published_or_final_version / Earth Sciences / Doctoral / Doctor of Philosophy

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In this thesis we study GaAs one dimensional hole systems with strong spin-orbit interaction effects. The primary focus is the Zeeman splitting of 1D subbands in the two orthogonal in-plane magnetic field directions. We study two types of 1D hole systems based on different (311)A grown heterostructures: a modulation doped GaAs/AlGaAs square quantum well and an undoped induced GaAs/AlGaAs triangular quantum well. The results from the modulation doped 1D wire show enhanced anisotropy of the effective Lande g-factor for the two in-plane field directions (parallel and perpendicular to the wire), compared to that in 2D hole systems. This enhancement is explained by the confinement induced reorientation of the total angular momentum ^ J from perpendicular to the 2D plane to in-plane and parallel to the wire. We use the intrinsic anisotropy of the in-plane g-factors to probe the 0:7 structure and the zero bias anomaly in 1D hole wires. We find that the behaviour of the 0:7 structure and the ZBA are correlated and depend strongly on the orientation of the in-plane field. This result proves the connection between the 0:7 and the ZBA and their relation to spin. We fabricate the first induced hole 1D wire with extremely stable gate characteristics and characterize this device. We also fabricate devices with two orthogonal induced hole wires on one chip, to study the interplay between the confinement, crystallographic anisotropy and spin-orbit coupling and their effect on the Zeeman splitting. We find that the ratios of the g-factors in the two orthogonal field directions for the two wires show opposite behaviour. We compare absolute values of the g-factors relative to the magnetic field direction. For B || [011] the g-factor is large for the wire along [011] and small for the wire along [233]. Whereas for B || [233], the g-factors are large irrespective of the wire direction. The former result can be explained by reorientation of ^ J along the wire, and the latter by an additional off-diagonal Zeeman term, which leads to the out-of-plane component of ^ J when B || [233], and as a result, to enhanced g-factors via increased exchange interactions.

Due to the complex characteristics of tunneling problems, tunneling engineering is perhaps one of the areas in which numerical methods are more frequently adopted in practice. One important application is to examine the influence of an excavation and construction procedures on the stress distribution and deformation in the ground surrounding the opening and on the tunnel lining. Another important aspect of tunneling problems that can be accounted for in a numerical analysis is the complex geometry associated with typical applications. This is not only related to the shape of the opening, but also to the presence of non-homogenous or non-isotropic soil strata. / A constitutive model that is suitable for the analysis of structured clays has been developed in this study based on the multilaminate framework. The model takes into account the elastic unloading-reloading, inherent and induced anisotropy, destructuration and bonding effects. The model is implemented into Plaxis finite element program, successfully calibrated and used to investigate the response of structured sensitive clay to the construction of the Gatineau tunnel in Gatineau, Quebec and the Ottawa sewer tunnel in Ottawa, Ontario. Numerical results were compared to the field measurements taken during the tunnel construction. To improve the performance of the numerical model, an implicit integration algorithm is implemented and proven to be very effective as compared to the conventional explicit integration methods. The effect of different soil parameters including bonding and anisotropy on the tunneling induced displacements and lining stresses is also examined using a comprehensive parametric study. The results indicated that soil bonding and anisotropy have significant effects on the shape of the settlement trough as well as the magnitudes of surface displacements and lining stresses induced by tunneling.

Bibliography: leaves 91-95. / x, 155 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis contains methods of solution for a number of different problems within the area of the elasticity of anisotropic materials. The first problem concerns the calculation of stresses and strains within a concentric arrangement of cylindrical shells, where each shell has a differing set of anisotropic properties. This has immediate application to the design of yacht masts, and the particular example of the "Moth" yacht mast is considered. The second problem considered is the uncoupled thermo-elastic problem, where a boundary element method is derived for solving the class of boundary value problems governing plane thermo-elastic deformations of isotropic and anisotropic materials. The final class of problems deals with mixed boundary value problems in which the stresses become singular at some points, for instance in elastic problems containing cracks. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1998

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A wind turbine array was constructed in the wind tunnel at Portland State University in a standard Cartesian arrangement. Configurations of the turbine array were tested with rotor blades set to rotate in either a clockwise or counter-clockwise sense. Measurements of velocity were made with stereo particle-image velocimetry. Mean statistics of velocities and Reynolds stresses clearly show the effect of direction of rotation of rotor blades for both entrance and exit row turbines. Rotational sense of the turbine blades is visible in the mean spanwise velocity W and the Reynolds shear stress -[macron over vw]. The normalized anisotropy tensor was decomposed yielding invariants [lowercase eta] and [lowercase xi], which are plotted onto the Lumley triangle. Invariants of the normalized Reynolds stress anisotropy tensor indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids are composed with the eigenvalues from the decomposition yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates streamwise trends, especially trailing the top rotor tip and below the hub of the rotors. Direction of rotation of rotor blades is evidenced in the orientation of characteristic spheroids according to principle axes. The characteristic spheroids of the anisotropy tensor and their relate alignments varies between cases clearly seen in the inflows to exit row turbines. There the normalized Reynolds stress anisotropy tensor shows cumulative effects of the rotational sense of upstream turbines. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean mechanical energy equation indicate a correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associate with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates more isotropy compared to the regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.

Recent advances in machine learning have unlocked new potential for innovation in engineering science. Neural networks are used as universal function approximators that harness high-dimensional data with excellent learning capacity. While this is an opportunity to accelerate computational mechanics research, application in constitutive modeling is not trivial. Machine learning material response predictions without enforcing physical constraints may lack interpretability and could be detrimental to high-risk engineering applications. This dissertation presents a meta-modeling framework for automating the discovery of elastoplasticity models across material scales with emphasis on establishing interpretable and, hence, trustworthy machine learning modeling tools. Our objective is to introduce a workflow that leverages computational mechanics domain expertise to enforce / post hoc validate physical properties of the data-driven constitutive laws. Firstly, we introduce a deep learning framework designed to train and validate neural networks to predict the hyperelastic response of materials. We adopt the Sobolev training method and adapt it for mechanics modeling to gain control over the higher-order derivatives of the learned functions. We generate machine learning models that are thermodynamically consistent, interpretable, and demonstrate enhanced learning capacity. The Sobolev training framework is shown through numerical experiments on different material data sets (e.g. β-HMX crystal, polycrystals, soil) to generate hyperelastic energy functionals that predict the elastic energy, stress, and stiffness measures more accurately than the classical training methods that minimize L2 norms. To model path-dependent phenomena, we depart from the common approach to lump the elastic and plastic response into one black-box neural network prediction. We decompose the elastoplastic behavior into its interpretable theoretical components by training separately a stored elastic energy function, a yield surface, and a plastic flow that evolve based on a set of deep neural network predictions. We interpret the yield function as a level set and control its evolutionas the neural network approximated solutions of a Hamilton-Jacobi equation that governs the hardening/softening mechanism. Our framework may recover any classical literature yield functions and hardening rules as well as discover new mechanisms that are either unbeknownst or difficult to express with mathematical expressions. Through numerical experiments on a 3D FFT-generated polycrystal material response database, we demonstrate that our novel approach provides more robust and accurate forward predictions of cyclic stress paths than black-box deep neural network models. We demonstrate the framework's capacity to readily extend to more complex plasticity phenomena, such as pressure sensitivity, rate-dependence, and anisotropy. Finally, we integrate geometric deep learning and Sobolev training to generate constitutive models for the homogenized responses of anisotropic microstructures (e.g. polycrystals, granular materials). Commonly used hand-crafted homogenized microstructural descriptors (e.g. porosity or the averaged orientation of constitutes) may not adequately capture the topological structures of a material. This is overcome by introducing weighted graphs as new high-dimensional descriptors that represent topological information, such as the connectivity of anisotropic grains in an assemble. Through graph convolutional deep neural networks and graph embedding techniques, our neural networks extract low-dimensional features from the weighted graphs and, subsequently, learn the influence of these low-dimensional features on the resultant stored elastic energy functionals and plasticity models.

Many hydrocarbon reservoirs have sufficient porosity but low permeability (for example, tight gas sands and coal beds). However, such reservoirs are often naturally fractured. The fracture patterns in these reservoirs can control flow and transport properties, and therefore, play an important role in drilling production wells. On the scale of seismic wavelengths, closely spaced parallel fractures behave like an anisotropic media, which precludes the response of individual fractures in the seismic data. There are a number of fracture parameters which are needed to fully characterize a fractured reservoir. However, seismic data may reveal only certain fracture parameters and those are fracture orientation, crack density and fracture infill. Most of the widely used fracture characterization methods such as Swave splitting analysis or amplitude vs. offset and azimuth (AVOA) analysis fail to render desired results in laterally varying media. I have conducted a systematic study of the response of fractured reservoirs with laterally varying elastic and fracture properties, and I have developed a scheme to invert for the fracture parameters. I have implemented a 3D finite-difference method to generate multicomponent synthetic seismic data in general anisotropic media. I applied the finite-difference algorithm in both Standard and Rotated Staggered grids. Standard Staggered grid is used for media having symmetry up to orthorhombic (isotropic, transversely isotropic, and orthorhombic), whereas Rotated Staggered grid is implemented for monoclinic and triclinic media. I have also developed an efficient and accurate ray-bending algorithm to compute seismic traveltimes in 3D anisotropic media. AVOA analysis is equivalent to the first-order Born approximation. However, AVOA analysis can be applied only in a laterally uniform medium, whereas the Born-approximation does not pose any restriction on the subsurface structure. I have developed an inversion scheme based on a ray-Born approximation to invert for the fracture parameters. Best results are achieved when both vertical and horizontal components of the seismic data are inverted simultaneously. I have also developed an efficient positivity constraint which forbids the inverted fracture parameters to be negative in value. I have implemented the inversion scheme in the frequency domain and I show, using various numerical examples, that all frequency samples up to the Nyquist are not required to achieve desired inversion results.

O presente trabalho trata de construir um modelo computacional utilizando o método dos volumes finitos para malhas não-estruturadas, a fim de se calcular a carga hidráulica num meio poroso, considerando este meio não homogêneo e anisotrópico. A anisotropia é uma característica de muitos materiais encontrados na natureza e depende da propriedade estudada no meio. Primeiramente apresenta-se a dedução da equação do transporte advectivo dispersivo e a formulação matemática para a equação de Laplace, esta última utilizada para o cálculo da carga hidráulica. Em seguida, apresenta-se o algoritmo de solução de um programa computacional em linguagem C++ que permite calcular a velocidade do fluxo em cada face de um volume de controle. Finalmente são feitos vários testes para validação do código computacional utilizado, o que levou a crer que o método utilizado é eficaz para os tipos de malhas testados, apresentando algumas diferenças quanto ao erro da solução. / The present work build a computational model using the finite volumes method for unstructured meshes, with the purpose of calculating the hydraulic load in a porous medium, considering it material non - homogeneous and anisotropic. The Anisotropy is a characteristic of many materials found in the nature and it depends on the property studied in this material. First, we present the deduction of the equation of advective-dispersive transport and the mathematical formulation for the Laplaces equation, this last one used for the calculation of the hydraulic load. Soon afterwards, we present the solution algorithm of a computational program in the C++ language that allows to calculate the speed of the flow in each face of the control volume. Finally several tests for validation of the code are made, which makes it that the plausible to assume method is effective for the types of meshes tested, presenting some differences for the wrong solution.