We aim to explain the intuition behind several large cardinal axioms, give characterization theorems for these axioms, and then discuss a few of their properties. As a capstone, we hope to introduce a new large cardinal notion and give a similar characterization theorem of this new notion. Our new notion of near strong compactness was inspired by the similar notion of near supercompactness, due to Jason Schanker.

Strong coupling of light and matter is an essential element of cavity quantum electrodynamics (cavity-QED) and quantum optics, which may lead to novel mixed states of light and matter and to applications such as quantum computation. In the strong-coupling regime, where the coupling strength exceeds the dissipation, the light-matter interaction produces a characteristic vacuum Rabi splitting. Therefore, strong coupling can be utilized as an effective coherent interface between light and matter (in the form of electron charge, spin or superconducting Cooper pairs) to achieve components of quantum information technology including quantum memory, teleportation, and quantum repeaters. Semiconductor quantum dots, nuclear spins and paramagnetic spin systems are only some of the material systems under investigation for strong coupling in solid-state physics. Mixed states of light and matter coupled via electric dipole transitions often suffer from short coherence times (nanoseconds). Even though magnetic transitions appear to be intrinsically more quantum coherent than orbital transitions, their typical coupling strengths have been estimated to be much smaller. Hence, they have been neglected for the purposes of quantum information technology. However, we predict that strong coupling is feasible between photons and a ferromagnetic nanomagnet, due to exchange interactions that cause very large numbers of spins to coherently lock together with a significant increase in oscillator strength while still maintaining very long coherence times. In order to examine this new exciting possibility, the interaction of a ferromagnetic nanomagnet with a single photonic mode of a cavity is analyzed in a fully quantum-mechanical treatment. Exceptionally large quantum-coherent magnet-photon coupling with coupling terms in excess of several THz are predicted to be achievable in a spherical cavity of ∼ 1 mm radius with a nanomagnet of ∼ 100 nm radius and ferromagnet resonance frequency of ∼ 200 GHz. This should substantially exceed the coupling observed in solids between orbital transitions and light. Eigenstates of the nanomagnet-photon system correspond to entangled states of spin orientation and photon number over 105 values of each quantum number. Initial coherent state of definite spin and photon number evolve dynamically to produce large coherent oscillations in the microwave power with exceptionally long dephasing times of few seconds. In addition to dephasing, several decoherence mechanisms including elementary excitation of magnons and crystalline magnetic anisotropy are investigated and shown to not substantially affect coherence upto room temperature. For small nanomagnets the crystalline magnetic anisotropy of the magnet strongly localize the eigenstates in photon and spin number, quenching the potential for coherent states and for a sufficiently large nanomagnet the macrospin approximation breaks down and different domains of the nanomagnet may couple separately to the photonic mode. Thus the optimal nanomagnet size is predicted to be just below the threshold for failure of the macrospin approximation. Moreover, it is shown that initially unentangled coherent states of light (cavity field) and spin (nanomagnet spin orientation) can be phase-locked to evolve into a coherent entangled states of the system under the influence of strong coupling.

This thesis presents a stable fluid structural interaction technique to simulate the dynamics of tissue valves including bio-prosthetic heart valves and natural heart valves under physiological Reynolds numbers. A partitioned approach is implemented where the equations governing the flow and the displacement of the structure are solved using two distinct solvers. A FEAP based solid solver is strongly coupled to the p-ELAFINT flow solver using subiteration procedure. The flow solver has been massively parallelized so that the domain can be distributed among several processors. The fixed Cartesian method with adaptive mesh refinement in p-ELAFINT enables us to perform fast and efficient flow computations of problem involving moving boundaries such as heart valve leaflets. To capture the structure deformation, Enhanced Assumed Solid shell element has been implemented into the solid solver which is known for its locking free and superior bending characteristics. Aitken Relaxation method which dynamically computes the relaxation parameter is used for relaxing the solid displacement in the FSI coupling. This helps the subiteration procedure to achieve a faster convergence compared to traditional Subiterative procedures with fixed relaxation parameter. Fung type material model with experimentally derived parameters is used as the constitutive model to capture the realistic solid deformation. Opening phase of a bicuspid aortic valve (BAV) model derived from a patient specific data and a pericardial bioprosthetic valve model were simulated using the FSI algorithm with realistic material parameters under physiological flow conditions. It was observed that the valves attained its fully open position under 35 milliseconds which is similar to the physiological opening. The bioprosthetic valve attained a fully circular orifice while the BAV attained an ellipsoidal shaped orifice at its fully open position. In the BAV, strong vortical patterns were observed at peak systole and recirculation zones were observed near the sino-tubular junction. The work presented in this thesis be seen as a platform from which complex patient specific data can be modeled under physiological conditions and as a base to include contact mechanics with which complete cardiac cycle can be simulated.

The strong Black woman ideal is a long-established image in U.S. society pressuring Black women to maintain a facade of strength at all times. The strength ideal is internalized as an integral aspect of their identity, so much so that Black women socialize each other to habituate behaviors reflecting strength. The Strong Black Woman Collective Theory (SBWC; Davis, 2015a) posits that Black women re-appropriate the strong Black woman image and use certain communication behaviors to affirm strength in each other. By exhibiting these behaviors, they delineate a safe space to promote solidarity within the group and confront oppressors collectively. This new theory needs to be corroborated with empirical data to examine how the theoretical tenets are actualized in a real-world communication context. To this end, the present study conducts a partial test of the SBWC theory by observing Black women friend groups engage in supportive discussions about racial discrimination. This is an ideal context to test the SBWC theory because the friends are gathering together as a group of same race-gendered persons; they are discussing the wrongdoing of an identifiable external hostility that they are motivated to retreat from and confront; and strength gets reified as a form of support during the conversation. The study advances a path model to represent the empirical associations among four key variables: strength regulation, group identification and solidarity, verbal confrontation, and relational quality with the out-group member. Fifty-two Black women friends groups (three in each) aged 18-89 years were sampled but only the data from the support seeker were used for analyses (n = 52). All data were collected in the home of one of the participants as a way to observe the supportive conversation in a safe, naturalistic environment. Structural Equation Modeling was used to test the Strong Black Woman Collective path model. The findings revealed that strength regulation was positively associated with group identification/solidarity, such that women felt more connected to the group when strength was regulated and reinforced. Also verbal derogation was inversely associated with relational satisfaction with the White woman aggressor. That is, support seekers reported lower levels of relational satisfaction with the White woman after she was verbally derogated during the discussion. The results also showed that strength regulation was positively correlated with verbal derogation, even though the relationship was approaching significance. Finally, verbal derogation had a very weak and nonsignificant association with group identification/solidarity. Findings from this study demonstrate that strength is functional in the context of Black women’s communication spaces and has important implications for their relationships with in-group affiliates and outsiders. The conclusion of this dissertation discusses the implications of these findings in relation to future articulations of the SBWC theory, extent research in Feminist Studies and Communication, and Black women’s day-to-day encounters with discrimination.

The generation of high-order harmonics opened an era of attosecond science wherein coherent light bursts are used to probe dynamic processes in matter with a time resolution short enough to resolve the motions of electrons. It enabled the development of extreme ultraviolet (XUV) and X-ray table-top sources with both temporal and spatial coherence, which provides the ability to shape the temporal and spatial structure of the XUV pulses. Scientists developed techniques to control and measure the temporal structure high harmonic emissions. These techniques exploited control of the driving laser pulse in the time domain and facilitated development of more advanced high-harmonic based XUV sources that have greatly impacted ultrafast measurements. In this thesis, I apply techniques to control and measure the spatial structure of high harmonic emissions, and discuss the underlying physics and potential applications of the interaction between spatially structured laser beams and materials. This study exploits the spatial degree of freedom in strong field interaction, which has not been given as much attention as the temporal degree of freedom. I use liquid crystal devices to shape the wave front of a fundamental laser beam to a vortex structure, then imprint this structured wave front onto XUV beams through high harmonic generation. This method provides an alternative to special XUV optics, which can manipulate the wave front of XUV radiation by all optical means. This result also reveals the conservation of orbital angular momentum in this extreme nonlinear wave mixing process. In addition to shaping the wave front, shaping the polarization of the driving beam also allows generation of circularly polarized the XUV radiation using a high harmonic source. This thesis also highlights the interplay between shaping the wave front and polarization in the high harmonic generation process. The topology of the structured beam can be maintained through this extreme nonlinear interaction due to the spin selection rules and spin-orbit conservation. Moreover, this thesis demonstrates an approach to integrate a vector beam into a broadband ultrafast light source and overcome the bandwidth limitation of mode converters. We use this approach to generate a few-cycle structured beam. In the future, this beam will be used to generate a strong ultrafast magnetic impulse in gas and solid targets by driving currents in a loop, which is a valuable tool for the future of magnetic metrology. The novel properties of structured laser beams discussed in this thesis expanded the capabilities of high harmonic based XUV sources and have opened a new field to explore this additional degree of freedom in strong field interactions.

This thesis is divided into two sections; a theoretical section which looks at the analytic construction of collective identities, and a section which applies the theory to two Australian novels. The first four chapters use the theories of Roy Wagner, Benedict Anderson, Jacques Lacan and Homi Bhabha to look at the often unconscious construction of culture and national, and at the process of hybridity to which those constructions are continually subject.The next three chapters examine Glenda Adamss Games of the Strong and Nicholas Haslucks The Bellarmine Jug showing how an unconscious development of Australian themes runs through the novels, regardless of a lack of Australian characters and setting. The novels show the complex, unique and frequently misunderstood position Australia holds between the cultures, nations and civilisations of the East and the West.The conclusion draws together the principal arguments of the thesis and highlights some concerns which they imply for Australian and its national imagination.

Ce travail porte sur la réalisation de dispositifs quantiques fonctionnant en régime de couplage fort entre une excitation d'un gaz d'électrons dans un puits quantique semiconducteur et un mode de cavité dans le moyen infra- rouge. Les quasi-particules issues de ce couplage lumière-matière sont appelées "polaritons intersousbande". La première partie de ce manuscrit est consacrée à l'étude d'un dis- positif électroluminescent basé sur une structure à cascade quantique in- sérée dans une microcavité planaire. Par une analyse détaillée des spectres d'électroluminescence à différents voltages, je démontre que les états de po- laritons sont peuplés de façon résonante, à une énergie qui dépend du voltage appliqué à la structure. Les résultats expérimentaux sont analysés et in- terprétés à l'aide d'un modèle reliant les spectres d'électroluminescence aux propriétés de l'injecteur de la structure à cascade. Pour augmenter la sélectivité de l'injection et observer ainsi une exaltation de l'émission spontanée, un nouveau type de cavité est développé dans la sec- onde partie de ce travail. Il s'agit d'une cavité basée sur un confinement plas- monique, dans laquelle la lumière est confinée entre deux plans métalliques, dans une épaisseur très inférieure à la longueur d'onde. Le miroir supérieur est façonné en réseau. L'influence des différents paramètres du réseau est étudiée et deux régimes sont mis en évidence: un régime où le mode de cavité se couple à un mode de plasmon de surface et un régime où le mode de cavité ne présente pas de dispersion en énergie. En insérant des puits quantiques dopés dans une cavité de ce deuxième type, les régimes de couplage fort puis de couplage ultra-fort lumière-matière sont démontrés jusqu'à température ambiante. La valeur importante du dédoublement de Rabi et la forte densité d'états polaritoniques obtenues dans ce type de cavité en font un candidat très prometteur pour la réalisation de dispositifs électroluminescents infrarouges de grande efficacité radiative et fonctionnant sans inversion de population.

<p align="justify">In a context of restoration of historical masonry structures, it is crucial to properly estimate the residual strength and the potential structural failure modes in order to assess the safety of buildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonry presents preferential damage orientations, strongly localised failure modes and damage-induced anisotropy, which are complex to incorporate in structural computations. Furthermore, masonry structures are generally subjected to complex loading processes including both in-plane and out-of-plane loads which considerably influence the potential failure mechanisms. As a consequence, both the membrane and the flexural behaviours of masonry walls have to be taken into account for a proper estimation of the structural stability.</p> <p align="justify">Macrosopic models used in structural computations are based on phenomenological laws including a set of parameters which characterises the average behaviour of the material. These parameters need to be identified through experimental tests, which can become costly due to the complexity of the behaviour particularly when cracks appear. The existing macroscopic models are consequently restricted to particular assumptions. Other models based on a detailed mesoscopic description are used to estimate the strength of masonry and its behaviour with failure. This is motivated by the fact that the behaviour of each constituent is a priori easier to identify than the global structural response. These mesoscopic models can however rapidly become unaffordable in terms of computational cost for the case of large-scale three-dimensional structures.</p> <p align="justify">In order to keep the accuracy of the mesoscopic modelling with a more affordable computational effort for large-scale structures, a multi-scale framework using computational homogenisation is developed to extract the macroscopic constitutive material response from computations performed on a sample of the mesostructure, thereby allowing to bridge the gap between macroscopic and mesoscopic representations. Coarse graining methodologies for the failure of quasi-brittle heterogeneous materials have started to emerge for in-plane problems but remain largely unexplored for shell descriptions. The purpose of this study is to propose a new periodic homogenisation-based multi-scale approach for quasi-brittle thin shell failure.</p> <p align="justify">For the numerical treatment of damage localisation at the structural scale, an embedded strong discontinuity approach is used to represent the collective behaviour of fine-scale cracks using average cohesive zones including mixed cracking modes and presenting evolving orientation related to fine-scale damage evolutions.</p> <p align="justify">A first originality of this research work is the definition and analysis of a criterion based on the homogenisation of a fine-scale modelling to detect localisation in a shell description and determine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale transition incorporating strong embedded discontinuities driven by the damaging mesostructure is proposed for the case of in-plane loaded structures. Finally, this continuous-discontinuous homogenisation scheme is extended to a shell description in order to model the localised behaviour of out-of-plane loaded structures. These multi-scale approaches for failure are applied on typical masonry wall tests and verified against three-dimensional full fine-scale computations in which all the bricks and the joints are discretised.</p>

This dissertation examines the role of ethical monism in the theology of Augustus Hopkins Strong. Chapter 1 discusses some of the reasons for examining Strong's theology and some of the difficulties entailed in such a study. Chapter 2 surveys the life of Strong up until the time when he returned to Rochester Theological Seminary and assumed the dual role of president and professor of theology in 1872. Special attention is given to factors which affected or pointed toward his later decision to embrace ethical monism. Chapter 3 explores the writings of several German thinkers who seem to have provided some of the philosophical building blocks which Strong used to construct his ethical monism. It also examines the writings of several English-speaking philosophers who emphasized the doctrine of divine immanence and who appear to have pushed Strong's thinking toward ethical monism. Chapter 4 discusses the various stages in Strong's decision to adopt ethical monism. It also traces his early incorporation of ethical monism into his larger theological system. Chapter 5 examines the impact which ethical monism had on other areas of Strong's theology. In particular, it discusses how ethical monism affected Strong's view of Scripture and experience, evolution and miracles, and sin and the atonement. Chapter 6 explores how other theologians viewed Strong's final theology and how Strong's theological journey affected the institution and people whom he impacted most. It argues that neither Rochester Theological Seminary nor the integrity of his theological system remained unaffected by his decision to embrace ethical monism. It also notes that both theological liberals and theological conservatives were generally critical of Strong's ethical monism, though for different reasons. This work contends that ethical monism was a means by which Strong attempted to reconcile Christian theology and modern thought while also trying to solve tensions within his own theology. In the end, Strong was unable to persuade modernists to embrace ethical monism or to convince conservatives that ethical monism was a legitimate theological option. Strong's attempt at a theological synthesis failed due largely to the contradictions which ethical monism produced within both Christian theology and philosophical monism.

在迪菲方塊中，我們將正方形的四個頂點皆填入數值，再利用相鄰兩頂點相減，再取絕對值的方式觀察其數列行為，發現四個頂點的數字最後皆會收斂至0。在本文中，我們將之推廣至五邊形，我們稱它為迪菲五邊形。我們套用同樣的運算模式後，發現亦有特殊的收斂行為。 / In Diffy box, we write down numbers on the four vertices of square, and then on the midpoint of each side write the difference between the two numbers at its endpoints. It is known that the numbers on the four vertices of a square will converge to zero finally. In this article, we use the same operations as Diffy box to discuss pentagons which we call" Diffy pentagon ". We find it will converge, too.