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ArticleOriginal scientific text

Title

Numerical application of knot invariants and universality of random knotting

Authors 1, 2

Affiliations

  1. Department of Physics, Ochanomizu University, Ohtsuka 2-1-1, Bunkyo-ku, Tokyo 112, Japan
  2. Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan

Abstract

We study universal properties of random knotting by making an extensive use of isotopy invariants of knots. We define knotting probability (PK(N)) by the probability of an N-noded random polygon being topologically equivalent to a given knot K. The question is the following: for a given model of random polygon how the knotting probability changes with respect to the number N of polygonal nodes? Through numerical simulation we see that the knotting probability can be expressed by a simple function of N. From the result we propose a universal exponent of PK(N), which may be a new numerical invariant of knots.

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Banach Center Publications
1998/42/1
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Pages:
77-85
Main language of publication
English
Published
1998
Exact and natural sciences