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We describe the development of a new software tool, called “Pomelo”, for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pears.

In this paper, we report experimental results on granular compaction in a model system made of mono- and bidisperse ellipsoidal packings as well as sand packings with grain size polydispersity. The packings are subject to vertical tapping of varying duration (number of taps) and their internal three-dimensional structure is obtained using x-ray computed tomography. Particles positions and orientations are reconstructed and the global packing densities are computed. The analysis of the vertical and horizontal local packing fraction profiles reveal a homogeneous densification in the ellipsoidal packings, however, sand packings exhibit radial density gradient, possibly linked to the onset of convection.