A introduction to metacalibration methods and their application. This includes a new proof of the double bubble conjecture, new results in the area of equitent problems (isoperimetric problems with boundary), and comments on a mapping conjecture.

We approximate the vibrational energies of the symmetric and asymmetric stretches of the hydrogen bonds of the molecules H_3O_2^- and H_5O_2^+ by applying an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei differently than the heavier oxygen nuclei. This results in significantly more accurate approximations for the stretching vibrational energies, which we compare to experimental measurements. / Master of Science

Yes / This paper presents the behaviour of circular concrete-filled double-skin steel tubular (CFDST) stub columns compressed under concentric axial loads. To predict the performance of such columns, a finite element analysis is conducted. Herein, for the accurate modelling of the double-skin specimens, the identification of suitable material properties for both the concrete infill and steel tubes is crucial. The applied methodology is validated through comparisons of the results obtained from the finite element analysis with those from past experiments. Aiming to examine the effect of various diameter-to-thickness (D/t) ratios, concrete cube strengths and steel yield strengths on the overall behaviour and ultimate resistance of the double-skin columns, a total of twenty-five models are created to conduct the parametric study. In addition, four circular concrete-filled steel tubes (CFST) are included to check the dissimilarities, in terms of their behaviour and weight, when compared with identical double-skin tubes. A new formula based on Eurocode 4 is proposed to evaluate the strength of the double-skin specimens. Based on the comparison between the results derived from the analysis, the proposed formulae for the concrete filled double-skin would appear to be satisfactory.

Proper functioning of instruments requires precise calibration and routine quality assurance. In a clinical setting, this is achieved through the use of phantoms, which mimic the physical characteristics of tissues. Polyvinyl alcohol (PVA), a non-toxic, water-soluble polymer is well-suited for use as clinical phantom material. Through successive freezing and thawing, solutions of PVA in water can be solidified into rigid cryogels (PVA-C). The number of freeze-thaw cycles affects the properties of the material, including its optical characteristics. A double integrating sphere system was used in conjunction with the Inverse Adding Doubling (IAD) algorithm to characterize the optical properties of thin slab samples. The setup was evaluated using liquid phantoms. Liquid emulsion and food colouring were used to impart scattering and absorbing properties in the range characteristic of human tissue. Measured values of normalized reflectances and transmittances were entered into IAD, and a set of optical properties (μ′s,μa,g) retrieved. The reduced scattering coefficient was found to increase linearly with increasing lipid concentration, while a consistent overestimation of the absorption coefficient was observed. Measurements of PVA cryogels revealed a linear increase in the reduced scattering coefficient with an increasing number of freeze-thaw cycles up to five cycles. Scattering was also observed to increase with concentration up to PVA concentrations of 15%, and to spontaneously increase during the lifetime of the slab samples. These findings suggest it is possible to tune the optical scattering of PVA-C via different purely physical mechanisms. / Thesis / Master of Science (MSc)

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A 2 cm ostectomy was performed on 10 pairs of canine cadaveric humeri proximal to the supratrochlear foramen. Stabilization was with a double plate construct (DB-PLATE) (n=10) or external skeletal fixator with intramedullary pin tie-in configuration (ESF-IMP) (n=10). Cyclic testing was performed. Axial compressive load to failure testing followed. Data analyzed included dynamic stiffness, stiffness and yield load. No constructs failed during cyclic testing or lost stiffness over time, although mean dynamic stiffness was greater for DB-PLATE compared to ESF-IMP. Mean stiffness of DB-PLATE in load-toailure testing was not significantly different than ESF-IMP. Yield force of DB-PLATE was significantly higher than ESF-IMP. These results suggest that both DB-PLATE and ESF-IMP would be appropriate fixation techniques for stabilization of comminuted supracondylar humeral fractures in dogs with appropriate exercise restriction. Double plate fixation may be preferable when prolonged healing or inadequate post-operative restraint was anticipated because it was stronger in destructive testing.

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