In this thesis, we study the unconventional superconductivity in Sr2RuO4 (SRO) and related systems. The superconducting state in SRO remains a puzzle after more than 28 years of study. Early experiments had pointed toward a topological non-trivial time-reversal symmetry breaking (TRSB) chiral p-wave order. This pairing candidate has attracted a large amount of attention, partly in relation to the possibility of topological quantum computation, and has stimulated studies on higher chirality superconducting systems. In the first part of this thesis, we study the spontaneous edge current in chiral d- and f-wave superconductors. We show that these currents, which vanish in the continuum limit at zero temperature, are generally non-vanishing but tiny, compared to the simplest chiral p-wave case. In the presence of strong surface roughness, the direction of the edge current in the chiral d-wave case can be reversed, compared with that of a specular ideal surface with specular scattering. However, it is shown that this current reversal is non-universal beyond the continuum limit. The chiral p-wave scenario in SRO is overturned by recent Knight shift measurements, highlighting the importance of exploring different pairing symmetries for SRO. Recently, $d_{x^2-y^2} \pm ig_{(x^2-y^2)xy}$, $s' \pm id_{xy}$ and mixed helical p-wave pairings have been proposed as order parameter candidates. However, the stability of these states, especially of the $d_{x^2-y^2} \pm ig$ pairing, remains unclear. In the second part of the thesis, we study the leading superconducting instabilities in SRO in the presence of sizable atomic spin-orbit coupling (SOC), non-local SOC, and non-local interactions. We find that it is difficult to stabilize chiral p-wave pairing in SRO models; this is because, among the triplet p-wave states, the atomic SOC favors helical states over the chiral state. The presence of both d- and g-wave pairings, including a $d_{x^2-y^2} \pm ig$ state, is found when the second nearest neighbor (in-plane) repulsions, together with orbital-anisotropy of the non-local interactions and/or the B2g channel non-local SOC are included. We further analyze the properties, such as nodal structures, in-plane field spin-susceptibility, and spontaneous edge current, of the realized $d_{x^2-y^2} \pm ig$ pairing and find that this state is more compatible with existing experimental measurements than the $s' \pm id_{xy}$ and the mixed helical p-wave proposals. / Dissertation / Doctor of Philosophy (PhD)

Weak optical signals have to be measured in different fields of sciences including chemistry and biology. For example, very low levels of fluorescence emission should be detected from the spots on a DNA microarray that correspond to weakly expressed genes. High sensitivity charge-coupled devices (CCDs) are used in these applications. CCDs require special fabrication and are difficult to integrate with other circuits. CMOS is the technology used for fabrication of CPUs and other widely used digital components. CMOS is not optimized for light detection. CMOS circuits are however cheap, low power and can integrate several components. Active pixel sensor (APS) is the most common pixel structure for CMOS photodetector arrays. In this work we provide an accurate analysis of the APS signal using new models for the capacitance of the photodiode. We also provide a complete noise analysis of the pixel to calculate the SNR of the pixel and provide optimum operation points. We propose a new mode of operation for APS that can achieve at least l 0 dB higher SNR, than conventional APS, at light levels of less than 1 μW/cm^2. We fabricated several APS pixels in CMOS 0.18 μm technology and measured them to confirm the proposed analyzes. There are applications like fluorescence lifetime imaging that require both sensitivity and fast response. Photomultiplier tubes (PMTs) are commonly used in these applications to detect single photons in pico- to nano-seconds regime. PMTs are bulky and require high voltage levels. Avalanche photodiodes (APDs) are the semiconductor equivalent of PMTs. We have fabricated different APDs along with different peripheral circuitries in CMOS 0.18 μm technology. Our APDs have a 5.5 percent peak probability of detection of a photon at an excess bias of 2 V, and a 30 ns dead time, which is less than the previously reported results. The low price of CMOS makes modem diagnosis devices more available. The low power of CMOS leads to battery-driven hand-held imaging solutions, and its high integration leads to miniaturized imaging and diagnosis systems. A low-light-level CMOS imager paves the way for the future generation of biomedical diagnosis solutions. / Thesis / Doctor of Philosophy (PhD)

The decision to adopt a formalized charter of rights is a momentous expression of a nations commitment to according and protection certain rights for its citizens. They usually contain complex and ambiguous moral concepts about which people have good faith disagreements. This thesis examines and ultimately rejects the belief put forward by Jeremy Waldron that judicial review is only democratically justifiable if the power of the last word in the interpretation of statutes and charter rights belongs to the democratically appointed legislature instead of the appointed judiciary. This thesis argues that a procedural conception of democracy is too limited and we would do better to base a justification of judicial review using a constitutional conception of democracy. It matters less which party has the authority of the final say with respects to rights-determining decisions and more on whether or not the democratic principle of equal concern for all is satisfied. This thesis introduces the concepts of deference, constitutional conventions, and principles and argues that these, among other things, will inform the constitutional theorists about which powers are actually present in a practice of judicial review. Once the contours of the practice are filled out one can then begin to deliberate about whether a particular conception of judicial review has democratic justification. / Thesis / Master of Arts (MA)

I present spectroscopic measurements for 260 sources from the Gemini Near Infrared Spectrograph–Distant Quasar Survey (GNIRS-DQS). Being the largest uniform, homogeneous survey of its kind, it represents a flux-limited sample of Sloan Digital Sky Survey (SDSS) quasars at 1.5 < z < 3.5. A combination of the GNIRS and SDSS spectra covers principal quasar diagnostic features, chiefly the C IV λ1549, Mg II λλ2798, 2803, Hβ λ4861, and [O III] λλ4959, 5007 emission lines, in each source. The spectral inventory is utilized primarily to develop prescriptions for obtaining more accurate and precise redshifts, black hole masses, and accretion rates for all quasars. Additionally, the measurements facilitate an understanding of the dependence of rest-frame ultraviolet–optical spectral properties of quasars on redshift, luminosity, and Eddington ratio, and test whether the physical properties of the quasar central engine evolve over cosmic time.

The following thesis investigates how social relations affect the type of information that people acquire without actively looking for it. To do this Karen Fisher’s concept of information grounds is being used, together with Mark Granovetter’s theory about the strength of weak ties. The population in the study is new university students. A combination of diaries and interviews was used to gather the empirical material, which was then analyzed using thematic analysis. The analysis showed that the most commonly shared type of information was information about people. Conversations with strong ties were usually more in depth, while conversations with weak ties tended to be more superficial. This finding contributes to the reason why information from weak ties tend to appear more surprising than information from strong ties. Factors other than those officially used together with the information grounds concept turned out to be of both interest and importance to understand why certain information was shared between people, while other information was not. These factors included language, culture, and time.

Mutually unbiased bases is an important topic in the recent quantum system researches. Although there is much work in this area, many problems related to mutually unbiased bases are still open. For example, constructing a complete set of mutually unbiased bases in the Hilbert spaces with composite dimensions has not been achieved yet. This thesis defines a weaker concept than mutually unbiased bases in the Hilbert spaces with composite dimensions. We call this concept, weak mutually unbiased bases. There is a duality between such bases and the geometry of the phase space Zd × Zd, where d is the phase space dimension. To show this duality we study the properties of lines through the origin in Zd × Zd, then we explain the correspondence between the properties of these lines and the properties of the weak mutually unbiased bases. We give an explicit construction of a complete set of weak mutually unbiased bases in the Hilbert space Hd, where d is odd and d = p1p2; p1, p2 are prime numbers. We apply the concept of weak mutually unbiased bases in the context of quantum tomography and quantum cryptography. / Egyptian government.

In this thesis, we study six Ginzburg-Landau minimization problems in the context of two-dimensional nematic liquid crystals with the intention of finding conditions for the existence of boundary vortices. The first minimization problem consists of the standard Ginzburg-Landau energy on bounded, simply connected domains Ω ⊂ R2 with boundary energy penalizing minimizers who stray from being parallel to some smooth S1-valued boundary function g of degree D ≥ 1. The second and third minimization problems consider the same Ginzburg-Landau energy but now with divergence and curl penalization in the interior and boundary function taken to be g = τ, the positively oriented unit tangent vector to the boundary. The remaining three problems involve minimizing the same energies, but now over the set for which all functions are precisely parallel to the given boundary data (up to a set for which their norms can be zero). These six problems are classified under two categories called the weak and strong orthogonal problems. In each of the six problems, we show that conditions exist for which sequences of minimizers converge to a limiting S1-valued vector field describing an equilibrium configuration for nematic material with defects. In some cases, energy estimates are obtained that show vortices belong to the boundary exclusively and the exact number of these vortices are known. A special case is also studied in the strong orthogonality setting. The analysis here suggests that geometries exist for which boundary vortices may be energetically preferable to interior vortices in the case where interior and boundary vortices have similar energy contributions. / Thesis / Doctor of Philosophy (PhD)

Many distributed energy resource (DER) systems are remotely located and are often interfaced at low or medium voltage levels through power electronics converters such as voltage-sourced converters (VSC). Therefore, a weak-grid situation is encountered where the voltage and frequency at the point of DER coupling can experience fluctuations. A power converter designed to operate in normal and strong grid conditions may not perform satisfactorily during such weak and distorted grid conditions. Hence, considering the full dynamics of the system during weak-grid conditions in the design of converter control is indispensable to ensure the stability of the DER and the grid. For instance, the phase-locked loop (PLL) has been identified as a critical component of the VSC controller that can compromise the DER performance during weak-grid conditions. This dissertation investigates and enhances the performances of inverters connected to weak and polluted grids. It primarily presents a novel approach of enhancing the inverter current controller by including the PLL state variables among the entire system state and use them to optimally generate the control input for the VSC. This mitigates the loop interactions between the PLL and other control loops resulting in a mitigation of the oscillations that could cause system instabilities. The procedure is accomplished using the recently developed linear model of the enhanced PLL (EPLL) for single-phase applications and using a model of the three-phase PLL developed in this dissertation. Extensive simulation and experimental results are presented to evaluate and validate the proposed control approaches. Full practical models of all system components are considered for simulation studies. The experimental tests are done on a practical inverter connected to the utility grid. Significant improvement of the inverter performance in weak-grid conditions is confirmed. This dissertation offers a systematic way of integrating and designing the PLL and controller in a VSC to achieve a robust performance in weak-grid conditions.

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