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Untangling knots via reaction-diffusion dynamics of vortex strings

Maucher, F.; Sutcliffe, P.M.

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Authors

F. Maucher



Abstract

We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.

Citation

Maucher, F., & Sutcliffe, P. (2016). Untangling knots via reaction-diffusion dynamics of vortex strings. Physical Review Letters, 116(17), Article 178101. https://doi.org/10.1103/physrevlett.116.178101

Journal Article Type Article
Acceptance Date Apr 14, 2016
Online Publication Date Apr 27, 2016
Publication Date Apr 27, 2016
Deposit Date Apr 28, 2016
Publicly Available Date Mar 28, 2024
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 116
Issue 17
Article Number 178101
DOI https://doi.org/10.1103/physrevlett.116.178101
Related Public URLs https://arxiv.org/abs/1604.04542

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.





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