Best packing of identical helices

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

Research output: Contribution to journalArticle

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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
StatePublished - 2016 Sep 23


  • double helix
  • identical helix
  • knot energy
  • ropelength

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