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Helicity, Reconnection and Seifert Surfaces

Presented by: 
De Witt Sumners Florida State University
Date: 
Friday 22nd September 2017 - 09:40 to 10:20
Venue: 
INI Seminar Room 1
Abstract: 
Co-author: Renzo Ricca (University of Milano-Bicocca)

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the total helicity of a linked configuration of flux tubes can be calculated in terms of linking, writhe and twist contributions. We prove that writhe helicity is conserved under anti-parallel reconnection [1]. We discuss the Seifert framing (isophase surfaces in GPE models) for a link. We give necessary and sufficient conditions for the existence of a Seifert surface for a framed link. We give a rigorous topological proof of the result that total helicity is zero for linked vortices with Seifert framing. We will discuss parallels between the links in the Belusov-Zhabotinsky reaction and links in fluid dynamics. This is joint work with Renzo Ricca.

[1] Laing, C.E., Ricca, R.L. & Sumners, De W. L. (2015) Conservation of writhe helicity under anti-parallel reconnection. Nature Sci. Rep. 5, 9224.
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    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons