Abstract
In this paper we prove the unique existence of a ropelength-minimizing conformation of the θ-spun double helix in a mathematically rigorous way, and find the minimal ropelength Rop∗(θ)= 8π/t where t is the unique solution in [-θ, 0] of the equation . 2-2 cos(t +θ) = t2.Using this result, the pitch angles of the standard, triple and quadruple helices are around , and , respectively, which are almost identical with the approximated pitch angles of the zero-twist structures previously known by Olsen and Bohr. We also find the ropelength of the standard N-helix.
Original language | English |
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Article number | 415205 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 49 |
Issue number | 41 |
DOIs | |
Publication status | Published - 2016 Sept 23 |
Externally published | Yes |
Bibliographical note
Funding Information:The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The fourth author was supported by the BK21 Plus Project through the National Research Foundation of Korea (NRF) grant funded by the Korean Ministry of Education (22A20130011003).
Publisher Copyright:
© 2016 IOP Publishing Ltd.
Keywords
- double helix
- identical helix
- knot energy
- ropelength
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy