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.
Cite
@article{arxiv.cond-mat/0607760,
title = {To knot or not to knot},
author = {J. Hickford and R. Jones and S. Courrech du Pont and J. Eggers},
journal= {arXiv preprint arXiv:cond-mat/0607760},
year = {2007}
}