Toroidal Vortex Filament Knots and Links: Existence, Stability and Dynamics

2020 ◽  
Vol 19 (4) ◽  
pp. 2403-2427
Author(s):  
Theodore Kolokolnikov ◽  
Chris Ticknor ◽  
Panayotis Kevrekidis
Keyword(s):  
Vortex Filament ◽  
Toroidal Vortex ◽  
Knots And Links

Knots and Links

2004 ◽  
Author(s):  
Peter R. Cromwell
Keyword(s):  
Knots And Links

Magnetic helicity and electromagnetic vortex filament flows under the influence of Lorentz force in MHD

Optik ◽  
2021 ◽  
pp. 167302
Author(s):  
Talat Körpınar ◽  
Rıdvan Cem Demirkol ◽  
Zeliha Körpınar
Keyword(s):  
Lorentz Force ◽  
Vortex Filament ◽  
Magnetic Helicity

Vortex Filament Simulation of the Turbulent Boundary Layer

AIAA Journal ◽  
2010 ◽  
Vol 48 (8) ◽  
pp. 1757-1771 ◽  
Author(s):  
Peter S. Bernard ◽  
Pat Collins ◽  
Mark Potts
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Vortex Filament

Dynamics of a vortex filament in a shear flow

1984 ◽  
Vol 148 ◽  
pp. 477-497 ◽  
Author(s):  
Hassan Aref ◽  
Edward P. Flinchem
Keyword(s):  
Mixing Layer ◽  
Background Field ◽  
Nucleation Site ◽  
Finite Amplitude ◽  
Vortex Filament ◽  
Attractive Alternative ◽  
Morphological Similarity ◽  
Single Vortex ◽  
Linearized Stability ◽  
Model Equations

Motions of a single vortex filament in a background flow are studied by numerical simulation of a set of model equations. The model, which in essence is due to Hama, treats the self-interaction of the filament through the so-called ‘localized-induction approximation’ (LIA). Interaction with the prescribed background field is treated by simply advecting the filament appropriately. We are particularly interested in elucidating the evolution of sinuous vortices such as the ‘wiggle’ seen by Breidenthal in the transition to three-dimensionality in the mixing layer. The model studied embodies two of the simplest ingredients that must enter into any dynamical explanation: induction and advection. For finite-amplitude phenomena we make contact with the theory of solitons on strong vortices developed by Betchov and Hasimoto. In a shear, solitons cannot exist, but solitary waves can, and their interactions with the shear are found to be key ingredients for an understanding of the behaviour of the vortex filament. When sheared, a soliton seems to act as a ‘nucleation site’ for the generation of a family of waves. Computed sequences are shown that display a remarkable morphological similarity to flow-visualization studies. The present application of fully nonlinear dynamics to a model presents an attractive alternative to the extrapolations from linearized stability theory applied to the full equations that have so far constituted the theoretical basis for understanding the experimental results.

scholarly journals Invariants of Random Knots and Links

2016 ◽  
Vol 56 (2) ◽  
pp. 274-314 ◽  
Author(s):  
Chaim Even-Zohar ◽  
Joel Hass ◽  
Nati Linial ◽  
Tahl Nowik
Keyword(s):  
Knots And Links ◽  
Random Knots

Stick numbers of Montesinos knots

2021 ◽  
pp. 2150013
Author(s):  
Hwa Jeong Lee ◽  
Sungjong No ◽  
Seungsang Oh
Keyword(s):  
Upper Bound ◽  
Crossing Number ◽  
Number Formula ◽  
Knots And Links

Negami found an upper bound on the stick number [Formula: see text] of a nontrivial knot [Formula: see text] in terms of the minimal crossing number [Formula: see text]: [Formula: see text]. Huh and Oh found an improved upper bound: [Formula: see text]. Huh, No and Oh proved that [Formula: see text] for a [Formula: see text]-bridge knot or link [Formula: see text] with at least six crossings. As a sequel to this study, we present an upper bound on the stick number of Montesinos knots and links. Let [Formula: see text] be a knot or link which admits a reduced Montesinos diagram with [Formula: see text] crossings. If each rational tangle in the diagram has five or more index of the related Conway notation, then [Formula: see text]. Furthermore, if [Formula: see text] is alternating, then we can additionally reduce the upper bound by [Formula: see text].

Piecewise-linear embeddings of knots and links with rotoinversion symmetry

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
Michael O'Keeffe ◽  
Michael M. J. Treacy
Keyword(s):  
Piecewise Linear ◽  
Infinite Family ◽  
Knots And Links

This article describes the simplest members of an infinite family of knots and links that have achiral piecewise-linear embeddings in which linear segments (sticks) meet at corners. The structures described are all corner- and stick-2-transitive – the smallest possible for achiral knots.

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