Magnetohydrodynamics as a field theory: topological and group theoretical aspects
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| Description: |
Yahalom, A (Ariel University of Samaria, Israel)
Thursday 11 October 2012, 11:30-12:30 |
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| Created: | 2012-10-12 11:43 |
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| Collection: | Topological Dynamics in the Physical and Biological Sciences |
| Publisher: | Isaac Newton Institute |
| Copyright: | Yahalom, A |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | The combination of electrodynamic fields and flow fields yields the novel field theory of magnetohydrodynamics [2]. This field theory has unique topological and symmetry properties which are absent in each of one of its ingredients. Although the standard equations of magnetohydrodynamics depend on seven quantities: the magnetic vector field B, the velocity vector field V and the density, mathematical analysis [2] shows that only four scalar functions are needed to describe magnetohydrodynamics. This analysis is based on previous work of Yahalom & Lynden-Bell [1]. The four functions include two surfaces whose intersections consist the magnetic field lines, the part of the velocity field not defined by the co-moving magnetic field and the density. The Lagrangian describing magnetohydrodynamics admits a novel group of diffeomorphism [3]. Moreover, the conservation of the topology of magnetic fields, leads to effects which are classical analogous of the quantum Aharonov-Bohm effect [4].
Bibliography [1] Asher Yahalom and Donald Lynden-Bell "Simplified Variational Principles for Barotropic Magnetohydrodynamics". [Los-Alamos Archives - physics/0603128], Journal of Fluid Mechanics, Volume 607, pages 235-265 (2008). [2] Asher Yahalom "A Four Function Variational Principle for Barotropic Magnetohydrodynamics". EPL 89 (2010) 34005, doi: 10.1209/0295-5075/89/34005 [Los-Alamos Archives - arXiv: 0811.2309]. [3] Asher Yahalom, "A New Diffeomorphism Symmetry Group of Magnetohydrodynamics" Proceedings of the 9th International Workshop "Lie Theory and Its Applications in Physics" (LT-9), 20-26 June 2011, Varna, Bulgaria. [4] Asher Yahalom "Aharonov - Bohm Effects in Magnetohydrodynamics" submitted to EPL [arXiv: 1005.3977]. |
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