### 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 |
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Article number | 485203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 51 |

Issue number | 48 |

DOIs | |

Publication status | Published - 2018 Nov 7 |

### 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)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

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