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...

Are some paths and interactions immune to the gravitational curvature of spacetime? The paths of virtual particles might be – the effect is unexplored experimentally. Were a quantum theory of gravity moderated by virtual gravitons that are themselves susceptible to gravitational curvature, to obey the weak equivalence principle, and to follow null geodesics, then gravitational acceleration migh...

A path deviation equation in the Parameterized Absolute Parallelism (PAP) geometry is derived. This equation includes curvature and torsion terms. These terms are found to be naturally quantized. The equation represents the deviation from a general path equation, in the PAP-geometry, derived by the author in a previous work. It is shown that, as the effect of the torsion, on the deviation, incr...

The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not behave analogously to smooth surfaces with respect to negative curvature. We extend this curvature to vertices and faces in such a way that the problems with co...

Nonaccidental properties (NAPs) are image properties that are invariant over orientation in depth and are distinguished from metric properties (MPs) that can change continuously with variations over depth orientation. To a large extent NAPs allow facile recognition of objects at novel viewpoints. Two match-to-sample experiments with 2D or 3D appearing geons assessed sensitivity to NAP vs. MP di...

The time course of categorization was investigated in four experiments, which revealed graded competitive effects in a categorization task. Participants clicked one of two categories (e.g., mammal or fish) in response to atypical or typical exemplars (e.g., whale or cat) in the form of words (Experiments 1 and 2) or pictures (Experiments 3 and 4). Streaming x, y coordinates of mouse movement tr...

Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles > 2π. With an additional condition, we can weaken the requirement on one metric to ‘no conjugate points.’

The repetitive sequence (AGGGCCCTAGAGGGGCCC-TAG)n was previously shown to be curved by gel mobility assays. Here we show, using hydroxy radical/DNase I digestion and differential helical phasing experiments that the curvature is directed towards the major groove and is located in the GGGCCC, but not the CTAGAG segments. The effect of the GC step in the context of the GGGCCC motif is apparently ...

Detectability of contours may be affected by long-range interactions between neurons in early stages of visual cortex. Specifically, neurons with receptive fields arrayed along the length of a contour may facilitate each other in a position- and orientation-dependent manner. Accordingly, the overall geometry of a contour should significantly influence both the strength of these long-range inter...

Many applications of geometry processing and computer vision rely on geometric properties of curves, particularly their curvature. Several methods have already been proposed to estimate the curvature of a planar curve, most of them for curves in digital spaces. This work proposes a new scheme for estimating curvature and torsion of planar and spatial curves, based on weighted least–squares fitt...