Herr Dr Fabian Schaller : Packing placebo pills to understand aspherical granular matter
A belated congratulations to my PhD student Fabian Schaller who defended his PhD thesis in June 2017. Well done, Fabian!
Fabian has performed extensive computational and experimental research into the structure of aspherical granular media models, focusing on oblate ellipsoids. Throughout his PhD research, he collaborated far and wide, with Matthias Schröter / MPI Göttingen (who was his second supervisor), Gary Delaney / CSIRO Melbourne, Mohammad Saadatfar / ANU and many others.
Here’s the summary of Fabian’s thesis:
In particulate systems with short-range interactions, such as granular matter or simple fluids, the local structure is crucial for the macroscopic physical properties. This thesis advances understanding of granular matter by a comprehensive study of Voronoi-based local structure metrics applied to amorphous ellipsoid configurations. In particular, a methodology for a local, density-resolved analysis of structural properties
is developed. These methods are then applied to address the question when the global packing fraction alone is a sufficient descriptor of the structure, and the situations when this is not the case.
Packings of monodisperse spherical particles are a common simple model for granular matter and packing pro
blems. This work focuses on packings of ellipsoidal particles, a system which offers the possibility to study the influence of particle shape, particular particle anisotropy, on packing properties. A large scale experimental study of jammed packings of oblate mm-sized ellipsoids with various aspect ratios a is performed. Packings are prepared with different preparation protocols to achieve different global packing fractions fg and imaged by X-ray tomography. Additional datasets of packings are created by Discrete Element Method simulations of frictional and frictionless particles with and without gravity. Furthermore, packings of Ottawa sand samples are analyzed, in an attempt to investigate the relevance of the ellipsoid model system for real world granulates.
The structure of the packings is analyzed by Set Voronoi diagrams, an extension of the conventional Voronoi diagram to aspherical particles. We find some surprising structural properties, specifically related to the local packing fraction fl, defined as particle volume divided by its Voronoi cell volume. A universality is 
found in the probability density function to find a particle with fl in a given packing. The width of the density function is independent of the aspect ratio a. For spheres, Aste et al. [EPL 79(2):24003, 2007] proposed an analytic model for the distribution of Voronoi cell volumina. Their model strongly depends on the locally densest configuration, a quantity that was, prior to this work, not known for ellipsoids. We numerically investigate the locally densest structures and analyze their occurrence as local building blocks of granular packings. Knowledge of the densest structures allows to rescale the Voronoi volume distributions onto the single-parameter family of k-Gamma distributions. Remaining deviations are explained by an excessive
formation of distorted icosahedral clusters.
A robust tool to characterize spatial structures is provided by Minkowski tensors, which generalize the concepts of interface and moment tensors. We here investigate the shape properties of the Voronoi cells by anisotropy indices br,s n derived from these tensors. These local anisotropy indices point towards a significant difference in the local structure of random packings of spheres and ellipsoids. While the average
cell shape br,s n of all cells with a given value of fl is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true.
Fabian’s research outcomes are published in a number of articles:
- Fabian M. Schaller and Robert F. B. Weigel and Sebastian C. Kapfer, Densest Local Structures of Uniaxial Ellipsoids, Phys. Rev. X 6, 041032 (2016)
- Fabian M. Schaller, Sebastian C. Kapfer, James E. Hilton, Paul W. Cleary, Klaus Mecke, Cristiano De Michele, Tanja Schilling, Mohammad Saadatfar, Matthias. Schröter, Gary W. Delaney, Gerd E. Schröder-Turk, Non-universal Voronoi cell shapes in amorphous ellipsoid packs, EPL (Europhysics Letters) 111(2), 24002 (2015)
- Fabian M. Schaller, Max Neudecker, Mohammad Saadatfar, Gary W. Delaney, Gerd E. Schröder-Turk, Mathias Schröter, Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings, Phys. Rev. Lett. 114, 158001 (2015)
- Fabian M. Schaller, Sebastian C. Kapfer, Myfanwy E. Evans, Matthias J.F. Hoffmann, Tomaso Aste, Mohammad Saadatfar, Klaus Mecke, Gary W. Delaney, Gerd E. Schröder-Turk, Set Voronoi diagrams of 3D assemblies of aspherical particles, Philosophical Magazine 93(31-33), 3993-4017 (2013)
and a few others, see link here.