scholarly journals Molecular Trefoil Knot from a Trimeric Circular Helicate

2018 ◽  
Vol 140 (15) ◽  
pp. 4982-4985 ◽  
Author(s):  
Liang Zhang ◽  
David P. August ◽  
Jiankang Zhong ◽  
George F. S. Whitehead ◽  
Iñigo J. Vitorica-Yrezabal ◽  
...  
Keyword(s):  
Trefoil Knot

Selective construction and stability studies of molecular trefoil knot and Solomon link

2021 ◽  
Author(s):  
Li-Long Dang ◽  
Ting-Ting Li ◽  
Zheng Cui ◽  
Sui Dong ◽  
Lufang Ma ◽  
...  
Keyword(s):  
Stacking Interactions ◽  
Stability Studies ◽  
Reversible Transformation ◽  
Π Stacking ◽  
Trefoil Knot

Two novel compounds, a molecular trefoil knot and a Solomon link, were constructed successfully through the cooperation of multiple π-π stacking interactions. A reversible transformation between the trefoil knot and...

Topological transformation of a trefoil knot into a [2]catenane

2017 ◽  
Vol 46 (47) ◽  
pp. 16474-16479 ◽  
Author(s):  
Thirumurugan Prakasam ◽  
Rana A. Bilbeisi ◽  
Roberto El-Khoury ◽  
Loïc J. Charbonnière ◽  
Mourad Elhabiri ◽  
...  
Keyword(s):  
Thermodynamic Investigation ◽  
Topological Transformation ◽  
Trefoil Knot

Kinetic and thermodynamic investigation of topological transformation of a trefoil knot into a [2]catenane in water.

Folding of Trefoil Knot and its Graph

2006 ◽  
Vol 2 (2) ◽  
pp. 378-385
Author(s):  
M. El-Ghoul ◽  
A.I. Elrokh ◽  
M.M. Al-Shamiri
Keyword(s):  
Trefoil Knot

scholarly journals Quantum Computing, Seifert Surfaces, and Singular Fibers

2019 ◽  
Vol 1 (1) ◽  
pp. 12-22 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Klee Irwin
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Complete Information ◽  
Singular Fiber ◽  
Dynkin Diagrams ◽  
Singular Fibers ◽  
Seifert Surfaces ◽  
Trefoil Knot ◽  
Universal Quantum

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

Topological molecular nanocarbons: All-benzene catenane and trefoil knot

Science ◽  
2019 ◽  
Vol 365 (6450) ◽  
pp. 272-276 ◽  
Author(s):  
Yasutomo Segawa ◽  
Motonobu Kuwayama ◽  
Yuh Hijikata ◽  
Masako Fushimi ◽  
Taishi Nishihara ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Energy Transfer ◽  
Magnetic Resonance ◽  
Dynamic Behavior ◽  
Enantiomer Separation ◽  
Hydrogen Atoms ◽  
Interlocked Molecules ◽  
Benzene Rings ◽  
Trefoil Knot ◽  
Synthetic Routes

The generation of topologically complex nanocarbons can spur developments in science and technology. However, conventional synthetic routes to interlocked molecules require heteroatoms. We report the synthesis of catenanes and a molecular trefoil knot consisting solely of para-connected benzene rings. Characteristic fluorescence of a heterocatenane associated with fast energy transfer between two rings was observed, and the topological chirality of the all-benzene knot was confirmed by enantiomer separation and circular dichroism spectroscopy. The seemingly rigid all-benzene knot has rapid vortex-like motion in solution even at –95°C, resulting in averaged nuclear magnetic resonance signals for all hydrogen atoms. This interesting dynamic behavior of the knot was theoretically predicted and could stimulate deeper understanding and applications of these previously untapped classes of topological molecular nanocarbons.

Resolution of a Molecular Trefoil Knot

1996 ◽  
Vol 118 (44) ◽  
pp. 10932-10933 ◽  
Author(s):  
Gwénaël Rapenne ◽  
Christiane Dietrich-Buchecker ◽  
Jean-Pierre Sauvage
Keyword(s):  
Trefoil Knot

Length of the tightest trefoil knot

2004 ◽  
Vol 70 (5) ◽  
Author(s):  
Justyna Baranska ◽  
Piotr Pieranski ◽  
Sylwester Przybyl ◽  
Eric J. Rawdon
Keyword(s):  
Trefoil Knot
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