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.
|Journal of Physics A: Mathematical and Theoretical
|Published - 2018 Nov 7
Bibliographical noteFunding 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).
© 2018 IOP Publishing Ltd.
- torus knot
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy