Ropelength, crossing number and finite-type invariants of links

Komendarczyk, Rafal; Michaelides, A.

doi:10.2140/agt.2019.19.3335

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…Determining the precise ropelength is inherently challenging. Consequently, extensive efforts have focused on establishing bounds and deducing asymptotic behaviors through rigorous mathematical methodologies and numerical simulations [15][16][17][18][19][20][21][22][23][24][25]. For example, it has been proven that, for any knot type K, there exists a relationship of the form…”

Section: Introductionmentioning

confidence: 99%

Efficiency of non-identical double helix patterns in minimizing ropelength of torus knots

Kim,

Oh,

Huh

2024

Phys. Scr.

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The ropelength of a knotted string with volume is defined as the ratio of the length of its central curve to the radius of its sectional disc. In a physical context, achieving minimal ropelength corresponds to a state of minimal potential energy, and geometrically, it signifies a tightly-packed conformation. The quest to establish a connection be- tween the topological complexity of knotted strings and their minimal ropelength has persisted into recent years. In this paper, we introduce a new upper bound on the minimal ropelength of (2, n)-torus knots and links: Rop(T (2, n)) ≤ 7.3163 Cr(T (2, n)) + 17.1657. This upper bound is derived from a torus knot conformation constructed based on a tight- ened pattern of double helix with non-identical radii of winding. A comparative analysis with conformations generated from a superhelix and a circular helix underscores the efficiency of the non-identical dou- ble helix pattern, particularly when it appears as a long repeated motif in knotted strings.

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Section: Introductionmentioning

confidence: 99%

Efficiency of non-identical double helix patterns in minimizing ropelength of torus knots

Kim,

Oh,

Huh

2024

Phys. Scr.

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Tight conformation of 2-bridge knots using superhelices

Huh

Kim

2021

Journal of Mathematical Physics

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The ropelength is a mathematical quantity that regulates the tightness of flexible strands in the three-dimensional space. The superhelical conformation of long twisted strands is known to be more efficient in terms of ropelength compared with the circular double helical conformation. In this paper, we present a conformation of 2-bridge knots by using ropelength-minimizing superhelical curves and derive an upper bound on the ropelength of 2-bridge knots. Our superhelical model of 2-bridge knots is shown to be more efficient than the standard double helical one if the iterative twisted parts are long enough.

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Tree invariants and Milnor linking numbers with indeterminacy

Komendarczyk¹,

Michaelides²

2016

Preprint

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Ropelength, crossing number and finite-type invariants of links

Cited by 3 publications

References 37 publications

Efficiency of non-identical double helix patterns in minimizing ropelength of torus knots

Efficiency of non-identical double helix patterns in minimizing ropelength of torus knots

Tight conformation of 2-bridge knots using superhelices

Tree invariants and Milnor linking numbers with indeterminacy

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