an isolated imperfect ring as an example, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 116–122. DOI: 10.18721/JPM.10311 10.18721/JPM.10311 539.3:534.1 ring resonator wave solid-state gyroscope bending frequency spectrum radial oscillation https://physmath.spbstu.ru/article/2017.37.11/ 11_116_122_10_3_2017.pdf

RAR RUS 123-139 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

Testing of various schemes with quasi-one-dimensional reconstruction of gasdynamic variables in the case of unstructured-grid calculations Several schemes of the second-order approximation worked out in the literature for unstructured-grid-based computations of gasdynamic flows are described. The convective fluxes on the control-volume’s faces are evaluated using the Roe’s approximate Riemann solver. The MUSCL approach with the use of various quasi-one-dimensional schemes of reconstruction of gasdynamic variables and limiters making the solution monotonic is applied in order to improve the approximation accuracy. Comparative analysis of the working capacity of the schemes under consideration has been carried out through solving two problems of inviscid gas flow. Namely, the transonic NACA-0012 airfoil flow and the superpersonic flow in the duct with the central ramp were computed. The smoothness of solution, obtained with different schemes, dissipativity features of the schemes and computational process stability were evaluated. Citation: E.V. Kolesnik, E.M. Smirnov, Testing of various schemes with quasi-one-dimensional reconstruction of gasdynamic variables in the case of unstructured-grid calculations, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 123–139. DOI: 10.18721/JPM.10312 10.18721/JPM.10312 519.6:533.6.011 compressible flow numerical simulation MUSCL approach unstructured grid quasi-one-dimensional reconstruction https://physmath.spbstu.ru/article/2017.37.12/ 12_123_139_10_3_2017.pdf

RAR RUS 140-151 Ovchinnikova Evgeniya elfimovaevgeniya@gmail.com Charikov Yuri y.charikov@yandex.ru Shabalin Alexander TaoAstronomer@gmail.com Vasil’ev Gennadiy Gennady.Vasilyev@mail.ioffe.ru The contribution of the albedo for photons to the intensity of the hard X-ray emission of solar flares The albedo contribution to the total hard X-ray solar-flare emission has been considered. First, the distribution of primary hard X-ray photons localized along the flare loop was found, and finally, the Monte Carlo calculations of the Compton scattered hard X-ray photons were obtained. The albedo for photons was shown to contribute to the total X-ray flux only in the energy range from 30 to 100 keV. Backscattered photons flux depends on the loop’s position and on the localization of the source of primary radiation along the loop. For an isotropic distribution of primary photons, the backscattered photons’ contribution to the total flux is maximal for the loop in the center of the Sun and reduces when shifting to a limb. In the case of an anisotropic source the angle at which the contribution being maximal depends on the degree of anisotropy and on X-ray directivity in the source. Citation: E.P. Ovchinnikova, Yu.E. Charikov, A.N. Shabalin, G.I. Vasilyev, The contribution of the albedo for photons to the intensity of the hard X-ray emission of solar flares, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 140–151. DOI: 10.18721/JPM.10313 10.18721/JPM.10313 523.985.3 solar flare hard X-ray electron kinetics compton scattering https://physmath.spbstu.ru/article/2017.37.13/ 13_140_151_10_3_2017.pdf

RAR RUS 152-160 Savchenko Mikhail Mikhail.Savchenko@mail.ioffe.ru Vatagin Pavel pavelvat@gmail.com Lazutkov Vadim Vadim.Lazutkov@mail.ioffe.ru Skorodumov Dmitriy Dmitri.Skorodumov@mail.ioffe.ru Kudryavtsev Igor Igor.Koudriavtsev@mail.ioffe.ru Charikov Yuri y.charikov@yandex.ru The two solar flares diagnostics based on the soft X-ray emission recording The time history of the temperature and the emission measure of the solar flare plasma have been studied relying upon the experimental data on the soft X-rays recorded by the IRIS spectrometer on June 29, 2002 (F1) and March 27, 2003 (F2). F1 was a thermal one and was not accompanied by hard X-rays. This data analysis revealed that at least two sequential energy-release processes occurred during F1 event. F2 event took place behind the limb, so only the top part of the flare loop being the soft X-ray source was recorded by the satellite-based spectrometer. From this data analysis it appeared that the fast plasma heating occurred in the initial stage of F2 and then the flare region expanded and the emission measure of flare plasma increased. Citation: M.I. Savchenko, P.V. Vatagin, V.P. Lazutkov, D.V. Skorodumov, I.V. Kudryavtsev, Yu.E. Charikov, The two solar flares diagnostics based on the soft X-ray emission recording, St. Petersburg Polytechnical State University Journal. Physics and Mathematics. 10 (3) (2017) 152–160. DOI: 10.18721/JPM.10314 10.18721/JPM.10314 УДК 523.985.3 solar flare hot plasma flare loop X-ray emission https://physmath.spbstu.ru/article/2017.37.14/ 14_152_160_10_3_2017.pdf