Computational aspects of modular parametrizations of elliptic curves

Thesis (Ph.D.)--University of Washington, 2016-06

Mode II delamination testing in uniaxially oriented PVC pipes

The mode II fracture toughness of an oriented PVC pipe was measured using an End Notched Flexure test geometry. A relatively low value of G(IIC) was found of 1.07 kJ m(-2) and this indicates that it is energetically more favorable for a crack to propagate in the tangential direction rather than radially through the wall of the pipe. Examination of the mechanism of crack advanced showed that although the crack was propagating globally in mode II, micro-cracks were opening ahead of the crack in mode I or in mixed mode. Growth of the crack occurred by linking up of these micro-cracks. This is similar to the mechanism found for mode II cracking in carbon fibre epoxy composites. (C) 2004 Kluwer Academic Publishers.

Scabies: more than just an irritation

Human scabies, caused by skin infestation with the arthropod mite, Sarcoptes scabiei, typically results in a papular, intensely pruritic eruption involving the interdigital spaces, and flexure creases. Recent research has led to a reassessment of the morbidity attributable to this parasite in endemic communities, particularly resulting from secondary skin sepsis and postinfective complications including glomerulonephritis. This has led to studies of the benefits of community based control programmes, and to concerns regarding the emergence of drug resistance when such strategies are employed. The renewed research interest into the biology of this infection has resulted in the application of molecular tools. This has established that canine and human scabies populations are genetically distinct, a finding with major implications for the formulation of public health control policies. Further research is needed to increase understanding of drug resistance, and to identify new drug targets and potential vaccine candidates.

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.

PÊNDULO ANCORADO EM MINI-IMPLANTES - ANÁLISE EM MODELOS DIGITAIS

A distalização dos molares superiores é uma opção de tratamento da má oclusão de Classe II, quando o envolvimento é principalmente dentoalveolar. Dispositivos intrabucais como o aparelho Pêndulo, dispensam a colaboração do paciente quanto ao uso, porém promovem efeitos muitas vezes indesejáveis como a vestibularização dos dentes anteriores que participam na ancoragem e a inclinação dos molares distalizados. Após o surgimento dos Dispositivos de Ancoragem Temporária (DATs), como o mini-implante pode-se alcançar a ancoragem de forma previsível e eficiente. Com isto, por meio de um estudo prospectivo, foram avaliadas as alterações dentárias, promovidas pela distalização de molares superiores com um aparelho Pêndulo modificado, apoiado em dois mini-implantes instalados no palato de 10 indivíduos, sendo 2 do sexo feminino e 8 do masculino, com média de idade de 14,3 anos. A amostra foi composta por 20 modelos digitalizados em 3D, obtidos de em duas fases: no início do tratamento (T1) e após distalização com sobrecorreção de 1 mm (T2), permitindo quantificar as alterações dentárias sagitais, transversais e possíveis movimentos de rotação, angulação e movimentos verticais. Os resultados obtidos mostraram que no sentido sagital, houve uma efetiva distalização com significância estatística, para os segundos molares superiores; primeiros molares superiores em média de 4,34 mm e 3,91mm para o lado direito e esquerdo, respectivamente, e para os segundos pré-molares do lado direito e esquerdo de 2,06 mm e 1,95 mm, respectivamente. Porém, para os dentes anteriores, foi constatada a perda de ancoragem. No sentido transversal, o maior aumento ocorreu na região dos dentes posteriores. Os movimentos de rotação, angulação e vertical dos primeiros molares superiores, indicam que houve rotação mesiovestibular e inclinação distal das coroas destes dentes de ambos os lados; as medidas verticais, demonstram que houve movimento significativo apenas para o primeiro molar direito, com inclinação distal pela intrusão da cúspide distal. Este dispositivo mostrou-se eficaz na correção da Classe II em um tempo médio de 6,2 meses.(AU)

AVALIAÇÃO DAS ALTERAÇÕES DENTÁRIAS E DO PERFIL FACIAL OBTIDAS NO TRATAMENTO ORTODÔNTICO COM BRAQUETES AUTOLIGADOS

Este trabalho teve como objetivo principal avaliar as inclinações dentárias e o perfil facial de pacientes tratados ortodonticamente com braquete autoligado Damon 2, prescrição padrão. Para este estudo, foi selecionada uma amostra de 18 indivíduos, sendo 12 do sexo masculino e 6 do feminino, com idades que variaram de 12 a 20 anos (idade média de 15 anos) e que apresentavam discrepância de modelo negativa (de 4 mm a 15 mm). Como critério de inclusão, os pacientes deveriam apresentar dentição permanente completa até os segundos molares, má oclusão de Classe I de Angle, telerradiografias em norma lateral do início e final do tratamento ortodôntico e modelos de estudo em gesso dos arcos dentários superiores e inferiores do início e final do tratamento ortodôntico. As medições das inclinações ântero-posteriores dos incisivos centrais superiores e incisivos centrais inferiores e alterações do perfil facial foram realizadas por meio das telerradiografias em norma lateral. As distâncias transversais das regiões de cúspide e cervical inter-caninos, primeiros e segundos pré-molares e primeiros molares, foram obtidas medindo-se os modelos de gesso. Todas as mensurações foram realizadas nas telerradiografias e modelos de gesso obtidos antes do início do tratamento ortodôntico (T1) e no final do tratamento (T2). Após a coleta de todos os dados aplicou-se o teste t de Student para comparar as medidas dos dois tempos avaliados neste estudo. Verificou-se diferença estatisticamente significante (p<0,05) na inclinação dos incisivos centrais inferiores e nas dimensões transversais inter-cúspides e inter-cervicais dos primeiros e segundos pré-molares e primeiros molares na maxila. Na mandíbula todas as distâncias transversais (inter cúspides e cervicais) de caninos, primeiros e segundos pré-molares e primeiros molares apresentaram significância estatística (p<0,05), exceto a distância inter-cervical dos caninos inferiores. Concluímos que o tratamento ortodôntico sem extrações de pacientes com má oclusão de Classe I realizados com os braquetes Damon 2, prescrição padrão, não promoveu alteração na inclinação vestíbulo-lingual dos incisivos centrais superiores, aumentou a inclinação vestibular dos incisivos centrais inferiores, não alterou o perfil facial e aumentou de modo significativo a dimensão transversal da maxila e da mandíbula por meio de inclinação vestibular de coroa.(AU)

Mechanism of action of the tetraflex accommodative intraocular lens

PURPOSE:To investigate the mechanism of action of the Tetraflex (Lenstec Kellen KH-3500) accommodative intraocular lens (IOL). METHODS:Thirteen eyes of eight patients implanted with the Tetraflex accommodating IOL for at least 2 years underwent assessment of their objective amplitude-of-accommodation by autorefraction, anterior chamber depth and pupil size with optical coherence tomography, and IOL flexure with aberrometry, each viewing a target at 0.0 to 4.00 diopters of accommodative demand. RESULTS:Pupil size decreased by 0.62+/-0.41 mm on increasing accommodative demand, but the Tetraflex IOL was relatively fixed in position within the eye. The ocular aberrations of the eye changed with increased accommodative demand, but not in a consistent manner among individuals. Those aberrations that appeared to be most affected were defocus, vertical primary and secondary astigmatism, vertical coma, horizontal and vertical primary and secondary trefoil, and spherical aberration. CONCLUSIONS:Some of the reported near vision benefits of the Tetraflex accommodating IOL appear to be due to changes in the optical aberrations because of the flexure of the IOL on accommodative effort rather than forward movement within the capsular bag.

Analysis of flexural isostasy of the northern Andes

The mode in which a lithosphere plate supports overlying topography is greatly driven by the strength of the plate. By analyzing the geophysical signature of lithosphere flexure, in the space and spectral domains, the strength of the plates that support the north Andean mountains and adjacent basins, and the topography of Kenya was investigated. In addition, the effect of windowing on elastic thickness estimates obtained via the coherence method was evaluated. ^ The coherence between the topography and Bouguer gravity spectra of northern South America suggests that the average elastic thickness of the lithosphere is 30 km. Although lateral variations were not resolved by the coherence implementation, these became apparent by modeling the foreland stratigraphy of the Llanos, Barinas and Maracaibo sub-Andean basins. Flexural models reveal a zone of lithosphere weakness beneath the eastern flank of the Eastern Cordillera and western flank of the Venezuelan Andes. The gravity anomaly calculated from these models is consistent with the observed Bouguer gravity anomaly. This zone of weakness appears to separate the strong, old Guyana shield lithosphere from the weaker and probably younger Andean lithosphere. The zone of weakness may correspond to a Paleozoic feature at the western margin of cratonic South America, or a Mesozoic rift arm that weakened the proto-Andean lithosphere. ^ Using synthetic data as well as the northern South America topography and gravity, this study demonstrates that lithosphere strength calculated from the coherence of mirrored data may overestimate the true lithosphere strength. As a result, many lithosphere plates may be weaker than currently thought. In light of this observation, gravity and topography data from Kenya were reevaluated using multitaper spectral techniques. The elastic thickness of this plate, currently undergoing rifting, was estimated at 7 to 8 km, a factor of 2 less than previously estimated. These estimates suggest that despite intense fracturing and sustained tensile stresses, continental lithosphere plates undergoing rifting are able to retain some strength. ^

Seismic performance of hybrid fiber reinforced polymer-concrete pier frame systems

As an alternative to transverse spiral or hoop steel reinforcement, fiber reinforced polymers (FRPs) were introduced to the construction industry in the 1980’s. The concept of concrete-filled FRP tube (CFFT) has raised great interest amongst researchers in the last decade. FRP tube can act as a pour form, protective jacket, and shear and flexural reinforcement for concrete. However, seismic performance of CFFT bridge substructure has not yet been fully investigated. Experimental work in this study included four two-column bent tests, several component tests and coupon tests. Four 1/6-scale bridge pier frames, consisting of a control reinforced concrete frame (RCF), glass FRP-concrete frame (GFF), carbon FRP-concrete frame (CFF), and hybrid glass/carbon FRP-concrete frame (HFF) were tested under reverse cyclic lateral loading with constant axial loads. Specimen GFF did not show any sign of cracking at a drift ratio as high as 15% with considerable loading capacity, whereas Specimen CFF showed that lowest ductility with similar load capacity as in Specimen GFF. FRP-concrete columns and pier cap beams were then cut from the pier frame specimens, and were tested again in three point flexure under monotonic loading with no axial load. The tests indicated that bonding between FRP and concrete and yielding of steel both affect the flexural strength and ductility of the components. The coupon tests were carried out to establish the tensile strength and elastic modulus of each FRP tube and the FRP mold for the pier cap beam in the two principle directions of loading. A nonlinear analytical model was developed to predict the load-deflection responses of the pier frames. The model was validated against test results. Subsequently, a parametric study was conducted with variables such as frame height to span ratio, steel reinforcement ratio, FRP tube thickness, axial force, and compressive strength of concrete. A typical bridge was also simulated under three different ground acceleration records and damping ratios. Based on the analytical damage index, the RCF bridge was most severely damaged, whereas the GFF bridge only suffered minor repairable damages. Damping ratio was shown to have a pronounced effect on FRP-concrete bridges, just the same as in conventional bridges. This research was part of a multi-university project, which is founded by the National Science Foundation (NSF) - Network for Earthquake Engineering Simulation Research (NEESR) program.

Development of thresholds for surface preparation in repair systems with wet lay -up fiber reinforced polymers

Bonded repair of concrete structures with fiber reinforced polymer (FRP) systems is increasingly being accepted as a cost-efficient and structurally viable method of rapid rehabilitation of concrete structures. However, the relationships between long-term performance attributes, service-life, and details of the installation process are not easy to quantify. Accordingly, there is currently a lack of generally accepted construction specifications, making it difficult for the field engineer to certify the adequacy of the construction process. ^ The objective of the present study, as part of the National Cooperative Highway Research Program (NCHRP) Project 10-59B, was to investigate the effect of surface preparation on the behavior of wet lay-up FRP repair systems and consequently develop rational thresholds that provide sufficient performance. ^ The research program was comprised of both experimental and analytical work for wet lay-up FRP applications. The experimental work included flexure testing of sixty-seven (67) reinforced concrete beams and bond testing of ten (10) reinforced concrete blocks. Four different parameters were studied: surface roughness, surface flatness, surface voids and bug holes, and surface cracks/cuts. The findings were analyzed from various aspects and compared with the data available in the literature. As part of the analytical work, finite element models of the flexural specimens with surface flaws were developed using ANSYS. The purpose of this part was to extend the parametric study on the effects of concrete surface flaws and verify the experimental results based on nonlinear finite element analysis. ^ Test results showed that surface roughness does not appear to have a significant influence on the overall performance of the wet lay-up FRP systems with or without adequate anchorage, and whether failure was by debonding or rupture of FRP. Both experimental and analytical results for surface flatness proved that peaks on concrete surface, in the range studied, do not have a significant effect on the performance of wet lay-up FRP systems. However, valleys of particular size could reduce the strength of wet lay-up FRP systems. Test results regarding surface voids and surface cracks/cuts revealed that previously suggested thresholds for these flaws appear to be conservative, as also confirmed by analytical study. ^

Movement Effects on the Flow Physics and Nutrient Delivery in Engineered Valvular Tissues

Mechanical conditioning has been shown to promote tissue formation in a wide variety of tissue engineering efforts. However the underlying mechanisms by which external mechanical stimuli regulate cells and tissues are not known. This is particularly relevant in the area of heart valve tissue engineering (HVTE) owing to the intense hemodynamic environments that surround native valves. Some studies suggest that oscillatory shear stress (OSS) caused by steady flow and scaffold flexure play a critical role in engineered tissue formation derived from bone marrow derived stem cells (BMSCs). In addition, scaffold flexure may enhance nutrient (e.g. oxygen, glucose) transport. In this study, we computationally quantified the i) magnitude of fluid-induced shear stresses; ii) the extent of temporal fluid oscillations in the flow field using the oscillatory shear index (OSI) parameter, and iii) glucose and oxygen mass transport profiles. Noting that sample cyclic flexure induces a high degree of oscillatory shear stress (OSS), we incorporated moving boundary computational fluid dynamic simulations of samples housed within a bioreactor to consider the effects of: 1) no flow, no flexure (control group), 2) steady flow-alone, 3) cyclic flexure-alone and 4) combined steady flow and cyclic flexure environments. We also coupled a diffusion and convention mass transport equation to the simulated system. We found that the coexistence of both OSS and appreciable shear stress magnitudes, described by the newly introduced parameter OSI-t , explained the high levels of engineered collagen previously observed from combining cyclic flexure and steady flow states. On the other hand, each of these metrics on its own showed no association. This finding suggests that cyclic flexure and steady flow synergistically promote engineered heart valve tissue production via OSS, so long as the oscillations are accompanied by a critical magnitude of shear stress. In addition, our simulations showed that mass transport of glucose and oxygen is enhanced by sample movement at low sample porosities, but did not play a role in highly porous scaffolds. Preliminary in-house in vitro experiments showed that cell proliferation and phenotype is enhanced in OSI-t environments.

Regulation of Bone Marrow Stem Cells through Oscillatory Shear Stresses - A Heart Valve Tissue Engineering Perspective

Heart valve disease occurs in adults as well as in pediatric population due to age-related changes, rheumatic fever, infection or congenital condition. Current treatment options are limited to mechanical heart valve (MHV) or bio-prosthetic heart valve (BHV) replacements. Lifelong anti-coagulant medication in case of MHV and calcification, durability in case of BHV are major setbacks for both treatments. Lack of somatic growth of these implants require multiple surgical interventions in case of pediatric patients. Advent of stem cell research and regenerative therapy propose an alternative and potential tissue engineered heart valves (TEHV) treatment approach to treat this life threatening condition. TEHV has the potential to promote tissue growth by replacing and regenerating a functional native valve. Hemodynamics play a crucial role in heart valve tissue formation and sustained performance. The focus of this study was to understand the role of physiological shear stress and flexure effects on de novo HV tissue formation as well as resulting gene and protein expression. A bioreactor system was used to generate physiological shear stress and cyclic flexure. Human bone marrow mesenchymal stem cell derived tissue constructs were exposed to native valve-like physiological condition. Responses of these tissue constructs to the valve-relevant stress states along with gene and protein expression were investigated after 22 days of tissue culture. We conclude that the combination of steady flow and cyclic flexure helps support engineered tissue formation by the co-existence of both OSS and appreciable shear stress magnitudes, and potentially augment valvular gene and protein expression when both parameters are in the physiological range.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Design and analysis of a compliant parallel pan-tilt platform

In combination of the advantages of both parallel mechanisms and compliant mechanisms, a compliant parallel mechanism with two rotational DOFs (degrees of freedom) is designed to meet the requirement of a lightweight and compact pan-tilt platform. Firstly, two commonly-used design methods i.e. direct substitution and FACT (Freedom and Constraint Topology) are applied to design the configuration of the pan-tilt system, and similarities and differences of the two design alternatives are compared. Then inverse kinematic analysis of the candidate mechanism is implemented by using the pseudo-rigid-body model (PRBM), and the Jacobian related to its differential kinematics is further derived to help designer realize dynamic analysis of the 8R compliant mechanism. In addition, the mechanism’s maximum stress existing within its workspace is tested by finite element analysis. Finally, a method to determine joint damping of the flexure hinge is presented, which aims at exploring the effect of joint damping on actuator selection and real-time control. To the authors’ knowledge, almost no existing literature concerns with this issue.

Evaporation maps for ternary non-ideal liquid mixtures

This thesis deals with the evaporation of non-ideal liquid mixtures using a multicomponent mass transfer approach. It develops the concept of evaporation maps as a convenient way of representing the dynamic composition changes of ternary mixtures during an evaporation process. Evaporation maps represent the residual composition of evaporating ternary non-ideal mixtures over the full range of composition, and are analogous to the commonly-used residue curve maps of simple distillation processes. The evaporation process initially considered in this work involves gas-phase limited evaporation from a liquid or wetted-solid surface, over which a gas flows at known conditions. Evaporation may occur into a pure inert gas, or into one pre-loaded with a known fraction of one of the ternary components. To explore multicomponent masstransfer effects, a model is developed that uses an exact solution to the Maxwell-Stefan equations for mass transfer in the gas film, with a lumped approach applied to the liquid phase. Solutions to the evaporation model take the form of trajectories in temperaturecomposition space, which are then projected onto a ternary diagram to form the map. Novel algorithms are developed for computation of pseudo-azeotropes in the evaporating mixture, and for calculation of the multicomponent wet-bulb temperature at a given liquid composition. A numerical continuation method is used to track the bifurcations which occur in the evaporation maps, where the composition of one component of the pre-loaded gas is the bifurcation parameter. The bifurcation diagrams can in principle be used to determine the required gas composition to produce a specific terminal composition in the liquid. A simple homotopy method is developed to track the locations of the various possible pseudo-azeotropes in the mixture. The stability of pseudo-azeotropes in the gas-phase limited case is examined using a linearized analysis of the governing equations. Algorithms for the calculation of separation boundaries in the evaporation maps are developed using an optimization-based method, as well as a method employing eigenvectors derived from the linearized analysis. The flexure of the wet-bulb temperature surface is explored, and it is shown how evaporation trajectories cross ridges and valleys, so that ridges and valleys of the surface do not coincide with separation boundaries. Finally, the assumption of gas-phase limited mass transfer is relaxed, by employing a model that includes diffusion in the liquid phase. A finite-volume method is used to solve the system of partial differential equations that results. The evaporation trajectories for the distributed model reduce to those of the lumped (gas-phase limited) model as the diffusivity in the liquid increases; under the same gas-phase conditions the permissible terminal compositions of the distributed and lumped models are the same.