On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists
Embargo Date
2017-02-01
OA Version
Citation
P. Robert Kotiuga. On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 215-234. doi: 10.3934/dcdss.2016.9.215
Abstract
The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with current-carrying links, as conjectured by Crager and Kotiuga, is shown to be necessary and conditions for sufficiency are given. Along the way a paradox is exposed: The seemingly unintuitive mathematical tools, often associated to higher dimensional topology, have their origins in three dimensional contexts but in the hands of late-onset visually impaired topologists. This paradox was previously exposed in the context of algorithms for the visualization of three-dimensional magnetic fields. For this reason, the paper concludes by developing connections between mathematics and cognitive science in this specific context.
Description
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in "Discrete And Continuous Dynamical Systems-Series S" following peer review. The definitive publisher-authenticated version P. Robert Kotiuga. On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 215-234 is available online at: http://dx.doi.org/10.3934/dcdss.2016.9.215.
License
Attribution-NonCommercial-NoDerivatives 4.0 International