Rubric: "1.2.2. Mathematical modeling, numerical methods and software packages (physical and mathematical sciences)"
521.19 The perturbation hollow spheres modelling for the gravity assists in the Solar system
Borovin G. K. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Golubev Y. F. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Grushevskii A. V. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Tuchin2 A. G. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes)
doi: 10.18698/2309-3684-2023-4-6473
One of the types of gravitational scattering in the Solar System within the framework of the circular restricted three-body problem (CR3BP) are the gravity assist maneuvers of "particles of insignificant mass" (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the scattering of beams of charged alpha-particles in the Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions on the ability to perform gravity assists associated with the limited size of the spheres of influence of the planet. At the same time, internal limitations on the possibility of performing gravity assists are known from the literature on CR3BP, estimated by the effective radii of planets (including gravitational capture by a planet falling into it). They depend on the asymptotic velocity of the particle relative to the planet. For obvious reasons, their influence makes it impossible to effectively use gravity assist maneuvers. The paper presents generalized estimates of the sizes of near-planetary regions (flat "perturbation rings" or "perturbation hollow spheres" rotating synchronously with a small body in the three-dimensional case), falling into which is a necessary condition for the implementation of gravity assists. A detailed analysis shows that Neptune and Saturn have characteristic of perturbation hollow spheres of the largest size in the Solar System, and Jupiter occupies only the fourth place in this list
Боровин Г.К., Голубев Ю.Ф., Грушевский А.В., Тучин А.Г. Моделирование пертурбационных оболочек для гравитационных маневров в Солнечной системе.Математическое моделирование и численные методы, 2023, № 4, с. 64–73.
Belkheeva R. K. (Новосибирский государственный университет)
doi: 10.18698/2309-3684-2024-1-317
A model of the low-parameter equation of state of diamond was constructed, and the parameters of this equation were found, which allow to describe reliably the behavior of solid and porous diamond samples and diamond-metal mixture. Porous substance and porous mixture of condensed components were considered as thermodynamically equilibrium mixtures. The comparison of calculated and experimental shock adiabats showed the applicability of the proposed two-parameter equation of state in a wide range of pressures and temperatures.
Бельхеева Р.К. Моделирование малопараметрического уравнения состояния в форме Ми-Грюнайзена для алмаза и смесей алмаз-металл. Математическое моделирование и численные методы, 2024, № 1, с. 3–17.
539.3 Finite element modeling of non-stationary thermal buckling of composite structures
Dimitrienko Y. I. (Bauman Moscow State Technical University), Bogdanov I. O. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Maremshaova A. A. (Bauman Moscow State Technical University), Anokhin D. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-1-3854
The problem of modeling for buckling analysis of the composite structures due to nonstationary thermal effects on them, taking into account the temperature dependence of the properties of the composite components, is considered. Systems of equations are formulated for calculating the basic and varied states of the structure. A classification of buckling analysis problems is proposed. The application of the finite element method to determine the critical temperature and the corresponding buckling mode of a structure is described. A local generalized eigenvalue problem was formulated and the proposed model was verified using the SMCM software package developed at the Simplex Research Center of Bauman Moscow State Technical University, as well as using ANSYS. It is shown that the results of calculating the eigenforms and eigenvalues in the test problem coincide quite well.
Димитриенко Ю.И., Богданов И.О., Юрин Ю.В., Маремшаова А.А., Анохин Д. Конечно-элементное моделирование нестационарной термоустойчивости композитных конструкций. Математическое моделирование и численные методы, 2024, № 1, с. 38–54.
550.388.2 Mathematical modeling of the impact of radio waves on the lower ionosphere
Stupitskij E. L. (Institute for Computer Aided Design of the Russian Academy of Sciences), Moiseeva D. S. (Institute for Computer Aided Design of the Russian Academy of Sciences), Motorin A. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2024-1-6792
The paper presents numerical studies of the parameters of the lower ionosphere when heated by high-frequency radio waves of various frequencies and powers. The main attention is paid to the interrelation between the energy and kinetic parameters of the disturbed D-region of the ionosphere in the processes that determine the absorption and transformation of the radio beam energy flux in space and time. The possibility of a significant difference in the behavior of the parameters of the disturbed region in the daytime and at nighttime, both in magnitude and in space-time distribution, is shown. In the absence of sufficiently reliable values of the rate constants for a number of important kinetic processes, numerical studies were carried out in stages with the gradual addition of individual processes and kinetic blocks corresponding at the same time to a certain physical content. It is shown that the energy thresholds for inelastic collisions of electrons with air molecules are the main ones. This approach made it possible to detect the effect of the emergence of a self-oscillating mode of changing parameters if the main channel for energy losses in inelastic processes is the most energy-intensive process – ionization. This effect may play a role in plasma studies using high-frequency inductive and capacitive discharges. The results of calculations of the ionization and optical parameters of the disturbed D-region for daytime conditions are presented. The electron temperature, density, emission coefficients in the visible and infrared ranges of the spectrum are obtained for various values of the power of the radio beam and its frequency in the lower ionosphere. The influence on the electron temperature and on the general behavior of the parameters of energy losses by electrons on the excitation of vibrational and metastable states of molecules has been studied in detail. It is shown that under nighttime conditions, when the electron concentration begins at altitudes of about 80 km, and the concentration of heavy particles decreases by two orders of magnitude compared to the average D-region, large-scale gas-dynamic motion can develop with sufficient radio emission power The algorithm was developed based on the McCormack method and two-dimensional gas-dynamic calculations of the behavior of the parameters of the perturbed region were performed with some simplifications of the kinetics.
Ступицкий Е.Л., Моисеева Д.С., Моторин А.А. Математическое моделирование воздействия радиоизлучения на нижнюю ионосферу. Математическое моделирование и численные методы, 2024, № 1, с. 67–92.
Polyanin A. D. (Ishlinsky Institute for Problems in Mechanics)
doi: 10.18698/2309-3684-2024-1-124142
Rather general nonstationary strongly nonlinear partial differential equations with three independent variables are investigated, which contain the first time derivative and a quadratic combination of the second derivatives with respect to spatial variables of the Monge–Ampere type (such equations are often called parabolic Monge–Ampere equations). Some equations of this type are found in differential geometry and electron magnetohydrodynamics. This paper describes multiparameter transformations that preserve the form of the considered class of nonlinear equations, which is given by an arbitrary function. Two-dimensional and one-dimensional reductions leading to simpler partial differential equations with two independent variables or ordinary differential equations are also considered. Using methods of generalized separation of variables, a number of exact solutions have been constructed, many of which can be represented in elementary functions. The obtained results and exact solutions can be used to assess the accuracy and analyze the adequacy of numerical methods for solving problems described by strongly nonlinear partial differential equations.
Полянин А.Д. Преобразования, редукции и точные решения широкого класса нестационарных уравнений с нелинейностью типа Монжа – Ампера. Математическое моделирование и численные методы, 2024, № 1, с. 124–142.
Abdikarimov N. I. (Ургенчский государственный университет Адрес: 220100, Узбекистан, город Ургенч, улица Х. Олимжона, 14.), Navruzov K. N. (Ургенчский государственный университет Адрес: 220100, Узбекистан, город Ургенч, улица Х. Олимжона, 14.)
doi: 10.18698/2309-3684-2024-2-3545
The problems of oscillatory flow of an elastic-viscous fluid in a flat channel for a given harmonic oscillation of fluid flow are solved based on the generalized Maxwell model. The “impedance” function was determined, and with the help of this function the dependence of the hydrodynamic resistance on the dimensionless oscillation frequency was studied for various values of the elastic Deborah number and the concentration of the Newtonian fluid. It is shown that in the oscillatory flow of an elastic-viscous fluid, the hydrodynamic resistance decreases depending on the Deborah number. This effect makes it possible to estimate the hydrodynamic resistance for a given law of change in the longitudinal velocity averaged over the cross section of the channel, with oscillatory flow and, thereby, allows us to determine the dissipation of the energy of the medium, which is important in the regulation of hydraulic and pneumatic systems.
Абдикаримов Н.И., Наврузов К.Н. Математическое моделирование гидродинамических сопротивлений при колебательном течении упруговязкой жидкости в плоском канале. Математическое моделирование и численные методы, 2024, № 2, с. 35–45.
519.7 Modeling and efficiency analysis of perceptual hash functions for segmented image search
Valishin A. A. (Bauman Moscow State Technical University), Zaprivoda A. V. (Bauman Moscow State Technical University), Tsukhlo S. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-4667
This research paper explores the use of perceptual hash functions to improve the retrieval efficiency of aerial photography and satellite remote sensing images segmented by a convolutional neural network. This paper describes three hashing algorithms. The first algorithm is based on the use of a low-pass filter and is aimed at reducing image detail in order to highlight the most stable image features. The second algorithm uses a two-dimensional discrete cosine transform to create an image hash. The third algorithm is based on the Radon transform, which allows you to extract information about the directions of lines in the image, as well as provide maximum invariance to the rotation transformation of the input image. The article also tests these algorithms, including analysis of their invariance to transformations for rotation, scaling and shifting of the source image. Test results show that the algorithm based on the Radon transform exhibits good rotation invariance, but is sensitive to the quality of segmentation, which can lead to frequent collisions when searching for similar images. Algorithms using a two-dimensional discrete cosine transform and an algorithm using a low-pass filter turned out to be more stable and have a smaller spread of values. However, it should be noted that algorithms using a low-pass filter and 2D discrete cosine transform may not be applicable to rotated images. Based on the results of analysis and comparison of the performance of the algorithms, it is recommended to give preference to either the second or third algorithm, because each of them has its own advantages and disadvantages, and the decision to use a specific algorithm in the task of finding the most similar image must take into account the specific conditions and limitations of the problem, as well as the requirements for the quality of image comparison.
Валишин А.А., Запривода А.В., Цухло С.С. Моделирование и сравнительный анализ эффективности перцептивных хеш-функций для поиска сегментированных изображений. Математическое моделирование и численные методы, 2024, № 2, с. 46-67.
Zakharov I. I. (Moscow State University of Civil Engineering), Aleroev T. S. (Moscow State University of Civil Engineering)
doi: 10.18698/2309-3684-2024-2-100111
This paper is devoted to an approximate method for solving the first boundary value problem for the inhomogeneous fractional-differential advection-diffusion (dispersion) equation. The aim of the work is to construct, and realize an effective approximate method for solving physical and mathematical problems. The boundary value problem is studied for the two-dimensional case. The problems of finding eigenvalues and constructing surfaces of solutions of the first boundary value problem for the inhomogeneous differential equation are considered. The method of estimating the accuracy of the approximate solution is shown. An algorithm for finding an approximate solution based on the analytical method of separation of variables (Fourier method) is described. The exact results of calculations, both numerical and graphical, are given for specific examples.
Захаров И.И., Алероев Т.С. Решение первой краевой задачи для неоднородного дробного дифференциального уравнения. Математическое моделирование и численные методы, 2024, № 2, с. 100-111.
Tlibekov A. T. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-112125
The comparison of existing and developed new methods of converting optimality criteria into a scalar function of the goal is performed. New converting methods are used in the problems of interpolation of experimental data by a modified fractional-power Newton–Puiseux series. Coefficients and degrees of a fractional-power series are calculated by evolutionary or infinite-step optimization methods, where the modules of the difference between experimental data and the values obtained by calculating the interpolation polynomial are used as optimality criteria. Under such conditions, the optimization task becomes multi-criteria, for which, during the search process, part of the optimality criteria increases, the rest decrease and reduce the scalar goal function and creating the illusion that the search is effective. For new converting methods, all optimality criteria in the search process are reduced. The errors obtained by interpolating the time of laser cutting of steel sheet and forecasting the production program of parts are shown. The use of modified fractional power series and new methods of converting optimality criteria for the implementation of the neural network learning function is proposed.
Тлибеков А.Х. Сравнительный анализ методов свертывания критериев оптимальности в задачах многокритериальной оптимизации. Математическое моделирование и численные методы, 2024, № 2, с. 112-125.