Swarming patterns in Microorganisms: Some new modeling results

In previous years, many examples of swarming patterns have been found in systems of microorganisms. These examples range from the adaptive branching structures built by surface-resident bacteria to the swirling localized vortices seen during amoeba aggregation in Dictyostelium discoideum colonies. Modeling these systems allows us to understand the connection between microscopic interactions among the cellular constituents and the resultant collective macroscopic patterns. After a very brief review of some of these phenomena, we present new results along two disparate directions: the derivation of a reaction-diffusion equation capable of dealing with chiral branching (i.e. the breaking of left-right symmetry) and the introduction of a new flocking model to study cell-sorting (aka phase separation) in localized vortices