4.7 Article

Length of excitable knots

期刊

PHYSICAL REVIEW E
卷 96, 期 1, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.96.012218

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资金

  1. Leverhulme Trust Research Programme [RP2013-K-009]
  2. SPOCK: Scientific Properties Of Complex Knots
  3. STFC [ST/J000426/1]
  4. Science and Technology Facilities Council [ST/J000426/1, ST/L000407/1] Funding Source: researchfish
  5. STFC [ST/J000426/1, ST/L000407/1] Funding Source: UKRI

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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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