相关论文: Capturing knots in polymers

This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.

We study numerically the tightness of prime flat knots in a model of self-attracting polymers with excluded volume. We find that these knots are localised in the high temperature swollen regime, but become delocalised in the low temperature…

A knot theoretic algorithm is proposed to model `fragile topology' of quantum physics.

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.

Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local" and, for several ring polymer models, we provide both theoretical and numerical…

We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite type invariants. These savings are achieved in comparison…

We introduce a two-dimensional lattice model for the description of knotted polymer rings. A polymer configuration is modeled by a closed polygon drawn on the square diagonal lattice, with possible crossings describing pairs of strands of…

In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…

We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.

We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to…

We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…

In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.

Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may…

This is an expository article on diagrammatic representations of knots and links in various settings via braids.

The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we…

An extensive study of single block copolymer knots containing two kinds of monomers $A$ and $B$ is presented. The knots are in a solution and their monomers are subjected to short range interactions that can be attractive or repulsive. In…

We present a numerical study of the effect of knotting on the ejection of flexible and semiflexible polymers from a spherical, virus-like capsid. The polymer ejection rate is primarily controlled by the knot, which moves to the hole in the…

Inspired by recent advances in the chromosome capture techniques, a method is proposed to study the structural organization of systems of polymers rings with topological constraints.To this purpose, the system is divided into compartments…

We construct new knot polynomials. Let $V$ be the standard solid torus in 3-space and let $pr$ be its standard projection onto an annulus. Let $M$ be the space of all smooth oriented knots in $V$ such that the restriction of $pr$ is an…

We describe an algorithm that recognizes some (perhaps all) intrinsically knotted (IK) graphs, and can help find knotless embeddings for graphs that are not IK. The algorithm, implemented as a Mathematica program, has already been used by…