This project is concerned with the development and implementation of a novel preconditioning method for the iterative solution of linear systems that arise in the finite element discretisation of the incompressible Navier-Stokes equations with weakly imposed boundary conditions. In this context we studied an augmented approach where the Schur complement associated with the momentum block of the Navier-Stokes equations has special sparse structure. We follow the standard inf-sup stable method of discretising the Navier-Stokes equations by the Taylor-Hood elements with the Lagrange multiplier constraints discretised using the same order approximation on matching grids. The resulting system of nonlinear equations is solved iteratively by Newton's method. The spectrum of the linearised Oseen's problem, preconditioned by the exact augmentation preconditioner was analysed. Then we developed inexact versions of the preconditioner aimed at achieving optimal scaling of the algorithm in terms of computational resources and wall-clock times. The experimental evaluation of the methodology involve a number of benchmark problems in two and three spatial dimensions. The obtained results demonstrate efficiency, robustness and almost optimal scaling of the solution algorithm with respect to the discrete problem size. We used OOMPH-LIB as a testbed for our experiments. The preconditioning strategies were implemented using OOMPH-LIB's Parallel Block Preconditioning Framework. The initial version of the software was significantly upgraded during the course of this project with newly implemented functionalities to facilitate the rapid development of sophisticated hierarchical design of parallel block preconditioners. Parallel performance analysis of the newly introduced functionalities demonstrate negligible overhead in terms of wall-clock time and the framework demonstrate good weak and strong parallel scaling.

Ao longo da última década o método adjunto tem sido consolidado como uma das mais versáteis e bem sucedidas ferramentas de otimização aerodinâmica e projeto inverso na Dinâmica dos Fluidos Computacional. Ele se tornou uma área de pesquisa por si só, criando uma grande variedade de aplicações e uma literatura prolífica. Entretanto, alguns aspectos relevantes do método permanecem ainda relativamente pouco explorados na literatura. Como é o caso das condições de contorno adjuntas e, mais especificamente, com respeito a fronteiras permeáveis. Esta dissertação discute detalhadamente uma nova forma de tratar o problema de contorno, que tem como objetivo assegurar que as equações adjuntas sejam bem-postas. O principal objetivo da otimização aerodinâmica consiste na tentativa de minimizar (ou maximizar) uma determinada medida de mérito. As aplicações de projeto inverso são desenvolvidas para escoamentos Euler 2-D ao redor de aerofólios, representados com a parametrização CST (Class-Shape function Transformation) proposta por Kulfan e Bussoletti (2006), em regime de vôo transônico e com domínio discretizado por malhas não-estruturadas de triângulos através de um ciclo de projeto, que utiliza o método steepest descent como algoritmo de busca da direção que minimiza (ou maximiza) a função de mérito. As equações adjuntas são derivadas na sua formulação contínua e suas condições de contorno são determinadas por equações diferenciais características adjuntas e relações de compatibilidade compatíveis com as variações realizáveis da física do escoamento. As variáveis adjuntas são, então, vistas como forças de vínculo generalizadas, que asseguram a realizabilidade de variações do escoamento. / Over the last decade the adjoint method has been consolidated as one of the most versatile and successful tools of aerodynamic optimization and inverse design in Computational Fluid Dynamics. It has become a research area of its own, spawning a large variety of applications and a prolific literature. Yet, some relevant aspects of the method remain relatively less explored in the literature. Such is the case with the adjoint boundary conditions and, more specifically, with regard to permeable boundaries. This dissertation discusses at length a novel approach to the boundary problem, which aims at ensuring the well-posedness of the adjoint equations. The main goal of aerodynamic optimization consists in attempting to minimize (or maximize) a certain mesure of merit. The inverse design applications are developed for 2-D Euler flows around airfoils, represented with the CST (Class-Shape function Transformation) parameterization proposed by Kulfan and Bussoletti (2006), in the transonic flight regime and domain discretized by triangle unstructured meshes in a design loop which makes use of the steepest descent method as search direction that minimizes (or maximizes) the mesure of merit. Adjoint equations are derived in the continuous formulation and their boundary conditions are determined by adjoint characteristic differential equations and compatibility relations. The latter are derived so as to be compatible with the realizable variations of physical quantities. The adjoint variables are seen as generalized constraint forces, which ensure the realizability of flow variations.

The Irwin River catchment, located in the central western region of Western Australia, has been the scene of significant geomorphological change over both historical and geological timescales. This thesis focuses on the most recent of these changes, the anthropogenic imprint, through the development of a catchment-scale understanding of system behaviour. Analysis and modelling of changes in the hydrological behaviour of the system indicates that while the Irwin River has displayed a natural susceptibility to large flood events, these have been exacerbated by the widespread clearing of native vegetation throughout the catchment. As a result, when such events do occur, the catchment response is now larger, more direct and has a greater ability to cause erosion. However, the nature and detail of sediment yield processes and stream channel response varies markedly throughout the system. A series of representative channel reaches, as defined by their planform characteristics, geometry and architecture, are presented to illustrate spatial changes in stream channel behaviour. A distinct variation in river morphotypes is seen both downstream throughout the system as well as across the tributary sub-catchments of the Irwin River, Lockier River and Green Brook. This inter and intra sub-catchment variation in stream channel response can be attributed to changes in the boundary conditions and coupling mechanisms in operation throughout the Irwin River system. The pronounced spatial variability in response to human disturbance and the changing nature of catchment-scale connectivity seen in the Irwin River system differs markedly to that reported elsewhere in the literature. Appreciation of the variability in form, behaviour and evolutionary history throughout the Irwin River catchment not only provides the foundation for effective management but also contributes to a wider understanding of fluvial system behaviour. Unlike the majority of existing literature, which tends to identify and measure channel changes in a single catchment where historical variation to the sediment and discharge regime is well known, this study demonstrates the role of boundary conditions in determining the response of the fluvial system to changing environmental controls.

Sunken oil is difficult to locate because remote sensing techniques cannot as yet provide views of sunken oil over large areas. Moreover, the oil may re-suspend and sink with changes in salinity, sediment load, and temperature, making deterministic fate models difficult to deploy and calibrate when even the presence of sunken oil is difficult to assess. For these reasons, together with the expense of field data collection, there is a need for a statistical technique integrating limited data collection with stochastic transport modeling. Predictive Bayesian modeling techniques have been developed and demonstrated for exploiting limited information for decision support in many other applications. These techniques brought to a multi-modal Lagrangian modeling framework, representing a near-real time approach to locating and tracking sunken oil driven by intrinsic physical properties of field data collected following a spill after oil has begun collecting on a relatively flat bay bottom. Methods include (1) development of the conceptual predictive Bayesian model and multi-modal Gaussian computational approach based on theory and literature review; (2) development of an object-oriented programming and combinatorial structure capable of managing data, integration and computation over an uncertain and highly dimensional parameter space; (3) creating a new bi-dimensional approach of the method of images to account for curved shoreline boundaries; (4) confirmation of model capability for locating sunken oil patches using available (partial) real field data and capability for temporal projections near curved boundaries using simulated field data; and (5) development of a stand-alone open-source computer application with graphical user interface capable of calibrating instantaneous oil spill scenarios, obtaining sets maps of relative probability profiles at different prediction times and user-selected geographic areas and resolution, and capable of performing post-processing tasks proper of a basic GIS-like software. The result is a predictive Bayesian multi-modal Gaussian model, SOSim (Sunken Oil Simulator) Version 1.0rc1, operational for use with limited, randomly-sampled, available subjective and numeric data on sunken oil concentrations and locations in relatively flat-bottomed bays. The SOSim model represents a new approach, coupling a Lagrangian modeling technique with predictive Bayesian capability for computing unconditional probabilities of mass as a function of space and time. The approach addresses the current need to rapidly deploy modeling capability without readily accessible information on ocean bottom currents. Contributions include (1) the development of the apparently first pollutant transport model for computing unconditional relative probabilities of pollutant location as a function of time based on limited available field data alone; (2) development of a numerical method of computing concentration profiles subject to curved, continuous or discontinuous boundary conditions; (3) development combinatorial algorithms to compute unconditional multimodal Gaussian probabilities not amenable to analytical or Markov-Chain Monte Carlo integration due to high dimensionality; and (4) the development of software modules, including a core module containing the developed Bayesian functions, a wrapping graphical user interface, a processing and operating interface, and the necessary programming components that lead to an open-source, stand-alone, executable computer application (SOSim - Sunken Oil Simulator). Extensions and refinements are recommended, including the addition of capability for accepting available information on bathymetry and maybe bottom currents as Bayesian prior information, the creation of capability of modeling continuous oil releases, and the extension to tracking of suspended oil (3-D).

Current design of cemented paste backfill (CPB) barricades tends to be of unknown conservativeness due to limited understanding of their behaviour. Previous work done to characterize barricade response has not accounted for the effects of the surrounding rock stiffness, which can have significant impact on the development of axial forces which enhance capacity via compressive membrane action. Parametric analyses were performed with the finite element analysis program Augustus-2 to determine the effects of various material and geometric properties on barricade capacity. Equations based on Timoshenko and Boussinesq solutions were developed to model rock stiffness effects based on boundary material properties. An iterative simulation process was used to account for secondary moment effects as a proof of concept. It was found that, for a range of typical rock types, barricade capacity varied significantly. The commonly made design assumption of a fully rigid boundary resulted in unconservative overpredictions of strength.

Current design of cemented paste backfill (CPB) barricades tends to be of unknown conservativeness due to limited understanding of their behaviour. Previous work done to characterize barricade response has not accounted for the effects of the surrounding rock stiffness, which can have significant impact on the development of axial forces which enhance capacity via compressive membrane action. Parametric analyses were performed with the finite element analysis program Augustus-2 to determine the effects of various material and geometric properties on barricade capacity. Equations based on Timoshenko and Boussinesq solutions were developed to model rock stiffness effects based on boundary material properties. An iterative simulation process was used to account for secondary moment effects as a proof of concept. It was found that, for a range of typical rock types, barricade capacity varied significantly. The commonly made design assumption of a fully rigid boundary resulted in unconservative overpredictions of strength.

Social service organizations have changed dramatically during the last decade in an effort to increase effectiveness and control. This has placed new demands on those in leadership roles, and the need for knowledge of how to lead these transformed organizations has increased. Transformational leadership is a leadership model based on vision and empowerment, one suggested to increase both employee effectiveness and well-being, but the usefulness of this model in the public sector has been questioned. The general aim of this thesis is therefore to increase our understanding of the transformational leadership process in the context of social service organizations by investigating factors that explain when and why transformational leadership emerges and is effective. Questionnaire data from social service employees as well as interview data from managers were used in three empirical studies. Results from Studies 1 & 2 show that transformational leadership is positively associated with employee outcomes including commitment, role clarity, and well-being. Factors that might influence the effectiveness of transformational leadership were addressed in Study 1. It was found that leader continuity enhanced the effect of transformational leadership on role clarity and commitment, indicating that it takes time before transformational leaders actually have an effect on employees. Furthermore, co-worker support enhanced the effect on commitment, reflecting the role of followers in the transformational leadership process. The way in which transformational leaders influence employees was examined in Study 2, and climate for innovation mediated the relationship between transformational leadership and well-being both cross-sectionally and one year later. Finally, organizational factors that may hinder the emergence of transformational leadership were addressed in Study 3, and newly recruited managers were interviewed during their first year of leadership. Eight hindering factors in the organization to exhibit transformational leadership were identified, including the organizational structure, ongoing change, and the leaders’ working conditions. In all, this thesis has demonstrated the usefulness of transformational leadership in social services in terms of being associated with employee positive attitudes and well-being, and has also identified factors that may both help and hinder the transformational leadership process in this context.

The complicated process may cause the internal defects of multi-layered ceramic capacitors (MLCCs) and result in the malfunctions. This work aims to investigate the deformations of MLCCs that composed of nearly a hundred of BaTiO3 and Ni electrode films interleaved and stacked due to high pressure at elevated temperature. This study focuses on theoretical and numerical analyses. Classical laminated plate theory, linear elastic assumptions and equilibrium equations were adopted. Associated with the texts by Timoshenko and practical manufacturing process, three types of boundary conditions were considered, such as all edges simple-supported, two opposite edges simple-supported and the other two free, and four edges free. Also, two more conditions need be added, including four fixed points at corners and the elastic foundation at bottom. The numerical simulation by finite element method (FEM) incorporated with software ANSYS was used to obtain the displacement field of MLCCs due to high pressure at elevated temperature. The MLCCs were divided into nine regions with suitably different boundary conditions. Compared with the numerical results the analytical solutions of nine regions were found satisfactorily acceptable, i.e., the errors were about 0.1% - 6.2% for the boundary conditions of four edges free and four corners fixed. The errors about 0.13% - 6.15% were also acceptable for the boundary conditions of two opposite edges simple-supported and the others free. However, the analytical solutions did not agree with the numerical results for the case of all the boundary conditions simple-supported. Finally the proposed theoretical methodology provides an analytical method alternatively, instead of FEM and ANSYS, to analyze a nearly hundred layered MLCCs.

This thesis is presented in two sections. Two different multiscale models are developed in order to increase the computational speed of two well known atomistic algorithms, Molecular Dynamics (MD) and Kinetic Monte Carlo (KMC). In Section I, the MD method is introduced. Following this, a multiscale method of linking an MD simulation of heat conduction to a finite element (FE) simulation is presented. The method is simple to implement into a conventional MD code and is independent of the atomistic model employed. This bridge between the FE and MD simulations works by ensuring that energy is conserved across the FE/MD boundary. The multiscale simulation allows for the investigation of large systems which are beyond the range of MD. The method is tested extensively in the steady state and transient regimes, and is shown to agree with well with large scale MD and FE simulations. Furthermore, the method removes the artificial boundary effects due to the thermostats and hence allows exact temperatures and temperature gradients to be imposed on to an MD simulation. This allows for better study of temperature gradients on crystal defects etc. In Section II, the KMC method is introduced. A continuum model for the KMC method is presented and compared to the standard KMC model of surface diffusion. This method replaces the many discrete back and forth atom jumps performed by a standard KMC algorithm with a single flux that can evolve in time. Elastic strain is then incorporated into both algorithms and used to simulate atom deposition upon a substrate by Molecular Beam Epitaxy. Quantum dot formation due to a mismatch in the lattice spacing between a substrate and a deposited film is readily observed in both models. Furthermore, by depositing alternating layers of substrate and deposit, self-organised quantum dot super-lattices are observed in both models.

This Thesis is concerned with the quasiclassical theory of meso-scopic superconductivity. The aim of the Thesis is to introduce the boundary conditions for a quasiclassical Green’s function on partially transparent interfaces in mesoscopic superconducting structures and to analyze the range of applicability of the quasiclassical theory. The linear boundary conditions for Andreev amplitudes, factoring the quasiclassical Green’s function, are presented.  The quasiclassical theory on classical trajectories is reviewed and then generalized to include knots with paths intersections.  The main focus of the Thesis is on the range of validity of the quasiclassical theory. This goal is achieved by comparison of quasiclassical and exact Green’s functions.  The exact Gor’kov Greens function cannot be directly used for the comparison because of its strong microscopic variations on the length-scale of λF. It is the coarse-grain averaged exact Green’s function which is appropriate for the comparison. In most of the typical cases the calculations show very good agreement between both theories. Only for certain special situations, where the classical trajectory contains loops, one encounters discrepancies. The numerical and analytical analysis of the role of the loop-like structures and their influence on discrepancies between both exact and quasiclassical approaches is one of the main results of the Thesis. It is shown that the terms missing in the quasiclassical theory can be attributed to the loops formed by the interfering paths.  In typical real samples any imperfection on the scale larger than the Fermi wavelength disconnects the loops and the path is transformed into the tree-like graph. It is concluded that the quasiclassical theory is fully applicable in most of real mesoscopic samples. In the situations where the conventional quasiclassical theory is inapplicable due to contribution of the interfering path, one can use the modification of the quasiclassical technique suggested in the Thesis.