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Routing in circulant graphs based on a virtual coordinate system 基于虚拟坐标系的环状图中的路由选择
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.282-293
A. M. Sukhov, A. Y. Romanov, E. V. Glushak
{"title":"Routing in circulant graphs based on a virtual coordinate system","authors":"A. M. Sukhov, A. Y. Romanov, E. V. Glushak","doi":"10.26907/2541-7746.2023.3.282-293","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.282-293","url":null,"abstract":"This article explores routing methods in two-dimensional circulant graphs where each vertex is linked to four neighboring ones. The unique symmetries of the circulant graph make it a viable topology for high-performance computing devices, such as networks-on-chip and cluster supercomputers. It was shown that the coordinates of the vertices can be determined as the minimum number of transitions along the generators from the initial vertex. Two virtual coordinate-based routing methods were developed. The first method entails restoring the vertex numbers and finding the difference between them, with the coordinates of the corresponding vertex setting the route. The second method involves calculating the difference between the final and initial vertex coordinates, while minimizing the route based on the proposed algorithm.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"37 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509567","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 formulation of thermomechanical problems 热力学问题的变式表述
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.246-263
S. A. Lurie, P. Belov, A. V. Volkov
{"title":"Variational formulation of thermomechanical problems","authors":"S. A. Lurie, P. Belov, A. V. Volkov","doi":"10.26907/2541-7746.2023.3.246-263","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.246-263","url":null,"abstract":"This article proposes that a 4D space-time continuum is used for building variational thermomechanical continuum models. In order to identify physical constants in reversible processes, physically justified hypotheses were formulated. They are the hypotheses of complementary shear stress, classical dependence of momentum on velocity, and heat flow potentiality (generalized Maxwell–Cattaneo law). The Duhamel–Neumann law was assumed to be classical. In the considered model, the generalized Maxwell–Cattaneo and Duhamel–Neumann laws were not introduced phenomenologically. They were derived from the compatibility equations by excluding thermal potential from the constitutive equations for temperature, heat flow, and pressure. Dissipation channels were considered as the simplest non-integrable variational forms, which are linear in the variations of arguments. As a result, a variational principle that generalizes L.I. Sedov’s principle was developed. It is a consequence of the virtual work principle and termed as the difference between the variation of the Lagrangian of reversible thermomechanical processes and the algebraic sum of dissipation channels. It was proved that for the classical thermomechanical processes, with second-order differential equations, there can only exist six dissipation channels. Two of them determine dissipation in an uncoupled system – in the equations of motion and heat balance. The remaining four channels define coupling effects in coupled problems of dissipative thermomechanics.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"38 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509627","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 Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries 具有任意数量移动相变边界的复合材料的斯特凡问题
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.236-245
E. L. Kuznetsova, S. I. Zhavoronok
{"title":"A Stefan problem for composite materials with an arbitrary number of moving phase-transition boundaries","authors":"E. L. Kuznetsova, S. I. Zhavoronok","doi":"10.26907/2541-7746.2023.3.236-245","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.236-245","url":null,"abstract":"A Stefan problem of heat transfer in semi-infinite bodies with an arbitrary number of unsteady moving boundaries during phase transitions was solved. Such problems arise when composite materials are heated at high temperatures, causing the binding agents to decompose (destruct) thermally, which leads to the formation of moving boundaries in the onset and end of phase transitions, mass transfer, etc. An analytical solution of the Stefan problem with an arbitrary number of unsteady moving boundaries was obtained. The heat transfer process with two moving boundaries was analyzed.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"31 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140510070","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 system for automatic construction of knowledge graphs of mathematical documents 自动构建数学文件知识图谱的系统
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.264-281
A. O. Nevzorova, B. Gizatullin
{"title":"A system for automatic construction of knowledge graphs of mathematical documents","authors":"A. O. Nevzorova, B. Gizatullin","doi":"10.26907/2541-7746.2023.3.264-281","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.264-281","url":null,"abstract":"This article outlines the process of creating an automated system for knowledge graph construction from collections of mathematical documents in LATEX format. The MathCollectionOntology, which defines the types of objects and relationships in knowledge graphs, was developed. The introduced toolkit includes methods for extracting mathematical terms, browsing and identifying document topics, extracting entities from LATEX code, and calculating statistical parameters of the graph. The parsed entities are mathematical terms, topics generated through the Latent Dirichlet Allocation, UDC codes, used formulas, author affiliations, cited literature, and others. The knowledge graph captures each extracted object using specific types of relationships defined in the MathCollectionOntology. Here, a knowledge graph was coined for a collection of articles published in Izvestiya VUZov. Matematika journal (1114 Russian-language documents in LATEX format). The thematic terms of the document topics were described. The quantitative parameters of the constructed knowledge graph were obtained.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509290","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
Problems of heat and mass transfer in chemically reacting boundary layers on blunted bodies 钝体上化学反应边界层的传热和传质问题
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.294-306
O. Tushavina, M. S. Egorova
{"title":"Problems of heat and mass transfer in chemically reacting boundary layers on blunted bodies","authors":"O. Tushavina, M. S. Egorova","doi":"10.26907/2541-7746.2023.3.294-306","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.294-306","url":null,"abstract":"This article considers a nonlinear system of partial differential equations describing the boundary layer. Such a system is commonly solved by numerical methods. Here, the Dorodnitsyn–Lees variables were used to carry out an analysis and derive the formulas for calculating the body temperatures and the heat fluxes to the body generated by the reacting compressible gradient boundary layer.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509446","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 the oxidation process of TiAl and Ti3 Al intermetallic compounds due to grain-boundary diffusion of oxygen 氧的晶界扩散导致的 TiAl 和 Ti3 Al 金属间化合物氧化过程建模
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.307-321
M. V. Chepak-Gizbrekht, A. G. Knyazeva
{"title":"Modeling the oxidation process of TiAl and Ti3 Al intermetallic compounds due to grain-boundary diffusion of oxygen","authors":"M. V. Chepak-Gizbrekht, A. G. Knyazeva","doi":"10.26907/2541-7746.2023.3.307-321","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.307-321","url":null,"abstract":"A diffusion-kinetic model was proposed to analyze the oxidation process in a nanostructured material with explicit identification of grain boundaries. It was assumed that oxygen migrates faster along the boundaries than it does in the grain volume. The model takes into account the stages of decomposition and formation of intermetallic compounds, as well as the formation of oxides, both within the boundaries and in the grain volume. The problem was solved numerically, and the oxidation dynamics were compared for various materials with different grain properties.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"22 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140510143","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 effect of stress on the nonequilibrium viscosity of glasses 应力对玻璃非平衡粘度的影响
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-12 DOI: 10.26907/2541-7746.2023.3.219-235
U. P. Karaseva, A. В. Freidin
{"title":"On the effect of stress on the nonequilibrium viscosity of glasses","authors":"U. P. Karaseva, A. В. Freidin","doi":"10.26907/2541-7746.2023.3.219-235","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.219-235","url":null,"abstract":"Two processes related to the relaxation of a glassy material’s structure were discussed. One entails stress relaxation, while the other involves the relaxation of the structure to its equilibrium state following the stress relief and is described by the change of fictive temperature. Both processes affect the viscosity coefficient. The nonequilibrium viscosity model was analyzed with account of these relaxation processes. The importance of considering stresses when modeling the viscoelastic behavior of glassy materials was showcased by solving the problem of stress relaxation in a plate under thermal stresses.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"19 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509653","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 cutting-plane method with internal iteration points for the general convex programming problem 针对一般凸编程问题的带内部迭代点的切割面方法
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-11 DOI: 10.26907/2541-7746.2023.3.208-218
I. Zabotin, K. Kazaeva, O. Shulgina
{"title":"A cutting-plane method with internal iteration points for the general convex programming problem","authors":"I. Zabotin, K. Kazaeva, O. Shulgina","doi":"10.26907/2541-7746.2023.3.208-218","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.208-218","url":null,"abstract":"A cutting method for solving the problem of convex programming was proposed. The method calculates iteration points based on approximation by polyhedral sets of the constraint region and the epigraph of the objective function. Its distinguishing feature is that the main sequence of approximations is constructed within the admissible region. At each step, it is also possible to assess how close the current value of the function is to the optimal value. The convergence of the method was proved. A few of its implementations were outlined.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"48 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509951","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 fully discrete finite element scheme for the nonlinear Klein–Gordon equation 非线性克莱因-戈登方程的保守全离散有限元方案
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-11 DOI: 10.26907/2541-7746.2023.3.190-207
R. Dautov, G. R. Salimzyanova
{"title":"A conservative fully discrete finite element scheme for the nonlinear Klein–Gordon equation","authors":"R. Dautov, G. R. Salimzyanova","doi":"10.26907/2541-7746.2023.3.190-207","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.190-207","url":null,"abstract":"This article proposes a family of the Petrov–Galerkin–FEM methods that can be used to solve the nonlinear Klein–Gordon equation. The discrete schemes were formulated based on the solution of the problem and its time derivative. They ensure that the total energy is conserved at a discrete level. The simplest two-layer scheme was studied numerically. Based on the solution of the test problems with smooth solutions, it was shown that the scheme can determine the solution of the problem, as well as its time derivative with an error of the order of O(h2 + τ 2) in the continuous L2 norm, where τ and h characterize the grid steps in time and space, respectively.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"44 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140510379","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
Painleve analysis of travelling wave solutions and analysis of energy estimates for a nonlinear Sobolev-type equation 非线性 Sobolev 型方程的行波解的 Painleve 分析和能量估计分析
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki Pub Date : 2024-01-11 DOI: 10.26907/2541-7746.2023.3.182-189
A. I. Aristov
{"title":"Painleve analysis of travelling wave solutions and analysis of energy estimates for a nonlinear Sobolev-type equation","authors":"A. I. Aristov","doi":"10.26907/2541-7746.2023.3.182-189","DOIUrl":"https://doi.org/10.26907/2541-7746.2023.3.182-189","url":null,"abstract":"There is considerable interest in studying unbounded solutions of nonlinear partial equations. In many cases, energy estimates can be used to prove that the solution tends to infinity in finite time, while also providing an estimate for the latter. Here, an equation in which energy estimates fail to gauge the cases when solutions exhibit such behavior was analyzed. A class of unbounded solutions was explored using the Painleve analysis.","PeriodicalId":516762,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki","volume":"47 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140509954","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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