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Abstract: Granular matter is pervasive in nature, technology and every-day life. It shares properties with solids, liquids and gases, but also has some it does not share with any of these, which is why some go as far as calling granulates a fourth state of matter. The microscopic behavior of these complex systems is difficult to observe experimentally and numerical simulation is increasingly becoming a valid alternative. We present a powerful implementation and some new applications of the Discrete Element Method (DEM) based on neighborhood detection using weighted Delaunay triangulations. One particular novelty is our ability to treat large populations of general-shaped objects called sphero-polyhedra, obtained as Minkowski sums of polyhedra and spheres. The method has been validated by faithfully reproducing several phenomena like e.g. jamming, crystallization, Brazil-nut-effect and reverse Brazil-nut-effect.
Joint work with Lionel Pournin, Marco Ramaioli, and Michel Tsukahara
Colloquium - 16:00
Abstract: The vertex-edge-face poset of a planar map is the poset whose elements are the vertices, edges and faces of the map ordered by inclusion. The vertex-face poset is the subposet induced by the vertices and faces. Brightwell and Trotter proved that the dimension of the vertex-edge-face poset of a planar map is at most 4. However, little is known about which planar maps have vertex-edge-face posets or vertex-face posets of dimension at most 3. It turns out that outerplanar maps and subdivisions of outerplanar maps are the key to understanding this.
I will talk about recent work (with Stefan Felsner) on characterizing outerplanar maps with vertex-face or vertex-edge-face posets of dimension 3.