Relativistic Fluids of Topological Defects
2015-09
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Relativistic Fluids of Topological Defects
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2015-09
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A number of papers on the topic of string fluids written by Vitaly Vanchurin and myself are reviewed. A network of Nambu-Goto strings is coarse-grained and the equations for a generalized fluid are derived. Besides the symmetric energy-momentum tensor, the fluid also has a conserved antisymmetric tensor $F$ related to the topological flux of strings. This $F$ tensor obeys the homogeneous Maxwell equations, and there is a topological constraint similar to Gauss's law for magnetism. The fluid is isentropic and pressureless and foliated by two-dimensional submanifolds which can be considered to be worldsheets of macroscopic strings. The macroscopic strings are shown to obey the known equations of motion of a wiggly string. The fluid can be generalized to have pressure and be foliated by arbitrary current carrying strings by introducing a natural variational principle. An action is constructed as a functional of three scalar fields which can be identified as the Lagrangian coordinates of the fluid. This same variational principle for a specific choice of functional is shown to lead to the equations of magnetohydrodynamics, in which the $F$ tensor above is indeed the electromagnetic tensor. Furthermore a minor modification in the fields varied leads to the equations for a model of vortices in a superfluid. The effect of dissipation can be introduced by allowing the $F$ tensor and energy-momentum tensor to depart from their equilibrium forms. The condition that entropy must increase restricts the form of the non-equilibrium components of these tensors, and leads to the analogue of the Navier-Stokes equations for a string fluid. Besides terms involving viscosity there are additional terms dependent on the curvature of the lines of flux. In the case of magnetohydrodynamics these additional terms are shown to be equivalent to Ohm's law and the thermoelectric Nernst effect. The condition that the non-equilibrium terms vanish is used to derive conditions for hydrostatic equilibrium that may be useful in astrophysical situations.
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University of Minnesota M.S. thesis. September 2015. Major: Physics. Advisor: Vitaly Vanchurin. 1 computer file (PDF); ii, 92 pages.
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Schubring, Daniel. (2015). Relativistic Fluids of Topological Defects. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/190577.
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