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Finding the exact spanning ratio of a Delaunay graph has been one of the longstanding open problems in Computational Geometry. Currently there are only four convex shapes for which the exact spanning ratio of their Delaunay graph is known: the equilateral triangle, the square, the regular hexagon and the rectangle. In this paper, we show the exact spanning ratio of the parallelogram Delaunay graph, making the parallelogram the fifth convex shape for which an exact bound is known. The worst-case spanning ratio is exactly $$\frac{\sqrt{2}\sqrt{1+A^2+2A\cos(\theta_0)+(A+\cos(\theta_0))\sqrt{1+A^2+2A\cos(\theta_0)}}}{\sin(\theta_0)},$$ where A is the aspect ratio and θ_0 is the non-obtuse angle of the parallelogram. Moreover, we show how to construct a parallelogram Delaunay graph whose spanning ratio matches the above mentioned spanning ratio.

This dissertation discusses topics related to the performance and long-term durability of glass-reinforced composites. The first portion of this dissertation describes work to assess the effect that post-curing has on widely used E-glass/vinyl-ester composites (E-glass/Derakane 510-A and E-glass/Derakane 8084). It is shown that post-curing can have significant positive effects on the initial material properties of glass-reinforced vinyl ester composites. Furthermore, the post-cure of 82ºC for four hours stabilizes the matrix, and as such reduces matrix-related material property evolution. By stopping or nearly stopping material property evolution due to matrix curing over time, the post-cure regime isolates and allows the study of other time-dependent effects, such as fatigue or hygrothermal degradation, and aids designers by establishing an unchanging base set of initial (undamaged) material design properties. The second portion of this dissertation discusses the effects that mean stress and R-ratio have on the fatigue performance of the same material. Qualitative and quantitative differences are seen in the performance as a function of the loading ratio. A residual strength based life prediction model developed at Virginia Tech is applied to the fatigue data, characterizing the material under constant-amplitude loading. Three curve-fitting parameters are then used along with the model to predict variable-amplitude fatigue lives, with remarkably good results. The final portion of the dissertation concerns the effect of hygrothermal and accelerated aging on glass-reinforced composites. A meta-study is performed on data from the literature, and a glass-degradation-based life-prediction model is applied to the data. It is seen that a static fatigue-based activation energy approach to residual strength can predict activation energies associated with glass-reinforced composite strength degradation in the case of glass-reinforced concrete quite well, predicting values of 80-100 kJ/mol, which are similar to those expected for glass dissolution via silica ring opening. The model may also hold some promise for doing the same for glass-reinforced polymer composites. / Ph. D.

The response of light-frame timber shear walls to lateral forces is the focus of the dissertation. The objective of this study was to obtain performance characteristics of shear walls with various aspect ratios and overturning restraint via experimental testing and analytical modeling. Presented are the test data of monotonic and cyclic tests on fifty-six light-frame timber shear walls with aspect ratios of 4:1, 2:1, 1:1, and 2:3. Overturning restraint conditions represent engineered construction and conventional construction practices. The walls representative of the engineered construction were attached to the base by means of tie-down anchors and shear bolts. As opposed to engineered construction, conventionally built walls were secured to the base by nails or shear bolts only. The specimens were tested in a horizontal position with oriented strandboard (OSB) sheathing on one side. To obtain conservative estimates, no dead load was applied in the wall plane during the tests. The nail-edge distance across the top and bottom plates varied from 10 mm (3/8 in.) to 19 mm (3/4 in.). Twelve walls were repaired after the initial tests and re-tested. A mechanics-based model was advanced to predict the racking resistance of conventional multi-panel shear walls using simple formulae. The deflections of engineered and conventional shear walls were predicted using the energy method combined with empirical formulae to account for load-deformation characteristics of sheathing-to-framing connections and overturning restraint. The proposed formulae were validated through comparison with test results obtained during this study. The results of the study serve to further development of a mechanics-based methodology for design of shear walls accounting for various wall configurations and boundary conditions. / Ph. D.

Hyperthyroidism is the most common feline endocrinopathy. 131I is the treatment of choice, and over 50,000 cats have been treated using an empirical fixed dose. Better treatment responses could be achieved by tailoring the dose based on the severity of disease. Scintigraphy is the best method to quantify the severity of the disease. Previously established scintigraphic quantitative methods, thyroid to salivary ratio (T:S ratio) and % dose uptake, are the most widely recognized measurements. Recently, the thyroid to background ratio (T:B ratio) has been proposed as an alternate method to assess function and predict 131I treatment response. The purpose of this study was to determine the best location of a background ROI, which should be reflective of blood pool activity. We also hypothesized that the T:B ratio using the determined background ROI would provide improved correlation to T4 when compared to T:S ratio and % dose uptake in hyperthyroid cats. Fifty-six hyperthyroid cats were enrolled. T4 was used as the standard measure of thyroid function and was obtained prior to thyroid scintigraphy and 131I therapy. Blood samples were collected at the time of scintigraphy and radioactivity within the sample was measured. The plasma radioactivity was compared to the background ROI count densities in 8 anatomic regions using linear regression analysis for 55 cats. One cat was excluded from the study because of an injection error during scintigraphy. T:B and T:S ratios, and % dose uptake on scintigraphy were then compared to serum T4 by linear regression analysis for 39 cats. Sixteen cats were excluded because of recent methimazole or Y/D diet use, or incomplete data. The heart ROI correlated best to plasma pertechnetate activity (r = 0.70). % dose uptake correlated best to serum T4 (r = 0.74), followed by T:S ratio (r = 0.66), followed by the T:B ratio using the heart ROI (r = 0.59). Placing an ROI over the heart is the best method of quantifying plasma radioactivity. T:B ratio using the heart ROI as the background is a good predictor T4 but percent dose uptake and T:S ratio proved to be better predictors of T4 than any of the T:B ratios. Therefore, our hypothesis was not supported. The T:B ratio may not provide the best scintigraphic measurement of thyroid function. Hence it is unlikely to accurately predict treatment response to 131I therapy. / Master of Science

Three strains of cyanobacteria (Anabaena PCC7120, A. variabilis and Nostoc commune), all belonging to the family Nostocaceae, were found to be capable of modulating the production and chemical composition of extracellular polysaccharides (EPS) in response to carbon and nitrogen availability as well as pH. While the carbohydrate compositions of the glycans produced by the different organisms were indicative of their recent evolutionary divergence, there were measurable differences that were dependent upon growth conditions. The EPS resulting from biofilm growth conditions was reduced in glucuronic acid levels in both Anabaena variabilis ATCC 29413 and Anabaena PCC 7120. Under planktonic conditions, the glycan from A. variabilis contained glucuronic acid when grown in nitrate-free BG-11₀ medium whereas A. PCC 7120 produced similar levels in standard BG-11 medium. This suggests that phylogeneticallyrelated cyanobacteria respond very differently to changes in their local environment. The pH of BG-11 cultures increased to 9-10 for all three strains of cyanobacteria. The increase resulted in an increase in the amount of dissolved inorganic carbon available in the medium, creating an imbalance in the carbon-nitrogen ratio, with the complete consumption of 17.65 mmol L⁻¹ nitrates raising the pH to near 10 in BG-11 medium. While increased carbon availability has been shown to induce capsulated morphologies in strains of cyanobacteria, only Nostoc commune DRH-1 exhibited this behavior, and only when grown in BG-11 medium. Carbon and nitrogen availability as well as pH modulate the monosaccharide composition of the glycan generated by cyanobacteria investigated. The different characteristics of the glycans produced can affect the survivability of the organisms and the community structure of cyanobacterial biofilms and microbial mats found in nature. As cyanobacteria are ubiquitous organism both now and in the past, they play a pivotal role in the biological and geological processes of the Earth, controlling the availability and cycling of carbon and nitrogen both actively and passively. / Master of Science in Life Sciences