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Best packing of identical helices

Title
Best packing of identical helices
Author
허영식
Keywords
double helix; ropelength; knot energy; identical helix
Issue Date
2016-09
Publisher
IOP PUBLISHING LTD
Citation
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, v. 49, NO. 41, Page. 415205-415212
Abstract
In this paper we prove the unique existence of a ropelength-minimizing conformation of the theta-spun double helix in a mathematically rigorous way, and find the minimal ropelength Rop(*)(theta) = -8 pi/t where t is the unique solution in [-theta, theta] 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 degrees, 42.8354 degrees and 43.8351 degrees, 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.
URI
http://iopscience.iop.org/article/10.1088/1751-8113/49/41/415205/metahttps://repository.hanyang.ac.kr/handle/20.500.11754/76805
ISSN
1751-8113; 1751-8121
DOI
10.1088/1751-8113/49/41/415205
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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