Corpus ID: 237940092

Knot Dynamics

@inproceedings{Kauffman2021KnotD,
  title={Knot Dynamics},
  author={Louis H. Kauffman},
  year={2021}
}
The paper studies the dynamics of knots under self-repulsion produced by artificial charges placed on the curve in space representing the knot. 

References

SHOWING 1-10 OF 16 REFERENCES
Knots and Physics
In this report, we introduce the basics of knots, knot polynomial invariants, and the Witten’s functional integral, which show relationships with topics in theoretical physics, such as theExpand
On the Classification of Rational Knots
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification ofExpand
On the classification of rational tangles
TLDR
Two new combinatorial proofs of the classification of rational tangles using the calculus of continued fractions are given and an elementary proof that alternatingrational tangles have minimal number of crossings is obtained. Expand
ENERGY FUNCTIONS FOR POLYGONAL KNOTS
We define a scale-invariant energy function for polygonal knots in ℜ3 based on the minimum distances between segments. The energy is bounded below by 2π. (minimum crossing number of the knot type).Expand
An enumeration of knots and links, and some of their algebraic properties
Publisher Summary This chapter describes knots and links, and some of their algebraic properties. An edge-connected 4-valent planar map is called a polyhedron, and a polyhedron is basic if no regionExpand
Bounds for the minimum step number of knots in the simple cubic lattice
Knots are found in DNA as well as in proteins, and they have been shown to be good tools for structural analysis of these molecules. An important parameter to consider in the artificial constructionExpand
Unknotting Unknots
TLDR
An introduction to the work of Dynnikov, who discovered the key use of arc-presentations to solve the problem of finding a way to detect the unknot directly from a diagram of the knot. Expand
Interactive topological drawing
The research presented here examines topological drawing, a new mode of constructing and interacting with mathematical objects in three-dimensional space. In topological drawing, issues such asExpand
BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices
In this paper, the elementary moves of the BFACF-algorithm (Aragao de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635–45, Aragao de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209–48, Berg andExpand
State Models and the Jones Polynomial
IN THIS PAPER I construct a state model for the (original) Jones polynomial [5]. (In [6] a state model was constructed for the Conway polynomial.) As we shall see, this model for the Jones polynomialExpand
...
1
2
...