This research presents a study of the hardness, electrical, and thermal properties AlMgB{sub 14} containing Al{sub 2}MgO{sub 4} spinel. This research also investigated how much Al{sub 2}MgO{sub 4} spinel consistently forms with AlMgB{sub 14}, if AlMgB{sub 14} materials can be produced by hot isostatic pressing (HIP), what effects TiC and TiB{sub 2} have on this composite material, and the importance of mechanical alloying. Included also is a study of the variation in hardness measurements and how they relate to SI units. Heretofore, all ultra-hard materials (hardness > 40 GPA) have been found to be cubic in structure, electrical insulators, and expensive; the behavior of AlMgB{sub 14}, which in certain specimens and compositions can have hardness values greater than 40 GPa, is therefore quite unusual since it is non-cubic, conductive, and moderate in cost. This offers an opportunity to investigate the relationship between hardness, thermal, and electrical properties from a new perspective. The main purpose of this project was to characterize the different properties of the AlMgB{sub 14} materials and to demonstrate that this material can be made in bulk. The technologies used for this study include microhardness measurement techniques, scanning electron microscopy, energy dispersive spectroscopy, x-ray diffraction spectroscopy, x-ray diffraction …

I present time-varying Reeb graphs as a topological framework to support the analysis of continuous time-varying data. Such data is captured in many studies, including computational fluid dynamics, oceanography, medical imaging, and climate modeling, by measuring physical processes over time, or by modeling and simulating them on a computer. Analysis tools are applied to these data sets by scientists and engineers who seek to understand the underlying physical processes. A popular tool for analyzing scientific datasets is level sets, which are the points in space with a fixed data value s. Displaying level sets allows the user to study their geometry, their topological features such as connected components, handles, and voids, and to study the evolution of these features for varying s. For static data, the Reeb graph encodes the evolution of topological features and compactly represents topological information of all level sets. The Reeb graph essentially contracts each level set component to a point. It can be computed efficiently, and it has several uses: as a succinct summary of the data, as an interface to select meaningful level sets, as a data structure to accelerate level set extraction, and as a guide to remove noise. I extend these uses …