본문 바로가기 메뉴바로가기
KOREA
main

Papers

Best packing of identical helices

https://doi.org/10.1088/1751-8113/49/41/415205

  • Research Fields산업수학센터
  • AuthorYoungsik Huh, Kyungpyo Hong, Hyoungjun Kim, Sungjong No and Seungsang Oh
  • JournalJournal of Physics A: Mathematical and Theoretical 49(41) (2016
  • Link https://doi.org/10.1088/1751-8113/49/41/415205
  • Classification of papersSCI

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 ${{\rm{Rop}}}_{* }(\theta )=-\tfrac{8\pi }{t}$ where tis the unique solution in $[-\theta ,0]$ of the equation $2-2\cos (t+\theta )={t}^{2}$. Using this result, the pitch angles of the standard, triple and quadruple helices are around $39.3771^\circ $, $42.8354^\circ $ and $43.8351^\circ $, 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.

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 ${{\rm{Rop}}}_{* }(\theta )=-\tfrac{8\pi }{t}$ where tis the unique solution in $[-\theta ,0]$ of the equation $2-2\cos (t+\theta )={t}^{2}$. Using this result, the pitch angles of the standard, triple and quadruple helices are around $39.3771^\circ $, $42.8354^\circ $ and $43.8351^\circ $, 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.