Ropelength of superhelices and (2, n)-torus knots

Youngsik Huh, Hyoungjun Kim, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper we investigate a ropelength-minimizing conformation of 4-strand superhelical strings whose axial curves constitute the standard double helix. In Huh et al (2016 J. Phys. A: Math. Theor. 49 415205) the authors found a specific conformation of standard double helix which was mathematically shown to be the unique ropelength-minimizing conformation. Adopting the conformation as axial curves we present a parametrization of superhelical curves so that the resulting shape is controlled by the twist number N and the helical radius r 2. For each N, the value of r 2 minimizing the ropelength is numerically estimated. A notable observation is that the ropelength per crossing of our 4-strand superhelical strings is minimized around 2.96 < N < 2.97 which suggests a moment of transition from tightly-packed status to unpacked status. As an application of our estimation, we derive an upper bound on the ropelength of -torus knots, which is 45.8237k + 28.4223. Finally the efficiency of our superhelix model for -torus knots is discussed in comparison with the circular helix model.

Original languageEnglish
Article number485203
JournalJournal of Physics A: Mathematical and Theoretical
Issue number48
Publication statusPublished - 2018 Nov 7

Bibliographical note

Funding Information:
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2016R1D1A1B01008044), the second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korea government Ministry of Science and ICT (NRF-2018R1C1B6006692), and the corresponding author (SO) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2017R1A2B2007216).

Publisher Copyright:
© 2018 IOP Publishing Ltd.


  • ropelength
  • supercoil
  • superhelix
  • torus knot

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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