Collective Dynamics in Active Biological Systems

Shawn D. Ryan

Department of Mathematical Sciences and Liquid Crystal Institute

Kent State University




In the first part of the talk a simple PDE/ODE model for a bacterial suspension is introduced with two goals in mind: (i) to better understand the non-trivial correlations leading to the onset of collective swimming and (ii) to study the effective viscosity. Here a bacterium is represented as a point force dipole subject to two types of interactions: hydrodynamic and excluded volume (collisions). The results of direct particle simulations confirm striking experimental observations: a drastic reduction in the effective viscosity of the suspension with increased concentration as well as the independence of the correlations on the concentration and swimming speed past the concentration threshold for collective motion. In addition, an explicit asymptotic formula for the effective viscosity in terms of known physical parameters is derived using a kinetic approach revealing that the alignment of asymmetrical particles and self-propulsion give rise to the decrease. The second part will focus on more recent work developing a model that captures collective motion in social insects, specifically army ants. In the absence of any external forces, the model shows a transition to an ordered phase and local traffic lane formation throughout the course of a raid. Both models capture the emergence of a collective state as the result of microscopic interactions and provide important insights into its mesoscopic nature.