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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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602364
Yu. N. Sviridenko
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602388
T. Akinaga, P. M. J. Trevelyan, S. C. Generalis
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602601
R. Yu. Fadeev, V. M. Stepanenko
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602571
A. I. Aristov
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602182
D. A. Gubaidullin, R. R. Zaripov
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602558
G. V. Fedotenkov, A. A. Orekhov, L. N. Rabinskiy
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602455
A. Kuleshov, K. Belyaev, I. Smirnov, N. Tuchkova
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602467
Ek. L. Kuznetsova, O. V. Egorova, A. S. Novikov
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602613
S. A. Lychev, K. G. Koifman, N. A. Pivovaroff
{"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
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602509
O. V. Tushavina, M. S. Egorova, P. F. Pronina
{"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
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