Maucher, Fabian and Sutcliffe, Paul (2017) 'Length of excitable knots.', Physical review E., 96 (1). 012218.
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.
| Item Type: | Article |
|---|---|
| Full text: | (VoR) Version of Record Download PDF (682Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1103/PhysRevE.96.012218 |
| Publisher 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. |
| Date accepted: | No date available |
| Date deposited: | 31 July 2017 |
| Date of first online publication: | 20 July 2017 |
| Date first made open access: | 31 July 2017 |
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