Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods. Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational structure. For such an equation or system, a weak solution can be found through finding the critical point of a corresponding energy functional. If this equation or system is also invariant under a certain symmetric group, multiple solutions are often expected. In this work, an integer-valued function that measures symmetries of CNLS was used to determine critical values. Besides variational methods, bifurcation methods may also be used to find solutions of a differential equation or system, if some trivial solution branch exists and the system is degenerate somewhere on this branch. If local bifurcations exist, then new solutions can be found in a neighborhood of each bifurcation point. If global bifurcation branches exist, then there is a continuous solution branch emanating from each bifurcation point. We consider two types of CNLS. First, for a fully symmetric system, we introduce a new index and use it to construct a sequence of critical energy levels. Using variational methods and the symmetric structure, we prove that there is at least one solution on each one of these critical energy levels. Second, we study the bifurcation phenomena of a two-equation asymmetric system. All these bifurcations take place with respect to a positive solution branch that is already known. The locations of the bifurcation points are determined through an equation of a coupling parameter. A few nonexistence results of positive solutions are also given

Design and performance of fully-printed Ku-band aperture coupled patch antennas fabricated by a direct digital manufacturing (DDM) approach that integrates fused deposition modeling (FDM) of acrylonitrile butadiene styrene (ABS) thermoplastic with in-situ micro-dispensing of conductive silver paste (CB028) are reported. Microstrip line characterizations are performed and demonstrate that misalignment of ABS substrate deposition direction with microstrip line micro-dispensing direction can degrade the effective conductivity up to 60% within the Ku-band, and must be taken into consideration in antenna array feed network designs. Specically, over 125 µm thick ABS substrate, RF loss of 0.052 dB/mm is obtained at 18 GHz, demonstrating the feasibility of additively manufactured RF devices within the Ku-band. By varying ABS inll ratios and resorting to multi-layer printing with custom substrate thicknesses, single and stacked patch antennas are designed, fabricated, and characterized with bandwidth performances up to 35%, and radiation efficiencies up to 90%. This extensive utilization of the design flexibilities provided by the direct digital manufacturing (i.e. customized substrate thicknesses, multiple substrates with varying infill ratios, and in-situ micro-dispensing of conductors) distinguishes the present work from the recently reported 3-D printed antennas. Compared to the existing work in literature, the antennas presented within this thesis stand out as being fully printed structures, operating in higher frequency range (i.e. Ku-band), and exhibiting high radiation efficiencies with wide bandwidth performances.

Intrinsically disordered proteins (IDPs) do not form stable tertiary structures like their ordered partners. They exist as heterogeneous ensembles that fluctuate over a time scale. Intrinsically disordered regions and proteins are found across different phyla and exert crucial biological functions. They exhibit transient secondary structures in their free state and become folded upon binding to their protein partners via a mechanism called coupled folding and binding. Some IDPs form alpha helices when bound to their protein partners. We observed a set of cancer associated IDPs where the helical binding segments of IDPs are flanked by prolines on both the sides. Helix-breaking prolines are frequently found in IDPs flanking the binding segment and are evolutionarily conserved across phyla. Two studies have shown that helix flanking prolines modulate the function of IDPs by regulating the levels of disorder in their free state and in turn regulating the binding affinities to their partners. We aimed to study if this is a common phenomenon in IDPs that exhibit similar pattern in the conservation of helix flanking prolines. We chose to test the hypothesis in c-Myb-KIX : IDP-target system in which the disordered protein exhibits high residual helicity levels in its free state. c-Myb is a hematopoietic regulator that plays a crucial role in cancer by binding to the KIX domain of CBP. Studying the functional regulation of c-Myb by modulating the disorder levels in c-Myb and in IDPs in general provides a better understanding of the way IDPs function and can be used in therapeutic strategies as IDPs are known to be involved in regulating various cellular processes and diseases. To study the effect of conserved helix flanking prolines on the residual helicity levels of c-Myb and its binding affinity to the KIX domain of CBP, we mutated the prolines to alanines. Mutating prolines to alanines increased the helicity levels of c-Myb in its free state. This small increase in the helicity levels of a highly helical c-Myb showed almost no effect on the binding affinity between cMyb and KIX. We hypothesized that there is a helical threshold for coupled folding and binding beyond which helicity levels of the free state IDP have no effect on its binding to their ordered protein partner. To test this hypothesis, we mutated solvent exposed amino acid residues in c-Myb that reduce its overall helicity and studied its effect on the binding affinity between c-Myb and KIX. Over a broad range of reduction in helicity levels of the free state did not show an effect on the binding affinity but beyond a certain level, decrease in helicity levels showed pronounced effects on the binding affinity between c-Myb and KIX.

This work highlights slab coupled optical sensors (SCOS) and their ability to measure high voltages. Although other high voltage measurement techniques exist, most of these techniques are electrical devices and are therefore more susceptible to stray ground currents and other electromagnetic interferences (EMI), which may cause signal distortion. Optical sensors are less susceptible to such interferences and these sensors, such as the Pockels cell, have been used in measuring high voltage. SCOS offer an alternative method of measuring high voltage optically. Consisting of an optical fiber and an electro-optic slab waveguide, SCOS have the advantage of being very small in size (0.2 mm x 0.3 mm cross-section), simpler composition, and potentially less coupling losses. Issues associated with high voltage measurements are addressed such as unwanted corona, arcing, and EMI. Solutions are also explored which include insolating materials, electrode geometries, Faraday cages, and using optical sensors such as SCOS. Although the SCOS has been traditionally used to measure electric field, the SCOS is able to measure high voltage through the use of an electrode structure. The SCOS' ability to measure high voltage is showcase through the construction and output measurements of several high voltage systems: an ignition coil-based circuit, a dual ignition coil circuit, a Marx generator, and a 200 kV generator used in a capacitor discharge configuration. These measurements show the SCOS' ability to measure at least 111 kV capacitor discharges with 6.6 ns rise times and other various high voltage waveforms.

Les acteurs neuroendocriniens régulant la physiologie des Lophotrochozoaires, groupe frère des Ecdysozoaires parmi les Protostomiens, demeurent peu connus. Grâce à l’émergence récente de ressources génomiques, transcriptomiques et peptidomiques chez l’huître creuse Crassostrea gigas, l’étude des couples ligand(s)/récepteur(s) régulant les fonctions physiologiques est désormais facilitée. Ainsi, par une approche d’endocrinologie inverse consistant à éprouver l’activité d’un panel de ligands potentiels, plusieurs récepteurs couplés aux protéines G (RCPGs), jusqu’alors orphelins ont pu être caractérisés sur le plan fonctionnel. Trois voies de signalisation ont été étudiées : la voie de type cholécystokinine/sulfakinine (CCK/SK) la voie de type calcitonine (CT) et la voie de type dopamine (DA). Grâce à des tests fonctionnels, deux neuropeptides et deux récepteurs de type CCK/SK ont pu être caractérisés. Des tests d’activité biologique in vitro et des expériences de conditionnement alimentaire ont montré la potentielle implication de ces couples dans la régulation de la digestion et de la satiété chez l’huître. Par ailleurs, deux couples neuropeptide/récepteur de type CT ont été caractérisés montrant, à l’image de leurs homologues chez les vertébrés, leur possible rôle dans la régulation hydrique ou ionique. D’autre part, un récepteur activé de manière spécifique par la dopamine et la tyramine a été caractérisé. Ce système de signalisation semble être impliqué dans la médiation du stress et intervenir dans les processus régulateurs de la reproduction au niveau de la gonade. Ainsi, les différents résultats obtenus au cours de ces travaux ont permis d’identifier des couples ligands/récepteurs d’huître homologues de systèmes de signalisation présents chez les Ecdysozoaires et les vertébrés confirmant l’origine de ces systèmes neuroendocriniens depuis l’ancêtre commun des Bilatériens. Les résultats obtenus ont également permis de mieux comprendre comment l’huître intègre les paramètres du milieu et donc s’acclimate aux différentes contraintes environnementales. / The neuroendocrine regulators of the physiology of Lophotrochozoa, the sister clade of Ecdysozoa among Protostoma, remain poorly understood. Thanks to the recent emergence of genomic, transcriptomic and peptidomic resources in the Pacific oyster Crassostrea gigas, the functional characterization of ligand/receptor pairs regulating a diversity of physiological functions has been facilitated. Using a reverse endocrinology approach, a number of orphan G Protein-Coupled Receptors (GPCRs) have been functionally characterized. Three signalling systems have been studied in the oyster: The cholecystokinin/sulfakinin (CCK/SK), the calcitonin (CT) and the dopamine (DA) signalling systems. Two CCK/SK receptors and ligands have been characterized. In vitro bioassays and feeding conditions suggested the potential involvement of this signalling system in the regulation of digestion and satiety. Besides, two couples of CT-type peptides and receptors have been characterized showing, as for their vertebrate counterparts, their possible role in the regulation of water and ion balance. A receptor specifically activated by dopamine and by tyramine has also been characterized. This signalling system appeared to be implicated in the mediation of stress and to play a role in the regulatory processes of reproduction in the gonads. This study allowed the characterization in the oyster of ligand receptor pairs homolog to known signalling systems present in Ecdysozoa and vertebrates, thus confirming the origin of these neuroendocrine systems in the common ancestor of Bilateria. The results of this study also contributed to understand how the oyster integrates external parameters and adapts to various environmental constrains.

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This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplished / Faculty of Business and Technology