«Вестник Южно-Уральского университета» серия «Математика. Механика. Физика» – рецензируемый журнал, публикующий на бесплатной основе оригинальные статьи, обзоры и краткие сообщения российских и зарубежных ученых, сотрудников ЮУрГУ, университетов и научно-исследовательских организаций России, посвященные актуальным вопросам математики, механики и физики. Полная версия статьи находится в сети Интернет на официальном сайте Научной электронной библиотеки eLIBRARY.RU, и в разделе сайта Южно-Уральского государственного университета «Вестник ЮУрГУ» в свободном доступе. Серия основана в 2009 году, является продолжением серии «Математика, физика, химия», издаваемой с 2001 года. Подписной индекс серии через объединенный каталог «Пресса России» – 29211, интернет-каталог агентства «Книга-Сервис» — Е29211. Периодичность издания – 4 выпуска в год. Объем 70—80 страниц, формат А4. Учредитель – ФГБОУ ВПО «Южно-Уральский государственный университет». Решением Президиума Высшей аттестационной комиссии (ВАК) Минобрнауки России от 19 февраля 2010 г. №6/6 журнал вошел в «Перечень ведущих рецензируемых научных журналов и изданий, в которых должны быть опубликованы основные научные результаты диссертаций на соискание ученых степеней доктора и кандидата наук» Журнал представлен: в Научной Электронной Библиотеке (РУНЭБ) (elibrary.ru); включен в специализированную базу данных «Российский индекс научного цитирования» (РИНЦ); Сведения о публикациях ежегодно размещаются в международной справочной системе по периодическим и продолжающимся изданиям «Ulricht's Periodicals Directory»; Выпуски размещаются в свободном доступе на Общероссийском математическом портале Math-Net.Ru. Издание зарегистрировано в Международном центре ISSN, номер ISSN 2075-809Х (Print), 2409-6547 (online) Основной целью серии «Математика. Механика. Физика» редакционная коллегия и редакционный совет серии считают публикацию оригинальных результатов научных исследований в области математики, механики и физики, а также их приложений в естественных, технических и экономических науках. Эти результаты могут быть представлены в форме как обзорных, так и оригинальных статей, а также (для молодых ученых, магистрантов и аспирантов) в форме кратких сообщений. Приоритетное право на публикацию имеют: результаты исследований аспирантов и докторантов ЮУрГУ; результаты исследований, проводимых сотрудниками ЮУрГУ, при поддержке научных фондов РФ или правительства России.
To the 70th Anniversary of Vasiliy Buchel'nikov
Vasily Dmitrievich Buchelnikov, Doctor of Physico-Mathematical Sciences, Professor, Honored Worker of Higher Education, celebrated his 70th birthday on April 3, 2025.
Copyright (c) 2025 Mathematics. Mechanics. Physics
Phase Stability and Electronic Structure of Heusler Alloys Ti2VZ (Z = Al, As, Ga, Ge, In, P, Sb, Si, Sn)
The article deals with the chemical stability, structural, magnetic, and electronic properties of Ti2VZ (Z = Al, As, Ga, Ge, In, P, Sb, Si, Sn) alloys using density functional theory methods. All compounds are found thermodynamically stable, and their stability correlates with the valence electron concentration (e/a) and decreases for heavier elements. The magnetic properties depend on composition and the degree of tetragonality: in the cubic phase, an increase in e/a reduces magnetization intensity, whereas lattice distortion increases it. Half-metallic behavior with 100 % spin polarization appears at e/a = 4 and 4,25, while Ti2VSb (e/a = 4,5) acquires a semiconducting state with a narrow gap ~0,1 eV. The results agree with PBE functional calculations and demonstrate the advantages of the SCAN functional for accurate description of complex alloys.
The Role of Impurity Ions in Nonlinear Dielectric Response Formation of Nematic Liquid Crystal Cell
The study considers the nonlinear dielectric response of a nematic liquid crystal (NLC). Odd harmonics are found in the dielectric response in the low-frequency region of the spectrum from 0.5 mHz to 600 Hz. The transporting of impurity ions causes two relaxation effects: space charge polarization and the formation of electric double layers.
On Selecting Optimal Parameters for Delay Time Measurement Using the Hong–Ou–Mandel Effect
The paper deals with the measurement error of the delay time between the arrivals at the beam splitter of two photons traveling through different channels in an optical system based on a Hong-Ou-Mandel (HOM) interferometer. We consider the source of two-photon light to be the radiation of spontaneous parametric scattering (SPS) of light of the second type. The photon delay in one of the HOM interferometer channels can be induced by a change in the optical path length due to various factors: mechanical displacement of interferometer parts, changes in the refractive index of the medium caused by temperature variations, electric fields, etc. In the scheme, the outputs of the beam splitter are connected to single-photon detectors, which send signals to a coincidence counter upon photon detection. The coincidence counter data determine the delay time. The authors determine the absolute error in estimating the delay time in terms of the biphoton spectral width, the visibility, calculated from the maximum and minimum values of the coincidence counter signal, and the estimated delay time value itself. The derived expression facilitates finding the estimated delay time value. The study reveals that for a fixed biphoton field width, the delay time corresponding to the minimum absolute error value approaches the inflection point of the coincidence-time curve with decreasing visibility. This should be taken into account when designing measuring devices based on the Hong-Ou-Mandel interferometer.
Computer Modeling of Magnetic Properties of Disordered BCC Phase of Fe100-xMex Alloys (Me = Al, Ga, Ge)
In this paper, within the framework of density functional theory for the disordered phase A2 of Fe-Me alloys (Me = Al, Ga, Ge) the magnetic exchange constants Jij are calculated and the Curie temperatures TC are estimated in dependence of the concentration of Me = Al, Ga, Ge (in the range of 0 ≤ x ≤ 14 at. %) and the crystal lattice parameter (in the range of 2,7 ≤ a ≤ 3,0 Å). The Jij distribution obtained in the paper demonstrates non-linear behavior. The highest ferromagnetic interaction in the first coordination sphere is ≈23 meV. In the third coordination sphere, antiferromagnetic exchange interaction is observed, which reaches a value of ≈ –2,5 meV. Magnetic transition temperatures calculated using the mean field approximation based on the experimental values and the a0 parameters calculated within the density functional theory show the presence of a concentration range of 4 ≤ x ≤ 8 at. % in which TC increases. The cross-section of the calculated Curie temperature distribution shows that for all studied Fe-Me alloys with the lattice parameter a0 = 2,94 Å, it is possible to construct a dependence TC(x) that is in quality agreement with the experimental one.
Algorithm for Analyzing Noisy Video Data for Autonomous Robots Navigation
Autonomous robots are widely used for various purposes, including monitoring, research, defense, emergency situations, etc. The main advantages of autonomous robots are mobility, ease of deployment and real efficiency. The problem of autonomous robot navigation based on data obtained from a video channel is relevant. The study aims to implement an algorithm for analyzing noisy video data to detect key points of navigation objects. Traditional approaches to detecting key points of navigation objects apply iterative algorithms without the use of neural networks. YOLOv11 neural network model and RGB images as input data can solve the problem. The work results in finding the coordinates for the key points of navigation objects. The algorithm test data on the dataset and data obtained from testing the demonstrator of an engine with a central body are provided. The OKS (Object Keypoint Similarity) metric is used. The study results in developing a neural network, trained to detect navigation objects and their key points. Defining the key points of objects enables to correct inertial navigation systems. The obtained neural network is resistant to various noises, including overlaps.
Preparing the Images of Complex Shape Transparent Objects to Detect Defects by the Computer Vision System
The article deals with the preprocessing of images by the computer vision system to find possible defects in transparent objects of complex shape made of amorphous materials. It is not always possible to obtain high-quality images with high contrast for such objects due to the small difference in the refractive indices of the product materials and the defect. The previously developed defect detection method is based on a modern neural network architecture and shows that image quality and contrast are critical indicators for effective defect detection. Therefore, the authors apply a special image frequency filtering technique to increase the contrast. The technique is based on dividing the image into narrow bands located perpendicular to the intensity gradient of the detail components image. One-dimensional forward Fourier transform, frequency filtering, and inverse Fourier transform are used for each band. Processing of a real image of the PS-70E (U70) insulator shows that the use of such frequency filtering reduces the contrast in the area of the components image and increases the contrast in the area of the defect image against a contrasting background. This property enables either identifying smaller size defects, or using images with resolutions up to and including 1024x1024 pixels, which can be useful when implementing computer vision systems in real industrial conditions.
Generalized Solvability of Initial-Boundary Value Problems for Quasihydrodynamic System of Equations in Weighted Sobolev Spaces
The paper considers the analog of the first initial boundary value problem for a quasihydrodynamic system of equations in the case of a weakly compressible fluid in weighted Sobolev spaces. The system is an elliptic-parabolic system: its first part is an elliptic equation for the pressure gradient, and its second part is a parabolic system for the velocity vector. The unknown variables of the pressure gradient and velocity vector belong to the principal parts of the elliptic equation and the parabolic system. The fixed part of the system is not uniformly elliptic, thus complicating the study of the problem. T.G. Elizarova and B.N. Chetverushkin introduce the system by averaging the known kinetic model. The first versions of the system are the system of quasi-gasodynamic equations. Later, Y.V. Sheretov, based on a more general equation of state, obtains another model, which is called quasihydrodynamic system of equations, and thoroughly analyses its properties. However, the issues of generalized solvability of initial boundary value problems for such systems have not been studied in detail yet. There are only some partial results. The paper aims to fill this gap. We prove generalized solvability of the system in some weight classes characterizing the behavior of solutions at t→∞ according to the Galerkin method and the obtained prior estimates. The decreasing (growing) behavior of the solution depends on the decreasing (growing) right-hand side of the system. The decrease (growth) at t→∞ of the used weight functions can be both exponential and power.
Stabilization of Solutions for the Wentzell Stochastic Dynamical System in a Circle and on Its Boundary
The paper considers the problem of stabilizing the solutions of the deterministic and stochastic Wenzel equations, which describe the filtration of a liquid in a circle and on its boundary. The authors address the issue of exponential stability and instability of the deterministic Wenzell equations solutions. They consider different signs of the parameters that describe the medium and the properties of the liquid. The instability gives rise to solving the problem of stabilization using a feedback loop. The obtained results are used in the stochastic Wenzell equations. The Nelson–Gleich derivative is considered, and a stochastic process is a solution.
The editorial team announces with deep sorrow that on January 30th, 2025, after a long illness, Honoured Professor of Moscow University, Professor of the Department of Elasticity Theory at Moscow State University, member of the editorial board of our journal Georgy Leonidovich Brovko passed away.
Method of Dispersing Silicon in a Silumin Melt Crystallizing in an Inhomogeneous Magnetic Field
This paper deals with the problem of controlling the process of silicon dispersion in a crystallizing silumin melt by means of an inhomogeneous permanent magnetic field. It is established that during crystallization of the silumin melt in an inhomogeneous permanent magnetic field, diffusive and convective flows of silicon are activated near the crystallization front. A physical and mathematical model of the process of influence of an inhomogeneous permanent magnetic field on secondary silicon ions near the crystallization front is proposed. The total flux of silicon atoms (ions) caused by two mechanisms is calculated: the first is classical diffusion caused by the silicon concentration gradient at the crystal-melt boundary; and the second is the force effect of an inhomogeneous magnetic field on magnetic dipoles of silicon near the crystallization front. Microstructural analysis of silumin specimen slits obtained during their crystallization in an inhomogeneous permanent magnetic field confirms the effect of this field on the formation of a given structure.
Contribution of Impurity Ions to Spatial-Temporal Distribution of Local Electric Field in Nematic Liquid Crystal Cell
The influence of impurity ions on the spatiotemporal distribution of the local electric field in a planar nematic liquid crystal (NLC) cell with blocking electrodes has been investigated. Numerical simulation of the switching dynamics of the NLC director has been performed using the Poisson–Nernst–Planck and nonlinear Ericksen–Leslie equations at the driving electrical voltage exceeding the Fredericksz threshold. The authors take into account the influence of the effective permittivity associated with the reorientation of the NLC director on the dynamics of electrodiffusion of impurity ions. Spectral analysis of the local electric field reveals the presence of higher harmonics caused by the spatial inhomogeneity of ionic impurity distribution. It has been proven that the presence of these harmonics in the spectral composition of the local electric field leads to a nonlinearity of the NLC director switching dynamics.
Determination of Elastic Constants of Energetic Materials based on Experimental Data on Mechanical Impact
The article addresses the problem of developing a mathematical model for the numerical analysis of potential emergency situations involving energetic materials (EMs), which are highly sensitive to mechanical and thermal loads. The mathematical model and calculations are based on dynamic and thermodynamic material properties obtained from experiments involving mechanical impact by a metallic striker on an EM. This allows the use of an elastic-plastic homogeneous medium model to describe the deformation process of the EM. The article presents the problem formulation corresponding to experiments on striker impact on the EM and describes the system of continuum mechanics differential equations in Lagrangian variables. The Prandtl–Reuss model is used to simulate plastic flow, along with material state equations and boundary conditions accounting for the mechanical and thermal interaction between the striker and the EM. Based on experimental data from the impact of a metallic striker on an octogen-containing EM, numerical modeling of the elastic-plastic flow of the EM is performed, enabling the determination of the material's elastic constants. The calculated results on the dynamics of striker penetration into the EM have shown good agreement with experimental data, confirming the adequacy of the proposed mathematical model.
Mathematical Modeling of Oxidation and Ignition Processes of Unalloyed Plutonium
The article discusses the problem of oxidation and ignition of plutonium at various temperatures. It is shown that to determine the critical conditions for the ignition of plutonium samples with a characteristic size of up to 2 cm at the stage of the steady-state thickness of the oxide layer, it is sufficient to use the outcomes of the thermal explosion theory formulated by N.N. Semenov. Calculations of the critical ambient temperature above which plutonium ignites are in satisfactory agreement with the experimental results. A model of the oxidation of a spherical plutonium sample in the form of a system of ordinary differential equations is formulated and substantiated. Using this model, it is possible to determine the time before ignition and the amount of oxidized plutonium at any given moment. The model’s operability was tested in an experiment on dynamic heating of a plutonium sample before ignition. As a result, a satisfactory correspondence of the calculated temperature value at the time of ignition to the experimentally recorded value was obtained. Based on the conclusions of the thermal explosion theory, an approach to the determination of the kinetic parameters for the reaction rate of plutonium oxidation is proposed.
Modification of the Mathematical Apparatus of almost Periodic Analysis for Processing Spatio-Temporal Data with an Ordered Argument
This paper discusses the mathematical apparatus of almost periodic analysis based on shift functions to solve the problem of identifying characteristic almost periods using vector computation. A process for converting an image from a Cartesian coordinate system to a polar coordinate system is presented, which allows structural almost periodic analysis using vector representation of the computation of the generalized shift function underlying almost periodic analysis. The process consists of two steps: the first step involves the determination of four rectangular grid nodes, for each polar grid node; and the second step interpolates the brightness values for the polar grid nodes from the rectangular grid. Thus, the image in Cartesian coordinates is converted to polar coordinates for further analysis. The mechanism for estimating a set of nearly periods in empirical data with ordered argument, represented by nonlinear oscillations with trend, is to investigate the results of matching the shift parameters on the argument Δt and the parameter τ - the nearly period in the generalized shift function. The inner summands of the generalized shift function are the result of trend exclusion. The paper considers the case of trend exclusion based on geometric progression. As a result, a modified method of calculating the results of the generalized shift function based on vector calculations is proposed in order to calculate the resulting near-periods from image slices. Such calculation method allows obtaining the results of almost periodic analysis of centric structures in images at a qualitative level and with an acceptable speed of data processing.
Representation of the Green’s Function for the Biharmonic Navier Problem
The Green's function of the biharmonic Navier problem in the unit ball is investigated. Unlike the form of the Green's function previously obtained by the author, here is a representation in which the singularity of the fundamental solution of the biharmonic equation is explicitly expressed. Then, based on the Green's function, an integral representation of the solution to the Navier problem in the unit ball is given. In conclusion, a representation of the solution to the homogeneous Navier problem is given without using the Green's function. An illustrative example is given.
Analytical Review of Neural Network Algorithms for Fire Detection in Emergency Situations
Advances in neural networks have enabled unmanned aerial vehicles (UAVs) to detect and recognize objects in real time, which has facilitated the use of UAVs autonomously in a variety of scenarios, including fire detection in emergency situations. The paper reviews a number of existing neural network-based detection algorithms, including convolutional neural networks, regional convolutional neural networks and their variants, deep neural networks with convolutional long short-term memory (ConvLSTM), methods integrating deep learning with correlation filtering through self-training, Siamese neural networks for target tracking, and the YOLO (You Only Look Once) family of algorithms. The main characteristics and differences between neural network algorithms are described, and a comparison of their performance in terms of mean average precision (mAP) and frame rate per second (FPS) is given. The conclusions of the article provide insight into the trade-offs between accuracy, speed and task-specific requirements in de
Analysis of a Screened Harmonic System under Dirichlet and Neumann Boundary Conditions
In this paper, a screened harmonic system with Dirichlet and Neumann boundary conditions in a domain with complex geometry is considered, and a method for analyzing such a system is proposed. The development of this method is especially relevant for solving boundary value problems for the screened Poisson equation in domains with complex geometry, which are used to describe various physical systems in mechanics, hydrodynamics, electrical engineering, and heat engineering. The proposed algorithm for analyzing a screened harmonic system under these boundary conditions makes a significant contribution to this area. The proposed method includes the continuation of the screened harmonic system through boundaries with Dirichlet and Neumann conditions. Then, the continuation is discretized by a system of linear algebraic equations. An asymptotically optimal analysis of the discrete continued screened harmonic system and an algorithm implementing the method for analyzing the screened harmonic system with optimal asymptotics in the number of arithmetic operations are carried out.
Application of a priori Estimates of the Integral Load of the Kirchhoff Hyperbolic Equation for its Reduction to a Linear Equation
The aim of this work is to establish a priori estimates for the integral load of the Kirchhoff equation. This equation models some nonlinear oscillatory processes. Here, the load is the rational degree m/n of a linear function of the norm of the desired solution in the space H1(Ω). To achieve the specified goal, integral transformations of the terms of the scalar product of the original equation and the time derivative of its solution are performed. The application of Gronwall-Bellman type integral inequality leads to the desired estimates. A priori inequalities limiting the integral load of the Kirchhoff equation to a known function are established. This function depends on the right-hand side of the equation and the initial conditions, as well as on the sign and type of the exponent. The article shows a method for reducing the Kirchhoff equation to a linear equation by replacing the integral load with the right-hand sides of these estimates. An example of such a reduction is given. The described method of establishing a priori estimates and subsequent reduction of a nonlinear equation to a linear one can be applied to a wide class of loaded equations containing the modulus of the integral of the rational degree of the desired function or its derivative
To the 80th Anniversary of Sergey Gurevich
Editorial staff of the journal "Bulletin of SUSU. The series "Mathematics. Mechanics. Physics" cordially congratulates Sergey Gurevich, Doctor of Engineering Sciences, Professor, Honored Worker of Higher Education, on the 80th anniversary! A respected and beloved teacher by colleagues and students, a prominent scientist who has made a great contribution to the fundamental theory of the interaction of pulsed laser, electromagnetic and acoustic fields in ferromagnetic metals at magnetic phase transition temperatures, and to the creation of the physical foundations of high-temperature and high-speed methods and means of contactless acoustic quality control of metal products, he enjoys well-deserved authority in the scientific community not only in our country, but also abroad. Congratulations to Sergey Yurievich on this significant date, we wish him health and longevity, creative inspiration, success and new achievements for the benefit of science and education.
To the 70th Anniversary of Aleksey Kaperko
The Editorial Board of the scientific journal "Bulletin of SUSU" and the members of the editorial Board of the series "Mathematics. Mechanics. Physics" sincerely congratulates Alexey Kaperko, twice winner of the Russian Government Prize in science and technology, Deputy Chairman of the Expert Council of the Higher Attestation Commission for Management, Computer and Information Sciences at the Ministry of Education and Science of the Russian Federation, on his 70th birthday and wishes him happiness, well-being, new bright creative successes and achievements!
The Effect of Electromagnetic Pulses on Surface Roughness and Fluctuations in Electrical Conductivity of Metal Films
The effect of pulsed electromagnetic fields on metal films, which are the basis of modern micro- and nanoelectronics, can lead to changes in their conductivity characteristics and surface properties. The paper aims to study the effect of electromagnetic pulses on the surface condition of thin metallic films of Bi, Cr and Fe and to investigate the effect of electromagnetic pulses on their conductivity and conductivity variations of the films. Surface roughness measurements were performed using a SOLVER PRO probe scanning microscope. In order to study the fluctuations of the film conductivity, a setup was set up that allowed measurements to be made around the clock for several months. The samples were exposed to nanosecond electromagnetic pulses without carrier frequency for 30 minutes. It was found that such exposure most strongly changed the surface roughness of chromium film, to a lesser extent - bismuth film, and for iron film exposure did not cause significant changes in the surface. The iron film also proved to be the most resistant to exposure in the conductivity study. Its resistivity and variation remained virtually unchanged. Exposure of the film to bismuth resulted in a 2–3 times decrease in the average number of conductivity jumps and bursts. Exposure to chromium film resulted in a similar effect and a twofold decrease in the level of small-scale fluctuations of electrical conductivity.
Evolution and Destruction of the Crystal Growth Line in a Supercooled Melt
The paper studies the macroscopic shape of the crystal growth line in a supercooled melt of a pure substance. The analysis focuses on the spatial heterogeneity of supercooling at the crystallization phase boundary. The paper shows that there is a threshold value of the heterogeneity parameter, and this threshold corresponds to the cellular structure of the crystallization front which is periodic along the coordinate transverse to the growth direction. The ratio of the structure period to the curvature radius of an individual cell is equal to π. The tip of the growth line is wedge-shaped on both sides of the threshold. When crossing the threshold, bifurcated situations are observed, since the cells are an intermediate structure between the flat front and the dendrites. The paper analyses the case when the small value of the first order of smallness is the angle between the normal and the symmetry axis of the growth line. Under this approximation, the growth equation has the form of the Burgers equation. A new physical interpretation is given to the exact solutions of this equation known in the literature, which allows considering the following processes: a disturbance wave caused by the curvature rupture; a destruction wave is a precursor of tip splitting; a rupture is a strong discontinuity of the sharpness angle; overturning of the growth line is a precursor to the tip neck introvolution. The paper comprehensively analyses stable and unstable ruptures of the growth line. It reveals that the differences between the blunting of the tip behind the rupture and overturning are explained by the direction of the transition through the threshold value of the heterogeneity parameter. The paper gives calculation examples illustrating the properties of the velocity of disturbance and destruction waves.
The Comparative Results of the Thermodynamic and First-Principle Modeling of Disordered Solutions of the Fe–V System
Experimental studies have shown that the precipitation of vanadium carbide significantly increases the hardness of steels. However, little is known about the process itself. The article presents the calculations of a number of energy parameters within the framework of density functional theory. This allows us to understand the formation of vanadium carbides and to describe the energy of their boundary with the ferrite phase.
Notes on Formulas for the Rayleigh Wave Velocity
The paper derives the expression for the velocity of surface waves on the boundary of an elastic half-space (Rayleigh waves) through the velocities of volume elastic waves. It presents the generalized D. Nkemzi and P.G. Malischewsky’s formulas, proposes the solution to the equation expressed through trigonometric and hyperbolic functions and considers some approximate formulas.
Structure and Electronic Properties of Fluorographene and Fluorographite Crystals
The paper presents the study of the structure and electronic properties of two-dimensional and three-dimensional crystals composed of monolayers of graphene polymorphs L6, L4-8, L3-12, L4-6-12, L5-7 functionalized by fluorine atoms with various types of attachment of fluorine atoms. It reveals that the interlayer distances in the studied crystals vary within a wide range from 4,73 to 5,96 Å and volumetric densities vary from 2,43 to 3,98 g/cm3. The value of the band gap in three-dimensional fluorographite crystals is on average 0,4 eV less than the band gap in the corresponding two-dimensional fluorographenes. The studied three-dimensional structures demonstrated a pattern: with an increase in the interlayer distance, the energy of the interlayer interaction decreases, and the volumetric density increases. The band gap of the fluorographenes and fluorographites decreases with an increase of sublimation energy. The paper establishes a correlation between the degree of C-C bond length variation of and the presence or absence of repulsive flagpole forces between the attached fluorine atoms. It proves that during functionalization, the values of the average C-C bond length increase for monolayers L6, L4-8, L3-12, L4-6-12 and L5-7. The values of the average lengths of C-C bonds practically do not change during the formation of fluorographite from fluorographene. The variation of C-C bond lengths in fluorographites is minimal for F-L6 T1 and equal to 0,2 %, while the maximum is observed for F-L4-6-12 T1, which is 10,7 %.
Investigation of Two-Component Flow “Liquid–Gas” Influence on a Coriolis Flowmeter Dynamic Parameters
In connection with the development of methods for determining the volume-mass parameters of “liquid–gas” performed by a team of scientists from the South Ural State University, the paper presents the results of full-scale tests and modeling of the operation of a Coriolis flowmeter with a gas-liquid mixture flow. The study aims to establish the causes of reduction of measurement accuracy by the device with an increase in the gas phase in the fluid flow. For this purpose, a series of pouring tests were performed on a specialized stand with the possibility of injecting a gas fraction into the liquid flow. The gas volume fraction in the fluid was calculated. A simulation model of the measuring tube of the Coriolis flowmeter was built and a non-stationary calculation was performed in the mechanical and hydrodynamic module with two-way transmission of pressure and displacement fields at each time step. The gas-liquid mixture was modeled using the VOF model. Based on the simulation results, it was found that the reduction in mass flow measurement accuracy is affected by the physics of the process occurring in the “flow tube – gas-liquid flow” system. A comparative analysis of the calculation and test results was performed, and their qualitative coincidence was shown. It was found that in the case of a two-phase flow, the control electronics and signal processing algorithms are not the main source of measurement error.
Rational Design of Composite Materials Tubular Elements of the Prosthetic Leg
The paper considers a thin-walled tubular shell of a prosthetic leg made of a composite material based on single-directional, fabric or chaotic reinforcement structures. The character of loading is compression with bending. The paper presents an analytical study of the stability of the orthotropic shell under compression and a numerical study of the stability under compression with bending, taking into account embedded connecting elements. It also provides an assessment of the strength. It proves that the most rational reinforcement structure is a fabric one. With practically feasible thicknesses, sizes and loads of prosthesis operation, there is no loss of stability of the tubular elements of the prostheses.
On the Topological Classification of Generic Singular Points of a Planar Vector Field with the Zero (m–1)-Jet
According to the Grobman-Hartman theorem, a dynamical system defined by a finite-dimensional vector field in the neighborhood of a singular point is topologically equivalent (and even topologically conjugate) to the dynamical system defined by the linearized vector field in the generic case when the eigenvalues of the matrix of the linear part of the field at the singular point have nonzero real parts. The topological classification of such singular points is simple: the number of eigenvalues with negative real part is a complete topological invariant. The paper proposes the following generalization of these results. It shows that for a planar vector field with a zero (m–1)-jet at a singular point, the m-jet (m > 1) in the “generic case” determines the topological type of the singular point. It also presents a topological classification of such singular points.
The Pareto Equilibrium of Objections and Counterobjections in Linear-Quadratic Games of N Person
Publications on mathematical game theory with many (not less than 2) players can be conditionally distributed in four directions: non-cooperative, hierarchical, cooperative and coalition games. The last two, in turn, are divided into games with side and non-side payments and games with transferable and nontransferable payoffs, respectively. If the first ones are actively studied (St. Petersburg State Faculty of Applied Mathematics and Control Processes, St. Petersburg Institute of Economics and Mathematics, Institute of Applied Mathematical Research of Karelian Research Centre RAS), the games with non-transferable payoffs are not covered. The paper proposes the conception of objections and counter-objections. The initial investigations were published in two monographs of E.I. Vilkas, the Lithuanian mathematician (the student of N.N. Vorobjev, the professor of St. Petersburg University). For the differential games this conception was first applied by E.M. Waisbord in 1974, then it was continued by the first author of the present article together with E.M. Waisbord in the book Introduction to the theory of differential games of n-persons and its application (1980), and in the monograph Equilibrium of objections and counterobjections (2010) by V.I. Zhukovskiy. The paper proves that in еру mathematical model there is no Nash equilibrium but there are equilibria of objections and conterobjections and simultaneously Pareto maximality.