Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics最新文献_第10页

Computer modelling of the state of stress and strain of the Tunguska and Vilyui syneclises 通古斯河和维柳河的应力和应变状态的计算机模拟

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/75/5

A. Akhmetov, I. Smolin

{"title":"Computer modelling of the state of stress and strain of the Tunguska and Vilyui syneclises","authors":"A. Akhmetov, I. Smolin","doi":"10.17223/19988621/75/5","DOIUrl":"https://doi.org/10.17223/19988621/75/5","url":null,"abstract":"The states of stress and strain are numerically analyzed under conditions of the geodynamic process of tension in the south part of the Vilyui syneclise and the middle part of the Tunguska syneclise. Two-dimensional models of geological structures of the south part of the Vilyui syneclise and the middle part of the Tunguska syneclise are constructed based on the Kimberlit-1981 geological profile obtained using deep seismic sounding. To describe the plastic strain in the geomedia, the model of elastic-plastic media with the non-associated plastic flow rule based on the Drucker-Prager-Nikolaevskii model is used. In this model, the “jelly sandwich” strength model is adopted for the analysis of the stress state of the lithosphere. The results of the numerical modeling of the state of the stress and strain of the chosen parts of the Siberian Craton are presented. The localization of plastic strain, the region of positive values of horizontal stresses, and the negative deviation of the calculated pressure from the lithostatic pressure correspond to mineral deposits.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89171529","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}

引用次数: 0

Exact solution of the fundamental equation of acoustics for a pressure wave developing in two directions 两个方向上压力波的声学基本方程的精确解

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/79/1

V. Borodin, A. Lun-Fu, M. Bubenchikov, A. Bubenchikov, D. Mamontov

{"title":"Exact solution of the fundamental equation of acoustics for a pressure wave developing in two directions","authors":"V. Borodin, A. Lun-Fu, M. Bubenchikov, A. Bubenchikov, D. Mamontov","doi":"10.17223/19988621/79/1","DOIUrl":"https://doi.org/10.17223/19988621/79/1","url":null,"abstract":"The authors proceed from the hyperbolic equation for acoustic pressure. Using the integral Fourier transform along the axial coordinate, an equation in partial derivatives for the kernel of this transformation is found. This equation contains only one spatial coordinate and time. Applying the integral Laplace transform in time to the last equation, we obtain an ordinary differential equation with respect to the radial coordinate for the corresponding image. It turns out that the solution of the last equation is the well-known Macdonald function. For this function, it was possible to find the original image according to Laplace. All this made it possible to write an integral formula for the pressure in a sound wave. If the function of the initial pressure distribution along the pipe axis is taken in the form of a Gaussian impulse, then the integrals included in the representation of the desired solution are taken explicitly. As a result, we obtain an explicit compact formula for the acoustic pressure distribution in the axisymmetric case. It is convenient to use this formula to analyze the distribution of sound disturbances both along the pipe axis and in the radial direction. Therefore, the results are presented as isobars in the (z, r) plane corresponding to different times.","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":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89697370","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}

引用次数: 0

On the shape of the brachistichrone rotating in a vertical plane 在垂直平面上旋转的计时表的形状上

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/78/7

S. Gladkov, S. B. Bogdanova

{"title":"On the shape of the brachistichrone rotating in a vertical plane","authors":"S. Gladkov, S. B. Bogdanova","doi":"10.17223/19988621/78/7","DOIUrl":"https://doi.org/10.17223/19988621/78/7","url":null,"abstract":"The paper aims to study the influence of the brachistochrone rotating in its own plane on the gutter shape along which a body moves. The problem is solved with a moving basis, which allows one to account for all forces exerted on the body. Introduction of the moving basis yields a compact system of dynamical equations, whose validity was proven in previous author's papers. In limiting cases, such an approach is used to solve analytically the obtained equations of motion and to determine the shape of curves depending on the parameters in the equations by tabular integration. The latter is illustrated in the figures presented. According to the energy conservation law, which accounts for the rotation of the entire system as a whole, the resulting equations also include the angular frequency of rotation as an additional parameter. In this paper, the case of steady rotation is studied. Such conditions have a significant impact on the brachistochrone. In the limiting case of low rotational speeds, the curve, as it should be, degenerates smoothly into a classical brachistochrone, which is justified by the numerical methods used.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"67 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77558343","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}

引用次数: 1

Application of the Loewner-Kufarev theory to the construction of a parametric set of univalent functions of a certain form Loewner-Kufarev理论在构造某形式一元函数参数集中的应用

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/75/1

O. Zadorozhnaya, V. Kochetkov

{"title":"Application of the Loewner-Kufarev theory to the construction of a parametric set of univalent functions of a certain form","authors":"O. Zadorozhnaya, V. Kochetkov","doi":"10.17223/19988621/75/1","DOIUrl":"https://doi.org/10.17223/19988621/75/1","url":null,"abstract":"This work relates to the theory of Loewner-Kufarev differential equations, which are a part of the geometric function theory. We apply the well-known second Loewner-Kufarev differential equation to construct a parametric family of univalent functions in the unit disk g(z, t) for each fixed non-negative value of the parameter t generalizing the known parametric families. The article also uses various alternative approaches and provides their comparative analysis. The results of the study can be considered as one sufficient condition for the uniqueness of regular functions in a unit disk. Leading Russian scientists made a great contribution to the development of the geometric function theory based the variational-parametric method for studying functionals and found some Loewner-Kufarev differential equations. There are three sections in the work. The first one applies the Loewner-Kufarev equation to construct a parametric set of univalent functions of a certain type. In the second section, we introduce a special class of regular functions in the unit disk with a fixed convex function, and prove the univalence property for functions of this class. Here we also show one more method for constructing a parametric family of univalent functions different from the methods described in the first paragraph. The third section is devoted to alternative methods for constructing one-parameter sets of univalent functions. AMS Mathematical Subject Classification: 35С15","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84681230","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}

引用次数: 0

Numerical simulation of air quality over a Tomsk city in light wind 微风下托木斯克市上空空气质量的数值模拟

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/79/3

A. Starchenko, E. Shelmina, L. I. Kizhner, S. Odintsov

引用次数: 0

Algorithmization of the solution of dynamic boundary value problems of the theory of flexible plates taking into account shift and rotation inertia 考虑位移和转动惯量的柔性板理论动态边值问题的求解算法

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/75/13

Adash Yu. Yuldashev, Sh.T. Pirmatov

{"title":"Algorithmization of the solution of dynamic boundary value problems of the theory of flexible plates taking into account shift and rotation inertia","authors":"Adash Yu. Yuldashev, Sh.T. Pirmatov","doi":"10.17223/19988621/75/13","DOIUrl":"https://doi.org/10.17223/19988621/75/13","url":null,"abstract":"Most of the problems on flexible plates are solved in the Föppl-von Karman formulation, which is Love's special case. The constructed algorithms are not economical in terms of implementation on a computer. Therefore, construction of algorithms for the complete calculation of flexible plates with a given degree of accuracy with allowance for the shear and inertia of rotation is becoming a topical issue. The problem of creating an automated inference system and solving the equations of the theory of elasticity and plasticity were first posed in the monograph by V.K. Kabulov. In this work, for the first time, the main problems of algorithmization are formulated and ways of their machine solution are outlined. The problem of algorithmization is solved as follows: depending on geometric characteristics of the object and physical properties of the material, a design scheme of this model is selected; derivation of the initial differential equations and the corresponding boundary and initial conditions; selection of a computational algorithm and numerical solution of the obtained equations; analysis of the obtained numerical results describing the stress-strain state of the structure under consideration. This work consists of an introduction, three sections and a conclusion. In the first paragraph, the equations of motion of rectangular plates are given. Substituting the expression for the force of moments and shearing forces and introducing a dimensionless value, a system of equations in displacements is obtained. In the second section, using the central difference formulas, a system of quasilinear ordinary differential equations is obtained. Taking into account the boundary and initial conditions, the system of equations is reduced to matrix form, which can be solved by the Runge-Kutta method. In the third paragraph, an analysis of the results obtained is presented.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"70 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76112415","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}

引用次数: 0

Inhomogeneous Poiseuille flow 非均匀泊泽维尔流

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/77/6

N. Burmasheva, Anastasiya V. Dyachkova, E. Prosviryakov

{"title":"Inhomogeneous Poiseuille flow","authors":"N. Burmasheva, Anastasiya V. Dyachkova, E. Prosviryakov","doi":"10.17223/19988621/77/6","DOIUrl":"https://doi.org/10.17223/19988621/77/6","url":null,"abstract":"The paper presents an investigation of the isothermal steady flow of a viscous incompressible fluid in an extended flat layer using hydrodynamic equations. The bottom of the layer under consideration is limited by a stationary solid hydrophilic surface. At the upper boundary of the layer, the pressure field, which is inhomogeneous in both horizontal coordinates, and the velocity field are specified. These boundary conditions allow one to generalize the classical Poiseuille flow. The exact solution, satisfying the set boundary value problem, is described by a series of polynomials of different orders. The highest (fifth) degree of the polynomials corresponds to a homogeneous component of the horizontal velocity. Here, the pressure field depends only on the horizontal coordinates; the dependence is linear. The detailed analysis of the velocity field is carried out. The obtained results confirm that the determined exact solution can describe multiple stratification of the velocity field and the corresponding field of tangent stresses. The analysis of spectral properties of the velocity field is performed for a general case without specifying the values of physical constants that unambiguously identify the studied fluid. Therefore, the presented results are applicable to viscous fluids of various nature.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"100 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81089770","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}

引用次数: 0

Variational simulation of the spectral problem 谱问题的变分模拟

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/75/3

Evgeniya. A. Molchanova

引用次数: 0

Left-invariant para-Sasakian structure on the Heisenberg group Heisenberg群上的左不变para-Sasakian结构

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/75/4

V. I. Pan’zhenskii, A. O. Rastrepina

{"title":"Left-invariant para-Sasakian structure on the Heisenberg group","authors":"V. I. Pan’zhenskii, A. O. Rastrepina","doi":"10.17223/19988621/75/4","DOIUrl":"https://doi.org/10.17223/19988621/75/4","url":null,"abstract":"Among the eight three-dimensional Thurston geometries, there is the Heisenberg group, the nilpotent Lie group of real 3x3 matrices of a special form. It is known that this group has a left-invariant Sasakian structure. This article proves that there is also a paracontact metric structure on the Heisenberg group, which is also Sasakian. This group has a unique contact metric connection with skew-symmetric torsion, which is invariant under the group of automorphisms of the para-Sasakian structure. The discovered connection is proved to be a contact metric connection for any para-Sasakian structure. The concept of a connection compatible with the distribution is introduced. It is found that the Levi-Civita connection and the contact metric connection on the Heisenberg group endowed with a para-Sasakian structure are compatible with the contact distribution. Their orthogonal projections on this distribution determine the same truncated connection. It is proved that Levi-Civita contact geodesics and truncated geodesics coincide. It is found that contact geodesics are either straight lines lying in the contact planes or parabolas the orthogonal projections of which on the contact planes are straight lines. The results obtained in this article are also valid for the multidimensional Heisenberg group. AMS Mathematical Subject Classification: 53D10, 53C50","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"138 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77497421","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}

引用次数: 1

An analytical model of the fluid influx for a multilateral well in an anisotropic formation 各向异性地层分支井流体流入分析模型

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Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics Pub Date : 2022-01-01 DOI: 10.17223/19988621/77/8

A. Orlov, A. S. Russkikh

{"title":"An analytical model of the fluid influx for a multilateral well in an anisotropic formation","authors":"A. Orlov, A. S. Russkikh","doi":"10.17223/19988621/77/8","DOIUrl":"https://doi.org/10.17223/19988621/77/8","url":null,"abstract":"Depletion and deterioration of the structure of reserves in the fields of Western Siberia requires the involvement in the development and operation of hydrocarbon deposits represented by reservoirs with secondary filtration-volumetric properties and complex heterogeneous structure. A technology, which is successfully applied by resource companies, uses multilateral wells. Development of deposits using such wells is complicated by the choice of the optimal layout and development system for a particular field. Our goal is to propose a common approach to the creation of an optimal system for the development of oil fields. To solve this problem, it is reasonable to develop an analytical calculation method that performs express assessment of the fluid inflow to a dual-lateral well avoiding the use of multivariate and time-consuming calculations by hydrodynamic models built in a simulator. In this work, such an analytical method is developed and verified using the actual geological and geophysical data on the productive Neocomian deposits of the Severo-Ostrovnoye field in Khanty-Mansi autonomous okrug.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"74 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86997963","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}

引用次数: 0