This thesis addresses the need for an optimization method which can simultaneously optimize and balance an aerothermodynamic cycle. The method developed is be able to control cycle design variables at all operating conditions to meet the performance requirements while controlling any additional variables which may be used to optimize the cycle and maintaining all operating limits and engine constraints. The additional variables represent degrees of freedom above what is needed for conservation of mass and energy in the engine system. The motivation for such a method is derived from variable cycle engines, however it is general enough to use with most engine architectures. The method is similar to many optimization algorithms but differs in its implementation to an aircraft engine by combining the cycle balance and optimization using a Newton-Raphson cycle solver to efficiently find cycle designs for a wide range of engine architectures with extra degrees of freedom not needed to balance the cycle. Combination of the optimization with the cycle solver greatly speeds up the design and optimization process. A detailed process description for implementation of the method is provided as well as a proof of concept using several analytical test functions. Finally, the method is demonstrated on a separate flow turbofan model. Limitations and applications of the method are further explored including application to a multi-design point methodology.

The phrase "opportunities to learn" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.

The phrase "opportunities to learn" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.

In the current era of “precision cosmology”, measuring the expansion rate of the Universe (Hubble constant, or H0) more accurately and precisely helps to better constrain the properties of dark energy. Cepheid-based distances are a critical step in the Extragalactic Distance Scale and have been recently used to measure H0 with a total uncertainty of only 3.4%. I will present my work on Cepheid variables in three different galaxies as part of this effort. NGC 4258 is a galaxy with a very precise and accurate distance (3% uncertainty) based on radio interferometric observations of water masers orbiting its central massive black hole. Therefore, it can be used to obtain a robust absolute calibration of the Cepheid Period-Luminosity relation. I analyzed observations of NGC 4258 obtained at Gemini North over four years and increased the number of long-period Cepheids (P>45 days) known in this galaxy. NGC 5584 was the host of type Ia SN 2007af. I applied a difference imaging technique to Hubble Space Telescope (HST) observations of this galaxy and discovered several hundred Cepheids. I compared my results with previous work based on traditional PSF photometry. The distance estimates of the two samples matched within the errors of the measurements, and so the difference imaging technique was a success. Additionally, I validated the first “white-light” variability search with the HST F350LP filter for discovering Cepheids. NGC 4921 is located in the heart of the Coma cluster at a distance of about 100 Mpc. I conducted a search for Cepheid variables using HST, extending the reach of Hubble by a factor of 3 relative to previous Cepheid work. Since Coma is in the Hubble flow, this approach eliminates the need for a secondary distance indicator and enables a direct determination of H0 based exclusively on a Cepheid distance. I present preliminary results from this challenging project.

The work in this thesis is concerned with the mechanics of the initiation and growth of small fatigue cracks from notches under service load histories. Fatigue life estimates for components subjected to variable amplitude service loading are usually based on the same constant amplitude strain-life data used for constant amplitude fatigue life predictions. The resulting fatigue life estimates although they are accurate for constant amplitude fatigue, are always non conservative for variable amplitude load histories. Similarly fatigue life predictions based on small crack growth calculations for cracks growing from flaws in notches are non conservative when constant amplitude crack growth data are used. These non conservative predictions have, in both cases, been shown to be due to severe reductions in fatigue crack closure arising from large (overload or underload) cycles in a typical service load history. Smaller load cycles following a large near yield stress overload or underload cycle experience a much lower crack opening stress than that experienced by the same cycles in the reference constant amplitude fatigue tests used to produce design data. This reduced crack opening stress results in the crack remaining open for a larger fraction of the stress-strain cycle and thus an increase in the effective portion of the stress-strain cycle. The effective strain range is increased and the fatigue damage for the small cycles is greater than that calculated resulting in a non conservative fatigue life prediction. Previous work at Waterloo introduced parameters based on effective strain-life fatigue data and effective stress intensity versus crack growth rate data. Fatigue life calculations using these parameters combined with experimentally derived crack opening stress estimates give accurate fatigue life predictions for notched components subjected to variable amplitude service load histories. Information concerning steady state crack closure stresses, effective strain-life data, and effective stress intensity versus small crack growth rate data, are all obtained from relatively simple and inexpensive fatigue tests of smooth specimens in which periodic underloads are inserted into an otherwise constant amplitude load history. The data required to calibrate a variable amplitude fatigue crack closure model however, come from time consuming measurements of the return of crack closure levels for small cracks to a steady state level following an underload (large cracks for which crack closure measurements are easier to make cannot be used because at the high stress levels in notches under service loads a test specimen used would fracture). For low and moderately high hardness levels in metals crack growth and crack opening stress measurements have been made using a 900x optical microscope for the small crack length at which a test specimen can resist the high stress levels encountered when small cracks grow from notches. For very hard metals the crack sizes may be so small that the measurements must be made using a confocal scanning laser microscope. In this case the specimen must be removed from the test machine for each measurement and the time to acquire data is only practical for an extended research project. The parameters for the crack closure model relating to steady state crack closure levels vary with material cyclic deformation resistance which in turn increases with hardness. One previous investigation found that the steady state crack opening level was lower and the recovery to a steady state crack opening stress level after an underload was more rapid for a hard than for a soft metal. This observation can be explained by the dependence of the crack tip plastic zone size that determines crack tip deformation and closure level on metal hardness and yield strength. Further information regarding this hypothesis has been obtained in this thesis by testing three different steels of varying hardness levels (6 HRC, 35 HRC, and 60 HRC) including a very hard carburized steel having a hardness level (60 HRC) for which no crack opening stress data for small cracks had yet been obtained. This thesis introduced a new test procedure for obtaining data on the return of crack opening stress to a steady state level following an underload. Smooth specimens were tested under load histories with intermittent underload cycles. The frequency of occurrence of the underloads was varied and the changes in fatigue life observed. The changes in damage per block (the block consisted of an underload cycle followed by intermittent small cycles) were used to determine the value of the closure model parameter governing the recovery of the crack opening stress to its steady state level. Concurrent tests were carried out in which the crack opening stress recovery was measured directly on crack growth specimens using optical microscope measurements. These tests on metals ranging in hardness from soft to very hard were used to assess whether the new technique would produce good data for crack opening stress changes after underloads for all hardness levels. The results were also used to correlate crack closure model parameters with mechanical properties. This together with the steady state crack opening stress, effective strain-life data and the effective intensity versus crack growth rate data obtained from smooth specimen tests devised by previous researchers provided all the data required to calibrate the two models proposed in this investigation to perform strain-life and small crack growth fatigue analysis.

The automotive industry has been in a marathon of advancement over the past decades. This is partly due to global environmental concerns about increasing amount of air pollutants such as NOx (oxides of nitrogen), CO (carbon monoxide) and particulate matters (PM) and decreasing fossil fuel resources. Recently due to stringent emission regulations such as US EPA (Environmental Protection Agency) and CARB (California Air Resource Board), improvement in fuel economy and reduction in the exhaust gas emissions have become the two major challenges for engine manufacturers. To fulfill the requirements of these regulations, the IC engines including gasoline and diesel engines have experienced significant modifications during the past decades. Incorporating the fully flexible valvetrains in production IC engines is one of the several ways to improve the performance of these engines. The ultimate goal of this PhD thesis is to conduct feasibility study on development of a reliable fully flexible hydraulic valvetrain for automotive engines. Camless valvetrains such as electro-hydraulic, electro-mechanical and electro-pneumatic valve actuators have been developed and extensively studied by several engine component manufacturers and researchers. Unlike conventional camshaft driven systems and cam-based variable valve timing (VVT) techniques, these systems offer valve timings and lift control that are fully independent of crankshaft position and engine speed. These systems are key technical enablers for HCCI, 2/4 stroke-switching gasoline and air hybrid technologies, each of which is a high fuel efficiency technology. Although the flexibility of the camless valvetrains is limitless, they are generally more complex and expensive than cam-based systems and require more study on areas of reliability, fail safety, durability, repeatability and robustness. On the contrary, the cam-based variable valve timing systems are more reliable, durable, repeatable and robust but much less flexible and much more complex in design. In this research work, a new hydraulic variable valve actuation system (VVA) is proposed, designed, prototyped and tested. The proposed system consists of a two rotary spool valves each of which actuated either by a combination of engine crankshaft and a phase shifter or by a variable speed servo-motor. The proposed actuation system offers the same level of flexibility as camless valvetrains while its reliability, repeatability and robustness are comparable with cam driven systems. In this system, the engine valve opening and closing events can be advanced or retarded without any constraint as well as the final valve lift. Transition from regenerative braking or air motor mode to conventional mode in air hybrid engines can be easily realized using the proposed valvetrain. The proposed VVA system, as a stand-alone unit, is modeled, designed, prototyped and successfully tested. The mathematical model of the system is verified by the experimental data and used as a numerical test bench for evaluating the performance of the designed control systems. The system test setup is equipped with valve timing and lift controllers and it is tested to measure repeatability, flexibility and control precision of the valve actuation system. For fast and accurate engine valve lift control, a simplified dynamic model of the system (average model) is derived based on the energy and mass conservation principles. A discrete time sliding mode controller is designed based on the system average model and it is implemented and tested on the experimental setup. To improve the energy efficiency and robustness of the proposed valve actuator, the system design parameters are subjected to an optimization using the genetic algorithm method. Finally, an energy recovery system is proposed, designed and tested to reduce the hydraulic valvetrain power consumption. The presented study is only a small portion of the growing research in this area, and it is hoped that the results obtained here will lead to the realization of a more reliable, repeatable, and flexible engine valve system.

The problem of reconstruction of digital images from their degraded measurements has always been a problem of central importance in numerous applications of imaging sciences. In real life, acquired imaging data is typically contaminated by various types of degradation phenomena which are usually related to the imperfections of image acquisition devices and/or environmental effects. Accordingly, given the degraded measurements of an image of interest, the fundamental goal of image reconstruction is to recover its close approximation, thereby "reversing" the effect of image degradation. Moreover, the massive production and proliferation of digital data across different fields of applied sciences creates the need for methods of image restoration which would be both accurate and computationally efficient. Developing such methods, however, has never been a trivial task, as improving the accuracy of image reconstruction is generally achieved at the expense of an elevated computational burden. Accordingly, the main goal of this thesis has been to develop an analytical framework which allows one to tackle a wide scope of image reconstruction problems in a computationally efficient manner. To this end, we generalize the concept of variable splitting, as a tool for simplifying complex reconstruction problems through their replacement by a sequence of simpler and therefore easily solvable ones. Moreover, we consider two different types of variable splitting and demonstrate their connection to a number of existing approaches which are currently used to solve various inverse problems. In particular, we refer to the first type of variable splitting as Bregman Type Splitting (BTS) and demonstrate its applicability to the solution of complex reconstruction problems with composite, cross-domain constraints. As specific applications of practical importance, we consider the problem of reconstruction of diffusion MRI signals from sub-critically sampled, incomplete data as well as the problem of blind deconvolution of medical ultrasound images. Further, we refer to the second type of variable splitting as Fuzzy Clustering Splitting (FCS) and show its application to the problem of image denoising. Specifically, we demonstrate how this splitting technique allows us to generalize the concept of neighbourhood operation as well as to derive a unifying approach to denoising of imaging data under a variety of different noise scenarios.

The actual service loading histories of most engineering components are characterized by variable amplitudes and are sometimes rather complicated. The goal of this study was to estimate the fatigue life of nickel-chromium-molybdenum 30CrNiMo8HH steel alloy under axial and pure torsion variable amplitude loading (VAL) conditions. The investigation was directed at two primary factors that are believed to have an influence on fatigue life under such loading conditions: load sequence and mean stress. The experimental work for this research included two-step loading, non-zero mean strain loading, and VAL tests, the results of which were added to previously determined fully reversed strain-controlled fatigue data. The effect of load sequence on fatigue life was examined through the application of the commonly used linear damage accumulation rule along with the Manson and Marco–Starkey damage accumulation methods, the latter of which takes load sequence into account. Based on the two-step experimental results, both the Manson and Marco–Starkey methods were modified in order to eliminate the empirically determined constants normally required for these two methods. The effect of mean stress on fatigue life was investigated with the use of three life prediction models: Smith–Watson–Topper (SWT), Fatemi–Socie (FS), and Jahed–Varvani (JV). The cycles from the VAL histories were counted using a rainflow counting procedure that maintains the applied strain sequence, and a novel method was developed for the estimation of the total energy density required for the JV model. For two-step loading and for all three fatigue models employed, the modified damage accumulation methods provided superior fatigue life predictions. However, regardless of the damage accumulation method applied, the most satisfactory fatigue life correlation for VAL was obtained using the energy-based JV model.

In this work the effect of rotation on oscillation frequencies have been inves- tigated . Rotation has been treated as a perturbation and detailed calculations were done on the infuence of second order rotation . We used an evolutionary model of DELTA-Scuti star V1162 Ori with a mass of 1:8 solar mass. The eigenfrequencies were calculated in two cases , the slow rotation case with vsini = 46km/s and the fast rotation case with vsini = 61.9km/s. Calculation were carried out by a modifed oscillation program and results were compared to observations .

In this thesis the design of a MMIC vector modulator operating in 9GHz-10GHz band is investigated and performed. Sub-sections of the vector modulator are 4-port (4.8dB) 1200 phase shift relative to the dedicated port power splitter, digitally controlled variable gain amplifier and the in phase power combiner. Alternative methods are searched in order to implement the structure properly in the given frequency band. The final design is appropriate for MMIC structure. 4-port (4.8dB) 1200 phase shift relative to the dedicated port power splitter is studied. The performance is simulated and optimized first on Microwave Office, then on Advanced Design System (ADS) tools. Various methods to design a digitally controlled variable gain amplifier are studied. The final topology is simulated and optimized on ADS tool. An in phase power combiner is designed. The performance of the combiner is simulated and optimized on ADS tool. Lumped element models are replaced with CASWELL H-40 models to achieve a MMIC structure and a layout is drawn. The finalized vector modulator is simulated and optimized on ADS tool. Key words: MMIC, Vector Modulator, Digitally Controlled Variable Gain Amplifier, Layout