To knot or not to knot

TL;DR

This study investigates how macroscopic chains form knots when shaken, revealing that beyond a critical length, knotting probability stabilizes while the time to untie increases with chain length.

Contribution

It demonstrates that knotting probability becomes independent of chain length beyond a critical point and analyzes the dynamics of knot formation and release.

Findings

Knotting probability saturates for long chains

Time to untie knots increases with chain length

Knotting probability is governed by a balance of formation and release processes

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.