The ropelength is a mathematical quantity that regulates the tightness of flexible strands in the three-dimensional space. The superhelical conformation of long twisted strands is known to be more efficient in terms of ropelength compared with the circular double helical conformation. In this paper, we present a conformation of 2-bridge knots by using ropelength-minimizing superhelical curves and derive an upper bound on the ropelength of 2-bridge knots. Our superhelical model of 2-bridge knots is shown to be more efficient than the standard double helical one if the iterative twisted parts are long enough.
Bibliographical noteFunding Information:
Youngsik Huh was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (Grant No. NRF-2016R1D1A1B01008044), Hyoungjun Kim 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 (Grant No. NRF-2018R1C1B6006692), and Seungsang Oh was supported by the Institute for Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea government (MSIT) (Grant No. 2019-0-00033, 30%, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity).
© 2021 Author(s).
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics