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Stable and unstable vortex knots in excitable media

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Binysh, Jack, Whitfield, Carl A. and Alexander, Gareth P. (2019) Stable and unstable vortex knots in excitable media. Physical Review E, 99 (1). 012211. doi:10.1103/PhysRevE.99.012211 ISSN 1539-3755.

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Official URL: http://dx.doi.org/10.1103/PhysRevE.99.012211

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Abstract

We study the dynamics of knotted vortices in a bulk excitable medium using the FitzHugh-Nagumo model. From a systematic survey of all knots of at most eight crossings we establish that the generic behavior is of unsteady, irregular dynamics, with prolonged periods of expansion of parts of the vortex. The mechanism for the length expansion is a long-range “wave-slapping” interaction, analogous to that responsible for the annihilation of small vortex rings by larger ones. We also show that there are stable vortex geometries for certain knots; in addition to the unknot, trefoil, and figure-eight knots reported previously, we have found stable examples of the Whitehead link and 6 2 knot. We give a thorough characterization of their geometry and steady-state motion. For the unknot, trefoil, and figure-eight knots we greatly expand previous evidence that FitzHugh-Nagumo dynamics untangles initially complex geometries while preserving topology

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science
Faculty of Science, Engineering and Medicine > Science > Mathematics
Faculty of Science, Engineering and Medicine > Science > Physics
Library of Congress Subject Headings (LCSH): Mathematical physics, Waves
Journal or Publication Title: Physical Review E
Publisher: American Physical Society
ISSN: 1539-3755
Official Date: 16 January 2019
Dates:
DateEvent
16 January 2019Published
16 November 2018Accepted
Volume: 99
Number: 1
Article Number: 012211
DOI: 10.1103/PhysRevE.99.012211
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 17 January 2019
Date of first compliant Open Access: 17 January 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/L015374/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/N007883/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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