منابع مشابه
Approximating Ropelength by Energy Functions
The ropelength of a knot is the quotient of its length by its thickness. We consider a family of energy functions R for knots, depending on a power p, which approach ropelength as p increases. We describe a numerically computed trefoil knot which seems to be a local minimum for ropelength; there are nearby critical points for R, which are evidently local minima for large enough p. 1. Thickness ...
متن کاملRopelength of Tight Polygonal Knots
A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is shown. Two ways of calculating the ropelength of tight polygonal knots are compared. An analytical calculation performed for a model knot shows that an appropria...
متن کاملPolygonal Knot Space near Ropelength-minimized Knots
For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which we can see small trefoil and figure-eight su...
متن کاملEnergy, ropelength, and other physical aspects of equilateral knots
Closed macromolecular chains may form physically knotted conformations whose relative occurrence and spatial measurements provide insight into their properties and the mechanisms acting upon them. Under the assumption of a degree of structural homogeneity, equilateral spatial polygons are a productive context within which to create mathematical models of these knots and to study their mathemati...
متن کاملLower Bounds for the Ropelength of Reduced Conformations
This paper generalizes the results of Sadjadi [4] and Alley [1] by providing an algorithm to find a lower bound on the ropelength of any knot which admits a reduced diagram. This lower bound is found by changing this problem of geometry into one of linear programming, which is then solved by the simplex algorithm.
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2014
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2014.18.1973