Numerical upper bounds on ropelengths of large physical knots

Y. Diao; C. Ernst; V. Kavuluru; U. Ziegler

doi:10.1088/0305-4470/39/18/004

Numerical upper bounds on ropelengths of large physical knots

Y. Diao, C. Ernst, V. Kavuluru, U. Ziegler

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

7 Scopus citations

Abstract

Numerical computations explored for this paper show that an upper bound on the ropelength of large knots with crossing number n grows as fast as nln ²n. The algorithms to randomly generate samples of such large knots and to determine an upper bound on the ropelength for each knot are described. The numeric results are presented and compared to the smallest known theoretical upper bounds on ropelength.

Original language	English
Pages (from-to)	4829-4843
Number of pages	15
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	18
DOIs	https://doi.org/10.1088/0305-4470/39/18/004
State	Published - May 5 2006

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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10.1088/0305-4470/39/18/004

Cite this

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title = "Numerical upper bounds on ropelengths of large physical knots",

abstract = "Numerical computations explored for this paper show that an upper bound on the ropelength of large knots with crossing number n grows as fast as nln 2n. The algorithms to randomly generate samples of such large knots and to determine an upper bound on the ropelength for each knot are described. The numeric results are presented and compared to the smallest known theoretical upper bounds on ropelength.",

author = "Y. Diao and C. Ernst and V. Kavuluru and U. Ziegler",

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AU - Ernst, C.

AU - Kavuluru, V.

AU - Ziegler, U.

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N2 - Numerical computations explored for this paper show that an upper bound on the ropelength of large knots with crossing number n grows as fast as nln 2n. The algorithms to randomly generate samples of such large knots and to determine an upper bound on the ropelength for each knot are described. The numeric results are presented and compared to the smallest known theoretical upper bounds on ropelength.

AB - Numerical computations explored for this paper show that an upper bound on the ropelength of large knots with crossing number n grows as fast as nln 2n. The algorithms to randomly generate samples of such large knots and to determine an upper bound on the ropelength for each knot are described. The numeric results are presented and compared to the smallest known theoretical upper bounds on ropelength.

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JO - Journal of Physics A: Mathematical and General

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Numerical upper bounds on ropelengths of large physical knots

Abstract

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