Local anisotropy of fluids using Minkowski tensors - Kapfer, Sebastian; Mickel, Walter; Schaller, Fabian; Spanner, Markus; Goll, Christian; Nogawa, T.; Ito, Nobuyasu; Mecke, Klaus; Schröder-Turk, Gerd (Journal of Statistical Mechanics-Theory and Experiment, 2010)
Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices 0 <= beta(a,b)(v) <= 1 of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from beta(a,b)(v) approximate to 0.3 for vapor phases to beta(a,b)(v) -> 1 for ordered solids. We find that for fluids, local anisotropy decreases monotonically with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices beta(a,b)(v) are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs.
Keywords: granular matter; random/ordered microstructures (theory); monodisperse fluids; mixtures and polydisperse fluids

Motion by stopping: Rectifying Brownian motion of nonspherical particles - Sporer, Susan; Goll, Christian; Mecke, Klaus (Physical Review E, 2008)
We show that Brownian motion is spatially not symmetric for mesoscopic particles embedded in a fluid if the particle is not in thermal equilibrium and its shape is not spherical. In view of applications to molecular motors in biological cells, we sustain nonequilibrium by stopping a nonspherical particle at periodic sites along a filament. Molecular dynamics simulations in a Lennard-Jones fluid demonstrate that directed motion is possible without a ratchet potential or temperature gradients if the asymmetric nonequilibrium relaxation process is hindered by external stopping. Analytical calculations in the ideal gas limit show that motion even against a fluid drift is possible and that the direction of motion can be controlled by the shape of the particle, which is completely characterized by tensorial Minkowski functionals.