COLLECTIVE MOTION OF BROWNIAN PARTICLES WITH HYDRODYNAMIC INTERACTIONS

Abstract

Biological motion and human traffic require energy supply from external sources. We develop here a model for the dynamics of driven entities which includes hydrodynamic interactions in order to adapt the model to the dynamics of swarms moving in dense fluids. Our entities have the ability to use the energy contained in an internal energy depot or an external energy inflow for the acceleration of motion. As a prototype of such entities we study Brownian particles having the ability to take up energy from their environment, to store it in an internal energy depot and to convert internal energy into kinetic energy. The motion of the particles is described by Langevin equations which include a dissipative force term resulting from the driving and equations for the dynamics of the depot. The hydrodynamic interactions are modeled by an Oseen-type tensorial force. It is shown that hydrodynamic interactions lead to the synchronization of the directions of motion leading to several new collective modes of the dynamics, including spontaneous rotations of the swarm.