Braid theory and Zipf relation used in dynamics of magnetic microparticles

Abstract We have studied the two-dimensional dynamics of a few body system of microparticles using rank-ordering statistics. The world lines from the microspheres were captured and converted to a braid notation according to mathematical braid theory. Rank-ordering statistics of the dynamical modes in the system shows a power law region consistent with the Zipf relation. A simple numerical simulation of the experimental system shows similar behavior. To exemplify the diversity of our system a result showing anomalous diffusion is also given.