相关论文: Stiff knots
We solve the Cauchy problem for the relativistic closed string in Minkowski space $M^{3+1}$, including the cases where the initial data has a knot like topology. We give the general conditions for the world sheet of a closed knotted string…
New results on the groundstate energy of tight, magnetic knots are presented. Magnetic knots are defined as tubular embeddings of the magnetic field in an ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear…
The trunk of a knot in $S^3$, defined by Makoto Ozawa, is a measure of geometric complexity similar to the bridge number or width of a knot. We prove that for any two knots $K_1$ and $K_2$, we have $tr(K_1 \# K_2) =…
Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of…
Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in…
This paper explores the problem of unknotting closed braids and classical knots in mathematical knot theory. We apply evolutionary computation methods to learn sequences of moves that simplify knot diagrams, and show that this can be…
Motivated by the increased interest in modeling nondissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretch-limited elastic strings: the string cannot be…
The contents of this 6-page paper have been subsumed into the 13-page paper, "A note on closed 3-braids", arXiv:0802.1072 [math.GT]. This paper is correct, but contains less information than the new one. The topological classification of…
We employ computer simulations and thermodynamic integration to analyse the effects of bending rigidity and slit confinement on the free energy cost of tying knots, $\Delta F_{\rm knotting}$, on polymer chains under tension. A…
Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…
In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case,…
We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question whether the fiber can spontaneously knot itself. Using a 1D Cosserat model, a simple local viscous drag model and…
Probably the most natural energy functional to be considered for knotted strings is the one given by the electrostatic repulsion. In the absence of counter-charges, a charged, knotted string evolving along the energy gradient of…
We produce embeddings of knots in thin position that admit compressible thin levels. We also find the bridge number of tangle sums where each tangle is high distance.
The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction…
Knots and links which are closed 3-braids are a very special class. Like 2-bridge knots and links, they are simple enough to admit a complete classification. At the same time they are rich enough to serve as a source of examples on which,…
This is an expository article on diagrammatic representations of knots and links in various settings via braids.
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which…
A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots,…
QCD strings are color-electric flux tubes between quarks with a finite thickness and thus a finite curvature stiffness. Contrary to an earlier rigid-string by Polyakov and Kleinert, and motivated by the properties of a magnetic flux tubes…