Math @ Duke

Publications [#166444] of Elizabeth L. Bouzarth
Papers Published
 E.L. Bouzarth and H. Pfister, Helicity conservation under Reidemeister Moves,
American Journal of Physics, vol. 74 no. 2
(February, 2006),
pp. 141144 [doi]
(last updated on 2010/10/27)
Abstract: We discuss a connection between two fields that appear to have little in common: plasma physics
and mathematical knot theory. Plasma physicists are interested in studying helicity conservation in
magnetic flux ropes and knot theorists commonly consider “Reidemeister moves,” transformations
that preserve a property called “knottedness.” To study the tangling, twisting, and untwisting of
magnetic flux ropes, it is helpful to know which topological transformations conserve helicity.
Although the second and third types of Reidemeister moves applied to a magnetic flux rope clearly
conserve the helicity of the flux rope, the first type of Reidemeister move appears to be in conflict
with helicity conservation.We show that all three Reidemeister moves conserve helicity in magnetic
flux ropes.


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