Physics of disordered materials and packing problems

Granular materials & aspherical particle models

“…, but if such demonics are ignored,…” (Edwards & Oakeshott, 1989)

This quote was made by Edwards in the context of the statistical mechanics description of granular powders. It specifically alludes to the fact that in these athermal many-particle systems some macroscopic properties (including e.g. global packing fraction) adopt well-defined averages with typical values across all microstates.

A lot of work in granular matter and disordered packings, including our own, relates to the question which macroscopic variables provide useful (and unifying) information to understand the complex phase space of the microstates. This is not only useful in the context of the statistical mechanics analogy investigated by many (following Edwards & Oakeshott’s vision), but also more generally for making sense of the multitude of structural measures that can be used to describe the structure of grain packings.

Our work on granular materials has focused on aspherical particle models (mostly ellipsoids) and been conducted using extensive tomographic image analysis as well as simulations. Our key message in the articles below is that Voronoi-based structure metrics (Minkowski tensor anisotropies) and a local (density-resolved analysis) are useful elements towards understanding the observed “universalities” in random sphere packings and the lack of some of those universalities in ellipsoid packings:

F.M. Schaller, S.C. Kapfer, J.E. Hilton, P. Cleary, K. Mecke, C. de Michele, T. Schilling, M. Saadatfar, M. Schröter, G.W. Delaney, G.E. Schröder-Turk, “Non-universal Voronoi cell shapes in amorphous ellipsoid packings“, EPL (Europhysics Letters) 111, 24002 (2015)
F.M. Schaller, M. Neudecker, M. Saadatfar, G.W. Delaney, G.E. Schröder-Turk, and M. Schröter, “L ocal Origin of Global Contact Numbers in Frictional Ellipsoid Packings“, Phys. Rev. Lett. 114, 158001 (featured on PRL cover)
S. Weis, G.E. Schröder-Turk and M. Schröter, “Structural similarity between dry and wet sphere packings“, under review for New Journal of Physics (2019)
F. Schaller, H. Punzmann, G.E. Schröder-Turk and M. Saadatfar, “Towards minimal models for realistic granular materials: Tomographic analysis of bidispersed assemblies of ellipsoids“, Powders and Grains, EPJ Web of Conferences 140, 06030 (2017)
N. Topic, F.M. Schaller, G.E. Schröder-Turk and T. Pöschel, “Microscopic structure of mono-disperse granular heaps and sediments of particles on inclined surfaces”, Soft Matter 12, 3184 – 3188 (2016)
S.C. Kapfer, W. Mickel, K. Mecke, and G.E. Schröder-Turk, Jammed Spheres: Minkowski Tensors Reveal Onset of Local Crystallinity , Phys. Rev. E 85 , 030301(Rapid Communication) (2012)
G.E. Schröder-Turk, W. Mickel, K. Mecke, G. Delanay, M. Saadatfar, T. Senden, T. Aste, “Disordered Spherical Bead Packs are Anisotropic”, Europhys. Lett. 90 (3), 34001 (2010)

Surface-tension dominated soap froths

M.E. Evans, G.E. Schröder-Turk, A.M. Kraynik, “A geometric exploration of stress in deformed liquid foams“, J. Phys.: Condens. Matter 29, 124004 (2017)
A. Mughal, T. Libertiny, G.E. Schröder-Turk, “How bees and foams respond to curved confinement: level set boundary representations in the Surface Evolver“, Colloids and Surfaces A: Physicochemical and Engineering Aspects 534, 94 (2017)
M.E. Evans, A.M. Kraynik, D.A. Reinelt, K. Mecke and G.E. Schröder-Turk, “Networklike Propagation of Cell-Level Stress in Sheared Random Foams“, Phys. Rev. Lett. 111, 138301 (2013)
M.E. Evans, J. Zirkelbach, G.E. Schröder-Turk, A.M. Kraynik, and K. Mecke, Deformation of Platonic foam cells: Effect on growth rate , Phys. Rev. E 85 , 061401 (2012)

Quantizer problem and Lloyd’s algorithm

M.A. Klatt, J. Lovric, D. Chen, S.C. Kapfer, F.M. Schaller, P.W.A. Schönhöfer, B.S. Gardiner, A.-S. Smith, G.E. Schröder-Turk, S. Torquato, “Universal hidden order in amorphous cellular geometries“, Nature Communications 10, 811 (2019)

Transport through disordered porous materials

C. Scholz, F. Wirner, M. Klatt, D. Hirneise, G.E. Schröder-Turk, K. Mecke, C. Bechinger, “Direct Relations between Morphology and Transport in Boolean Models“, Physical Review E 92, 043023 (2015)
C. Scholz, F. Wirner, J. Götz, U. Rüde, G.E. Schröder-Turk, K. Mecke and C. Bechinger, “Permeability of Porous Materials Determined from the Euler Characteristic”, Physical Review Letters 109, 264504 (2012)

Percolation problems and vertex percolation

M.A. Klatt, G.E. Schröder-Turk, K. Mecke, “Anisotropy in finite continuum percolation: Threshold estimation by Minkowski functionals“, J. Stat Mech 2017(2), 023302 (2017)
S. Nachtrab, M.J.F. Hoffmann, S.C. Kapfer, G.E Schröder-Turk and Klaus Mecke, “Beyond the percolation universality class: the vertex split model for tetravalent lattices“, New J. Phys. 17, 043061 (2015) [pdf]

Anomalous diffusion and Lorenz models

M. Spanner, F. Höfling, S.C. Kapfer, K. Mecke, G.E. Schröder-Turk, and T. Franosch, “Splitting of the universality class of anomalous transport in crowded media”, Physical Review Letters 116, 060601 (2016)
T. Franosch, M. Spanner, T. Bauer, G.E. Schröder-Turk, E. Frey, F. Höfling, “Space-resolved dynamics of a tracer in a disordered solid”, J. Non-Cryst. Solids 357, 472 (2011)

M. Spanner, F. Höfling, G.E. Schröder-Turk, K. Mecke and Th. Franosch, “Anomalous transport of a tracer on percolating clusters”, J. Phys.: Condens. Matter. 23, 234120, (2010)

Mechanical properties of disordered cellular solids

S. Nachtrab, S.C. Kapfer, C.H. Arns, M. Madadi, K. Mecke and G.E. Schröder-Turk, “Morphology and Linear-Elastic Moduli of Random Network Solids”, Advanced Materials 23, 2633-2637 (2011)
S. Nachtrab, S. Kapfer, D. Rietzel, D. Drummer, M. Madadi, C.H. Arns, A.M. Kraynik, G.E. Schröder-Turk and K. Mecke, “Tuning elasticity of open-cell solid foams and bone scaffolds via randomized vertex connectivity”, Advanced Engineering Materials 14, 120-124 (2012)
M. Saadatfar, M. Mukherjee, M. Madadi, G.E. Schröder-Turk, F. Garcia-Moreno, F.M. Schaller, S. Hutzler, A.P. Sheppard, J. Banhart, U. Ramamurty, Structural and Finite Element analysis of tomographic data for closed cell aluminum foam subject to uniaxial compression, Acta Materialia 60 (8), 36043615 (2012)

Groundstates & low-temperatures of disordered stat mech models

G.E. Schröder, T. Knetter, M.A. Alava and H. Rieger, “Ground states versus low-temperature equilibra in random field Ising chains”, Eur. Phys. J. B 24, 101-105 (2001)
T. Knetter, G.E. Schröder, M.A. Alava and H. Rieger, “Disorder-induced roughening transition of many elastic lines in a periodic potential”, Europhys. Lett. 55, 719-725 (2001)
G.E. Schröder, T. Knetter, H. Rieger, “Solution of the multifluxline ground state problem in disordered systems”, in Computer Simulation Studies in Condensed Matter Physics XIII, p118-122, Springer, Heidelberg, Berlin (2000)
T. Knetter, G.E. schröder, H. Rieger, “Disorder-driven roughening transition of flux lines in a periodic potential”, in Computer Simulation Studies in Condensed Matter Physics XIII, p118-122, Springer, Heidelberg, Berlin (2000)

Facebook Tweet Pin