The goal of this thesis is to develop an efficient finite element model of a particular micro-positioning(MP) system, known as the 3RRR Mechanism. MP systems are capable of delivering accurate and controllable motion in the micro-metre to sub-micrometre range. Conventional mechanisms, which are often composed of rigid links with pinned connections are prone to friction, backlash and stiction, which are magnified at small displacements. As such MP systems utilize a new structure known as the compliant mechanism. The structure of most compliant mechanisms is based on conventional mechanisms; however they are monolithic devices which utilize flexible elements, instead of pins, to transform the input to a useful output position. One common flexible element found in compliant mechanisms is the right circular flexure hinge. The seminal work on flexure hinges was done by Paros and Weisbord(1965), the basis of which was to calculate compliance (the reciprocal of stiffness) in order to characterize the behaviour of the hinge when loaded. However they essentially modelled the flexure hinge as a 1-D beam, when it is in fact 3-D in nature. Researchers completing finite element models of MP systems and flexure hinges have extended the model to 2-D elements, still resulting in poor results when compared to experimental data. The task of completing a full 3-D finite element model of a MP system, let alone a right circular flexure hinge, is a major computational effort. For instance, a full 3-D model of the 3RRR mechanism would require over 1,000,000 degrees of freedom(DOF) dedicated to the flexure hinges alone. A 2-D model requires approximately 45,000 DOF in total; however, this number is still regarded as large. Given these facts, a new technique called the Equivalent Beam Methodology(EBM) has been developed to model the 3-D stiffness of any right circular flexure hinge with a low number of DOF. This method essentially maps the 3-D stiffness of the hinge to a number of 1-D beam elements. For comparison, the finite element model of the 3RRR mechanism which incorporates the beams of the EBM has under 300 DOF in total, and is more accurate than the 2-D model. This method is extremely accurate, easy to use, and has a very low number of DOF, which makes it suitable to many advanced finite element modelling analyses such as topographic optimization, dynamic and modal analysis.

This thesis aims to reveal the magnitude of the income elasticity of health expenditure and the impact of non-income determinants of health expenditures in the Canadian Provinces. Health can be seen as a luxury good if the income elasticity exceeds unity and as a necessity good if the income elasticity is below unity. The motivation behind the analysis of the determinants of health spending is to identify the forces that drive the persistent increase in health expenditures in Canada and to explain the disparities in provincial health expenditures, thereby to prescribe sustainable macroeconomic policies regarding health spending. Panel data on real per capita GDP, relative price of health care, the share of publicly funded health expenditure, the share of senior population and life expectancy at birth have been used to investigate the determinants of Canadian real per capita provincial total, private and government health expenditures for the period 1975-2002. Dynamic models of health expenditure are analyzed via Generalized Instrumental Variables and Generalized Method of Moments techniques. Evidence confirms that health is far from being a luxury for Canada and government health expenditures are constrained by the relative prices. Results also cast doubt upon the power of quantitative analysis in explaining the increasing health expenditures.

This thesis is an extension of a recent study into the relationship between merger size and profitability. It studies a class of Cournot oligopoly with linear cost and quadratic demand. Its focus is to analyze how a mergers profitability is affected by its size and by the demand elasticity. Such results have not yet been reported in previous studies, perhaps due to the complexity of the equilibrium equation involved. It shows an increase in the demand elasticity also raises a mergers profitability. Consequently, an increase in the demand elasticity reduces merged members critical combined per-merger market share for the merger to be profit enhancing. Comparing with 80% minimum market share requirement for a profitable merger in Salant, Switzer, and Reynolds (1983), a greater market share is needed when the demand function is concave (demand is relatively inelastic), while a smaller market share may still be profitable when the demand function is convex (demand is relatively elastic). In our model, mergers are generally detrimental to public interests by increasing market price and reducing output. However, the merger will be less harmful when the goods are very inelastic.

This thesis aims to reveal the magnitude of the income elasticity of health expenditure and the impact of non-income determinants of health expenditures in the Canadian Provinces. Health can be seen as a luxury good if the income elasticity exceeds unity and as a necessity good if the income elasticity is below unity. The motivation behind the analysis of the determinants of health spending is to identify the forces that drive the persistent increase in health expenditures in Canada and to explain the disparities in provincial health expenditures, thereby to prescribe sustainable macroeconomic policies regarding health spending. Panel data on real per capita GDP, relative price of health care, the share of publicly funded health expenditure, the share of senior population and life expectancy at birth have been used to investigate the determinants of Canadian real per capita provincial total, private and government health expenditures for the period 1975-2002. Dynamic models of health expenditure are analyzed via Generalized Instrumental Variables and Generalized Method of Moments techniques. Evidence confirms that health is far from being a luxury for Canada and government health expenditures are constrained by the relative prices. Results also cast doubt upon the power of quantitative analysis in explaining the increasing health expenditures.

In the study of the mechanical behavior of biological tissues, many complex tissues are often modeled as poroelastic systems due to their high fluid content and mobility. Fluid content and fluid transport mechanisms in tissues are known to be highly correlated with several pathologies. Thus, imaging techniques capable of providing accurate information about these mechanisms can potentially be of great diagnostic value. Ultrasound elastography is an imaging modality that is currently used as a complement to sonographic methods to detect a variety of tissue pathologies. Poroelastography is a new elastographic technique that has been recently proposed to image the mechanical behavior of tissues that can be modeled as poroelastic media. The few poroelastographic studies retrievable focus primarily on homogeneous poroelastic media. In this study, a statistical analysis of the performance of poroelastographic techniques in a non-homogeneous poroelastic simulation model under different loading conditions was carried out. The two loading conditions simulated were stress relaxation (application of constant strain) and creep compression (application of constant stress), both of which have been commonly used in the field of poroelastography. Simulations were performed using a FE poroelastic simulation software combined with ultrasound simulation software techniques and poroelastography processing algorithms developed in our laboratory. The non-homogeneous poroelastic medium was modeled as a cube (background) containing a cylindrical inclusion (target). Different permeability, Young’s modulus and Poisson’s ratio contrasts between the underlying matrix of the background and the target were considered. Both stress relaxation and creep compression loading conditions were simulated. The performance of poroelastography techniques was quantified in terms of accuracy, elastographic contrast–to–noise ratio and contrast transfer efficiency. The results of this study show that, in general, image quality of both axial strain and effective Poisson’s ratio poroelastograms is a complex function of time, which depends on the contrast between the poroelastic material properties of the background and the poroelastic material properties of the target and the boundary conditions. The results of this study could have important implications in defining the clinical range of applications of poroelastographic techniques and in the methodologies currently deployed.

The objective of this research is to synthesize and characterize microstructures and some elastic properties of bioactive glasses subject to relaxation and/or devitrification treatments. We synthesize two kinds of bioglasses, i.e. P-richer 45S5 and P-poorer 55S4.3. After tempering, the as-prepared bioactive glasses are transparent, 55S4.3 being colorless while 45S5 pale pink in color. The thermal events in DTA analysis indicated that the crystallization of 45S5 and 55S4.3 starts at 620oC and 680oC, respectively. The two bioactive glasses became ivory upon heating at 715oC, and the degree of being opaque increases with dwelling time. The crystalline phase for 45S5 is Na2CaSiO4 -derived Na2Ca2Si3O9 or Na4CaSi3O9. By XRD traces and polarizing optical micrographs, we conclude that the crystal is based on simple cubic structure with a=7.5054Å and space group P213 (198). Due to poor crystallization rate, the crystal in P-poor 55S4.3 glass was not investigated in detail. However, according to the similarity of Raman spectra for devitrified 45S5 and 55S4.3, we suggest that the crystal is similar for the two devitrified glasses. Raman spectra indicated that the relaxed 45S5 has predominant Q2 and Q3 species and the Q3/Q2 ratio decreases with firing time at 715oC. As for relaxed 55S4.3, the major structural unit is Q3, and the intensity of Q3 is higher for 55S4.3 than 45S5. As the Na+/Si4+ ratio increases, the intensity of 946 (or 947) cm-1 increases while bands near 1100 cm-1 decrease. Based on the Raman spectra of devitrified 45S5 and 55S4.3, the crystals in the two glasses have a common structural unit of SiO32- (Q2). The elasticity measurement by Brillouin scattering indicated that the moduli for devitrified glass 45S5 are greater than undevitrified 45S5 and 55S4.3 glass. The elasticity of the present bioactive glasses is lower than hydroxyapatite and fluorapatite.

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The finite element method since its development in the 1950’s has been used extensively in solving complex problems involving partial differential equations. The conventional finite element methods use piecewise Lagrange interpolation functions for approximating displacements. The aim of this research is to explore finite element analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves which provide higher continuity of derivatives than piecewise Lagrange interpolation functions. This work focuses on the implementation and comparison of the B-spline finite elements in contrast with the conventional finite elements. This thesis observes that the use of B-spline interpolation functions can reduce the computational cost significantly. It is an efficient technique and can be conveniently implemented into the existing finite element programs.

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Thesis (Ph. D.)--University of Chicago, Dept. of Physics, 2001. / Includes bibliographical references. Also available on the Internet.