Best packing of identical helices

Youngsik Huh, Kyungpyo Hong, Hyoungjun Kim, Sungjong No, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Article number415205
JournalJournal of Physics A: Mathematical and Theoretical
Issue number41
Publication statusPublished - 2016 Sept 23
Externally publishedYes

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.


  • 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


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