Length of excitable knots

Maucher, Fabian; Sutcliffe, Paul

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.

Citation

Maucher, F., & Sutcliffe, P. (2017). Length of excitable knots. Physical Review E, 96(1), Article 012218. https://doi.org/10.1103/physreve.96.012218

• 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
• DOI: https://doi.org/10.1103/physreve.96.012218
• Public URL: https://durham-repository.worktribe.com/output/1352581