Time-dependent Knotting of Agitated Chains

Agitated strings serve as powerful macroscopic models of knot formation, providing insight in knotting dynamics at the microscale while retaining the ability to explicitly characterize knot topology. Here we present an experimental setup in which knot formation is driven by a tumbling motion along with a software interface to process complex knot data with high crossing numbers. Using this setup, we characterize knotting probability, knot complexity and knot formation dynamics for knots with as many as 50 crossings. We find that the probability of knotting saturates below 80% within 100 seconds of tumbling and that this saturation probability does not increase for chains above a critical length. This is an indication of non-equilibrium knot-formation conditions in our experiment. Despite this saturation in knot formation, we show that longer chains still tend to form knots of higher complexity, likely due to the mobility of the free end which can access a greater number of loops during tumbling.