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Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space 对三维空间镜面反射敏感的微极性固体的热传导
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-02-18 DOI: 10.26907/2541-7746.2023.4.389-403
E. Murashkin, Y. Radayev
{"title":"Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space","authors":"E. Murashkin, Y. Radayev","doi":"10.26907/2541-7746.2023.4.389-403","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.4.389-403","url":null,"abstract":"This article considers a variant of the heat conduction theory of thermal conductivity, in which the heat flux pseudovector has a weight of 1. The pseudoinvariants associated to the heat flux pseudovector are sensitive to mirror reflections and inversions of threedimensional space. The primary purpose of the study was to find a heat flux vector that is algebraically equivalent to the microrotation pseudovector and to measure elementary volumes and areas using pseudoinvariants that are sensitive to mirror reflections. To represent spinor displacements, a contravariant microrotation pseudovector with a weight of +1 was selected. Thus, the heat flux and mass density were expressed as odd-weight pseudotensors. The Helmholtz free energy per unit doublet pseudoinvariant volume was employed as the thermodynamic state potential of the following functional arguments: absolute temperature, symmetric parts, and accompanying vectors for the linear asymmetric strain tensor and the wryness pseudotensor. The results obtained show that the thermal conductivity coefficient and heat capacity of elastic micropolar solids are pseudoscalars of odd weight, indicating their sensitivity to mirror reflections.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"8 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959736","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
Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models 经典和广义热传导模型方程的基本解法
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-02-18 DOI: 10.26907/2541-7746.2023.4.404-414
A. A. Orekhov, L. N. Rabinskiy, G. Fedotenkov
{"title":"Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models","authors":"A. A. Orekhov, L. N. Rabinskiy, G. Fedotenkov","doi":"10.26907/2541-7746.2023.4.404-414","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.4.404-414","url":null,"abstract":"This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140452547","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 Local Stability Loss of Modified Composites with Whiskerized Fibers 论带须纤维改性复合材料的局部稳定性损失
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-02-18 DOI: 10.26907/2541-7746.2023.4.344-360
G. I. Kriven, D. S. Shavelkin
{"title":"On Local Stability Loss of Modified Composites with Whiskerized Fibers","authors":"G. I. Kriven, D. S. Shavelkin","doi":"10.26907/2541-7746.2023.4.344-360","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.4.344-360","url":null,"abstract":"This article examines the critical compressive stresses required for a modified fiber composite to remain straight while the fibers within it bend. It was assumed that the modified composite consists of three phases: fiber, whiskerized interfacial layer, and matrix. An example of a composite material made up of carbon fibers, a whiskerized layer of carbon nanotubes with an epoxy matrix, and an epoxy matrix was considered. Its physical parameters affecting the critical compressive stresses were assessed, and methods for determining them were proposed. The effective properties of the inclusion and binder composite material were identified using the Voigt and Reis methods. Similarly, the effective properties of the interfacial whiskerized layer were analyzed by the three-phase method. The influence of fiber wavelength and phase shift, which define the destruction of the composite material, on the critical compressive stress value was explored. The wavelengths at which the composite material is destroyed were found. The effect of the volume content of the modified inclusion on the minimum critical compressive stress value was shown. The results for the modified composites were compared with those for the classical composites with a similar volume content of inclusions.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"36 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140452720","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
Incompatible Deformations of Elastic Plates 弹性板的不相容变形
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-02-18 DOI: 10.26907/2541-7746.2023.4.361-388
S. Lychev
{"title":"Incompatible Deformations of Elastic Plates","authors":"S. Lychev","doi":"10.26907/2541-7746.2023.4.361-388","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.4.361-388","url":null,"abstract":"This article considers the methods for mathematical modeling of incompatible finite deformations of elastic plates by using the principles of the differential geometry theory underlying continuously distributed defects. Equilibrium equations were derived by asymptotic expansions of the finite strain measures with respect to two small parameters. One parameter defines the order of smallness of displacements from the reference shape (self-stressed state), while the other specifies the thickness. Asymptotic orders were different for the deflections and displacements in the plate plane, as well as for their derivatives. They were selected in such a way that, with additional assumptions on the possibility of ignoring certain terms in the resulting expressions and the compatibility of deformations, the equations could be reduced to the system of F¨oppl–von Ka´rm´an equations.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"5 44","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959283","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 Conservative Finite Element Scheme for the Kirchhoff Equation 基尔霍夫方程的保守有限元方案
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-18 DOI: 10.26907/2541-7746.2023.2.115-131
R. Dautov, M. V. Ivanova
{"title":"A Conservative Finite Element Scheme for the Kirchhoff Equation","authors":"R. Dautov, M. V. Ivanova","doi":"10.26907/2541-7746.2023.2.115-131","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.2.115-131","url":null,"abstract":"This article presents an implicit two-layer finite element scheme for solving the Kirchhoff equation, a nonlinear nonlocal equation of hyperbolic type with the Dirichlet integral. The discrete scheme was designed considering the solution of the problem and its derivative for the time variable. It ensures total energy conservation at a discrete level. The use of the Newton method was proven to be effective for solving the scheme on the time layer despite the nonlocality of the equation. The test problems with smooth solutions showed that the scheme can define both the solution of the problem and its time derivative with an error of O(h2+τ2) in the root-mean-square norm, where τ and h are the grid steps in time and space, respectively.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"108 49","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139640336","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
Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator 附带振子的浅壳特征振动数学建模
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-18 DOI: 10.26907/2541-7746.2023.2.153-166
D. M. Korosteleva, S. Solov’ev
{"title":"Mathematical Modeling of Eigenvibrations of the Shallow Shell with an Attached Oscillator","authors":"D. M. Korosteleva, S. Solov’ev","doi":"10.26907/2541-7746.2023.2.153-166","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.2.153-166","url":null,"abstract":"For the problem of eigenvibrations of the shallow shell with an attached oscillator, a new symmetric variational statement in the Hilbert space was proposed. It was established that there exist a sequence of positive eigenvalues of finite multiplicity with a limit point at infinity and the corresponding complete orthonormal system of eigenvectors. The problem was approximated by the mesh scheme of the finite element method with Hermite finite elements. Theoretical error estimates for the approximate solutions were proved. The theoretical findings were verified by the results of numerical experiments.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"104 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139640327","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
Dirichlet Solutions of Functional Differential Equations without Delay 函数微分方程的无延迟 Dirichlet 解法
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-18 DOI: 10.26907/2541-7746.2023.2.132-142
N. P. Evlampiev, V. S. Mokeichev, I. E. Filippov
{"title":"Dirichlet Solutions of Functional Differential Equations without Delay","authors":"N. P. Evlampiev, V. S. Mokeichev, I. E. Filippov","doi":"10.26907/2541-7746.2023.2.132-142","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.2.132-142","url":null,"abstract":"Necessary and sufficient conditions for the existence of a valid Dirichlet solution were obtained. A method was developed to find Dirichlet solutions of the functional differential equation with non-delayed linear argument deviation.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140503602","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
Development of an Isoline Modeling Method for Extended Small Celestial Objects 为扩展小天体开发等值线建模方法
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-18 DOI: 10.26907/2541-7746.2023.2.105-114
A. O. Andreev, Y. Nefedyev, N. Demina
{"title":"Development of an Isoline Modeling Method for Extended Small Celestial Objects","authors":"A. O. Andreev, Y. Nefedyev, N. Demina","doi":"10.26907/2541-7746.2023.2.105-114","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.2.105-114","url":null,"abstract":"This article presents a method for modeling extended small celestial (ESC) objects, which are mainly cometary systems. Special attention was given to the possibility of analyzing their structure and physical properties in line with the modern theories of the Solar System’s formation suggesting a rather complicated evolutionary dynamics. Modeling and investigating the structure of different extended celestial objects advance our understanding of the general evolutionary processes that have taken place in the Solar System because all its objects are evolutionarily related. The isoline modeling (IM) method was tested on the real comet data and proved effective in assessing the activity of the processes that occur as ESC objects move in space. The IM method is particularly useful for studying long-period comets that, in many cases, cross the perihelion only once within a foreseeable period of human existence.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"32 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140503729","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
Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape 解决任意形状物体的标量二维非线性衍射问题
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-18 DOI: 10.26907/2541-7746.2023.2.167-177
A. O. Lapich, M. Medvedik
{"title":"Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape","authors":"A. O. Lapich, M. Medvedik","doi":"10.26907/2541-7746.2023.2.167-177","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.2.167-177","url":null,"abstract":"In this study, the development, design, and software implementation of the methods for solving the nonlinear diffraction problem were performed. The influence of nonlinear medium defined by the Kerr law on the propagation of a wave passing through an object was examined. The differential and integral formulations of the problem and the nonlinear integral equation were considered. The problem was solved for different bodies with the use of various computational grids. Convergence graphs of the iterative processes were generated. The obtained graphical results were presented. The explicit and implicit methods for solving the integral equation were compared.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"47 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140504090","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 Relaxed Version of the Cutting Method with Approximation of the Constraint Region 近似约束区域的宽松切割法
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-18 DOI: 10.26907/2541-7746.2023.2.143-152
I. Zabotin, O. Shulgina, R. Yarullin
{"title":"A Relaxed Version of the Cutting Method with Approximation of the Constraint Region","authors":"I. Zabotin, O. Shulgina, R. Yarullin","doi":"10.26907/2541-7746.2023.2.143-152","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.2.143-152","url":null,"abstract":"A cutting method was proposed for solving the convex programming problem. The method assumes that the constraint region of the problem is embedded into some polyhedral sets for constructing iteration points. It involves the construction of a sequence of approximations that belongs to the admissible set and is relaxed, as well as implies that the ε-solution of the initial problem is fixed after a finite number of steps. The method also allows to obtain mixed convergent algorithms by using, if desired, any known or new relaxation algorithms for constructing the main iteration points.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"23 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140504507","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
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