Data and code from: Random knotting in very long off-lattice self-avoiding polygons

DRYAD

Abstract

We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, for each n between 10 and 27, we generated 243–n polygons of size 2*n*. Using a new knot diagram simplification and invariant-free knot classification code, we were able to determine the precise knot type of each polygon. The results show that the number of prime summands of knot type K in a random n-gon is very well described by a Poisson distribution. We estimate the characteristic length of knotting as 656,500 ± 2500. We also make new calculations for knotting rates and amplitude ratios of knot probabilities. We find that our calculations agree quite well with previous on-lattice computations. Our results support the idea of knot localization and the knot entropy conjecture.

Authors 4

1. Jason Cantarella

   University of Georgia

   Affiliation as printed

   University of Georgia

2. Tetsuo Deguchi

   Ochanomizu University

   Affiliation as printed

   Ochanomizu University

3. Clayton Shonkwiler

   Colorado State University

   Affiliation as printed

   Colorado State University

4. Erica Uehara

   Kyoto University

   Affiliation as printed

   Kyoto University