Three-dimensional nonequilibrium steady state of active particles: Symmetry breaking and clustering

Motile creatures are ubiquitous in the natural world. Spanning a broad range of length scales, they all have in common the fact that they convert energy from internal or external resources into motion. In most natural situations one such individual does not exist on its own but is part of a large group like a flock of birds, a school of fish, or a bacterial suspension. Often these groups show interesting and surprising structure formation which emerges in a self-organized fashion without any external forcing. Recently, the modeling of the dynamics of such large groups has attracted a lot of interest also among physicists with the aim to understand the simple, local mechanisms which lead to a complex, global behavior. The subject of this thesis are active particles at low Reynolds numbers in three dimensions which mimic, for example, bacteria in an aqueous environment. All particles move at a constant speed and align nematically with neighboring particles – they do not distinguish between head and tail. Large groups of active particles are investigated by means of molecular dynamics simulations in the limit of overdamped dynamics. We investigate the nonequilibrium phase diagram of these active particles in terms of density and rotational Péclet number. The latter compares the strength of the nematic alignment with the rotational diffusion. We find a phase transition from the isotropic to the nematically ordered state. Close to the transition point, traveling density waves occur which resemble solitons. In the nematic region of the phase diagram a spontaneous chiral symmetry breaking can be observed. This occurs via the formation of patterns which are characterized by a helical arrangement of the mean local orientations. We discuss their stability and study their formation. A comparison to a one-dimensional rotor model (similar to the XY -model) reveals the importance of fluctuations. Very interestingly, density waves traveling along the helix emerge. They differ, however, in nature from the ones occurring at the nematicisotropic transition. In the second part of the thesis, the active particles are immersed in a surrounding, mildly turbulent fluid (R 20) to mimic the conditions of plankton in the ocean. The fluid flow field is modeled by means of kinematic simulations to ensure reasonable computational times. However, for comparison, a number of simulations of the self-propelled particles are also performed using the result of state-of-the-art direct numerical simulations. We find a remarkably good agreement between these two methods. The particles show a turbulence-induced clustering in the form of smallscale patches in a specific region of the phase diagram. The strongest clustering occurs if the integral length scale of the vorticity of the turbulent field is equal to half of the nematic interaction range and the Kolmogorov time scale matches the time scale of nematic alignment. Finally, we discuss the implications of our results onto the famous “paradox of the plankton”