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Journal of Siberian Federal University. Mathematics and Physics最新文献

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High-Temperature Evolution of the Magnetization of Aluminum Reduction Cell Steel 铝还原电池钢的高温磁化演化
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2021-02-01 DOI: 10.17516/1997-1397-2021-14-1-5-11
D. Balaev, S. Semenov, Sergei N. Varnakov, E. Radionov, Y. Tretyakov
{"title":"High-Temperature Evolution of the Magnetization of Aluminum Reduction Cell Steel","authors":"D. Balaev, S. Semenov, Sergei N. Varnakov, E. Radionov, Y. Tretyakov","doi":"10.17516/1997-1397-2021-14-1-5-11","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-1-5-11","url":null,"abstract":"The magnetic properties of steel of a structural element of an aluminum reduction cell have been investigated in the temperature range of 300–900 K. The analysis of the temperature dependence of the saturation magnetization MS(T) showed (i) the applicability of the Bloch’s 3=2 law and a reason- able value of the Bloch’s constant for steel and (ii) the quadratic dependence MS(T) (1 - T2) in the temperature range of 380–700 K.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123790533","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
Problem of Determining a Multidimensional Kernel in One Parabolic Integro–differential Equation 一类抛物型积分-微分方程多维核的确定问题
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2021-02-01 DOI: 10.17516/1997-1397-2020-14-1-117-127
D. Durdiev, Zhavlon Zafarovich Nuriddinov
{"title":"Problem of Determining a Multidimensional Kernel in One Parabolic Integro–differential Equation","authors":"D. Durdiev, Zhavlon Zafarovich Nuriddinov","doi":"10.17516/1997-1397-2020-14-1-117-127","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-14-1-117-127","url":null,"abstract":"The multidimensional parabolic integro-differential equation with the time-convolution in- tegral on the right side is considered. The direct problem is represented by the Cauchy problem for this equation. In this paper it is studied the inverse problem consisting in finding of a time and spatial dependent kernel of the integrated member on known in a hyperplane xn = 0 for t > 0 to the solution of direct problem. With use of the resolvent of kernel this problem is reduced to the investigation of more convenient inverse problem. The last problem is replaced with the equivalent system of the integral equations with respect to unknown functions and on the bases of contractive mapping principle it is proved the unique solvability to the direct and inverse problems","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114331649","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: 3
Mass Transfer Between the Vortex Ring and the Surrounding Fluid, when the Density of the Fluid in the Vortex is Less than Outside it 当漩涡内流体密度小于漩涡外流体密度时，漩涡环与周围流体之间的传质
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2021-02-01 DOI: 10.17516/1997-1397-2021-14-1-42-46
V. Nikulin, E. Chashnikov
{"title":"Mass Transfer Between the Vortex Ring and the Surrounding Fluid, when the Density of the Fluid in the Vortex is Less than Outside it","authors":"V. Nikulin, E. Chashnikov","doi":"10.17516/1997-1397-2021-14-1-42-46","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-1-42-46","url":null,"abstract":"The mass transfer between the atmosphere of a vortex ring and the surrounding liquid was studied by the shadow method in the case, when the density of the liquid in the vortex is less than outside it. The obtained results were compared with experiments on the motion of vortex rings containing a fluid denser, than the surrounding fluid. The qualitative effects of changing the shadow image is established to be the same in both cases. The characteristic path and time of exchange are determined by analyzing of shadow images in depending on the speed and magnitude of the density difference","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133615369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On a Limiting Passage as the Thickness of a Rigid Inclusions in an Equilibrium Problem for a Kirchhoff-Love Plate with a Crack 含裂纹Kirchhoff-Love板平衡问题中作为刚性夹杂厚度的极限通道
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2021-02-01 DOI: 10.17516/1997-1397-2021-14-1-28-41
N. Lazarev, G. Semenova, N. A. Romanova
{"title":"On a Limiting Passage as the Thickness of a Rigid Inclusions in an Equilibrium Problem for a Kirchhoff-Love Plate with a Crack","authors":"N. Lazarev, G. Semenova, N. A. Romanova","doi":"10.17516/1997-1397-2021-14-1-28-41","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-1-28-41","url":null,"abstract":"The paper considers equilibrium models of Kirchhoff-Love plates with rigid inclusions of two types. The first type of inclusion is described by three-dimensional sets, the second one corresponds to a cylindrical rigid inclusion, which is perpendicular to the plate’s median plane in the initial state. For both models, we suppose that there is a through crack along a fixed part of the inclusion’s boundary. On the crack non-penetration conditions are prescribed which correspond to a certain known configuration bending near the crack. The uniqueness solvability of a new problems for a Kirchhoff-Love plate with a flat rigid inclusion is proved. It is proved that when a thickness parameter tends to zero, the problem for a flat rigid inclusion can be represented as a limiting task for a family of variational problems concerning the inclusions of the first type. A solvability of an optimal control problem with a control given by the size of inclusions is proved","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"593 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122935412","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: 4
New Classes of Solutions of Dynamical Problems of Plasticity 塑性动力学问题解的新类别
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-12-01 DOI: 10.17516/1997-1397-2020-13-6-792-796
S. I. Senashov, O. Gomonova, I. Savostyanova, O. Cherepanova
{"title":"New Classes of Solutions of Dynamical Problems of Plasticity","authors":"S. I. Senashov, O. Gomonova, I. Savostyanova, O. Cherepanova","doi":"10.17516/1997-1397-2020-13-6-792-796","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-6-792-796","url":null,"abstract":"Dynamical problems of the theory of plasticity have not been adequately studied. Dynamical problems arise in various fields of science and engineering but the complexity of original differential equations does not allow one to construct new exact solutions and to solve boundary value problems correctly. One-dimensional dynamical problems are studied rather well but two-dimensional problems cause major difficulties associated with nonlinearity of the main equations. Application of symmetries to the equations of plasticity allow one to construct some exact solutions. The best known exact solution is the solution obtained by B.D. Annin. It describes non-steady compression of a plastic layer by two rigid plates. This solution is a linear one in spatial variables but includes various functions of time. Symmetries are also considered in this paper. These symmetries allow transforming exact solutions of steady equations into solutions of non-steady equations. The obtained solution contains 5 arbitrary functions","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128577726","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
Three-Dimensional Simulation of a Tank Filling With a Viscous Fluid Using the VOF Method 用VOF法对粘性流体充注槽进行三维模拟
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-12-01 DOI: 10.17516/1997-1397-2020-13-6-670-677
E. Borzenko, E. Hegaj
{"title":"Three-Dimensional Simulation of a Tank Filling With a Viscous Fluid Using the VOF Method","authors":"E. Borzenko, E. Hegaj","doi":"10.17516/1997-1397-2020-13-6-670-677","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-6-670-677","url":null,"abstract":"This paper presents the results of 3D modeling of a Newtonian fluid flow with a free surface. The PLIC-VOF algorithm, which is developed to solve the problems of two-dimensional fluid flows with a free surface, is generalized to the case of three-dimensional flows. Efficiency of the developed algorithm and reliability of the obtained results are justified by comparing with available data in literature and by testing approximation convergence. Parametric calculations of a rectangular channel filling show that the free surface assumes a steady convex shape over time and then moves along the channel at a constant velocity. As a result of parametric studies, the dependences of geometric characteristics of the free surface shape on problem parameters have been plotted","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126965782","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 Construction of Solutions to a Problem with a Free Boundary for the Non-linear Heat Equation 非线性热方程自由边界问题解的构造
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-12-01 DOI: 10.17516/1997-1397-2020-13-6-694-707
L. Alexander, F. S. Lev, Lee Ming-Gong
{"title":"On the Construction of Solutions to a Problem with a Free Boundary for the Non-linear Heat Equation","authors":"L. Alexander, F. S. Lev, Lee Ming-Gong","doi":"10.17516/1997-1397-2020-13-6-694-707","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-6-694-707","url":null,"abstract":"The construction of solutions to the problem with a free boundary for the non-linear heat equation which have the heat wave type is considered in the paper. The feature of such solutions is that the degeneration occurs on the front of the heat wave which separates the domain of positive values of the unknown function and the cold (zero) background. A numerical algorithm based on the boundary element method is proposed. Since it is difficult to prove the convergence of the algorithm due to the non-linearity of the problem and the presence of degeneracy the comparison with exact solutions is used to verify numerical results. The construction of exact solutions is reduced to integrating the Cauchy problem for ODE. A qualitative analysis of the exact solutions is carried out. Several computational experiments were performed to verify the proposed method","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129462829","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: 2
Control of Stochastic Processes that Proceeds in the Limited Area 在有限区域内进行的随机过程的控制
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-12-01 DOI: 10.17516/1997-1397-2020-13-6-746-754
V. Alexander, D. Eugene
{"title":"Control of Stochastic Processes that Proceeds in the Limited Area","authors":"V. Alexander, D. Eugene","doi":"10.17516/1997-1397-2020-13-6-746-754","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-6-746-754","url":null,"abstract":"Stochastic process control is considered in the paper. New types of processes (H-processes) are described. Input variables are stochastically related in H-processes. The problem of identification and control of H-processes are considered in detail. The modification of the nonparametric dual control algorithm is developed. The proposed algorithm is compared with the PID algorithm. Application of the proposed algorithm for controlling the H-process with several output variables is presented","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122884733","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
Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains 外域的混合双调和Dirichlet-Neumann问题
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-12-01 DOI: 10.17516/1997-1397-2020-13-6-755-762
H. Matevossian
{"title":"Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains","authors":"H. Matevossian","doi":"10.17516/1997-1397-2020-13-6-755-762","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-6-755-762","url":null,"abstract":"We study the unique solvability of the mixed Dirichlet-Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions of the mixed Dirichlet-Neumann problem","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"22 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125496054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Patterns of Magnetohydrodynamic Flow in the Bent Channel 弯曲通道中磁流体动力流动模式
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-12-01 DOI: 10.17516/1997-1397-2020-13-6-774-780
A. Proskurin, A. Sagalakov
{"title":"Patterns of Magnetohydrodynamic Flow in the Bent Channel","authors":"A. Proskurin, A. Sagalakov","doi":"10.17516/1997-1397-2020-13-6-774-780","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-6-774-780","url":null,"abstract":"The article considers the flow patterns of an electrically-conductive fluid in a 90 degree bend. The magnetic field is directed parallel to the outlet branch of the bend. Magnetohydrodynamic equations in terms of the small magnetic Reynolds numbers approach and the spectral-element method were used. The flow patterns were studied at different values of the Reynolds and the Hartmann numbers, and with regard to different values of the bent radus. A reverse flow was found in the outlet branch of the channel","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127403483","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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