Topological Braids and Material Coherence

We are interested in studying particle trajectories to identify groups of particles that have the same dynamical fate, or conversely, groups of particles that disperse very quickly. We analyze the Burau representation of a braid of particle trajectories to identify distinct dynamical regimes. We apply our methods to study Aref's blinking vortex flow and a modified Duffing oscillator, which was studied by Allshouse and Thiffeault to test and illustrate the detection of coherent bundles.