The work is devoted to the study of algebras of invariants of finite unitary groups G' = G∩SL3(C), where G is a finite unitary irreducible primitive group generated by reflections in the unitary space U3. It is known that the system of invariants of the group G' that form an algebra is obtained from the system of invariants of the group G that form the algebra by adding all semi-invariants of the group G of a special form. In the paper, generators of the algebras of invariants of all the indicated groups G' are constructed.
{"title":"On basic invariants of some finite subgroups in SL3(C)","authors":"O. I. Rudnitskií","doi":"10.17223/19988621/81/4","DOIUrl":"https://doi.org/10.17223/19988621/81/4","url":null,"abstract":"The work is devoted to the study of algebras of invariants of finite unitary groups G' = G∩SL3(C), where G is a finite unitary irreducible primitive group generated by reflections in the unitary space U3. It is known that the system of invariants of the group G' that form an algebra is obtained from the system of invariants of the group G that form the algebra by adding all semi-invariants of the group G of a special form. In the paper, generators of the algebras of invariants of all the indicated groups G' are constructed.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"25 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73719334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Cauchy problem for differential equations with fractional derivatives is used in many spheres of science and technology. It was the reason for the development of various methods for its solution, both analytic and approximate ones. The search of an exact solution of differential equations with fractional derivatives by analytic methods is a complex and ineffective task; for this reason, an attempt to solve the considered problem approximately is undertaken in this paper. gated on the segment [0, T]. The method of finite differences which is relatively primary to implement is used for the numerical solution. A difference scheme approximating the Cauchy problem with the first order is constructed on a uniform grid. The difference problem is studied for stability and convergence with a fixed value of the function α(t). It is shown that the numerical solution of the problem converges to the exact solution in the first order. Explicit recurrent formulas for the numerical solution are obtained. A computational experiment upon analysis of the numerical solution of the Cauchy problem is carried out. It is shown on the basis of the computational experiment that if we take the average value for α(t), the first order exactness takes place.
{"title":"A numerical method of solving the Cauchy problem for one differential equation with the Caputo fractional derivative","authors":"Asiyat G. Omarova","doi":"10.17223/19988621/81/3","DOIUrl":"https://doi.org/10.17223/19988621/81/3","url":null,"abstract":"The Cauchy problem for differential equations with fractional derivatives is used in many spheres of science and technology. It was the reason for the development of various methods for its solution, both analytic and approximate ones. The search of an exact solution of differential equations with fractional derivatives by analytic methods is a complex and ineffective task; for this reason, an attempt to solve the considered problem approximately is undertaken in this paper. gated on the segment [0, T]. The method of finite differences which is relatively primary to implement is used for the numerical solution. A difference scheme approximating the Cauchy problem with the first order is constructed on a uniform grid. The difference problem is studied for stability and convergence with a fixed value of the function α(t). It is shown that the numerical solution of the problem converges to the exact solution in the first order. Explicit recurrent formulas for the numerical solution are obtained. A computational experiment upon analysis of the numerical solution of the Cauchy problem is carried out. It is shown on the basis of the computational experiment that if we take the average value for α(t), the first order exactness takes place.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"50 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77753717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the effect of the rotational motion of a body on the trajectory of its fastest descent into the gravity field. The body is considered as a ball rotating about its instantaneous axis, which is perpendicular to the pattern, with a variable angular frequency. The rotation of the ball creates a vortex flow that induces the highest pressure at the top of the ball and the least pressure at the bottom. Thus, the Magnus force (down-force), which is opposed to the reaction force of a trough, occurs. It provides an "antilifting" effect resulting in strong changes in the brachistochrone shape. Based on the fundamental principle of dynamics, a general vector equation of motion is obtained in the form of projections on a moving basis represented as unit vectors of the tangent and normal to the trajectory of the motion. A parametric solution to the equations describing the shape of the trough in Cartesian coordinates is obtained in the absence of dissipative forces. It follows from the resulting solution that the Magnus effect is most noticeable only for massive bodies of long radius. Using the numerical integration methods, various shapes of the deformed brachistochrone are presented as a result of the Magnus effect
{"title":"On the brachistochrone shape under the Magnus effect","authors":"S. Gladkov, S. B. Bogdanova","doi":"10.17223/19988621/81/8","DOIUrl":"https://doi.org/10.17223/19988621/81/8","url":null,"abstract":"This paper studies the effect of the rotational motion of a body on the trajectory of its fastest descent into the gravity field. The body is considered as a ball rotating about its instantaneous axis, which is perpendicular to the pattern, with a variable angular frequency. The rotation of the ball creates a vortex flow that induces the highest pressure at the top of the ball and the least pressure at the bottom. Thus, the Magnus force (down-force), which is opposed to the reaction force of a trough, occurs. It provides an \"antilifting\" effect resulting in strong changes in the brachistochrone shape. Based on the fundamental principle of dynamics, a general vector equation of motion is obtained in the form of projections on a moving basis represented as unit vectors of the tangent and normal to the trajectory of the motion. A parametric solution to the equations describing the shape of the trough in Cartesian coordinates is obtained in the absence of dissipative forces. It follows from the resulting solution that the Magnus effect is most noticeable only for massive bodies of long radius. Using the numerical integration methods, various shapes of the deformed brachistochrone are presented as a result of the Magnus effect","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"127 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88318991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents the experimental study results for the effect of ultrasound influence (USI) on the filling of the Hele-Shaw cells with glass spherules at a constant pressure drop, including the case with a stepwise constriction. The process considered represents a physical model of fractures in an oil reservoir. The experimental set-up is developed with the use of visualization methods for microfluidic studies. Exposure to the USI and constant pressure drop provides the close packing and uniform distribution of the spherules. The flow rate of the water with glass spherules, which are sieved through a 150 pm strainer in the measured model with a thickness of 200 pm, increases proportionally with an increase in the pressure drop, while for the model with the spherules sieved through a 70 pm strainer, the increase is more significant, and the flow rate is five times lower for a pressure drop of 50 kPa. The USI is revealed to be crucial for the uniform filling with the spherules, both in the volumetric models with and without constriction. When the spherules block the constriction, the USI reactivates the flow. Thus, it is a reliable method of influencing the dynamic blocking effect, which is promising for creating the technology intended to increase the ratio of hard-to-recover oil reserves in the total production balance.
{"title":"An experimental study of the ultrasound effect on the motion of glass spherules in Hele-Shaw cells","authors":"A. Rakhimov, A. A. Valiev","doi":"10.17223/19988621/80/11","DOIUrl":"https://doi.org/10.17223/19988621/80/11","url":null,"abstract":"This paper presents the experimental study results for the effect of ultrasound influence (USI) on the filling of the Hele-Shaw cells with glass spherules at a constant pressure drop, including the case with a stepwise constriction. The process considered represents a physical model of fractures in an oil reservoir. The experimental set-up is developed with the use of visualization methods for microfluidic studies. Exposure to the USI and constant pressure drop provides the close packing and uniform distribution of the spherules. The flow rate of the water with glass spherules, which are sieved through a 150 pm strainer in the measured model with a thickness of 200 pm, increases proportionally with an increase in the pressure drop, while for the model with the spherules sieved through a 70 pm strainer, the increase is more significant, and the flow rate is five times lower for a pressure drop of 50 kPa. The USI is revealed to be crucial for the uniform filling with the spherules, both in the volumetric models with and without constriction. When the spherules block the constriction, the USI reactivates the flow. Thus, it is a reliable method of influencing the dynamic blocking effect, which is promising for creating the technology intended to increase the ratio of hard-to-recover oil reserves in the total production balance.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"45 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82937373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the impact of high-speed particles on corrugated metal mesh shields. Numerical solutions to a number of problems on high-speed interaction at different corrugation angles and positions of the initial contact point of the shield and impactor are solved using the grid Wilkins Lagrangian method in a three-dimensional formulation. The parameters of the behind-the-barrier cloud of destruction products are compared for various problems with the same distance traveled by the particle perforating the shield. Thus, the optimal inclination angle of the corrugation is revealed.
{"title":"On some features of the destruction of high-speed particles on debris corrugated mesh shields","authors":"D. B. Dobritsa, Yu. F. Khristenko","doi":"10.17223/19988621/82/7","DOIUrl":"https://doi.org/10.17223/19988621/82/7","url":null,"abstract":"This paper studies the impact of high-speed particles on corrugated metal mesh shields. Numerical solutions to a number of problems on high-speed interaction at different corrugation angles and positions of the initial contact point of the shield and impactor are solved using the grid Wilkins Lagrangian method in a three-dimensional formulation. The parameters of the behind-the-barrier cloud of destruction products are compared for various problems with the same distance traveled by the particle perforating the shield. Thus, the optimal inclination angle of the corrugation is revealed.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"9 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82243927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose an analytical solution of the parameter problem of the Schwarz–Christoffel conformal mapping of the interior (exterior) of a circle onto the interior (exte-rior) of a polygon by use of the behavior of the Newtonian simple layer and logarithmic potentials equal to a constant inside of a simply connected domain.
{"title":"Solution of the parameter problem of the Schwarz–Christoffel conformal mapping of the interior (exterior) of a circle onto the interior (exterior) of a polygon","authors":"N. A. Trubaev","doi":"10.17223/19988621/82/3","DOIUrl":"https://doi.org/10.17223/19988621/82/3","url":null,"abstract":"We propose an analytical solution of the parameter problem of the Schwarz–Christoffel conformal mapping of the interior (exterior) of a circle onto the interior (exte-rior) of a polygon by use of the behavior of the Newtonian simple layer and logarithmic potentials equal to a constant inside of a simply connected domain.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"12 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82531155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One of popular mathematical models of filtration is the classical elastic regime model describing the nonstationary equilibrium filtration. It is also called the Muskat-Leverett model. Solving filtration problems by Monte Carlo methods makes it possible to find the solution of the problem at an individual point of the domain and to estimate derivatives of the solution. This paper is devoted to applying algorithms of the Monte Carlo method to problems of filtration. The Monte Carlo algorithms of random walk by spheres and on boundaries are used for solving the stationary problem of filtration of two immiscible inhomogeneous incompressible fluids in a porous medium and for estimating the solution and the derivatives of the solution of this problem.
{"title":"Application of Monte Carlo methods for solving the regular and degenerate problem of two-phase filtration","authors":"M. Tastanov, A. Utemissova, Fedor F. Mayer","doi":"10.17223/19988621/80/13","DOIUrl":"https://doi.org/10.17223/19988621/80/13","url":null,"abstract":"One of popular mathematical models of filtration is the classical elastic regime model describing the nonstationary equilibrium filtration. It is also called the Muskat-Leverett model. Solving filtration problems by Monte Carlo methods makes it possible to find the solution of the problem at an individual point of the domain and to estimate derivatives of the solution. This paper is devoted to applying algorithms of the Monte Carlo method to problems of filtration. The Monte Carlo algorithms of random walk by spheres and on boundaries are used for solving the stationary problem of filtration of two immiscible inhomogeneous incompressible fluids in a porous medium and for estimating the solution and the derivatives of the solution of this problem.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"50 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88005466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of longitudinal and transverse vibrations of a barrel with arbitrary cross-sectional shapes is considered and solved in the framework of a one-dimensional model. The study shows that the amplitude of transverse vibrations in the vertical plane significantly exceeds that in the horizontal plane. This paper proposes to reduce the amplitude of vibrations by changing the shape of the barrel cross-section, namely by adding stiffeners. The numerical algorithm for solving the problem is developed on the basis of the integro-interpolation method. The verification of the numerical integration method is carried out, and the grid convergence is verified by means of the modeling of barrel vibrations for a 30 mm automatic cannon. The study of the impact of the barrel cross-section shape shows that the use of stiffeners can reduce the initial deflection and the amplitude of muzzle vibrations when firing in bursts. The obtained results demonstrate a narrow spread of projectile departure angles, and, consequently, the improved shooting accuracy of the automatic cannon.
{"title":"A one-dimensional mathematical model of barrel vibrations with arbitrary cross-sectional shapes","authors":"I. G. Rusyak, V. Sufiyanov, D. A. Klyukin","doi":"10.17223/19988621/80/12","DOIUrl":"https://doi.org/10.17223/19988621/80/12","url":null,"abstract":"The problem of longitudinal and transverse vibrations of a barrel with arbitrary cross-sectional shapes is considered and solved in the framework of a one-dimensional model. The study shows that the amplitude of transverse vibrations in the vertical plane significantly exceeds that in the horizontal plane. This paper proposes to reduce the amplitude of vibrations by changing the shape of the barrel cross-section, namely by adding stiffeners. The numerical algorithm for solving the problem is developed on the basis of the integro-interpolation method. The verification of the numerical integration method is carried out, and the grid convergence is verified by means of the modeling of barrel vibrations for a 30 mm automatic cannon. The study of the impact of the barrel cross-section shape shows that the use of stiffeners can reduce the initial deflection and the amplitude of muzzle vibrations when firing in bursts. The obtained results demonstrate a narrow spread of projectile departure angles, and, consequently, the improved shooting accuracy of the automatic cannon.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72996984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses the capabilities of a two-fluid turbulence model for solving complex physical problems such as separated flow around a square cylinder and laminar-turbulent flow in a suddenly expanding channel. The numerical solution to the system of hydrodynamic equations is implemented using a finite-difference scheme. At each time step, the velocities are corrected through pressure calculations according to the SIMPLE algorithm. For verification purposes, the obtained numerical results are compared with available experimental data. A comparison of numerical results has shown that the two-fluid model is easy to implement, requires less computational resources and is capable of predicting laminar and turbulent flows with high accuracy.
{"title":"Numerical simulation of turbulent flows on the basis of a two-fluid model of turbulence","authors":"M. Madaliev","doi":"10.17223/19988621/82/10","DOIUrl":"https://doi.org/10.17223/19988621/82/10","url":null,"abstract":"This paper discusses the capabilities of a two-fluid turbulence model for solving complex physical problems such as separated flow around a square cylinder and laminar-turbulent flow in a suddenly expanding channel. The numerical solution to the system of hydrodynamic equations is implemented using a finite-difference scheme. At each time step, the velocities are corrected through pressure calculations according to the SIMPLE algorithm. For verification purposes, the obtained numerical results are compared with available experimental data. A comparison of numerical results has shown that the two-fluid model is easy to implement, requires less computational resources and is capable of predicting laminar and turbulent flows with high accuracy.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"15 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83644285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. V. Belov, Аleksey V. Bel’kov, A. Zhukov, M. Pavlov, S. Ponomarev
To reduce the cost of CubeSat satellites, an industrial level of performance for radio-electronic components designed for ground operations is applied. A specific tem-perature range should be maintained for such electronic components to operate under space flight conditions. Since the CubeSat spacecraft does not have an active temperature regulation system, the thermal conditions are determined by the balance between inactive absorbed and radiated energy flows, including internal heat release. This paper considers the effect of heat release from circuit boards of different packing density in the electronic equipment on the 1U CubeSat thermal conditions. Both the absorbed radiation from ex-ternal sources, the radiation from the CubeSat external surfaces, the inner heat release, and the re-radiation between the surfaces within the spacecraft are taken into account. The formulated problem is solved numerically. The results show the effect of circuit board packing density on the amplitudes of temperature oscillations and on the average temperatures of satellite structural elements.
{"title":"A thermal state of a small satellite at various packing density of electronic circuit boards","authors":"S. V. Belov, Аleksey V. Bel’kov, A. Zhukov, M. Pavlov, S. Ponomarev","doi":"10.17223/19988621/82/6","DOIUrl":"https://doi.org/10.17223/19988621/82/6","url":null,"abstract":"To reduce the cost of CubeSat satellites, an industrial level of performance for radio-electronic components designed for ground operations is applied. A specific tem-perature range should be maintained for such electronic components to operate under space flight conditions. Since the CubeSat spacecraft does not have an active temperature regulation system, the thermal conditions are determined by the balance between inactive absorbed and radiated energy flows, including internal heat release. This paper considers the effect of heat release from circuit boards of different packing density in the electronic equipment on the 1U CubeSat thermal conditions. Both the absorbed radiation from ex-ternal sources, the radiation from the CubeSat external surfaces, the inner heat release, and the re-radiation between the surfaces within the spacecraft are taken into account. The formulated problem is solved numerically. The results show the effect of circuit board packing density on the amplitudes of temperature oscillations and on the average temperatures of satellite structural elements.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"87 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82657110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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