2304-9782, 2618-8686, 2405-7223
St. Petersburg Polytechnic University Journal. Physics and Mathematics
2
242
2016
RAR
RUS
9-18
Romanov
Nikolay
nikromanov.90@gmail.com
Zakharova
Irina
Peter the Great St. Petersburg Polytechnic University
zakharova@rhpf.spbstu.ru
The composition and the structure of thin films based on metal porphyrin complexes
Thin films based on CuTPP, ZnTPP and FeClTPP (ТРР – TetraPhenylPorphyrin) complexes and manufactured by vacuum deposition under quasi-equilibrium conditions have been investigated. The hot-wall epytaxy method was chosen for the preparation of samples. The structure of objects and their composition were examined by scanning electron microscopy (SEM) and energy dispersive microanalysis (EDX). The CuTPP film was established to form whiskers about 20 nm in diameter and 5 μm in length. The structural features and morphology of ZnTPP and FeClTPP films’ surface were revealed. The theoretical interpretation of obtained results was proposed that made possible to relate the film structure with its composition.
10.5862/JPM.242.1
538.951
organic electronics
thin film
metal-porphyrin complex
https://physmath.spbstu.ru/article/2016.32.1/
01_9_18_2_242_2016.pdf
RAR
RUS
19-26
Slutsker
Alexander
Polykarpov
Yuri
Karov
Dmitry
Peter the Great St. Petersburg Polytechnic University
dmkarov@yandex.ru
Elastic strain energy behavior in the polymer nanocrystals
In the paper, the changes in the axial and the contour lengths of skeletal interatomic bonds in the chain molecules of polyethylene nanocrystals have been measured using X-ray diffractometry and Raman spectrometry. In the course of the measurements the samples were subjected to stretching and heating (mechanical and thermal actions). The measured force and temperature dependences were analyzed and the calculated description of the polymer nanocrystal’s strain was inferred from them. In so doing the original results were obtained for the thermal action. The potential energy components related to both the skeletalbond stretching and the chain-molecule bending were determined for the strained polymer crystal. The sharp distinction between the ratios of these components for the object under mechanical and thermal actions was found.
10.5862/JPM.242.2
536.4, 539.3
stretching
heating
axial length of chain molecule
potential energy
https://physmath.spbstu.ru/article/2016.32.2/
02_19_26_2_242_2016.pdf
RAR
RUS
27-36
Pankin
Dmitry
dima-pankin@mail.ru
Smirnov
Mikhail
smirnomb@rambler.ru
The applicability of Raman spectroscopy for estimation of interfaces thickness in the AlN/GaN superlattices
Polar optical phonons in quaternary nitride-based superlattices have been investigated in the framework of dielectric continuum model. In the considered systems, the superlattice period consisted of two main layers GaN and AlN and two interstitial layers Al0.5Ga0.5N. Such structure simulates binary superlattices with diffuse interfaces. The presence of the finite thickness interface layers was shown to give rise to appearance of several low-intensity additional phonon modes active in Raman scattering; frequency splitting of such modes is sensitive to relative thickness of intermediate layers. The fundamental Raman-intense polar phonon modes were also stated to be independent on the interface thickness, and these modes being very sensitive to the main layer thicknesses.
10.5862/JPM.242.3
538.911
polar phonon
dielectric continuum model
nitride-based superlattice
https://physmath.spbstu.ru/article/2016.32.3/
03_27_36_2_242_2016.pdf
RAR
RUS
37-43
Nelasov
Ivan
nelasow@bsu.edu.ru
Lipnitskii
Aleksey
lipnitskii@bsu.edu.ru
The study of Cu/Nb interface diffusion using molecular dynamics simulation
The peculiarities of interfacial boundary diffusion where the boundary goes between nonmiscible metals with body-centered cubic (BCC) and face-centered cubic (FCC)lattices have been studied taking, as a case in point, the Cu/Nb system, and using the molecular dynamics method. The diffusion atomic displacements were shown to occur mainly near the mismatch dislocations and their intersections. The diffusion of the high-melting component was found to be characterized by high anisotropy with the predominant atomic displacement along the dense-packed direction in the interfacial boundary plane being common to FCC and BCC lattices with the Kurdyumov-Sachs mutual orientation.
10.5862/JPM.242.4
539.219.3
interface diffusion
copper-niobium.
molecular dynamics
Kurdyumov-Sachs mutual orientation
https://physmath.spbstu.ru/article/2016.32.4/
ph_2_2016.37_43.pdf
RAR
RUS
44-54
Kartamyshev
Andrey
andrei_kart@mail.ru
Dat
Duy
duydat_bel@yahoo.com
Lipnitskii
Aleksey
lipnitskii@bsu.edu.ru
The interactions between some impurity atoms and vacancies in titanium and aluminum metals: an ab initio study
In this paper, we present binding energies between an atom of hydrogen (H), carbon (C), nitrogen (N) and oxygen (O) with a vacancy in the hexagonal closedpacked (HCP) lattice of titanium (Ti) and the face centered cubic (FCC) lattice of aluminum (Al), calculated using the density functional theory (DFT). We have also investigated the trapping of up to five hydrogen atoms by a vacancy and the reduction of the vacancy formation energy, due to the formation of a hydrogen–vacancy complex. We used the molecular-dynamics modeling with consecutive relaxation at 0 K to obtain an atomic configuration of the vacancy–impurity complex, corresponding to the global energy minimum. According to our calculations, C–V, H–V, C–(H–V), N–(H–V) complexes are stable in the Al lattice with only H–V complex being stable in Ti. The formation of C–(H–V) and N–(H–V) complexes in the Al lattice results in the negative vacancy formation energy. The formation of H–V complex decreases the vacancy formation energy by 0.26 eV in the Ti lattice. A vacancy in the Ti lattice can trap up to four hydrogen atoms.
10.5862/JPM.242.5
538.9
titanium
aluminium
vacancy
impurity
density functional theory
https://physmath.spbstu.ru/article/2016.32.5/
ph_2_2016.44_54.pdf
RAR
RUS
55-64
Pavlov
Vladimir
vova-gt@yandex.ru
Krasnova
Nadezhda
Peter the Great St. Petersburg Polytechnic University
n.k.krasnova@mail.ru
Synthesis of electrostatic fields for transportation of charged particle beams
In the article, an approach to creation of corpuscular-optical devices for transportation and transformation of charged particle beams has been elucidated. These devices are able to optimize and create the most convenient configuration of ionic or electron path. The approach relies upon the inverse dynamics problem formulated on a basis of the Hamilton-Jacobi equation. The motion in the symmetry plane of a threedimensional (3D) field was considered. The problem was solved by analytical methods. An algorithm for construction electric fields providing the particle motion on the desired trajectories was described. А key to this algorithm lies with a concept of conformal transformation from complex variable theory. This procedure was illustrated by examples. Quadratic potential was chosen as a basis. Three functions of conformal transformation were considered, they providing the rotation of the focused charged particle beam at fixed angle, the transformation of divergent flow to parallel one. The calculated two-dimensional potentials were extended into 3D-space by power series expansion on transverse coordinate. Device embodiments were suggested on a basis of the calculated field structures.
10.5862/JPM.242.6
537.533.3:537.291
inverse dynamics problem
charged particle optics
conformal transformation
ideal focusing
https://physmath.spbstu.ru/article/2016.32.6/
ph_2_2016.55_64.pdf
RAR
RUS
65-71
Korablev
Vadim
korablev@spbcas.ru
57193675419
Dubov
Victor
Peter the Great St. Petersburg Polytechnic University
dubov@spbstu.ru
The formation of the angular dependences of the inelastically scattered electrons by their quantum transport near the surface of a solid
Features of the formation of angular dependences of electrons emitted from a disordered solid and experienced inelastic scattering have been considered. Such fine details of the dependences are formed by the processes of the quantum transport of emitted particles. We took the cases of two-particle and multi-particle inelastic processes. Qualitative and quantitative assessments of the relative contributions of the different groups of particles were carried out. The effects related to quantum electron transport were shown to be generally more pronounced in the case of registration of electrons, generated inside the solid in the inelastic scattering of particles of the primary beam. This is true both to the electrons generated by ionization processes and Auger electrons. The obtained results point up the possibility of using this effect in the applied electron spectroscopy.
10.5862/JPM.242.7
530.145+539.1
electron scattering
quantum transport
weak localization
surface of a solid
https://physmath.spbstu.ru/article/2016.32.7/
ph_2_2016.65_71.pdf
RAR
RUS
72-81
Egorova
Polina
bio_polya@mail.ru
Vlasova
Olga
Peter the Great St. Petersburg Polytechnic University
olvlasova@yandex.ru
O-7971-2016
7006214225
0000-0001-7006-6951
Bezprozvanny
Ilya
UT Southwestern Med Ctr, Dept Physiol
mnlabspb@gmail.com
Dallas, USA
The limitation of the Purkinje cell’s impulse activity in the laboratory mice’s vermis by in vivo activation of SK channels
This study tested the effect of intravenous injections of CyPPA [the activator of small conductance calcium-activated potassium channels of types 2 and 3 (SK2/SK3)] on the firing frequency of cerebellar Purkinje cells of laboratory male mice at the age of 6 months via the method of extracellular in vivo recordings from Purkinje cells. This method revealed that 1 mM CyPPA tail vein injections lead to progressive reduction of Purkinje cells firing frequency. Thus, simple spike’s firing frequency decreases by 16% in one hour after injection, by 49% in two hours after injection, and by 61% in three hours. The obtained results confirmed the hypothesis about the important role of SK channels in the maintenance of Purkinje cells spontaneous activity in vivo. Since deterioration of biophysical and physiological functions is observed in many cerebellar ataxias, SK channels can serve as a potential target for the treatment of such disorders.
10.5862/JPM.242/8
577.35
ataxia
cerebellum
purkinje cells
SK channels
cyppa
https://physmath.spbstu.ru/article/2016.32.8/
ph_2_2016.72_81.pdf
RAR
RUS
82-86
Oktyabrskiy
Valeriy
vokt@yandex.ru
A new opinion of the greenhouse effect
The article analyzes the correspondence between actually occurring physical and chemical processes and the concept of the greenhouse effect. The absorption of the solar radiation by the gases existing in the Earth atmosphere has been examined. It was demonstrated that, despite the absorption of radiation from the Earth’s surface in the middle and long-wave infrared (IR) regions, there is a strong absorption of the overtones and combined frequencies of water vapor in the solar radiation (visible and near IR regions), i.e. the transmittance bandwidth of ‘the glass greenhouse’. Thus, the Earth atmosphere does not really function as a greenhouse, and the terms ‘greenhouse effect’ and ‘greenhouse gases’ lost their original meaning and have remained symbolical.
10.5862/JPM.242.9
535-1/3
absorption spectrum
greenhouse effect
greenhouse gas
water vapor overtone
https://physmath.spbstu.ru/article/2016.32.9/
ph_2_2016.82_86.pdf
RAR
RUS
87-94
Khokhlyuk
Vitaly
Principles for constructing the disjunctive cuts
This article focuses on solving the disjunctive problem. Various methods of constructing the disjunctive cuts (DC) from the logical limitations on the linear inequalities have been presented. A general principle of DC and a principle making possible to strengthen these cuts were stated. By virtue of the stated principles, solving the problems of optimization with a great number of limitations can be simplified. Two theorems were formulated and proved. Four examples illustrated various theoretical statements. The suggested principles and procedures on their basis provide the theoretical background to the elaboration of algorithms intended for the software implementation in solving the practical problems.
10.5862/JPM.242.10
519.854
mathematical logic
disjunctive problem
convex hull
closure of set
strengthening of cut
https://physmath.spbstu.ru/article/2016.32.10/
ph_2_2016.87_94.pdf
RAR
RUS
95-107
Pastukhov
Alexey
pastuhov1992@gmail.com
Prokofiev
Alexander
aaprokof@yandex.ru
Kohonen self-organizing map application to representative sample formation in the training of the multilayer perceptron
In this paper, we have considered an item of effective formation of a representative sample for training the neural network of the multilayer perceptron (MLP) type. The main problems arising in the process of the factor space division into the test, verification and training sets were formulated. An approach based on the use of clustering, that allowed one to increase the entropy of the training set was put forward. Kohonen selforganizing maps (SOM) were examined as an effective procedure of a clustering. Based on such maps, the clustering of factor spaces of different dimensions was carried out, and a representative sample was formed. To verify our approach we synthesized the MLP neural network and trained it. The training technique was performed with the sets formed both using the clustering and no doing it. The approach under consideration was concluded to have an influence on the increase in the entropy of the training set and (as a result) to lead to the quality improvement of training of MLP with the small dimensionality of the factor space.
10.5862/JPM.242.11
004.032.26
artificial neural network
Kohonen self-organizing map
clustering
sample formation
https://physmath.spbstu.ru/article/2016.32.11/
ph_2_2016.95_107.pdf
RAR
RUS
108-115
Berezin
Sergey
servberezin@yandex.ru
On analytic characteristic functions and processes governed by SDEs
We study analyticity of the characteristic function of a process defined by means of SDEs. Namely, starting with the simple case of a scalar Ito SDE we show that the corresponding characteristic function is entire. The proof is based on the Gröenwall’s inequality technique and the classic analyticity criterion in terms of moments. Further, we extend this criterion and derive a handy sufficient condition of analyticity in the multidimensional case. This condition is used to prove the corresponding general result of analyticity. We assume that the drift vector obeys the linear growth condition, and the diffusion matrix is time-onlydependent, but possibly degenerate. The approach used in the article can be extended to more general types of SDEs.
10.5862/JPM.242.12
519.213.2:519.217.4
stochastic differential equation
complex analytic function
holomorphic function
multivariate holomorphic function
https://physmath.spbstu.ru/article/2016.32.12/
ph_2_2016.108_115.pdf
RAR
RUS
116-125
Sharifulin
Albert
Poludnitsin
Anatoliy
panam.48@mail.ru
The borders of existence of anomalous convection flow in the inclined square cylinder: numerical determination
The article is devoted to the study of bifurcations of stationary convection regimes in a closed, heated from below and tilted square cylinder filled with air for cases of heat-insulated and perfectly heat-conducting sidewalls. The temperature and velocity fields were obtained using grid method for inclinations from a horizontal position up to 30 degrees in the range of Rayleigh numbers up to 20-fold excess of its critical value. The limit angle of anomalous-flow existence in the cylinder with the heat-insulated walls was established to be about 3 times greater than that in the cylinder with the heat-conducting ones. In the case of the heatconducting walls the maximum angle of the anomalous-flow existence reached 7.7 degrees at a 3.3-fold excess of the critical value of Rayleigh number.
10.5862/JPM.242.13
532.5.013.4.536.25+519.6
thermal convection
inclination of the cavity
anomalous flow
numerical simulation
https://physmath.spbstu.ru/article/2016.32.13/
ph_2_2016.116_125.pdf
RAR
RUS
126-135
Tikhomirov
Victor
Peter the Great St. Petersburg Polytechnic University
victikh@mail.ru
Russia, 195251, St.Petersburg, Polytechnicheskaya, 29
A semi-infinite crack of mode III in the bimaterial wedge
An exact solution of the antiplane problem for a semi-infinite interface crack in a piecewise-homogeneous wedge under a self-balanced load on its sides has been obtained. Three types of boundary conditions on the wedge sides were examined: the both sides being stress-free; both sides being clamped, and one side being stress-free with the second one clamped. As a result of using the Wiener-Hopf method, the solution was represented in quadratures. The Green’s functions were obtained for stress intensity factors; in the case of a geometrically symmetrical wedge structure simple formulae were found for these functions. The stress singularity in the apex of the wedge was studied. In contrast to the homogeneous wedge structure the asymptotic of the stresses near the apex was established to have sometimes two singular terms for some values of the composite parameters.
10.5862/JPM.242.14
539.3
interfacial mode III crack
bimaterial wedge
stress intensity factor
stress singularity
https://physmath.spbstu.ru/article/2016.32.14/
14_126-135_2(242)2016.pdf
RAR
RUS
136-140
Lobanov
Ivan
lobanov.111@yandex.ru
Denisov
Alexander
A.V.Denisov@inbox.ru
The exact analytical solution of the problem on the average number of spikes of the narrowband Gaussian stoсhastic process
In this article, the problem of the number of spikes (level crossings) of the stationary narrowband Gaussian process has been considered. The process was specified by the exponentially-cosine autocorrelation function. The problem had been solved earlier by S. Rice in terms of the joint probabilities’ density of the process and its derivative with respect to time, but in our article we obtained the solution using the functional of probabilities’ density (the functional was obtained by I.N. Amiantov), as well as an expansion of the canonical stochastic process. In this article, the optimal canonical expansion of narrowband stochastic process based on the work of A.P. Filimonov and A.V. Denisov was also considered to solve the problem. The application of all these resources allowed obtaining an exact analytical solution of the problem on spikes of stationary narrowband Gaussian process. The obtained formulae one could use to solve, for example, some problems about the residual resource of some radiotechnical products, about the breaking sea waves and others.
10.5862/JPM.242.15
519.21(075)
emission of stoсhastic process
density functional of probability
canonical expansion
https://physmath.spbstu.ru/article/2016.32.15/
ph_2_2016.136_140.pdf
SCO
RUS
141-144
Without
author
Vadim K. Ivanov (on the occasion of his 70th birthday)
https://physmath.spbstu.ru/article/2016.32.16/
ph_2_2016.141_144.pdf