title: Weaving Knotted Vector Fields with Tunable Helicity.
abstract: We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.
authors.affiliation: Department of Physics, James Franck Institute, Enrico Fermi Institute, The University of Chicago, 929 E 57th St., Chicago, Illinois 60637, USA.
authors.forename: Hridesh
authors.initials: H
authors.lastname: Kedia
authors.affiliation: HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK.
authors.forename: David
authors.initials: D
authors.lastname: Foster
authors.affiliation: HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK.
authors.forename: Mark R
authors.initials: MR
authors.lastname: Dennis
authors.affiliation: Department of Physics, James Franck Institute, Enrico Fermi Institute, The University of Chicago, 929 E 57th St., Chicago, Illinois 60637, USA.
authors.forename: William T M
authors.initials: WT
authors.lastname: Irvine