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To knot or not to knot

J. Hickford·R. Jones·S. Courrech du Pont·J. Eggers
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Abstract

We study the formation of knots on a macroscopic ball-chain, which is shaken on a horizontal plate at 12 times the acceleration of gravity. We find that above a certain critical length, the knotting probability is independent of chain length, while the time to shake out a knot increases rapidly with chain length. The probability if finding a knot after a certain time is the result of the balance of these two processes. In particular, the knotting probability tends to a constant for long chains.

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J. Hickford, R. Jones, S. Courrech du Pont, J. Eggers. 2006-07-28. To knot or not to knot. https://arxiv.org/abs/cond-mat/0607760

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