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Nature of collective motion in dilute suspensions of self-propelled particles

Recent years have witnessed a significant interest in physical, biological and engineering aspects of self-propelled particles, such as bacteria or synthetic microswimmers. The main distinction of this 'active matter' from its passive counterpart is the ability to extract energy from the environment (consume food) and convert it into directed motion. One of the most striking consequences of this distinction is the transition to collective motion in self-propelled particles suspended in a fluid observed in recent experiments: at low densities particles move around in an uncorrelated fashion, while at higher densities they organise into jets and vortices comprising many individual swimmers. Presently, very little is understood about the origin of this transition.

In this talk I will propose a possible mechanism responsible for the transition to collective motion in model swimmers. First I will present a numerical method based on a Lattice-Boltzmann algorithm to simulate hydrodynamic interactions between a large number of model swimmers (order 10^5), represented by extended force dipoles. Using this method we simulate the transition to large-scale structures, and use a simple hydrodynamic theory to characterise them. I will discuss the nature of the coherent state, velocity fluctuations and turbulent-like spectra observed in this state and present results on the influence of coherent motion on the enhanced diffusion of tracer particles suspended in a solution of microswimmers.