• 519.63 Математическое моделирование течения вязко–пластической жидкости в смешанных переменных «вихрь–скорость»

    Лебедев С. В. (Bauman Moscow State Technical University), Абдулин С. Р. (Bauman Moscow State Technical University)


    doi: 10.18698/2309-3684-2021-2-314


    В работе рассматривается задача о численном трехмерном моделировании движения вязко–пластических жидкостей Шведова–Бингама в цилиндрических установках. Такие задачи имеют практическое значения для ряда отраслей промышленности: химической, пищевой и некоторых, при создании перспективных установок с перемешиванием и/или обработкой жидких сред. Жидкости в данных установках проявляют, как правило, сильно вязкие свойства, которые наиболее адекватно описываются моделями неньютоновских вязкопластических сред. Неньютоновские свойства жидкостей усложняют уравнения движения, что приводит к необходимости разработки метода численного расчета данных уравнений стационарного пространственного течения жидкой среды. В данной работе предложен численный алгоритм решения трехмерной задачи движения жидкости Шведова–Бингама, основанный на использовании переменных «вихрь–скорость» и применении неявной конечно-разностной схемы расчета. Представлены некоторые результаты расчета трехмерного движения жидкости Шведова–Бингама в цилиндрической трубе.


    Лебедев С.В., Абдуллин С.Р., Бондаренко Н.И. Математическое моделирование течения вязко–пластической жидкости в смешанных переменных «вихрь–скорость». Математическое моделирование и численные методы, 2021, № 2, с. 3–14.





  • 539.3 Modeling the deformation of layered periodic composites based on the theory of plastic flow

    Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Черкасова М. С. (Bauman Moscow State Technical University)


    doi: 10.18698/2309-3684-2021-2-1537


    The aim of this work is to find the constitutive relations for a layered elastoplastic composite according to the flow theory using the method of asymptotic averaging. This goal is achieved by developing an algorithm for solving the problem of the theory of plastic flow for a layered composite material, taking into account various characteristics and properties of these layers of the material, followed by visualizing the result in the form of effective plasticity diagrams connecting the components of averaged stress tensors and components of averaged strain tensors.


    Димитриенко Ю.И., Губарева Е.А., Черкасова М.С. Моделирование деформирования слоистых периодических композитов на основе теории пластического течения. Математическое моделирование и численные методы, 2021, № 2, с. 15–37.





  • 551.513 Global climate model taking into account the biogeochemical carbon cycle of terrestrial vegetation

    Parkhomenko V. P. (Bauman Moscow State Technical University/Computing Centre of RAS)


    doi: 10.18698/2309-3684-2021-2-3853


    The aim of this work is to consider a global model of the carbon cycle. The model describes the production process of forest ecosystems taking into account the seasonal sicle of climatic factors. It is designed to simulate a long period of time as part of a global climate model of intermediate complexity. It has been established that the global characteristics of the climate system reach a steady state over a period of about 2000 years, and the model works steadily. The temporal and spatial distributions of the obtained climatic characteristics and the biogeochemical carbon cycle of terrestrial vegetation are given.


    Пархоменко В.П. Глобальная климатическая модель с учетом биогеохимического углеродного цикла растительности суши. Математическое моделирование и численные методы, 2021, № 2, с. 38–53.





  • 519.6 Optimization of low–mass satellites flight from Earth orbit to Mars orbit using ion engines

    Mozzhorina T. Y. (Bauman Moscow State Technical University), Чуванова Л. О. (Bauman Moscow State Technical University)


    doi: 10.18698/2309-3684-2021-2-5467


    In this paper, optimization of the transfer of a low–mass satellite from Earth orbit to Mars orbit using ion thrusters is considered. The ion engine allows you to minimize fuel consumption and accelerate the spacecraft to fairly high speeds far from the planets of the solar system. The heliocentric section of the flight is subject to consideration. The task is to minimize the flight time. The following assumptions are made in the work: the orbits of the Earth and Mars are circular and lying in the same plane. The angle between the tangential velocity of the spacecraft in the heliocentric system and the direction of thrust action is selected as a control. When compiling the optimization algorithm, the Pontryagin maximum principle was used, which leads the optimization problem of a functional to a boundary value problem for a system of ordinary differential equations. The solution to the boundary value problem was found by one of the numerical methods — the false position method, which gives the most accurate results. The analysis of the results obtained is carried out and a comparison with the data obtained earlier in similar calculations by foreign authors by another numerical solution method is carried out. The conclusion is made about the efficiency of the false position method when solving such problems.


    Мозжорина Т.Ю., Чуванова Л.О. Моделирование и оптимизация перелета спутников малой массы с Земной орбиты на орбиту Марса с помощью ионных двигателей. Математическое моделирование и численные методы, 2021, № 2, с. 54–67.





  • 517 Modeling of nonlinear dynamic and stationary systems based on Volterra integro–functional series and various classes of quadrature formulas

    Висам Махди Абас А. (SRSPU (NPI)), Arutyunyan R. V. (Bauman Moscow State Technical University)


    doi: 10.18698/2309-3684-2021-2-6885


    The article deals with the analysis of nonlinear dynamic and stationary systems based on Volterra integro–functional series and various classes of quadrature formulas. A mathematical model of the input–output type is used, which does not take into account the specific physical nature of the dynamic process, which is commonly called a black box. The methods of the article are applicable to the main variants of the Volterra integral–functional decomposition, including for the case of stationary dynamical systems, a vector input signal. An example of an optimization problem based on the considered integrative series is given. It is noted that when analyzing and optimizing nonlinear dynamical systems by the method of integro–functional series, the problem of calculating multidimensional integrals may arise. The article considers the application of the combined method based on the Volterra integrative series and grid methods for solving the corresponding one -— and multidimensional integral equations for the analysis of nonlinear dynamic and stationary systems. This article considers the case when a certain set of implementations of input and output signals is known, which can be in principle random processes. According to these data, the kernels are found in the decomposition based on the solution of the corresponding linear multidimensional Fredholm integral equation of the first kind. The corresponding problem belongs to the incorrectly posed ones and the regularization method according to A.N. Tikhonov is used to solve it. The article proposes to apply the quasi Monte–Carlo method, characterized by satisfactory convergence, in this problem in the case of large dimensions. The computational qualities in the considered problem of a semi-statistical method for solving integral equations of large dimension, the quasi Monte–Carlo method, the method of central rectangles (cells) and the quadrature formulas of Gauss–Legendre are studied. The approaches under consideration allow us to expand the range of problems to be solved in the theory of analysis and optimization of systems, since methods are proposed that are practically acceptable for large dimensions of integral equations in conditions of limited information about the system.


    Абас Висам Махди Абас, Арутюнян Р.В. Моделирование нелинейных динамических и стационарных систем на основе интегро–функциональных рядов Вольтерры и различных классов квадратурных формул. Математическое моделирование и численные методы, 2021, № 2, с. 68–85.





  • 519.8 Stochastic model of combat operations of the same type of combat units against ones of different types

    Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)


    doi: 10.18698/2309-3684-2021-2-8695


    On the basis of the theory of continuous Markov processes, a model of a two–way battle of two similar combat units of side X against two different types of enemy units is developed. Calculation formulas are obtained for calculating the current and final states for various tactics of fighting by the X–side. The developed model of two–way combat can be used to assess the combat effectiveness of multi-purpose weapons systems.


    Чуев В.Ю., Дубограй И.В. Стохастическая модель боевых действий однотипных боевых единиц против разнотипных. Математическое моделирование и численные методы, 2021, № 2, с. 86–95.





  • 001.4+001.8+001.9 The similarity index of mathematical and other scientific publications with equations and formulas and the problem of self–plagiarism identification

    Polyanin A. D. (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics/MEPhI), Shingareva I. K. (University of Sonora)


    doi: 10.18698/2309-3684-2021-2-96116


    The problems of estimating the similarity index of inhomogeneous scientific publications containing equations and formulas are discussed for the first time. It is shown that the presence of equations and formulas (as well as figures, drawings, and tables) is a complicating factor that significantly complicates the study of such texts. It has been proved that the method for determining the similarity index of publications, based on taking into account individual mathematical symbols and parts of equations and formulas, is ineffective and can lead to erroneous and even completely absurd conclusions. Possibilities of the most popular analytical systems Antiplagiat and iThenticate, currently used in scientific journals, are investigated for detecting plagiarism and self–plagiarism. The results of processing by the iThenticate system of specific examples and specific test problems containing equations and formulas are presented. It has been established that this analytical system, when analyzing heterogeneous texts, is often unable to distinguish self– plagiarism from pseudo-self-plagiarism, seeming real (but false and imaginary) self– plagiarism. A model complex situation is considered, in which the identification of self–plagiarism requires the involvement of highly qualified specialists of a narrow profile. Various ways to improve the work of analytical systems for comparing inhomogeneous texts are proposed. This article will be useful to researchers and university teachers in physics, mathematics, and engineering, programmers dealing with problems in image recognition and research topics of digital image processing, as well as a wide range of readers who are interested in issues of plagiarism and self–plagiarism.


    Полянин А.Д., Шингарева И.К. Индекс подобия математических и других научных публикаций с уравнениями и формулами и проблема идентификации самоплагиата. Математическое моделирование и численные методы, 2021, № 2, с. 96–116.