Composite flow simulation tools for LCM processing can be expensive and time-consuming but necessary to design a mold system with proper placement of resin inlets and vacuum outlets. Composites manufacturing engineers would benefit from data regarding the impact of mold curvature radius on resin flow. This could help determine whether or not a particular part and mold would require expensive simulation software designed to handle complex flow paths through curved fabric architectures exhibiting variable permeability over the curvature, or if simple flow modeling would provide accurate enough simulations for sound tooling setup decision making. Four molds, with double curvature having equal radii, were fabricated with radii ranging from 3.2 to 25.4 mm to characterize the permeability of two different fiber reinforcements 1) a carbon biaxial NCF and 2) a fiberglass CSM over the mold curvatures. Three infusions of each material type were conducted on each of the 4 molds for a total of 24 test infusions. Flow front position vs. time data was captured during each experimental infusion. The permeability in the bend regions, KB, was first estimated by the integrated form of Darcy's Law to evaluate the permeability for average flow across the entire bend region. This was done for both the convex and concave regions using a geometric estimate for the increased compaction in the bend regions. The permeability increases as the tool radius increases, and the rate of increase diminishes as the tool radius increases and the permeability approaches the flat region permeability. An estimate of KB for VI was then made by applying a ratio calculated from the resulting permeability from the rigid- and VI-based models in the flat regions. Generic power law fits are reported that could be used in LCM process simulation, to give a model to estimate the permeability for any bend in the reinforcement part geometry. The results suggest that any curve with a radius higher than 25 mm requires no adjustment to the flat permeability.

Charged or rotating black holes possess an inner horizon beyond which determinism is lost. However, the strong cosmic censorship conjecture claims that even small perturbations will turn the horizon into a singularity beyond which the spacetime is inextendible, preventing the loss of determinism. Motivated by this conjecture, this dissertation studies free scalar quantum fields on various black-hole spacetimes to test whether quantum effects can lead to the formation of a singularity at the inner horizon in cases where classical perturbations cannot. The starting point is the investigation of the behaviour of real-scalar-field observables near the inner horizon of Reissner-Nordström-de Sitter spacetimes. Using semi-analytical methods, we find that quantum effects can indeed uphold the censorship conjecture. Subsequently, we consider charged scalar fields on the same spacetime and observe that a first-principle calculation is essential to accurately describe the quantum effects at the inner horizon. As a first step towards an extension of these results to rotating black holes, we rigorously construct the Unruh state for the real scalar field on slowly rotating Kerr-de Sitter spacetimes. We show that it is a well-defined Hadamard state and can therefore be used to compute expectation values of the stressenergy tensor and other non-linear observables.:1 Introduction 7 2 An introduction to quantum fields and black holes 13 2.1 Notations and conventions . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 A brief introduction to AQFT . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 An introduction to microlocal analysis . . . . . . . . . . . . . . . . . . . 24 2.4 An introduction to black-hole spacetimes . . . . . . . . . . . . . . . . . 28 2.4.1 The Reissner-Nordström-de Sitter spacetime . . . . . . . . . . . 28 2.4.2 The Kerr-de Sitter spacetime . . . . . . . . . . . . . . . . . . . . 32 2.5 Free scalar fields in black-hole spacetimes . . . . . . . . . . . . . . . . . 37 3 Computing the energy flux of the real scalar field 43 3.1 Strong cosmic censorship on RNdS . . . . . . . . . . . . . . . . . . . . 43 3.2 The Klein-Gordon equation on RNdS . . . . . . . . . . . . . . . . . . . 45 3.3 Extension to the charged scalar field on RNdS . . . . . . . . . . . . . . . 52 3.4 The energy flux at the Cauchy horizon . . . . . . . . . . . . . . . . . . . 53 4 The charged scalar field in Reissner-Nordström-de Sitter 63 4.1 The Unruh state for the charged scalar field . . . . . . . . . . . . . . . . 65 4.2 The renormalized current . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3 The current in the Unruh state - numerical results . . . . . . . . . . . . . 80 4.4 The charged scalar field at the inner horizon . . . . . . . . . . . . . . . . 86 5 The Unruh state on Kerr-de Sitter 97 5.1 Null geodesics in the Kerr-de Sitter spacetime . . . . . . . . . . . . . . . 98 5.2 The Unruh state on Kerr-de Sitter . . . . . . . . . . . . . . . . . . . . . . 107 5.3 The Hadamard property of the Unruh state . . . . . . . . . . . . . . . . . 120 5.3.1 The Hadamard condition in O . . . . . . . . . . . . . . . . . . . 123 5.3.2 The Hadamard condition on M\O . . . . . . . . . . . . . . . . . 128 6 Summary and discussion 139 A Bibliography 143

A study of a thin-walled curved rectangular box beam under torsion and out-of-plane bending is documented in this thesis. A new one-dimensional theory that takes into account warping and distortion in the beam cross-sections is the main focus. Existing available theories for thin-walled curved beams lack rigorous theoretical development, and most have ignored the effects of warping and distortion. A higher order theory including two additional degrees of freedom corresponding to warping and distortion was derived. The conventional three degrees of freedom model was compared with the new five degrees of freedom model. The variation of beam thickness to control and decrease the high distortion variable is investigated.

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No description available.

<p>This work explores a new method of force generation for flying robots on the sub-cm wingspan scale: resonant curved piezoelectric cantilevers created using completely parallel MEMS fabrication. It theorizes that because a resonating curved beam has a different drag coefficient on the upstroke than the downstroke, it should act as a fluid diode: a partial one-way gate for fluids, and thereby generate an asymmetric force over a symmetric one-degree-of-freedom flapping cycle. It develops a simplified model for the large-amplitude resonant mode of thin circular arcs by analytically extending the resonant mode shape of straight cantilevers, shows that this shape is a better fit to experimental data than previous models, and shows that it accurately predicts the resonant frequency. It uses this resonant mode to compute the force on flapping curved arcs under a wide range of amplitudes, Reynolds numbers, and arc angles using computational fluid dynamics (CFD) simulations, and extends the concept of a drag coefficient from steady-flow fluid mechanics to steady-state oscillatory fluid mechanics both for net force generation and power dissipation. It develops a framework to analyze the CFD results in the broader context of a complete robot, and uses this framework to determine priorities for material selection, robot size, and flapping shape, depending on desired robot application. It tests these theoretical predictions by creating prototype 7.6 mm wings out of 7.5 micrometer thick x-cut quartz and SU-8, after developing and implementing a method to smoothly thin x-cut quartz leaving the surface free of dielectric-compromising pits using reactive ion etching (RIE). Finally, it constructs a test chamber to measure the force, amplitude, and electrical parameters of the flapping wings under a variety of air pressures and demonstrates that the results are consistent with the theoretical predictions, indicating that this approach can in fact lead to successful flying microrobots.</p> / Doctor of Philosophy (PhD)

The ping-pong lemma was introduced by Klein in the late 1800s to show that certain subgroups of isometries of hyperbolic 3-space are free and remains one of very few tools that certify when a pair of group elements generate a free subgroup or semigroup. Quantitatively applying the ping-pong lemma to more general group actions on metric spaces requires a blend of understanding the large-scale global geometry of the underlying space with local combinatorial and dynamical behavior of the action. In the 1980s, Gromov publish a sequence of seminal works introducing several metric notions of non-positive curvature in group theory where he asked which finitely generated groups have uniform exponential growth. We give an overview of various developments of non-positive curvature in group theory and past results related to building free semigroups in the setting of non-positive curvature. We highlight joint work with Radhika Gupta and Kasia Jankiewicz and with Carolyn Abbott and Davide Spriano that extends these tools and techniques to show several groups with that act on cube complexes and many hierarchically hyperbolic groups have uniform exponential growth. / Mathematics

This thesis presents a geometrically exact curved beam theory, with the assumption that the cross-section remains rigid, and its finite element formulation/implementation. The theory provides a theoretical view and an exact and efficient means to handle a large range of nonlinear beam problems. A geometrically exact curved/twisted beam theory, which assumes that the beam cross-section remains rigid, is re-examined and extended using orthonormal reference frames starting from a 3-D beam theory. The relevant engineering strain measures at any material point on the current beam cross-section with an initial curvature correction term, which are conjugate to the first Piola-Kirchhoff stresses, are obtained through the deformation gradient tensor of the current beam configuration relative to the initially curved beam configuration. The Green strains and Eulerian strains are explicitly represented in terms of the engineering strain measures while other stresses, such as the Cauchy stresses and second Piola-Kirchhoff stresses, are explicitly represented in terms of the first Piola-Kirchhoff stresses and engineering strains. The stress resultant and couple are defined in the classical sense and the reduced strains are obtained from the three-dimensional beam model, which are the same as obtained from the reduced differential equations of motion. The reduced differential equations of motion are also re-examined for the initially curved/twisted beams. The corresponding equations of motion include additional inertia terms as compared to previous studies. The linear and linearized nonlinear constitutive relations with couplings are considered for the engineering strain and stress conjugate pair at the three-dimensional beam level. The cross-section elasticity constants corresponding to the reduced constitutive relations are obtained with the initial curvature correction term. For the finite element formulation and implementation of the curved beam theory, some basic concepts associated with finite rotations and their parametrizations are first summarized. In terms of a generalized vector-like parametrization of finite rotations under spatial descriptions (i.e., in spatial forms), a unified formulation is given for the virtual work equations that leads to the load residual and tangent stiffness operators. With a proper explanation, the case of the non-vectorial parametrization can be recovered if the incremental rotation is parametrized using the incremental rotation vector. As an example for static problems, taking advantage of the simplicity in formulation and clear classical meanings of rotations and moments, the non-vectorial parametrization is applied to implement a four-noded 3-D curved beam element, in which the compound rotation is represented by the unit quaternion and the incremental rotation is parametrized using the incremental rotation vector. Conventional Lagrangian interpolation functions are adopted to approximate both the reference curve and incremental rotation of the deformed beam. Reduced integration is used to overcome locking problems. The finite element equations are developed for static structural analyses, including deformations, stress resultants/couples, and linearized/nonlinear bifurcation buckling, as well as post-buckling analyses of arches subjected to conservative and non-conservative loads. Several examples are used to test the formulation and the Fortran implementation of the element. / Master of Science

Event Detection is a process of identifying terrain flatness from which localized events such as potholes in the terrain surface can be found and is an important tool in pavement health monitoring and vehicle performance inspection. Repeated detection of terrain surfaces over an extended period of time can be used by highway engineers for long term road health monitoring. An accurate terrain map can allow maintenance personnel for identifying deterioration in road surface for immediate correction. Additionally, knowledge of the events in terrain surface can be used to predict the performance the vehicles would experience while traveling over it. Event detection is composed of two processes: event edging and stitching edges to events. Edge detection is a process of identifying significant localized changes in the terrain surface. Many edge detection methods have been designed capable of capturing edges in terrain surfaces. Gradient searches are frequently used in image processing to recover useful information from images. The issue with using a gradient search method is that it returns deterministic values resulting in edges which are less precise. In order to predict the precision of the terrain surface, the individual nodal probability densities must be quantified and finally combined for the precision of terrain surface. A Comparative Nodal Uncertainty Method is developed in this work to detect edges based on the probability distribution of the nodal heights within some local neighborhood. Edge stitching is developed to group edges to events in a correct sequence from which an event can be determined finally. / Master of Science

Two topics dealing with adhesion are addressed: an investigation of the cling of thin polymeric films and an analysis of the effects of viscoelasticity on adhesive systems involving curvature mismatch. The results of an investigation into the mechanisms of adhesion and debonding energy associated with the cling between polymeric films and various substrates is presented first. The thermodynamic work of adhesion, electrostatic attraction, and substrate roughness apparently play significant roles in the cling of a film to a substrate. Peel tests are conducted and strain energy release rates are determined which show different debonding energies for the various film-substrate systems. In the analysis of adhesive systems involving curvature mismatch, the focus of the work is on modeling the bond behavior using the solution to the beam on a viscoelastic foundation problem. In addition, the behavior of the adhesive is modeled with a recursive technique using a stress distribution obtained from the solution to the beam on an elastic foundation problem. Debond rate tests are described and conducted so that experimental results may be compared with analytical results. For both adhesion topics, the mechanisms and mechanics of adhesion are considered and experimental tests are conducted. / Master of Science