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

Youngsik Huh, Hyoungjun Kim, Seung Sang Oh

Research output: Contribution to journalArticle

Abstract

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
Volume51
Issue number48
DOIs
Publication statusPublished - 2018 Nov 7

Fingerprint

Torus knot
Conformation
helices
Conformations
strands
curves
strings
Helix
Curve
Circular helix
Strings
Twist
Parametrization
moments
radii
Radius
Upper bound
Moment
Model
Standards

Keywords

  • ropelength
  • supercoil
  • superhelix
  • torus knot

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Ropelength of superhelices and (2, n)-torus knots. / Huh, Youngsik; Kim, Hyoungjun; Oh, Seung Sang.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 51, No. 48, 485203, 07.11.2018.

Research output: Contribution to journalArticle

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