### 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 language | English |
---|---|

Article number | 485203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 51 |

Issue number | 48 |

DOIs | |

Publication status | Published - 2018 Nov 7 |

### Fingerprint

### 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

*Journal of Physics A: Mathematical and Theoretical*,

*51*(48), [485203]. https://doi.org/10.1088/1751-8121/aae969

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 51, no. 48, 485203. https://doi.org/10.1088/1751-8121/aae969

}

TY - JOUR

T1 - Ropelength of superhelices and (2, n)-torus knots

AU - Huh, Youngsik

AU - Kim, Hyoungjun

AU - Oh, Seung Sang

PY - 2018/11/7

Y1 - 2018/11/7

N2 - 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.

AB - 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.

KW - ropelength

KW - supercoil

KW - superhelix

KW - torus knot

UR - http://www.scopus.com/inward/record.url?scp=85056475867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056475867&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aae969

DO - 10.1088/1751-8121/aae969

M3 - Article

AN - SCOPUS:85056475867

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 48

M1 - 485203

ER -