Mathematics Colloquia and Seminars

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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 mathematical models for DNA site-specific recombination, and argue that the mathematics of DNA is directly applicable to vortex reconnection in fluid dynamics and plasma physics. We will prove that writhe is conserved in an anti-parallel reconnection event, and study 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. This talk will present the proof of the following: Theorem: Given an anti-parallel 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).