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


Breier,  Rebekka E.
Group Non-equilibrium soft matter, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Breier, R. E. (2017). Three-dimensional nonequilibrium steady state of active particles: Symmetry breaking and clustering. PhD Thesis, Georg-August-Universität, Göttingen.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-B9D0-3
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
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
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”.