Best packing of identical helices

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

doi:10.1088/1751-8113/49/41/415205

Best packing of identical helices

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

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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
Article number	415205
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	49
Issue number	41
DOIs	https://doi.org/10.1088/1751-8113/49/41/415205
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

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10.1088/1751-8113/49/41/415205

Cite this

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title = "Best packing of identical helices",

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.",

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AU - Hong, Kyungpyo

AU - Kim, Hyoungjun

AU - No, Sungjong

AU - Oh, Seungsang

N1 - 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.

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N2 - 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.

AB - 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.

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KW - identical helix

KW - knot energy

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ER -

Best packing of identical helices

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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