Ropelength of superhelices and (2, n)-torus knots
- Authors
- Huh, Youngsik; Kim, Hyoungjun; Oh, Seungsang
- Issue Date
- 30-11월-2018
- Publisher
- IOP PUBLISHING LTD
- Keywords
- ropelength; supercoil; superhelix; torus knot
- Citation
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, v.51, no.48
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Volume
- 51
- Number
- 48
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/71490
- DOI
- 10.1088/1751-8121/aae969
- ISSN
- 1751-8113
- Abstract
- In this paper we investigate a ropelength-minimizing conformation of 4-strand superhelical strings whose axial curves constitute the standard double helix. In IIuh 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 (2, 6k + 1)-torus knots, which is 45.8237k + 28.4223. Finally the efficiency of our superhelix model for (2, n)-torus knots is discussed in comparison with the circular helix model.
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