直纹曲面的磁球指标

IF 2.1 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

International Journal of Geometric Methods in Modern Physics Pub Date : 2023-11-03 DOI:10.1142/s0219887824500683

Alperen Yildirim, Emin Kasap

{"title":"直纹曲面的磁球指标","authors":"Alperen Yildirim, Emin Kasap","doi":"10.1142/s0219887824500683","DOIUrl":null,"url":null,"abstract":"The spherical indicatrix of a ruled surface is the image curve of its rulings on the sphere [Formula: see text]. In this paper, we present Lorentz forces and magnetic curves produced by the Frenet frame [Formula: see text] of the spherical indicatrix of a ruled surface in a magnetic field. We calculate magnetic vector fields of magnetic curves for [Formula: see text]. Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic spherical indicatrix. We obtain developability conditions for these surfaces. Finally, we give some examples to show magnetic flux surfaces.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"176 s418","pages":"0"},"PeriodicalIF":2.1000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Magnetic Spherical Indicatrix of a Ruled Surface\",\"authors\":\"Alperen Yildirim, Emin Kasap\",\"doi\":\"10.1142/s0219887824500683\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The spherical indicatrix of a ruled surface is the image curve of its rulings on the sphere [Formula: see text]. In this paper, we present Lorentz forces and magnetic curves produced by the Frenet frame [Formula: see text] of the spherical indicatrix of a ruled surface in a magnetic field. We calculate magnetic vector fields of magnetic curves for [Formula: see text]. Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic spherical indicatrix. We obtain developability conditions for these surfaces. Finally, we give some examples to show magnetic flux surfaces.\",\"PeriodicalId\":50320,\"journal\":{\"name\":\"International Journal of Geometric Methods in Modern Physics\",\"volume\":\"176 s418\",\"pages\":\"0\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2023-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Geometric Methods in Modern Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219887824500683\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Geometric Methods in Modern Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219887824500683","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

直纹曲面的球面指标是其直纹在球面上的像曲线[公式:见正文]。在本文中，我们给出了由磁场中直纹曲面的球面指标的弗莱内框架[公式:见文]所产生的洛伦兹力和磁曲线。我们计算了[公式:见原文]的磁曲线的磁场矢量。在此基础上，定义了磁矢量场沿磁球指标构成的磁通曲面。我们得到了这些曲面的可展性条件。最后，我们给出了一些例子来说明磁通面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Magnetic Spherical Indicatrix of a Ruled Surface

The spherical indicatrix of a ruled surface is the image curve of its rulings on the sphere [Formula: see text]. In this paper, we present Lorentz forces and magnetic curves produced by the Frenet frame [Formula: see text] of the spherical indicatrix of a ruled surface in a magnetic field. We calculate magnetic vector fields of magnetic curves for [Formula: see text]. Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic spherical indicatrix. We obtain developability conditions for these surfaces. Finally, we give some examples to show magnetic flux surfaces.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Geometric Methods in Modern Physics 物理-物理：数学物理

CiteScore

3.40

自引率

22.20%

发文量

274

审稿时长

6 months

期刊介绍： This journal publishes short communications, research and review articles devoted to all applications of geometric methods (including commutative and non-commutative Differential Geometry, Riemannian Geometry, Finsler Geometry, Complex Geometry, Lie Groups and Lie Algebras, Bundle Theory, Homology an Cohomology, Algebraic Geometry, Global Analysis, Category Theory, Operator Algebra and Topology) in all fields of Mathematical and Theoretical Physics, including in particular: Classical Mechanics (Lagrangian, Hamiltonian, Poisson formulations); Quantum Mechanics (also semi-classical approximations); Hamiltonian Systems of ODE''s and PDE''s and Integrability; Variational Structures of Physics and Conservation Laws; Thermodynamics of Systems and Continua (also Quantum Thermodynamics and Statistical Physics); General Relativity and other Geometric Theories of Gravitation; geometric models for Particle Physics; Supergravity and Supersymmetric Field Theories; Classical and Quantum Field Theory (also quantization over curved backgrounds); Gauge Theories; Topological Field Theories; Strings, Branes and Extended Objects Theory; Holography; Quantum Gravity, Loop Quantum Gravity and Quantum Cosmology; applications of Quantum Groups; Quantum Computation; Control Theory; Geometry of Chaos.