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Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds whose topological classification is known. There is a second family consisting of the Witten manifolds: they are the examples of compact simply connected spaces admitting Einstein metrics of positive Ricci curvature. Thirdly, there is a notion of generalized Witten manifold as well. Topologically, all three families share the same cohomology ring. This common ring structure motivates the definition of a manifold of type r, where r is the order of the fourth cohomology group. In 1991, M. Kreck and S. Stolz classified manifolds M of type r up to homeomorphism and dieomorphism using invariants s̄[subscript i](M) and s[subscript i](M), for i = 1, 2, 3. This gave rise to many new examples of nondieomorphic but homeomorphic manifolds. In this dissertation, new versions of the homeomorphism and dieomorphism classification of manifolds of type r are proven. In particular, we can replace s̄₁ and s̄₃ by the first Pontrjagin class and the self-linking number in the homeomorphism classification of spin manifolds of type r. As the formulas of the two latter invariants are in general much easier to compute, this simplifies the classification of these manifolds up to homeomorphism significantly. / Graduation date: 2012

Anodisation has been studied for almost eighty years, primary in the field of corrosion science, as a simple and efficient way of producing thick protective oxide coatings on Al, Ti or Zr alloys. Anodisation is an electrochemical oxidation process which relies on the migration of ions across solid films under the action of a large electric field. From the fundamental point of view, many aspects regarding the growth of anodic films have been studied extensively. However, so far, little interest has been devoted to the mechanical aspects involved in the growth process, despite their considerable importance both from an applied as well as from a fundamental point of view. A solid understanding of internal stresses development is indeed crucial in order to guarantee the durability of anodic coatings, their structural and functional properties. In addition, the stress evolution directly reflects the motion of the ions in the film and therefore provides a unique means to investigate in situ the growth mechanisms of anodic films. In this thesis, we have studied the evolution of the internal stresses in anodic TiO2 films in situ during their growth. The stresses have been obtained from changes in the curvature of cantilevered anode samples, measured using a high-resolution multi-beam optical sensor. We demonstrate, for the first time, the capability of this type of curvature sensor for monitoring processes in liquid environments. Experimental data on the internal stresses developing in anodic TiO2 films is provided, and trends regarding the influence of the experimental conditions on the stress evolution are identified. In particular, the evolution of the internal stresses is shown to be strongly correlated with the evolution of the electrochemical variables, which directly demonstrates the interest of curvature measurements as a fundamental technique for investigating the details of the growth process of anodic oxide films. The reversible and irreversible stress contributions associated, respectively, with electrostriction and with growth-related ionic transport have been separated from one another and quantified. A novel constitutive model for the electrostriction stress has been proposed which explicitly takes into account the effect of dielectrostriction.

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used for signal normalization. In conclusion, the studies implicate that for individual otitis diagnosis, the hyperaemic tympanic membrane was separated from the healthy by application of erythema indices using diffuse reflectance spectroscopy. Moreover, bulging and retracted positions of the tympanic membrane were separable by means of the source-detector intensity matrix. For further clinical studies it is reasonable to assume that data from both methods are needed for diagnosis.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

Aim: The primary aim of this study was to find if there is any correlation between the corneal radius of curvature and its eccentricity. Method: 45 subjects participated in this study, 24 emmetropes, 18 myopes and three hyperopes. All subjects were free of ocular abnormalities and had no media opacities. All the subjects had normal ocular health and good visual acuity of 1.0 or better for both distance and near. The values for eccentricity and corneal radius of curvature were obtained by using a Topcon CA-100F Corneal Analyzer. Results: For the 4.5 mm zone the only significant correlation between corneal radius of curvature and eccentricity was obtained for the mean of the meridian (p = 0.007). On the other hand, we found no significant correlation for the average of two meridians or for meridian 1 and meridian 2 separately in the 8.0 mm zone. Conclusions: We found no correlation between the corneal radius of curvature and the eccentricity for both zones. In addition, no correlation could be found between the spherical equivalent of the refractive errors and the corneal eccentricity. The reason for not finding any significant correlation between the two entities could be due to factors such as smaller sample size and poor distribution of refractive errors in the sample. Moreover, there may be other factors that could influence the overall corneal shape like eye shape, axial length and corneal diameter, which was not evaluated in this study.

A novel lensed plastic optical fiber (LPOF) scheme to achieve the high coupling efficiency with a long working distance between the light source and LPOF is proposed. The advantages of the proposed LPOF are demonstrated by proofs of the experiment. In this study, an aspheric convex-concave plastic lens (CCPLs) is bonded with a flattened end of the plastic fiber by using the laser transmission welding (LTW) to form an aspheric-endface fiber. The working distance between the light source and LPOF can be increased with high coupling efficiency by the design of the CCPLs. According to the proposed design in this study, the working distance and the coupling efficiency can reach to 300£gm and 80%, separately. Furthermore, the analysis shows that the LTW can achieve a high welding strength and a small heat affected zone that meets the commercial utilization. But the LTW technology has some restrictions, the disadvantages of the LTW technology are improved in this study to spread the application of the laser welding.