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Length of excitable knots

Maucher, Fabian; Sutcliffe, Paul

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Fabian Maucher


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.


Maucher, F., & Sutcliffe, P. (2017). Length of excitable knots. Physical Review E, 96(1), Article 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


Published Journal Article (697 Kb)

Copyright Statement
Reprinted with permission from the American Physical Society: Physical Review E 96, 012218 © (2017) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

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