Non-Riemannian Geometry of Twisted Flux Tubes
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Sociedade Brasileira de Física
2006
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| _version_ | 1876436159817580544 |
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| author | L. C. Garcia de Andrade |
| author_facet | L. C. Garcia de Andrade |
| contents | Non-Riemannian Geometry of Twisted Flux Tubes L. C. Garcia de Andrade Física, Astronomía y Matemáticas Non Twisted flux tubes Riemannanian geometry New examples of the theory recently proposed by Ricca [PRA(1991)] on the generalization of Da Rios-Betchov intrinsic equations on curvature and torsion of classical non-Riemannian vortex higher-dimensionalstring are given. In particular we consider applications to 3-dimesional fluid dynamics, including the case ofa twisted flux tube and the fluid rotation. In this case use is made of Da Rios equation to constrain the fluid.Integrals on the Cartan connection are shown to be related to the integrals which represent the total Frenettorsion and total curvature. By analogy with the blue phases twisted tubes in liquid crystals, non-Riemanniangeometrical formulation of the twisted flux tube in fluid dynamics is obtained. A theorem by Ricca and Moffatton invariant integrals for the Frenet curvature is used to place limits on the Cartan integrals. The stationaryincompressible flow case is also addressed in the non-Riemannian case where Cartan torsion scalars are shownto correspond to abnormalities of the congruence. Geodesic motion is shown to be torsionless. Vorticity is shownto be expressed in terms of abnormalities of the congruence, which is analogous to the result recenly obtained[Garcia de Andrade,PRD(2004)], where the vorticity of the superfluid plays the role of Cartan contortion vectorin the context of analog gravity. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436630 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.4A Vol.36 |
| format | Artículo científico |
| id | redalyc_46436630 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Non-Riemannian Geometry of Twisted Flux Tubes L. C. Garcia de Andrade Física, Astronomía y Matemáticas Non Twisted flux tubes Riemannanian geometry Non-Riemannian Geometry of Twisted Flux Tubes L. C. Garcia de Andrade Física, Astronomía y Matemáticas Non Twisted flux tubes Riemannanian geometry New examples of the theory recently proposed by Ricca [PRA(1991)] on the generalization of Da Rios-Betchov intrinsic equations on curvature and torsion of classical non-Riemannian vortex higher-dimensionalstring are given. In particular we consider applications to 3-dimesional fluid dynamics, including the case ofa twisted flux tube and the fluid rotation. In this case use is made of Da Rios equation to constrain the fluid.Integrals on the Cartan connection are shown to be related to the integrals which represent the total Frenettorsion and total curvature. By analogy with the blue phases twisted tubes in liquid crystals, non-Riemanniangeometrical formulation of the twisted flux tube in fluid dynamics is obtained. A theorem by Ricca and Moffatton invariant integrals for the Frenet curvature is used to place limits on the Cartan integrals. The stationaryincompressible flow case is also addressed in the non-Riemannian case where Cartan torsion scalars are shownto correspond to abnormalities of the congruence. Geodesic motion is shown to be torsionless. Vorticity is shownto be expressed in terms of abnormalities of the congruence, which is analogous to the result recenly obtained[Garcia de Andrade,PRD(2004)], where the vorticity of the superfluid plays the role of Cartan contortion vectorin the context of analog gravity. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46436630 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.4A Vol.36 |
| title | Non-Riemannian Geometry of Twisted Flux Tubes |
| topic | Física, Astronomía y Matemáticas Non Twisted flux tubes Riemannanian geometry |
| url | https://www.redalyc.org/articulo.oa?id=46436630 |