首页 > 最新文献

Lobachevskii Journal of Mathematics最新文献

英文 中文
The Use of Artificial Neural Networks to Determine the Aerodynamic Forces and Moments Acting on an Aircraft in a Vortex Wake 利用人工神经网络确定飞机在涡流中的空气动力和力矩
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602364
Yu. N. Sviridenko

Abstract

The article proposes a method based on the use of artificial neural networks to determine what additional forces and moments act on an aircraft in a vortex wake of another aircraft in real time. The method is based on neural-network approximating additional forces and moments acting on the aircraft. These are caused by the influence of individual vortex segments. To generate a set of data for training neural networks, the method of hydrodynamic singularities has been used. Estimates of the accuracy and speed of the proposed method have been carried out.

摘要 本文提出了一种基于人工神经网络的方法,用于实时确定在另一架飞机的涡流尾流中作用在飞机上的附加力和力矩。该方法基于神经网络近似作用在飞机上的附加力和力矩。这些都是由单个涡流段的影响造成的。为了生成一组用于训练神经网络的数据,使用了流体力学奇点法。对拟议方法的准确性和速度进行了评估。
{"title":"The Use of Artificial Neural Networks to Determine the Aerodynamic Forces and Moments Acting on an Aircraft in a Vortex Wake","authors":"Yu. N. Sviridenko","doi":"10.1134/s1995080224602364","DOIUrl":"https://doi.org/10.1134/s1995080224602364","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The article proposes a method based on the use of artificial neural networks to determine what additional forces and moments act on an aircraft in a vortex wake of another aircraft in real time. The method is based on neural-network approximating additional forces and moments acting on the aircraft. These are caused by the influence of individual vortex segments. To generate a set of data for training neural networks, the method of hydrodynamic singularities has been used. Estimates of the accuracy and speed of the proposed method have been carried out.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217097","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
Taylor Nearly Columnar Vortices in the Couette–Taylor System: Transition to Turbulence 库埃特-泰勒系统中的泰勒近柱状涡旋:向湍流的过渡
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602388
T. Akinaga, P. M. J. Trevelyan, S. C. Generalis

Abstract

The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, (beta), up to (betasim 3) rather narrow Taylor vortices may be realized for Reynolds number (R<80). These vortices will become unstable to states with columnar components with increasing (R). We show that for low (R), ((R,beta)sim(62.2,3.5)), a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers (alphasim 0.17) with (beta=3.5). We examine the bifurcation sequence of these states.

摘要 泰勒-库埃特问题在小间隙极限下的分析扩展到了近柱状(NC)解。理论结果是在小间隙近似条件下得出的,而在实验中并不总是能很好地近似。尽管如此,在笛卡尔框架下进行的研究与理论结果和观测结果进行比较后,还是得出了很好的一致结论。对于较高的轴向波数值((beta)),在雷诺数(R<80)下,可能会出现相当窄的((betasim 3))泰勒涡。随着(R)的增加,这些漩涡会变得不稳定,变成具有柱状成分的状态。我们表明,对于低雷诺数,((R,beta)sim(62.2,3.5)),在方位角波数((alphasim 0.17))和((beta=3.5)时,存在一个具有强柱状成分的流向漂移状态。我们研究了这些状态的分岔序列。
{"title":"Taylor Nearly Columnar Vortices in the Couette–Taylor System: Transition to Turbulence","authors":"T. Akinaga, P. M. J. Trevelyan, S. C. Generalis","doi":"10.1134/s1995080224602388","DOIUrl":"https://doi.org/10.1134/s1995080224602388","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, <span>(beta)</span>, up to <span>(betasim 3)</span> rather narrow Taylor vortices may be realized for Reynolds number <span>(R&lt;80)</span>. These vortices will become unstable to states with columnar components with increasing <span>(R)</span>. We show that for low <span>(R)</span>, <span>((R,beta)sim(62.2,3.5))</span>, a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers <span>(alphasim 0.17)</span> with <span>(beta=3.5)</span>. We examine the bifurcation sequence of these states.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216973","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 Aspects and Implementation of LAKE Scheme into a Global Atmospheric Model SLAV 在全球大气模型 SLAV 中采用 LAKE 方案的数值方面和实施情况
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602601
R. Yu. Fadeev, V. M. Stepanenko

Abstract

SLAV is a mathematical model of the Earth’s atmosphere that predicts weather in future based on current weather conditions. This paper describes and evaluates the numerical algorithm based on the energy balance for implementing the LAKE model into SLAV. LAKE is an extended one-dimensional model of lake that has been tested in respect to thermal and ice regime at a number of lakes in contrasting climate conditions in a standalone mode. The results obtained from numerical simulations for lead times up to 4 month and retrospective forecasts of weather anomalies with the same lead time indicate the applicability of the developed approach to reproduce lake-atmosphere coupling.

摘要 SLAV 是一种地球大气数学模型,可根据当前天气条件预测未来天气。本文介绍并评估了基于能量平衡的数值算法,以将 LAKE 模型应用到 SLAV 中。LAKE 是一个扩展的一维湖泊模型,已在一些气候条件截然不同的湖泊中以独立模式进行了热和冰机制测试。在长达 4 个月的准备时间内进行的数值模拟以及在相同准备时间内对天气异常进行的回顾性预测所获得的结果表明,所开发的方法适用于再现湖泊-大气耦合。
{"title":"Numerical Aspects and Implementation of LAKE Scheme into a Global Atmospheric Model SLAV","authors":"R. Yu. Fadeev, V. M. Stepanenko","doi":"10.1134/s1995080224602601","DOIUrl":"https://doi.org/10.1134/s1995080224602601","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>SLAV is a mathematical model of the Earth’s atmosphere that predicts weather in future based on current weather conditions. This paper describes and evaluates the numerical algorithm based on the energy balance for implementing the LAKE model into SLAV. LAKE is an extended one-dimensional model of lake that has been tested in respect to thermal and ice regime at a number of lakes in contrasting climate conditions in a standalone mode. The results obtained from numerical simulations for lead times up to 4 month and retrospective forecasts of weather anomalies with the same lead time indicate the applicability of the developed approach to reproduce lake-atmosphere coupling.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216977","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 Solutions of a Model Nonlinear Equation 非线性方程模型的精确解
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602571
A. I. Aristov

Abstract

Since the second half of the twentieth century, wide studies of Sobolev-type equations are undertaken. These equations contain items that are derivatives with respect to time of the second order derivatives of the unknown function with respect to space variables. They can describe nonstationary processes in semiconductors, in plasm, phenomena in hydrodinamics and other ones. Notice that wide studies of qualitative properties of solutions of Sobolev-type equations exist. Namely, results about existence and uniqueness of solutions, their asymptotics and blow-up are known. But there are few results about exact solutions of Sobolev-type equations. There are books and papers about exact solutions of partial equations, but they are devoted mainly to classical equations, where the first or second order derivative with respect to time or the derivative with respect to time of the first order derivative of the unknown function with respect to the space variable is equal to a stationary expression. Therefore it is interesting to study exact solutions of Sobolev-type equations. In the present paper, a third order model nonlinear partial equation is studied. Six classes of its exact solutions are built. They are expressed in terms of elementary and special functions (solutions of some ordinary differential equations).

摘要自二十世纪下半叶以来,对索伯列夫型方程进行了广泛的研究。这些方程包含的项目是未知函数相对于空间变量的二阶导数的时间导数。它们可以描述半导体、等离子体中的非稳态过程、流体力学现象和其他现象。我们注意到,对索伯列夫型方程的解的定性性质存在广泛的研究。也就是说,关于解的存在性和唯一性、其渐近性和炸毁的结果都是已知的。但是关于索波列夫方程的精确解的结果却很少。虽然也有关于偏方程精确解的书籍和论文,但它们主要针对的是经典方程,即未知函数相对于时间的一阶或二阶导数或相对于空间变量的一阶导数相对于时间的导数等于静止表达式。因此,研究 Sobolev 型方程的精确解很有意义。本文研究了一个三阶模型非线性偏方程。建立了六类精确解。它们用基本函数和特殊函数(某些常微分方程的解)表示。
{"title":"Exact Solutions of a Model Nonlinear Equation","authors":"A. I. Aristov","doi":"10.1134/s1995080224602571","DOIUrl":"https://doi.org/10.1134/s1995080224602571","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Since the second half of the twentieth century, wide studies of Sobolev-type equations are undertaken. These equations contain items that are derivatives with respect to time of the second order derivatives of the unknown function with respect to space variables. They can describe nonstationary processes in semiconductors, in plasm, phenomena in hydrodinamics and other ones. Notice that wide studies of qualitative properties of solutions of Sobolev-type equations exist. Namely, results about existence and uniqueness of solutions, their asymptotics and blow-up are known. But there are few results about exact solutions of Sobolev-type equations. There are books and papers about exact solutions of partial equations, but they are devoted mainly to classical equations, where the first or second order derivative with respect to time or the derivative with respect to time of the first order derivative of the unknown function with respect to the space variable is equal to a stationary expression. Therefore it is interesting to study exact solutions of Sobolev-type equations. In the present paper, a third order model nonlinear partial equation is studied. Six classes of its exact solutions are built. They are expressed in terms of elementary and special functions (solutions of some ordinary differential equations).</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216979","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
Interaction of Acoustic Waves with a Layer of Multifractional Polydispersed Vapor–Gas–Droplet Mixture with Account of Phase Transitions 声波与多分数多分散蒸汽-气体-液滴混合物层的相互作用及相变说明
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602182
D. A. Gubaidullin, R. R. Zaripov

Abstract

This work is devoted to the study of the interaction of acoustic waves with a layer of multifractional vapor–gas–droplet mixture with polydispersed inclusions of different sizes and materials. A mathematical model that determines the oblique incidence of an acoustic wave on a layer of finite thickness is presented.The calculations results of acoustic wave reflection from a layer of multifractional vapor–gas–droplet mixture are presented. The influence of layer thickness, mass concentration, inclusion sizes, phase transitions, and the angle of wave incidence on the reflection of acoustic waves from the layer of multifractional polydispersed vapor–gas–droplet mixture has been analyzed.

摘要 这项工作致力于研究声波与具有不同大小和材料的多分散夹杂物的多分数蒸汽-气体-液滴混合物层的相互作用。文中给出了确定声波在有限厚度层上斜入射的数学模型。分析了层厚度、质量浓度、夹杂物大小、相变和入射角对声波从多分数多分散蒸汽-气体-液滴混合物层反射的影响。
{"title":"Interaction of Acoustic Waves with a Layer of Multifractional Polydispersed Vapor–Gas–Droplet Mixture with Account of Phase Transitions","authors":"D. A. Gubaidullin, R. R. Zaripov","doi":"10.1134/s1995080224602182","DOIUrl":"https://doi.org/10.1134/s1995080224602182","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This work is devoted to the study of the interaction of acoustic waves with a layer of multifractional vapor–gas–droplet mixture with polydispersed inclusions of different sizes and materials. A mathematical model that determines the oblique incidence of an acoustic wave on a layer of finite thickness is presented.The calculations results of acoustic wave reflection from a layer of multifractional vapor–gas–droplet mixture are presented. The influence of layer thickness, mass concentration, inclusion sizes, phase transitions, and the angle of wave incidence on the reflection of acoustic waves from the layer of multifractional polydispersed vapor–gas–droplet mixture has been analyzed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217082","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
Unsteady Contact Interaction of Liquid and Solid Bodies 液体和固体物体的非稳态接触相互作用
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602558
G. V. Fedotenkov, A. A. Orekhov, L. N. Rabinskiy

Abstract

The processes of unsteady contact interaction of liquids described by different mathematical models with solid deformable bodies are considered. Closed mathematical formulations of unsteady contact problems in the case of various models of liquids and linear-elastic bodies are developed. The analytical solution of the nonstationary problem of interaction between an acoustic fluid and a deformable solid body is obtained. The time integral Laplace transform is used to construct the solution. The distributions of displacements and stresses in the solid body, as well as pressure and velocity fields in the fluid during unsteady contact interaction are analyzed.

摘要 研究了不同数学模型描述的液体与固体可变形体的非稳态接触相互作用过程。建立了各种液体模型和线性弹性体非稳态接触问题的封闭数学公式。获得了声学流体与可变形固体体之间相互作用的非稳态问题的解析解。解法采用时间积分拉普拉斯变换。分析了非稳态接触相互作用过程中固体中的位移和应力分布,以及流体中的压力和速度场。
{"title":"Unsteady Contact Interaction of Liquid and Solid Bodies","authors":"G. V. Fedotenkov, A. A. Orekhov, L. N. Rabinskiy","doi":"10.1134/s1995080224602558","DOIUrl":"https://doi.org/10.1134/s1995080224602558","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The processes of unsteady contact interaction of liquids described by different mathematical models with solid deformable bodies are considered. Closed mathematical formulations of unsteady contact problems in the case of various models of liquids and linear-elastic bodies are developed. The analytical solution of the nonstationary problem of interaction between an acoustic fluid and a deformable solid body is obtained. The time integral Laplace transform is used to construct the solution. The distributions of displacements and stresses in the solid body, as well as pressure and velocity fields in the fluid during unsteady contact interaction are analyzed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216978","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
Statistical Distribution of Characteristics of the Model Solution after Data Assimilation 数据同化后模型解决方案特征的统计分布
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602455
A. Kuleshov, K. Belyaev, I. Smirnov, N. Tuchkova

Abstract

The probability distribution of several characteristics, in particular, sea surface and subsurface temperature and sea salinity simulated by the ocean circulation model of Nucleus for European Modeling of the Ocean in conjunction with data assimilation are determined. The data assimilation method, called as the Generalized Kalman filter method developed by the authors earlier and published in a number of studies is used. For assimilation the Agro drifter data have been applied for different model levels from sea surface until 2000 m. In order to define the probability distribution of sought model characteristics the Karhunen–Loeve decomposition of the covariance function has been utilized. The results of numerical experiments have been presented and analyzed.

摘要 确定了欧洲海洋建模核心的海洋环流模型与数据同化相结合模拟的若干特征的概率分布,特别是海表和海下温度以及海水盐度的概率分布。使用的数据同化方法称为广义卡尔曼滤波法,由作者早先开发并在多项研究中发表。为了确定所寻求模型特征的概率分布,使用了协方差函数的卡尔胡宁-洛夫分解法。对数值实验结果进行了介绍和分析。
{"title":"Statistical Distribution of Characteristics of the Model Solution after Data Assimilation","authors":"A. Kuleshov, K. Belyaev, I. Smirnov, N. Tuchkova","doi":"10.1134/s1995080224602455","DOIUrl":"https://doi.org/10.1134/s1995080224602455","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The probability distribution of several characteristics, in particular, sea surface and subsurface temperature and sea salinity simulated by the ocean circulation model of Nucleus for European Modeling of the Ocean in conjunction with data assimilation are determined. The data assimilation method, called as the Generalized Kalman filter method developed by the authors earlier and published in a number of studies is used. For assimilation the Agro drifter data have been applied for different model levels from sea surface until 2000 m. In order to define the probability distribution of sought model characteristics the Karhunen–Loeve decomposition of the covariance function has been utilized. The results of numerical experiments have been presented and analyzed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216985","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
A New Economical Unconditional Stable Splitting Method for Numerical Solution of Problems of Mathematical Physics 用于数学物理问题数值求解的新型经济无条件稳定分割法
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602467
Ek. L. Kuznetsova, O. V. Egorova, A. S. Novikov

Abstract

In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.

摘要 本文提出了一种经济的无条件稳定的变向外推法,用于求解含有混合导数的抛物线方程问题的数值解,并从近似性和稳定性方面进行了论证,在与其他数值方法的对比分析中,该方法在改变网格特性时显示出最高的精度和独特的稳定余量。
{"title":"A New Economical Unconditional Stable Splitting Method for Numerical Solution of Problems of Mathematical Physics","authors":"Ek. L. Kuznetsova, O. V. Egorova, A. S. Novikov","doi":"10.1134/s1995080224602467","DOIUrl":"https://doi.org/10.1134/s1995080224602467","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216986","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
Configurations and Deformations in Relativistic Elasticity 相对论弹性中的配置与变形
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602613
S. A. Lychev, K. G. Koifman, N. A. Pivovaroff

Abstract

Configurations and deformations are the homeomorphisms that relate material manifold and shapes of a solid in conventional non-linear elasticity. They play fundamental role in kinematic description of deformable media and seem to be an essential part of non-linear continuum mechanics. These concepts nevertheless are rooted in Euclidean nature of space and time, adopted in non-relativistic physics, and their direct application in relativistic case is impossible. The paper develops the generalization for them within General Relativity. To this end the concept of relativistic shape is introduced, which is defined as an element of foliation over a congruence of worldlines that constitute the world-tube of the solid. This makes it possible to define displacements as a field of translations along elements of congruence beginning on one element of foliation and ending on another. Geometrically this is similar to Fermi–Walker transport. Each relativistic shape can be endowed with two metrics, one induced by ambient space, and another, given by pushforwarding of the metric induced on another shape (another element of foliation). These metrics are relativistic counterpart of Cauchy–Green measures of deformation. The conditions under which the foliation of congruence of worldlines exists are specified. When these conditions are violated, the natural generalization of the shape leads to a set that cannot be represented by the Riemann submanifold. This situation is similar to that which arises in the continuum theory of defects when trying to find a globally stress-free shape. To solve this problem, it is proposed to construct a material manifold whose elements represent shapes locally. The method of determination of geometry on material manifold, which turns out to be Weyl geometry, is proposed. All constructions are carried out within the framework of a variational approach to the derivation of field equations and Noether symmetries.

摘要构型和变形是传统非线性弹性力学中材料流形与固体形状之间的同构关系。它们在可变形介质的运动学描述中起着基础性作用,似乎是非线性连续介质力学的重要组成部分。然而,这些概念植根于欧几里得时空性质,为非相对论物理学所采用,不可能直接应用于相对论情况。本文在广义相对论中对它们进行了概括。为此,本文引入了相对论形状的概念,将其定义为构成实体世界管的世界线全等的对折元素。这样,就可以把位移定义为沿全等元素的平移场,从一个对折元素开始,到另一个对折元素结束。在几何学上,这与费米-沃克运移类似。每个相对论形状都可以被赋予两个度量,一个是由环境空间诱导的,另一个是由另一个形状(另一个折线元素)上诱导的度量的推转给出的。这些度量是考奇-格林变形度量的相对论对应度量。世界线全同的褶皱存在的条件是明确的。当这些条件被违反时,形状的自然广义化会导致一个无法用黎曼子曲面表示的集合。这种情况类似于缺陷连续理论中试图寻找全局无应力形状时出现的情况。为解决这一问题,建议构建一个材料流形,其元素代表局部形状。提出了在材料流形上确定几何形状的方法,该方法被证明是韦尔几何。所有构造都是在推导场方程和诺特对称性的变分法框架内进行的。
{"title":"Configurations and Deformations in Relativistic Elasticity","authors":"S. A. Lychev, K. G. Koifman, N. A. Pivovaroff","doi":"10.1134/s1995080224602613","DOIUrl":"https://doi.org/10.1134/s1995080224602613","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Configurations and deformations are the homeomorphisms that relate material manifold and shapes of a solid in conventional non-linear elasticity. They play fundamental role in kinematic description of deformable media and seem to be an essential part of non-linear continuum mechanics. These concepts nevertheless are rooted in Euclidean nature of space and time, adopted in non-relativistic physics, and their direct application in relativistic case is impossible. The paper develops the generalization for them within General Relativity. To this end the concept of relativistic shape is introduced, which is defined as an element of foliation over a congruence of worldlines that constitute the world-tube of the solid. This makes it possible to define displacements as a field of translations along elements of congruence beginning on one element of foliation and ending on another. Geometrically this is similar to Fermi–Walker transport. Each relativistic shape can be endowed with two metrics, one induced by ambient space, and another, given by pushforwarding of the metric induced on another shape (another element of foliation). These metrics are relativistic counterpart of Cauchy–Green measures of deformation. The conditions under which the foliation of congruence of worldlines exists are specified. When these conditions are violated, the natural generalization of the shape leads to a set that cannot be represented by the Riemann submanifold. This situation is similar to that which arises in the continuum theory of defects when trying to find a globally stress-free shape. To solve this problem, it is proposed to construct a material manifold whose elements represent shapes locally. The method of determination of geometry on material manifold, which turns out to be Weyl geometry, is proposed. All constructions are carried out within the framework of a variational approach to the derivation of field equations and Noether symmetries.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216987","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
Modeling of Heat Transfer in a Plate Made of Composite Material in the Presence of a Thermal Energy Sink 存在热能散热器的复合材料板中的传热模型
IF 0.7 Q2 MATHEMATICS Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602509
O. V. Tushavina, M. S. Egorova, P. F. Pronina

Abstract

The paper is focused on mathematical modeling of heat transfer in an anisotropic plate with heat energy drain due to various physical and chemical transformations inside the material and under conditions of exponential heat transfer at the boundary. The analytical solution of the second initial boundary value problem of heat conduction with nonlinear heat energy flow is obtained and investigated.

摘要 本文主要研究了各向异性板中的传热数学模型,由于材料内部的各种物理和化学变化以及边界的指数传热条件,导致热能耗尽。本文获得并研究了非线性热能流导热的二次初始边界值问题的解析解。
{"title":"Modeling of Heat Transfer in a Plate Made of Composite Material in the Presence of a Thermal Energy Sink","authors":"O. V. Tushavina, M. S. Egorova, P. F. Pronina","doi":"10.1134/s1995080224602509","DOIUrl":"https://doi.org/10.1134/s1995080224602509","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper is focused on mathematical modeling of heat transfer in an anisotropic plate with heat energy drain due to various physical and chemical transformations inside the material and under conditions of exponential heat transfer at the boundary. The analytical solution of the second initial boundary value problem of heat conduction with nonlinear heat energy flow is obtained and investigated.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"420 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216988","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
期刊
Lobachevskii Journal of Mathematics
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1