Anomalous transport of a tracer on percolating clusters - Spanner, Markus; Hoefling, Felix; Schröder-Turk, Gerd; Mecke, Klaus; Franosch, Thomas (Journal of Physics: Condensed Matter, 2011)
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as a response to an alternating electric field. Last, we discuss the non-Gaussian parameter as an indicator for heterogeneous dynamics.

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

Splitting of the Universality Class of Anomalous Transport in Crowded Media - Spanner, Markus; Hoefling, Felix; Kapfer, Sebastian; Mecke, Klaus; Schroeder-Turk, Gerd E.; Franosch, Thomas (Physical Review Letters, 2016)
We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle nonuniversal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics.