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Magnetohydrodynamics as a field theory: topological and group theoretical aspects

Presented by: 
A Yahalom [Ariel University of Samaria, Israel]
Thursday 11th October 2012 - 11:30 to 12:30
INI Seminar Room 1
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].


[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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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons