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Reconnection In Biology and Physics

Banff International Research Station for Mathematical Innovation and Discovery

Reconnection is an important event in many areas of science, including site- specific DNA recombination and the reconnection of field lines in astro- and plasma physics. We will discuss the conservation of writhe in a reconnection, and the behavior of twist in site-specific DNA recombination. Using the theorem of Moffatt and Ricca (Proc. Roy. Soc. 1992), the helicity of a magnetic flux tube can be calculated in terms of the writhe of the centerline and the twist of the ribbon determined by the centerline and one of the other field lines in the flux tube tube. This talk will present the proof of the following:\\r\\nTheorem: Given a reconnection event between a pair of magnetic flux tubes of identical flux, suppose that the twist of the reconnected tube is the sum of the twists of the individual tubes. Then helicity is conserved by the reconnection event — the helicity of the reconnected flux tube is the sum of the helicities of the individual tubes. Any deviation from helicity conservation is entirely due to twist inserted locally at the reconnection site (the writhe component of helicity is always conserved). This is joint with Christian Laing and Renzo Ricca.\\r\\n

Mathematics; Biology and other natural sciences; Manifolds and cell complexes; Mathematical biology

video/mp4

Author affiliation: Florida State University

2014-10-11

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50691

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/