Pub Date : 2024-04-18DOI: 10.1134/s106345412401014x
N. A. Vavilov
Abstract
The present survey describes the contribution of St. Petersburg mathematicians to the theory of linear, classical, and algebraic groups. The second part is devoted to the publications by Suslin of the 1970s and early 1980s, in the areas of classical algebraic K-theory and the theories of linear and classical groups. In addition, we describe the general context of these works and state some of the most important results by Suslin himself, and his students, and some of the most closely related follow-ups and subsequent results.
摘要 本概览介绍了圣彼得堡数学家对线性、经典和代数群理论的贡献。第二部分专门介绍苏斯林 20 世纪 70 年代和 80 年代初在经典代数 K 理论以及线性群和经典群理论领域发表的著作。此外，我们还介绍了这些著作的一般背景，阐述了苏斯林本人及其学生的一些最重要的成果，以及一些最密切相关的后续成果和后续结果。
{"title":"St. Petersburg School of Linear Groups: II. Early Works by Suslin","authors":"N. A. Vavilov","doi":"10.1134/s106345412401014x","DOIUrl":"https://doi.org/10.1134/s106345412401014x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The present survey describes the contribution of St. Petersburg mathematicians to the theory of linear, classical, and algebraic groups. The second part is devoted to the publications by Suslin of the 1970s and early 1980s, in the areas of classical algebraic <i>K</i>-theory and the theories of linear and classical groups. In addition, we describe the general context of these works and state some of the most important results by Suslin himself, and his students, and some of the most closely related follow-ups and subsequent results.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"55 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627189","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}
Pub Date : 2024-04-18DOI: 10.1134/s1063454124010072
M. A. Komarov
Abstract
In this paper, we study approximation properties of simple partial fractions (logarithmic derivatives of algebraic polynomials), all of whose poles lie on the unit circle. There are obtained criteria for the density of these fractions in classical integral spaces: in the spaces of functions summable with degree p on the unit segment with ultraspherical weight and (weighted) Bergman spaces, analytic in the unit disk and summable with degree p over the disk area. The well-known criteria of Chui and Newman and Abakumov, Borichev, and Fedorovsky for Bergman spaces with p = 1 and p = 2, respectively, are generalized by the obtained results to the case of an arbitrary exponent p > 0.
摘要 本文研究简单偏分数（代数多项式的对数导数）的近似性质，这些分数的极点都位于单位圆上。这些分数在经典积分空间中的密度标准是：在单位段上可求和度数为 p 的函数空间中，具有超球面权重和（加权）伯格曼空间，在单位圆盘中解析，在圆盘区域上可求和度数为 p。Chui 和 Newman 以及 Abakumov、Borichev 和 Fedorovsky 分别针对 p = 1 和 p = 2 的伯格曼空间所提出的著名标准，被所获得的结果推广到了任意指数 p > 0 的情况。
{"title":"Density of Simple Partial Fractions with Poles on a Circle in Weighted Spaces for a Disk and a Segment","authors":"M. A. Komarov","doi":"10.1134/s1063454124010072","DOIUrl":"https://doi.org/10.1134/s1063454124010072","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study approximation properties of simple partial fractions (logarithmic derivatives of algebraic polynomials), all of whose poles lie on the unit circle. There are obtained criteria for the density of these fractions in classical integral spaces: in the spaces of functions summable with degree <i>p</i> on the unit segment with ultraspherical weight and (weighted) Bergman spaces, analytic in the unit disk and summable with degree <i>p</i> over the disk area. The well-known criteria of Chui and Newman and Abakumov, Borichev, and Fedorovsky for Bergman spaces with <i>p</i> = 1 and <i>p</i> = 2, respectively, are generalized by the obtained results to the case of an arbitrary exponent <i>p</i> > 0.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627185","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}
Pub Date : 2024-04-18DOI: 10.1134/s1063454124010023
S. M. Ananjevskii, A. P. Chen
Abstract
A new model of the random filling of a segment of large length with intervals of smaller length is studied. A new statement of the problem is considered. A model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2 is considered. The position of the interval to be placed is subject to a uniform distribution law. The behavior of the average number of intervals placed is studied depending on the length of the segment to be filled. An exact expression is obtained for the analog of Rényi’s constant.
{"title":"A Continuous Version of the Selfish Parking Problem","authors":"S. M. Ananjevskii, A. P. Chen","doi":"10.1134/s1063454124010023","DOIUrl":"https://doi.org/10.1134/s1063454124010023","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new model of the random filling of a segment of large length with intervals of smaller length is studied. A new statement of the problem is considered. A model in which unit intervals are placed on a segment only if the segment being filled has a length of at least 2 is considered. The position of the interval to be placed is subject to a uniform distribution law. The behavior of the average number of intervals placed is studied depending on the length of the segment to be filled. An exact expression is obtained for the analog of Rényi’s constant.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630616","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}
Pub Date : 2024-04-18DOI: 10.1134/s1063454124010102
M. Revyakov
Abstract
The paper presents conditions under which the probability of hitting a linear combination of random vectors in a compressed (from above) polyhedral cone, in particular, a truncated cone is a Schur-concave function of the vector corresponding to this linear combination. It is required that the compressed cone be convex, contain the point 0, its edges be parallel to the coordinate axes, and the distribution density of the vectors be a logarithmically concave sign-invariant function. In addition, a characterization of functions that preserve one known preorder inside the majorization preorder is obtained in differential form.
{"title":"Probability of Random Vector Hitting Truncated Polyhedral Cone: Majorization Aspect","authors":"M. Revyakov","doi":"10.1134/s1063454124010102","DOIUrl":"https://doi.org/10.1134/s1063454124010102","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper presents conditions under which the probability of hitting a linear combination of random vectors in a compressed (from above) polyhedral cone, in particular, a truncated cone is a <i>Schur</i>-concave function of the vector corresponding to this linear combination. It is required that the compressed cone be convex, contain the point <b>0</b>, its edges be parallel to the coordinate axes, and the distribution density of the vectors be a logarithmically concave sign-invariant function. In addition, a characterization of functions that preserve one known preorder inside the majorization preorder is obtained in differential form.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630513","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}
Pub Date : 2024-01-24DOI: 10.1134/s1063454123040179
S. N. Burian
Abstract
The Darboux mechanism is considered. It is proved that this hinge mechanism allows the rotational movement of one link to be converted into (strictly) straight linear movement of its top H. The links of the Darboux mechanism can form geometric shapes such as triangles and squares (with diagonals drawn). In the “square”-shaped configuration of the mechanism, geometrically, branching may occur when the vertex H can move both along a straight line L and along a curve γ. In this case, the rank of the holonomic constraints of the system diminishes by one. For direct linear motion of the vertex H, the Lagrange equation of the second kind in terms of the point H coordinates is derived. The coefficients of this equation can be smoothly continued through a branching point. The “limiting” behavior of the reaction forces in the rods is studied when the mechanism moves to the branching point. An external force that does not do work on point H leads to unlimited reactions in the rods. The kinematics at the branching point is also studied. The inverse problem of dynamics at the point where the rank of the holonomic constraints is not a maximum is solvable. The Lagrange multipliers Λi at the branching point are not defined in a unique way, but the corresponding forces acting on the mechanism vertices are uniquely defined.
摘要 本文研究了达尔布机构。达布机构的链节可以形成三角形和正方形（画对角线）等几何形状。在机构的 "正方形 "构型中，当顶点 H 既能沿直线 L 运动，又能沿曲线 γ 运动时，就会出现几何分支。对于顶点 H 的直接直线运动，可以根据点 H 的坐标推导出第二类拉格朗日方程。该方程的系数可通过分支点平滑延续。当机构运动到分支点时，研究了杆中反作用力的 "极限 "行为。不对 H 点做功的外力会导致杆中产生无限的反作用力。同时还研究了分支点的运动学。在整体约束条件的秩不是最大值的点上的动力学逆问题是可解的。分支点上的拉格朗日乘数Λi 并非以唯一方式定义，但作用在机构顶点上的相应力却是唯一定义的。
{"title":"Specific Features of the Dynamics of the Rectilinear Motion of the Darboux Mechanism","authors":"S. N. Burian","doi":"10.1134/s1063454123040179","DOIUrl":"https://doi.org/10.1134/s1063454123040179","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The Darboux mechanism is considered. It is proved that this hinge mechanism allows the rotational movement of one link to be converted into (strictly) straight linear movement of its top <i>H</i>. The links of the Darboux mechanism can form geometric shapes such as triangles and squares (with diagonals drawn). In the “square”-shaped configuration of the mechanism, geometrically, branching may occur when the vertex <i>H</i> can move both along a straight line <i>L</i> and along a curve γ. In this case, the rank of the holonomic constraints of the system diminishes by one. For direct linear motion of the vertex <i>H</i>, the Lagrange equation of the second kind in terms of the point <i>H</i> coordinates is derived. The coefficients of this equation can be smoothly continued through a branching point. The “limiting” behavior of the reaction forces in the rods is studied when the mechanism moves to the branching point. An external force that does not do work on point <i>H</i> leads to unlimited reactions in the rods. The kinematics at the branching point is also studied. The inverse problem of dynamics at the point where the rank of the holonomic constraints is not a maximum is solvable. The Lagrange multipliers Λ<sub><i>i</i></sub> at the branching point are not defined in a unique way, but the corresponding forces acting on the mechanism vertices are uniquely defined.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557987","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}
Pub Date : 2024-01-24DOI: 10.1134/s1063454123040052
S. A. Bochkarev, S. V. Lekomtsev, V. P. Matveenko
Abstract
The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells, together with the corresponding geometric and physical relations, are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary-value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of the vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of the lowest vibration frequencies on the ply angle and the fluid level for simply supported, rigidly clamped, and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of lay-up scheme and the ply angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.
{"title":"Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid","authors":"S. A. Bochkarev, S. V. Lekomtsev, V. P. Matveenko","doi":"10.1134/s1063454123040052","DOIUrl":"https://doi.org/10.1134/s1063454123040052","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells, together with the corresponding geometric and physical relations, are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary-value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of the vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of the lowest vibration frequencies on the ply angle and the fluid level for simply supported, rigidly clamped, and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of lay-up scheme and the ply angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557972","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}
Pub Date : 2024-01-24DOI: 10.1134/s1063454123040027
V. A. Babeshko, O. V. Evdokimova, O. M. Babeshko, M. V. Zaretskaya, V. S. Evdokimov
Abstract
The paper presents for the first time one of the methods for studying and solving contact problems with a deformed stamp for those cases when there is a need to change the rheology of the stamp material. It is based on a new universal modeling method previously published by the authors, which is used in boundary-value problems for systems of partial differential equations. With its help, solutions of complex-vector boundary-value problems for systems of differential equations can be decomposed into solutions of scalar boundary-value problems for individual differential equations. Among them, the Helmholtz equations are the simplest. The solutions to the scalar boundary-value problems are represented as fractals, self-similar mathematical objects, first introduced by the American mathematician B. Mandelbrot. The role of fractals is performed by packed block elements. The transition from systems of differential equations in partial derivatives to individual equations is carried out using the transformation of Academician B.G. Galerkin or representation by potentials. It is known that the solutions of dynamic contact problems with a deformable stamp of complex rheology are cumbersome and their study is always difficult. The problem is complicated by the presence of discrete resonant frequencies in such problems, which were once discovered by Academician I.I. Vorovich. A contact problem with a deformable punch admits the construction of a solution if it is possible to solve the contact problem for an absolutely rigid punch and construct a solution to the boundary problem for a deformable punch. In earlier works of the authors, the deformable stamp was described by a separate Helmholtz equation. In this paper, we consider a contact problem on the action of a semiinfinite stamp on a multilayer base, described by the system of Lame equations. One of the methods of transition to other rheologies is shown when describing the properties of a deformable stamp in contact problems.
摘要 本文首次提出了一种研究和解决变形印章接触问题的方法，适用于需要改变印章材料流变性的情况。它基于作者之前发表的一种新的通用建模方法，该方法用于偏微分方程系统的边界值问题。在它的帮助下，微分方程系统的复向量边界值问题的解可以分解为单个微分方程的标量边界值问题的解。其中，亥姆霍兹方程最为简单。标量边界值问题的解以分形表示，分形是自相似的数学对象，由美国数学家 B. Mandelbrot 首次提出。分形的作用由打包的块元素承担。从偏导数微分方程系统到单个方程的转换是通过 B.G. Galerkin 院士的转换或电位表示来实现的。众所周知，具有复杂流变性的可变形印章的动态接触问题的求解非常繁琐，而且研究起来总是很困难。I.I. Vorovich院士曾发现此类问题中存在离散共振频率，这使得问题变得更加复杂。如果可以解决绝对刚性冲头的接触问题，并构建可变形冲头边界问题的解决方案，那么就可以构建可变形冲头接触问题的解决方案。在作者的早期著作中，可变形冲头由一个单独的亥姆霍兹方程描述。在本文中，我们考虑的是半无限冲头在多层底座上作用的接触问题，该问题由拉梅方程组描述。在描述接触问题中可变形印章的特性时，显示了过渡到其他流变学的方法之一。
{"title":"On Contact Problems with a Deformable Punch and Variable Rheology","authors":"V. A. Babeshko, O. V. Evdokimova, O. M. Babeshko, M. V. Zaretskaya, V. S. Evdokimov","doi":"10.1134/s1063454123040027","DOIUrl":"https://doi.org/10.1134/s1063454123040027","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper presents for the first time one of the methods for studying and solving contact problems with a deformed stamp for those cases when there is a need to change the rheology of the stamp material. It is based on a new universal modeling method previously published by the authors, which is used in boundary-value problems for systems of partial differential equations. With its help, solutions of complex-vector boundary-value problems for systems of differential equations can be decomposed into solutions of scalar boundary-value problems for individual differential equations. Among them, the Helmholtz equations are the simplest. The solutions to the scalar boundary-value problems are represented as fractals, self-similar mathematical objects, first introduced by the American mathematician B. Mandelbrot. The role of fractals is performed by packed block elements. The transition from systems of differential equations in partial derivatives to individual equations is carried out using the transformation of Academician B.G. Galerkin or representation by potentials. It is known that the solutions of dynamic contact problems with a deformable stamp of complex rheology are cumbersome and their study is always difficult. The problem is complicated by the presence of discrete resonant frequencies in such problems, which were once discovered by Academician I.I. Vorovich. A contact problem with a deformable punch admits the construction of a solution if it is possible to solve the contact problem for an absolutely rigid punch and construct a solution to the boundary problem for a deformable punch. In earlier works of the authors, the deformable stamp was described by a separate Helmholtz equation. In this paper, we consider a contact problem on the action of a semiinfinite stamp on a multilayer base, described by the system of Lame equations. One of the methods of transition to other rheologies is shown when describing the properties of a deformable stamp in contact problems.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"117 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558055","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}
Pub Date : 2024-01-24DOI: 10.1134/s1063454123040131
S. A. Petukhov, A. V. Stepanov
Abstract
Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables, the distribution functions of which are defined on a common support, are proposed in the present paper. Known algorithms of generation of record times and values are given in Introduction for the case when the initial random variables are independent and identically distributed. A brief review of the scientific literature associated with this topic is also given in Introduction. It is also pointed out there that all efficient algorithms of record generation are based on the Markov property of records. In Section 2, the distribution functions of record times and values are derived for the case when the initial random variables are independent and non-identically distributed. The corresponding record-generation algorithms are proposed for the first time. These algorithms are based on the derived distributions and the Markov property of records, which also holds in the case when the initial observations are independent but non-identically distributed. At the end of this work, in Section 3, the proposed algorithms are tested by simulation experiments. In these experiments the records are generated for the case when the initial random variables have Gumbel distribution functions.
{"title":"Generation of Records Obtained from Sequences of Independent and Non-Identically Distributed Variables","authors":"S. A. Petukhov, A. V. Stepanov","doi":"10.1134/s1063454123040131","DOIUrl":"https://doi.org/10.1134/s1063454123040131","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables, the distribution functions of which are defined on a common support, are proposed in the present paper. Known algorithms of generation of record times and values are given in Introduction for the case when the initial random variables are independent and identically distributed. A brief review of the scientific literature associated with this topic is also given in Introduction. It is also pointed out there that all efficient algorithms of record generation are based on the Markov property of records. In Section 2, the distribution functions of record times and values are derived for the case when the initial random variables are independent and non-identically distributed. The corresponding record-generation algorithms are proposed for the first time. These algorithms are based on the derived distributions and the Markov property of records, which also holds in the case when the initial observations are independent but non-identically distributed. At the end of this work, in Section 3, the proposed algorithms are tested by simulation experiments. In these experiments the records are generated for the case when the initial random variables have Gumbel distribution functions.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139557979","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}
Pub Date : 2024-01-24DOI: 10.1134/s1063454123040106
N. F. Morozov, D. A. Indeitsev, A. V. Lukin, I. A. Popov, L. V. Shtukin
Abstract
The present article is the second part of our study of the nonlinear dynamics of parametrically excited bending vibrations of a microbeam fixed at both ends, a basic sensitive element of a promising class of microsensors of various physical quantities, under laser thermo-optical action in the form of periodically generated pulses acting on a certain part of the surface of the beam element. The conceptual technical feasibility of laser generation of parametric oscillations of high-Q microresonators without implementation of scenarios with the loss of elastic stability of the sensitive element or unacceptable heating is shown. The nature of the zone of the primary parametric resonance is analyzed analytically. The resonant characteristics of the system are constructed in a geometrically non-linear formulation corresponding to the Bernoulli–Euler beam model.
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Pub Date : 2024-01-24DOI: 10.1134/s1063454123040088
K. P. Frolova, E. N. Vilchevskaya, V. A. Polyanskiy
Abstract
The work develops a universal approach to accounting for imperfect contacts in determining effective properties of various nature, namely, effective diffusivity and thermal and electrical conductivity. Imperfect contacts appear when fields at the microlevel are not continuous. The possibility of creating a unified approach is due to the similarity of the governing equations. At the same time, the appearance of imperfect contacts may be caused by microstructural features and by the specifics of the process itself. For concreteness, the effective diffusion permeability is determined, since various reasons for the appearance of imperfect contacts can be considered. The reasons can be associated both with the formation of structural defects and with the presence of the specific segregation effect. The paper generalizes and compares two approaches to accounting for imperfect contacts. In the first case, a field jump is set. In the second case, an inhomogeneity with a thin coating possessing extreme properties is introduced. A comprehensive analysis is carried out on the example of a material with spherical inhomogeneities. Analytical expressions for the contribution tensor of the equivalent inhomogeneity are obtained, which results in simplification of the generalization of various homogenization methods.
{"title":"Modeling of Imperfect Contacts in Determining the Effective Diffusion Permeability","authors":"K. P. Frolova, E. N. Vilchevskaya, V. A. Polyanskiy","doi":"10.1134/s1063454123040088","DOIUrl":"https://doi.org/10.1134/s1063454123040088","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The work develops a universal approach to accounting for imperfect contacts in determining effective properties of various nature, namely, effective diffusivity and thermal and electrical conductivity. Imperfect contacts appear when fields at the microlevel are not continuous. The possibility of creating a unified approach is due to the similarity of the governing equations. At the same time, the appearance of imperfect contacts may be caused by microstructural features and by the specifics of the process itself. For concreteness, the effective diffusion permeability is determined, since various reasons for the appearance of imperfect contacts can be considered. The reasons can be associated both with the formation of structural defects and with the presence of the specific segregation effect. The paper generalizes and compares two approaches to accounting for imperfect contacts. In the first case, a field jump is set. In the second case, an inhomogeneity with a thin coating possessing extreme properties is introduced. A comprehensive analysis is carried out on the example of a material with spherical inhomogeneities. Analytical expressions for the contribution tensor of the equivalent inhomogeneity are obtained, which results in simplification of the generalization of various homogenization methods.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139562517","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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