OF THE DISSERTATION Various Geometric Aspects of Condensed Matter Physics by Zhenyu Zhou Doctor of Philosophy in Physics Washington University in St. Louis, 2013 Professor Alexander Seidel, Chairperson Geometric aspect of condensed matter has arouse a lot of interests in recent years. The idea of Berry phase is highly appreciated in various systems. We explored the geometric features of two spe...

Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically show that there exists a point that is contained in many objects that are induced (spanned) by an underlying point set. In the first selection lemma, we conside...

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...

The Wedding Chamber fresco, also known as Camera Picta, or La Degli Sposi, painted by Andrea Mantegna at the dawn of Renaissance, epitomizes most outstanding expression personal creativity and innovation from an artist that transformed boundaries representation narrative inside architectural space, to mix illusion reality. He utilized trompe l'oeil effect, Oculus, cinematic imaging on walls, re...

This paper presents an application of photogrammetry on ceramic fragments from two excavation sites located north-west of France. The restitution by photogrammetry of these different fragments allowed reconstructions of the potteries in their original state or at least to get to as close as possible. We used the 3D reconstructions to compute some metrics and to generate a presentation support b...