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Postdoctoral Research Project: Dynamic density functional theory for active (Brownian) particles.

The study of interacting, active or self-propelled organisms has developed in
recent years to a very exciting field due to its numerous biological applications
exemplified by complex motional patterns in swimming sperm cells or bacteria.
Biofilms investgated in projects C1 and C2 are another very specific biological
example. On the other hand, research concentrates on basic properties of inter-
acting model swimmers such as coherent structure formation and the importance
of hydrodynamic interactions, or, as in project B4, tries to explore the potential
of active particles for microfluidic applications.
Collective penomena of active particles are studied either on the particle level or
with the help of coarse-grained models for particle densities. The latter are formu-
lated for specific problems such as the Keller-Segel model and its extensions
that apply to bacteria interacting by chemotaxis.
The aim of the project is to develop a systematic approach to coarse-grained
models for active Brownian particles in a highly viscous environment and to
explore the capacity of the formulated models. We will use the formalism of
dynamic density functional theory (DDFT) for Brownian particles which is currently
in the center of interest in the colloidal physics community and try to generalize
it to active Brownian particles. After early formulations of DDFT, the theory was
extended to include flowing solvents, anisotropic colloidal particles, and hydro-
dynamic interactions on the Rotne-Prager level.
In our treatment, we will follow the works of Archer et al. (J.Chem.Phys. 121, 4246)
and Rex et al. (Phys.Rev.Lett. 101, 148302) that start from the Smoluchowski
equation for the multi-particle probability distribution. First, one has to identify
where the property of self-propulsion of the Brownian particles is included in the
Smoluchowski equation. The derivation of DDFT will then be performed for increasing
degree of complexity starting with pair potentials between the interacting swimmers
and finally including hydrodynamic interactions.
The projects from areas B and C will benefit from the methodological developments
of this postdoctoral project.

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