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要旨:
Disordered packings of ellipsoidal particles are an important model for disordered
granular matter and can shed light on geometric features and structural transitions
in granular matter. In this thesis, the structure of experimental ellipsoid packings is
analyzed in terms of contact numbers and measures from mathematical morphometry
to characterize of Voronoi cell shapes. Jammed ellipsoid packings are prepared by
vertical shaking of loose configurations in a cylindrical container. For approximately
50 realizations with packing fractions between 0.54 and 0.70 and aspect ratios from
0.40 to 0.97, tomographic images are recorded, from which positions and orientations
of the ellipsoids are reconstructed. Contact numbers as well as discrete approximations
of generalized Voronoi diagrams are extracted. The shape of the Voronoi cells
is quantified by isotropy indexes b,r,s,n based on Minkowski tensors. In terms of the
Voronoi cells, the behavior for jammed ellipsoids differs from that of spheres; the
Voronoi Cells of spheres become isotropic with increasing packing fraction, whereas
the shape of the Voronoi Cells of ellipsoids with high aspect ratio remains approximately
constant. Contact numbers are discussed in the context of the jamming
paradigm and it is found that the frictional ellipsoid packings are hyperstatic, i.e.
have more contacts than are required for mechanical stability. It is observed, that the
contact numbers of jammed ellipsoid packings predominantly depend on the packing
fraction, but also a weaker dependence on the aspect ratio and the friction coefficient
is found. The achieved packing fractions in the experiments lie within upper and
lower limits expected from DEM simulations of jammed ellipsoid packings. Finally,
the results are compared to Monte Carlo and Molecular Dynamics data of unjammed
equilibrium ellipsoid ensembles. The Voronoi cell shapes of equilibrium ensembles of
ellipsoidal particles with a low aspect ratio become more anisotropic by increasing
the packing fraction, while the cell shape of particles with large aspect ratios does the
opposite. The experimental jammed packings are always more anisotropic than the
corresponding densest equilibrium configuration.
