On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists

P. Robert  Kotiuga

doi:10.3934/dcdss.2016.9.215

Article Contents

2016, Volume 9, Issue 1: 215-234. Doi: 10.3934/dcdss.2016.9.215

This issue Previous Article Stabilized Galerkin for transient advection of differential forms Next Article Spectral approximation of the curl operator in multiply connected domains

On the topological characterization of near force-free magnetic fields, and the work of late-onset visually-impaired topologists

P. Robert Kotiuga^1,

1.
Boston University, ECE Dept, 8 Saint Mary's Street, Boston, MA 02215

Received: September 2014

Revised: February 2015

Published: February 2016

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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.

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Mathematics Subject Classification: 37D55, 53D35, 58Z99, 78A25.

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