Displaying similar documents to “Modeling repulsive forces on fibres via knot energies”

Discrete thickness

Sebastian Scholtes (2014)

Molecular Based Mathematical Biology

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We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the...

Homogeneity of dynamically defined wild knots.

Gabriela Hinojosa, Alberto Verjovsky (2006)

Revista Matemática Complutense

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In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.

The Knot Spectrum of Confined Random Equilateral Polygons

Y. Diao, C. Ernst, A. Montemayor, E. Rawdon, U. Ziegler (2014)

Molecular Based Mathematical Biology

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It is well known that genomic materials (long DNA chains) of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant) bacteriophage P4, DNA molecules packed inside the bacteriophage head are considered to be circular...

Applications of topology to DNA

Isabel Darcy, De Sumners (1998)

Banach Center Publications

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The following is an expository article meant to give a simplified introduction to applications of topology to DNA.

Lissajous knots and billiard knots

Vaughan Jones, Józef Przytycki (1998)

Banach Center Publications

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We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.

On the Kauffman-Harary conjecture for Alexander quandle colorings.

Soichiro Asami (2006)

Revista Matemática Complutense

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The Kauffman-Harary conjecture is a conjecture for Fox's colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.

Unknotting number and knot diagram.

Yasutaka Nakanishi (1996)

Revista Matemática de la Universidad Complutense de Madrid

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This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.