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<p> Atherosclerosis generally occurs near the branching in the arteries where there tends to be flow irregularities. A build up of fatty deposits (plaque) occurs in the blood vessel in such regions making it to lose its elasticity. Such hardening of the arteries and the narrowing of the lumen can cause severe atheromas and even high blood pressure and blockage of the vessels. It is observed in North America that nearly 47% of the deaths are caused due to cardiovascular diseases and hence determination of such regions becomes very critical and can be very beneficial if done at an earlier stage. In this thesis, we present: an approach to model the pulsating flow of blood through such an atherosclerosis affected region of the artery using finite element method and further discuss the statistical model used to implement the optimization techniques to estimate the region of maximum rigidity. Here within we present a numerical and non-invasive approach to predict such regions. The computational modeling is carried out under two categories: a. The mathematical model and b. The statistical model. </p> <p> The mathematical model which is the forward model, comprises of the artery and the cardiac muscle as hyperelastic material modeled with the neo-hookean model and the three dimensional Navier-Stokes equations solve for the blood flowing through it. We perform fluid dynamic analysis for the blood flowing through the vessel to compute the velocity at different time instances and mechanical analysis to compute the deformation of the artery which is a function of the elasticity of the vessel. The two models are interconnected to each other by boundary conditions as the normal component of the surface force provides the coupling between the two models. The shear modulus represents a measure of the elasticity of the vessel. We use linear spatial basis functions to model the shear modulus which spatially varies along the geometry of the vessel thus we have a region of atherosclerosis and the geometry shows the stenosis. The change in the shear modulus affects the velocity of blood through the vessel. </p> <p> In the statistical model, we propose an inverse computational model for estimating the elasticity profile of the arterial wall where we implement the inverse modeling approach to estimate the maximum shear modulus which helps us to predict the region of atherosclerosis. The velocity and the deformation obtained for a particular shear modulus from our COMSOL forward model provide the realistic simulated measurements that are made noisy by introduction of white Gaussian noise with different SNR and we try to estimate the shear modulus that minimizes the error-function. We use COMSOL with MATLAB for simultaneous iterative computations of velocity and deformation measurements by running the optimization code. We estimate these unknown parameters using optimization algorithm that minimizes the cost function of our model. For our estimation we use the least squares estimator and we derive the maximum likelihood estimator. The unconstrained optimization is carried out with Neider Mead Simplex Method and the Trust Region Method which uses only the function evaluations to find the minimum: making it a very robust algorithm and very efficient for problems that are nonlinear or have a number of discontinuities. Our preliminary results demonstrate significant change in velocity of the blood and occurrence of vortices in the region of less elasticity and the tendency of the artery to deform minimum in the hardened less elastic region. Our estimation results show that the parameters are identifiable. The mean square error of the estimate as a function of SNR shows accuracy of the estimation. </p> / Thesis / Master of Applied Science (MASc)

Fundamental studies of surface forces in foam films are carried out to explain the stability of foams and froths in froth flotation. The thin film pressure balance (TFPB) technique was used to study the surface forces between air bubbles in water from equilibrium film thickness and dynamic film thinning measurements. The results were compared with the disjoining pressure predicted from the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The contribution from the non-DLVO force was estimated by subtracting the electrostatic double-layer and van der Waals forces from the total force (or pressure) measured. The results obtained in the present work suggest that a strong attractive force (referred to as hydrophobic force) exists at very low surfactant concentrations, and that it decreases with increasing surfactant and/or electrolyte concentrations. In contrast, pH changes have only minor effects on the hydrophobic force. The changes in the hydrophobic force observed at low surfactant concentration region have been related to foam stability in flotation. In addition, an analytical model applicable to a broad range of surfactant concentration was developed to calculate film elasticity from surface tension. The model finds, however, that the film elasticities change little at low surfactant concentrations. It is, therefore, suggested that bubble coalescence and foam stability at low surfactant concentrations may be largely affected by hydrophobic force. The TFPB technique was also used to study the surface forces in the foam films stabilized with various frothers such as pentanol, octanol, methyl isobutyl carbinol (MIBC), and polypropylene glycol (PPG). The results were compared with the foam stabilities measured using the shake tests and the film elasticity calculated using the model developed in the present work. It was found that at a low electrolyte concentration foam stability is controlled by film elasticity and surface forces, the relative contributions from each changing with frother concentration and type. It is, therefore, proposed that one can control the foam stability in flotation by balancing the elasticities of foam films and the disjoining pressure in the films, particularly the contributions from the hydrophobic force. / Ph. D.

The sonic testing method employed in this thesis provides data for the calculation of several of the mechanical properties or aluminum and for a qualitative analysis of the visco-elastic behavior of this material. Young's modulus of elasticity is determined for aluminum bars with various lengths and cross sections using the resonant frequency (in flexure) of each bar. This property varies linearly with the length to depth ratio of the test specimens, decreasing as the L/D ratio decreases. Certain nonlinear relationships exist between the length to depth ratios, resonant frequencies and Young's modulus, and are depicted in figures 8 and 9. In addition, the logarithmic decrement, a measure or the internal damping of the material, is computed from the nondimensional amplitude-frequency response curves and is observed to increase as the test specimens become shorter. This is an indication that the internal damping increases as the lengths of the test specimens become shorter. Due to the visco-elastic nature or aluminum, the manner in which this damping varies is unknown. An attempt to qualitatively analyze this phenomena is made by analyzing a one-dimensional mechanical model incorporating both a nonlinear restoring force and nonlinear viscous damping in its system. Observations of the test results show that the restoring force is best described by a linear spring, but that the damping can indeed be described, at least qualitatively, by a nonlinear dashpot. This qualitative analysis of aluminum can at best provide only a concept of the physical characteristics of this material in the light of experimental results. / Master of Science

When we stretch and contract a rubber band a hundred times, we expect the rubber band to fail. Yet our heart stretches and contracts the same amount every two minutes, and does not fail. Why is that? What causes the significantly higher elasticity of certain molecules and the rigidity of others? Equally importantly, can we use this information to design materials for precise mechanical tasks? It is the aim of this dissertation to illuminate key aspects of the answer to these questions, while detailing the work that remains to be done. In this dissertation, particular emphasis is placed on the nanoscale properties of elastomeric proteins. By better understanding the fundamental characteristics of these proteins at the nanoscale, we can better design synthetic rubbers to provide the same desired mechanical properties. / Ph. D.

This dissertation describes two essays in empirical international trade, focusing on trade costs and the pattern of trade along the intensive and extensive margins. In the first essay, I study the barriers that impede international trade. In the second paper, I examine the growth of U.S. agricultural trade in detail describing how U.S. agriculture and food trade has expanded along the margins. The first chapter introduces a relatively straightforward, yet empirically powerful, manipulation of the gravity equation. The gravity model has been dubbed the work horse model of empirical trade, and thus is a suitable foundation from which to derive an indirect measure of largely unobservable 'iceberg' trade costs. In this paper, I solve a sector level version of the gravity equation and study the pattern of agricultural trade costs and factors that impede world agricultural trade growth over a long time series, 1986-2011. In addition, I estimate sector-specific elasticity of substitution which is a key parameter in the computation of trade cost. In the second essay, I examine the growth of world and U.S. agricultural exports along the intensive and extensive margins of international trade over the period 1986 to 2010. The purpose of this essay is to decompose the growth of world and U.S. agricultural trade using qualitative methods from the marketing literature (i.e., market expansion grids) but modified to fit bilateral trade relationships and a theoretical index to measure the margins of trade at a single point in time. In addition, we examine often overlooked channels by which U.S. agricultural exports have expanded using very detailed agricultural product lines. Using information related to the pattern of a trade rather than trade volume itself, I estimate how much starting a trade relationship with a new partner or in a new product variety matters to agricultural trade growth and then conclude with a set of stylized facts to inform current theory. / Ph. D.