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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
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 | |||||||||
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| 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 |
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| 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: |
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| 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: |
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