Length of excitable knots

Fabian Maucher and Paul Sutcliffe
Phys. Rev. E 96, 012218 – Published 20 July 2017
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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.

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  • Received 17 March 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012218

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary PhysicsPhysics of Living SystemsGeneral Physics

Authors & Affiliations

Fabian Maucher1,2,* and Paul Sutcliffe1,†

  • 1Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom
  • 2Joint Quantum Centre Durham-Newcastle, Department of Physics, Durham University, Durham DH1 3LE, United Kingdom

  • *fabian.maucher@durham.ac.uk
  • p.m.sutcliffe@durham.ac.uk

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Issue

Vol. 96, Iss. 1 — July 2017

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