Condensed Matter


Knot Formation in Open and Closed Self-Avoiding Walks: an Empirical Comparative Study

Authors: Robert A.J. Matthews

We describe an empirical study of the formation of knots in open and closed self-avoiding walks (SAWs), based on a simple model involving randomly agitated cords. The results suggest that the probability of a closed SAW remaining knot-free follows a similar scaling law to that for open-ended SAWs. In particular, the process of closing a given SAW prior to random agitation substantially increases the probability that it will be knot-free following agitation. The results point to a remedy for the well-known problem of tangling of cord, rope, headphone cables etc. The simple act of connecting the two free ends to each other, thus creating a loop, greatly reduces the risk of such tangling. Other implications, in particular for DNA storage in cells, are briefly discussed.

Comments: 2 Pages.

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Submission history

[v1] 21 Nov 2009

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