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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Physics

On the construction and dynamics of knotted fields 
 
Tue, May 23, 2017,   03:00 PM at Physics Seminar Room 31, 2nd Floor, Main Building

Dr Hridesh Kedia
U Chicago and MIT

Abstract:

A knot - a closed loop tangled with itself, which can not be untangled without cutting the loop - preserves its identity when stretched or rotated. Remarkably, knots in the vortex lines of a dissipationless fluid, or in the magnetic field lines of an infinitely conducting plasma, stretch and rotate as they evolve, but never untangle, persisting forever. A consequence of this topology-preserving evolution, is an additional conserved quantity: helicity, which has far-reaching implications for the dynamics of fluids and plasmas. Seeking a better understanding of the persistence of knots, and the ensuing conservation of helicity, we begin by analytically constructing knotted vector fields. We then study if knots can persist in a linear theory such as Maxwell’s equations. Lastly, we ask if an additional conserved quantity analogous to helicity exists in superfluids since they also flow without dissipation.

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