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This thesis will argue that the Black Sea of the High Medieval period was an important and vibrant economic zone. During the two centuries before the fall of Constantinople to the Fourth Crusade in 1204, the Black Sea was bustling with economic activity. Not only did those dwelling on its coasts - the Byzantines, Russians, Georgians and later Seljuqs - make use of the maritime connections for local trade; but its markets also connected those further afield, across the Mediterranean and European worlds. As a result of its substantial commercial activity, and geopolitical import, the Black Sea figured significantly in Byzantine foreign policy; however, the Byzantines did not attempt to systematically close the sea off to foreign merchants, as has been suggested. Rather, they used it as a bargaining chip in their negotiations with the Italian merchant republics of Genoa and Venice. Due to the later flourishing of the Black Sea under the Pax Mongolica, historiography has tended to underestimate or dismiss this earlier period of Euxine activity; however, such side-lining of this earlier trade is based on mistaken premises or misevaluated sources. In all, the Black Sea was a substantial economic zone in its own right long before 1204, and deserves more thorough investigation than it has been given. This thesis will provide that examination.

In the wake of the recent wave of interest in the ties between Early Rus and the Latin world, this dissertation investigates conceptions and depictions of Latin Christians in Early Rusian texts. Unlike previous smaller-scale studies, the present study takes into consideration all indigenous Early Rusian narrative sources which make reference to Latins or the Latin world. Its contribution is twofold. Firstly, it overturns the still prevalent assumption that Early Rusian writers tended to portray Latins as religious Others. There was certainly a place in Early Rusian writing for religious polemic against the Latin faith, but as I show, this place was very restricted. Secondly, having established the considerable diversity and complexity of rhetorical approaches to Latins, this study analyses and explains rhetorical patterns in Early Rusian portrayals of Latins and Latin Christendom. Scholars have tended to interpret these patterns as primarily influenced by extra-textual factors (most often, a text’s time of composition). This study, however, establishes that textual factors—specifically genre and theme—are the best predictors of a text’s portrayal of Latins, and explains the appearance and evolution of particular generic and thematic representations. It also demonstrates that a text’s place of composition tends to have a greater influence on its depictions of Latins than its time of composition. Through close engagement with the subtleties and ambiguities of Early Rusian depictions of Latins, this study furthers contemporary debate on questions of narrative, identity and difference in Rus and the medieval world.

The objective of this dissertation is the development of both forward and inverse modeling frameworks that extend the nondestructive evaluation (NDE) capability of resonant ultrasound spectroscopy (RUS) for materials science applications through utilization of modern computational resources and a rigorous application of the fundamental physics of mechanical resonance. First, a forward modeling framework (FMF) based on 3D linear-elastic finite element models is developed to explain the complex manner in which resonance frequencies of a specimen change as damage is accumulated. Numerous examples of damage common to Ni-based superalloys for structural applications in extreme thermo-mechanical environments, like those found in turbine engines, are specifically addressed including: creep, fatigue and recrystallization. Then, an inverse modeling framework (IMF) devised with the goal of quantitative NDE of materials based on RUS measured resonance frequencies is introduced. Built upon a full-Bayesian approach to the inverse problem, the novel IMF devised here affords substantially simplified experimental methods by estimating elastic constants and crystal orientation parameters simultaneously. The potential of the IMF is demonstrated by evaluating a series of novel Co and CoNi-based single crystal superalloys, with robust convergence behavior as compared to optimizer-based approaches described in the literature. Together, the finite element-based FMF and the Bayesian IMF demonstrate the immense value and insight gained by coupling experiments with physics-based models for state-of-the-art materials characterization and NDE.

Tb6FeSb2 and Tb6FeBi2 are novel rare earth compounds with little prior research. These compounds show high and variable curie temperatures for rare-earth compounds. This has lead to a literature review which includes the discussion of: elasticity, resonance, and magnetism. This review is used to discuss the theory and methodology which can relate these various properties to each other. Furthermore, synthesis, x-ray analysis, and RUS sample preparation of Tb6FeSb2 and Tb6FeBi2 were completed. Resonant Ultrasound Spectroscopy (RUS) elastic studies were taken for Tb6FeSb2 and Tb6FeBi2 as a function temperature from 5-300K, in various magnetic fields ranging from 0-9T. Tb6FeSb2’s and Tb6FeBi2’s elastic moduli are related to their magnetic properties. Magnetization data, primarily M v. H, provides another measure the magnetic properties are used to help correlate the data to elasticity. Tb6FeSb2 and Tb6FeBi2 Curie temperatures are 253(3)K and 246(5)K respectively. The low temperature magnetic transition of Tb6FeSb2 is 65-90K and Tb6FeBi2 is 55-75K. RUS suggests that this low temperature transition is somehow related to a structural transition but this transition does not occur in these two compounds. Co-substitution of Tb6FeSb2 and Tb6FeBi2 seem to greatly affect this lower temperature transition in RUS. It does not greatly effect the curie temperature. Low temperature XRD shows that Co-substitution also creates a structural transition in this family of compounds.