Disentangling the Dynamics of Prime Knots

Many areas of physics describe entanglements— from vortex- to molecular knots, there is interest in understanding knots as dynamic objects. Formally, knots are defined as closed curves embedded in R³ that cannot be untangled without a cut. A subset of these curves, the prime knots, cannot be decomposed (i. e., expressed as a connected sum of two non-trivial knots). We investigate the dynamics of prime knots, capturing events like periodic breathing and other correlated motions, and relate these events to knot complexity, curvature, torsion and linking numbers. With the help of Molecular Dynamics simulations, we build a framework to analyze correlated motions in prime knots modeled as polymer chains, and study how these motions relate to their local structural properties. We investigate the link between dynamical arrest and local geometry in knotted polymers and present and characterize a novel type of motion discovered in knots that may have applications to nanoscale materials and machines.