2304-9782, 2618-8686, 2405-7223 3 201 2014

UNK RUS 9-19 Faddeev Ludvig.D. My life in the quantum fields (the report at the General Meeting of RAS on March 27, 2014) https://physmath.spbstu.ru/article/2014.25.1/ 01_9_19_3_201_2014.pdf

RAR RUS 20-34 St. Petersburg State University Grishchenko Alexei gai-gr@yandex.ru Peter the Great St. Petersburg Polytechnic University Melnikov Boris melnikovboris@mail.ru Peter the Great St. Petersburg Polytechnic University Semenov Artem semenov.artem@googlemail.com Finite element modeling of bone deformation at the submicroscopic scale By means of the direct finite element simulation and homogenization the analysis of variation influence in the morphological characteristics (hydroxyapatite crystals disorientation, sizes and orientation of mineral bridges, mineralization) on mechanical properties of the representative volume element of bone at the nanoscale (at the collagen fibrils level) is carried out. The morphological model of bone with an account of the mineral bridges between the associations of the hydroxyapatite crystals is used in the computations. The purpose of the paper is to analyze the influence of the nanostructure parameters of bone on its elastic and strength properties. Such studies are important for the creation of artificial bone-substitute materials. The analysis of the stress-strain state of the RVE of bone tissue has been performed in order to determine the location of the most critical points and deformation mechanisms of bridges. The most loaded elements are the corners of conglomerates and corners of bridges. Taking account of the bridges leads to the decrease of the von Mises stresses in the corner of the conglomerate and to the increase of the effective elastic moduli in the vertical and horizontal directions. The effects of orientation of conglomerates and bridges on the stress state of the representative volume were analyzed. The influence of the bone mineralization on the effective elastic moduli and stress state were investigated. The comparison of obtained results with experimental data was performed and discussed. 539.32 bone tissue representative volume element homogenization boundary condition of periodicity misalignment of conglomerates intercrystalline bridge elasticity viscoelasticity finite element method https://physmath.spbstu.ru/article/2014.25.2/ 03_30_37_4_206_2014.pdf

RAR RUS 35-46 0000-0003-2016-8612 Peter the Great St. Petersburg Polytechnic University Lukin Alexei lukin_av@spbstu.ru

Russian Federation, 195251, St. Petersburg, Polytechnicheskaya, 29

Peter the Great St. Petersburg Polytechnic University Modestov Victor modestov@compmechlab.com Finite element modeling and an analysis of the stress-strain state of reinforced concrete structures One of the tasks for engineers in the field of feasibility of strength of designs and constructions of nuclear power plants is the analysis of reactor buildings safety under dynamic loads such as earthquakes, fall aftereffects of a heavy passenger plane, etc. An application of linear-elastic material models and equations of the linear theory of elasticity results in excessively conservative outcomes, designs and constructions parameters being non-optimal economically and technologically. Reinforced concrete bearing elements of the reactor building of the nuclear power plant with wall thicknesses of up to two meters, according to requirements of standard documentation, offers a clear example. This work considers the present-day methods of computational mechanics and uses them for the analysis of stress-strain state of reinforced concrete designs taking into account nonlinear physical and mechanical properties of concrete and the cracking phenomenon. 539.42 NPP reinforced concrete stress analysis finite element method https://physmath.spbstu.ru/article/2014.25.3/ 03_30_37_4_206_2014.pdf

RAR RUS 47-56 Peter the Great St. Petersburg Polytechnic University Petrichenko Mikhail fonpetrich@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Kharkov Nikita nkharkov@mail.ru Boundary problems for the Crocco equation in the transport theory The Crocco boundary problem is more convenient than the Fourier limit problem when either is applied to the transfer problem of passive and conservative tracers for a number of advantages given below. Firstly, the concentration density distribution is generally sought on the standard compact interval from 0 to 1 in the distribution class of the limited growth instead of a semi-infinite interval. Secondly, the dual variational formulation of the problem being equivalent to the marginal one is admitted, and it reduces the solutions topology from C(2)(0, 1) to W2 (1)(0, 1). Thirdly, there are simple invariants of the solution which are convenient for estimating the solution norms and have a simple interpretation for moments of the density distribution. And finally, the Crocco boundary problem is “insensitive” to the nonlinearity of the equation coefficients. In this problem with piecewise-constant coefficients boundary conditions on the contact within the (0, 1) interval of variation in the density distribution are equivalent to the transversality conditions. The paper presents the demonstration of these arguments and the solution examples of the limiting problem for the Crocco equation with a power variation in the transfer coefficient. 501, 530.1 boundary problem solution extreme condition weak topology duality contact boundary https://physmath.spbstu.ru/article/2014.25.4/ 04_47_56_3_201_2014.pdf

RAR RUS 57-73 Peter the Great St. Petersburg Polytechnic University Chabanov Vladimir vtchabanov@mail.ru

29, Politechnicheskaya St., St. Petersburg, 195251, Russia

Peter the Great St. Petersburg Polytechnic University Zhukov Victor vic-zhukoff@yandex.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Сalculation and design of EMAT for ultra-sonic nondestructive testing The article focuses on the design of electromagnetic acoustic transducer (EMAT) for ultrasonic nondestructive testing of metal products. Some theoretical calculations of a number of the inverter parameters have been carried out; the influence of the screening, the transducer sensitivity dependence on the gap between EMAT and the testing surface have been considered. The article also includes theoretical calculations of magnetic field distribution and parameters of EMAT magnetic system. The measurement results of radiation patterns of direct and oblique EMAT for a number of wave types at different frequencies are given. The experimental and theoretical data were compared. The EMAT radiation directivity dependence on the number and the relative positions of the conductors carrying a current is also presented. The results of those studies can be used in optimizing the EMAT parameters in their design. 534.16 ultrasonic non-destructive testing electromagnetic acoustic transducer (EMAT) ultrasonic wave SV- and SH-polarized waves directional diagram https://physmath.spbstu.ru/article/2014.25.5/ 05_57-73_201_2014.pdf

RAR RUS 74-81 Golovkov Oleg Kuptsova Galina Ryazan State University named for S.A.Yesenin Stepanov Vladimir vl.stepanov@365.rsu.edu.ru Stationary solution of the  Tang – Statz – Demars system of equations for YAG:Nd-laser 621.373.826 wavelength YAG : Nd laser spectrum of generations laser mode Tang – Statz – Demars equations https://physmath.spbstu.ru/article/2014.25.6/ 06_74_81_ph3_201_2014.pdf

RAR RUS 82-91 St. Petersburg Academic University of the Russian Academy of Sciences Bayramov Farid pharrid@gmail.com

8/3 Khlopina St., St. Petersburg, 195220, Russia

Poloskin Egor е.poloskin@mail.ioffe.ru Chernev Andrei chernev.andrew@gmail.com Toporov Vladimir toporov@mail.ioffe.ru Dubina Michael michael.dubina@gmail.com Lähderanta Erkki Erkki.Lahderanta@lut.fi Lashkul Alexander Lipsanen Harri Bairamov Bakhysh bairamov@mail.ioffe.ru Raman scattering of light in oligonucleotides The purpose of our investigation was to develop a highly sensitive technique of the Raman light scattering spectroscopy with high spectral resolution for later use as an experimental procedure for closer examination of molecular structure and clarification of the chemical nature of intermolecular and intramolecular interactions in synthetic oligonucleotides.  This task has been accomplished with optimal results. High spectral resolution spectra being sensitive to secondary, tertiary, and quaternary structures were obtained by a highly sensitive method of non-resonant Raman scattering of light in biomacromolecules through the example of single-stranded short oligonucleotides (20G, 20T), where d – deoxynucleotide, G – guanine, T – thymine.  The high-quality compounds involved were synthesized using the solid-phase phosphoroamidite method. The detection of narrow spectral lines allowed to determine the characteristic scale of times and gave new opportunities for studying the dynamics of fast relaxation processes of vibrational motions of atoms in biomacromolecules.  The full width at its half-height for one of the narrowest lines (1355.4 cm–1) was found to be 14.6 cm–1; this line belongs to the vibrations of methyl group of dT. The corresponding lifetime was equal to 0.38 ps. 535.375.51; 577.2.08 raman scattering of light oligonucleotides solid-phase synthesis phosphoroamidite method https://physmath.spbstu.ru/article/2014.25.7/ 07_82-91_ph3(201)2014.pdf

RAR RUS 92-109 Ivankov Alexey a.vnkv1@gmail.com The software system for real-time investigation of autocontrol mechanisms of transcranial blood circulation The paper presents architecture and details of software implementation of a client-server system developed to investigate the hemodynamics in the brain in real-time mode. That is our own implementation of distributed registering, recording, an analysis of blood flow velocity (BFV), arterial blood pressure (BP). Input signals (BFV, BP) are treated as quasiperiodic stochastic processes. The analysis is performed by spectral methods of stochastic processes theory. FFT algorithm is in use to get spectra estimates. Modified Welch estimator is applied to evaluate consistent estimates of harmonics amplitudes. GUI is implemented in client software to display input signals and their estimates. The results of the software clinical testing in which course we studied the M-wave phenomenon are given. 61:577.3; 004.415.2.031.43 client-server architecture GUI hemodynamics investigation M-wave adaptation of nonparametric Welch method consistent estimate of spectra https://physmath.spbstu.ru/article/2014.25.8/ 08_92-109_ph3(201)2014.pdf

RAR RUS 110-117 Peter the Great St. Petersburg Polytechnic University Vinnichenko Maxim mvin@spbstu.ru Sofronov Anton sofronov@rphf.spbstu.ru J-6066-2013 35403302800 0000-0003-3947-4994 Peter the Great St. Petersburg Polytechnic University Firsov Dmitry firsov.da@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Dremov Sergei sales@atcsd.ru Ter-Martirosyan Aleksandr sales@atcsd.ru Investigation of photoditazin optical properties for expanding possibilities of photodynamic therapy Photodynamic therapy is a promising method for diagnostics and treatment of cancers of varying localization. Photodynamic diagnostic systems are based on fluorescence detection of photosensitizers. One of the much used photosensitizers is photoditazin, but it is characterized by too small fluorescence-absorption spectral separation. This property involves considerable difficulties in spectral selection of fluorescent emission and exciting laser radiation when working out diagnostic systems. Optical properties of photoditazin have been studied in this work. The absorption spectra were recorded to refine the spectral positions of line maxima. The efficient fluorescence in the spectral range between 670 and 800 nm was found to be obtainable under radiant excitation with not only conventional wavelength (660 nm) but with 405 nm wavelength as well. If the latter is the case the spectral selection of exciting radiation and fluorescent emission becomes much simpler. The studies conducted allowed us to determine requirements for spectral optical elements of photodynamic diagnostic systems. The fluorescence excitation with laser radiation at 405 nm wavelength was shown to be available for diagnostic systems with limited depth of light penetration into tissue. 57.043 photodynamic therapy photoditazin photosensitizer fluorescence photodynamic diagnostics https://physmath.spbstu.ru/article/2014.25.9/ 09_110-117_ph3(201)2014.pdf

RAR RUS 118-125 Peter the Great St. Petersburg Polytechnic University Petrichenko Mikhail fonpetrich@mail.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Additive and multiplicative doubling variables in autonomous equations The paper analyzes the Cauchy problem for a dynamic equation or for a dynamic system (1) of equations. In doing so, we take a flow and a tangential space Tx, the flow being the dynamic system or mapping X basis of segregation of Em subset on the Tx layer or a trivial tangential segregation. The segregation is given by diffeomorphism from X on E1, of Crr(T) class, r ≥ 1. The aim of this work is to elucidate the possibility of embedding this segregation into the field of extremals. A necessary and a sufficient condition for a trivial embedding is formulated as the intensification of Liouville’s condition in order to keep the phase volume or a condition of existence of invariant measure. The application of this condition allows to construct the dynamic system energy. The distribution which is a dual of Hamiltonian gives the Lagrangian density. In this manner a variational problem is obtained, in which the initial system plays the role of an intermediate integral and of coordination conditions for LaGrange’s system of equations. Procedures of different types of doubling variables (additive and multiplicative, external and internal) have been used in non-trivial embedding of the initial Cauchy problem characteristic into the field of extremals. Multiplicative doubling is analogous to the application of the integrating factor, and the additive one is identical to the addition of equations in variations to the initial system. 517.2 + 512.8 dynamic system flow field of extremals segregation basis of segregation diffeomorphism Hamiltonian Lagrange equations https://physmath.spbstu.ru/article/2014.25.10/ 10_118_125_ph3_201_2014.pdf

RAR RUS 126-130 Khokhlyuk Vitaly The group problem of minimization This problem was shown previously. The algorithm for reduction of an integer basic matrix to a normal form was used in the process. The speedup of calculations in this algorithm is gained due to the Euclidian algorithm. The following questions are considered in this article: (i) the statement of the group problem of minimization for a finite Abelian group; (ii) the numerical solution of this problem; (iii) the representation of the group elements is given for a cyclic group and for a direct sum of cyclic groups; (iiii) recurrence relations for the value function and the index function; (iiiii) calculation of the coefficients of the inequation, giving the facet of the polytope of the group equation; (iiiiii) a statement and a proof of the theorem on the steps number estimation. The recurrence relations and the theorem mentioned are the theoretical basis for the validation of the computational schemes. 519.854 finite abelian group cyclic group direct sum minimization group equation group minimization problem recurrence relation estimation of steps number polytope polytope facet https://physmath.spbstu.ru/article/2014.25.11/ 11_126-130_ph3(201)2014.pdf

RAR RUS 131-138 Khokhlyuk Vitaly The algorithm for completing the standard table The present article describes the computational scheme for numerical solving practical and theoretical problems. This scheme realizes the algorithm for completing the standard table (from top to bottom and from left to right). Among the computation features of this scheme are computer memory saving, the possibility to estimate the number of executed operations, parallelization of computations. The calculating formulae used in the scheme are given and the work of the algorithm for completing the standard table is illustrated with three numerical examples. The first example describes the simplest case when every coefficient of the group equation induces the whole finite group. The second example describes the general case. There could be some group elements among the coefficients of the group equation, which order is smaller than the finite group one. The third example shows that not all the points defining the hyperplane are the vertices of the polytope of the group equation. Note that in the applications the coefficients of the inequation, which defines the face of the polytope, are calculated with the filling of the standard table (this inequation is called the cut or the valid inequation in discrete optimization). 519.854 algorithm computational scheme computer memory number of executed operations calculating formula algorithm for completing standard table vertex of polytope facet of polytope https://physmath.spbstu.ru/article/2014.25.12/ 12_131_138_ph3_201_2014.pdf

RAR RUS 139-147 Pashkovsky Alexander alecsandr_607@rambler.ru Pashkovsky Vladimir Phan models of electric field of nucleons and electrons In this article, we construct a model which describes the potential of electric charges distribution using degenerate partial differential equations. It has been proved that the potential of the electron cloud in the hydrogen atom being in the ground state and a hydrogen atom itself can be described by such equations. This description obviates the need to use the notion of a point charge. The medium properties are modeled by the equation coefficients, which can turn into infinity, solutions being sought in a certain class of functions. We name the constructed models “phan models”. We put forward a construction technique of phan models for different media containing divided charges, such as colloids and biological media. The models may be used in suprachemistry to calculate force interactions between the particles. Phan models are close to the Maxwell ones. Their applications are promising for cases when the quantum-mechanical calculations are too complex and conventional electromechanical models are not able to reflect accurately the medium properties. The examples given show the possibilities for the further development of phan theory. 539.1.01 фан фановая модель нуклон электрон атом водорода точечный заряд потенциал вырождающееся уравнение с частными производными коллоидный раствор супрахимия https://physmath.spbstu.ru/article/2014.25.13/ 13_139_147_ph3_201_2014.pdf

CHR RUS 148-153 Sochava Alexander sochava@radio.rphf.spbstu.ru 7006360562 Peter the Great St. Petersburg Polytechnic University Cherepanov Andrey hsapst@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Zernov Nikolai zernov@paloma.spbu.ru Bityukov Alexander XXVII Всероссийская научная конференция студентов-радиофизиков The paper discusses the 17th All-Russian scientific conference of undergraduates specializing in radiophysics, which took place on April, 22–23, 2014 in Petrodvoretz in the educational center of Saint Petersburg State University (SPbSU). About forty undergraduates and postgraduates and lecturers from Saint Petersburg’s institutions of higher education took part in the conference. The most number of reports were presented by SPbSU (9) and SPbSPU (5), and their total number was 35. The reports presented were written on a diverse range of subject matter, such as vibration theory, radiation and propagation of electromagnetic waves, electronic devices and systems, quantum radiophysics, and physical phenomena studied by radiophysical methods. Two reports from SPbSU got the 1st degree awards: (i) I.V. Ageev's “The short review of results of high-temperature measurements of electromagnetic radiation scattering intensity in glasses and their melts”; (ii) E.A. Danilogorskaya's “On the horizontal gradients contribution in errors of object positions establishment with global navigation satellite systems”. 537.86 scientific conference undergraduate specializing in radiophysics scientific report award for conference https://physmath.spbstu.ru/article/2014.25.14/ 14_148_153_ph3_201_2014.pdf

CHR RUS 154-166 57034855700 0000-0002-4088-4707 Peter the Great St. Petersburg Polytechnic University Antonov Valerii hmath@spbstu.ru

Russia, 195251, St.Petersburg, Polytechnicheskaya, 29

Vasiliev Yuri president@spbstu.ru Department of higher mathematics, St. Petersburg state polytechnic university. History and the present The article outlines the main stages of formation and development of chair of higher mathematics - one of the largest departments universities of Russia. Much attention is paid to the history of development of the Polytechnic Institute, an integral part of of which since its foundation is the Chair of Higher Mathematics. Along with the story much attention is paid to modern state of mathematics education at the Polytechnic University, as well as the challenges facing the staff of the department at the moment. 51:378.662(470.23-25) higher mathematics professor department scientists algebra functions science https://physmath.spbstu.ru/article/2014.25.15/ 15_154-166_ph3(201)2014.pdf