Length of excitable knots

Maucher, Fabian; Sutcliffe, Paul

doi:10.1103/physreve.96.012218

Length of excitable knots

Maucher, Fabian; Sutcliffe, Paul

Authors

Fabian Maucher

Professor Paul Sutcliffe p.m.sutcliffe@durham.ac.uk
Professor

Abstract

In this paper, we present extensive numerical simulations of an excitable medium to study the long-term dynamics of knotted vortex strings for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presented, thereby providing a field theory approach to the study of knots. Furthermore, the evolution yields a well-defined minimal length for each knot that is comparable to the ropelength of ideal knots. We highlight the role of the medium boundary in stabilizing the length of the knot and discuss the implications beyond torus knots. We also show that there is not a unique attractor within a given knot topology.

Citation

Maucher, F., & Sutcliffe, P. (2017). Length of excitable knots. Physical Review E, 96(1), Article 012218. https://doi.org/10.1103/physreve.96.012218

Journal Article Type	Article
Online Publication Date	Jul 20, 2017
Publication Date	Jul 20, 2017
Deposit Date	Jul 21, 2017
Publicly Available Date	Jul 31, 2017
Journal	Physical review . E, Statistical, nonlinear, and soft matter physics
Print ISSN	2470-0045
Electronic ISSN	2470-0053
Publisher	American Physical Society
Peer Reviewed	Peer Reviewed
Volume	96
Issue	1
Article Number	012218
DOI	https://doi.org/10.1103/physreve.96.012218

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