Characterizing correlated and topologically driven dynamics of prime knots

Knots, as entangled objects, provide a natural platform for studying the link between the dynamics and structure of complex systems. Across the scales, knots have been used in modeling the magnetic flux loop of the sun and vortex formation in fluids. In polymers, knots are known to alter the properties of the polymer bulk such as relaxation time, fragility, and viscosity. In this work, we present a detailed examination of the dynamics of prime knots modelled as polymer chains. We disentangle their complex dynamics into three basis motions— orthogonal, aligned, and mixed— and identify their contributions to the overall dynamics that give rise to a unique set of motions for each knot topology. We also investigate dynamics that emerge purely as a result of topology, focusing on dynamical arrest— the suppression of motions as knot complexity increases.