Knot complexity and the probability of random knotting

Details Knot complexity and the probability of random knotting Knot complexity and the probability of random knotting

2002-07-11

arxiv.org/abs/cond-mat/0207282v2

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 4 figures

Scientific paper

10.1103/PhysRevE.66.040801

The probability of a random polygon (or a ring polymer) having a knot type $K$ should depend on the complexity of the knot $K$. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially with respect to knot complexity. Here we assume that some aspects of knot complexity are expressed by the minimal crossing number $C$ and the aspect ratio $p$ of the tube length to the diameter of the {\it ideal knot} of $K$, which is a tubular representation of $K$ in its maximally inflated state.

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