Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Time Reversed Electromagnetic Wave Propagation as a Novel Method of Wireless Power Transfer

We investigate the application of time-reversed electromagnetic wave propagation to transmit energy in a wireless power transmission system. “Time reversal” is a signal focusing method that exploits the time reversal invariance of the lossless wave equation to direct signals onto a single point inside a complex scattering environment. In this work, we explore the properties of time reversed microwave pulses in a low-loss ray-chaotic chamber. We measure the spatial profile of the collapsing wavefront around the target antenna, and demonstrate that time reversal can be used to transfer energy to a receiver in motion. We demonstrate how nonlinear elements can be controlled to selectively focus on one target out of a group. Finally, we discuss the design of a rectenna for use in a time reversal system. We explore the implication of these results, and how they may be applied in future technologies.

BEHAVIOR OF FIBER REINFORCED POLYMER COMPOSITE PILES WITH ELLIPTICAL CROSS SECTIONS IN INTEGRAL ABUTMENT BRIDGE FOUNDATIONS

Every year in the US and other cold-climate countries considerable amount of money is spent to restore structural damages in conventional bridges resulting from (or “caused by”) salt corrosion in bridge expansion joints. Frequent usage of deicing salt in conventional bridges with expansion joints results in corrosion and other damages to the expansion joints, steel girders, stiffeners, concrete rebar, and any structural steel members in the abutments. The best way to prevent these damages is to eliminate the expansion joints at the abutment and elsewhere and make the entire bridge abutment and deck a continuous monolithic structural system. This type of bridge is called Integral Abutment Bridge which is now widely used in the US and other cold-climate countries. In order to provide lateral flexibility, the entire abutment is constructed on piles. Piles used in integral abutments should have enough capacity in the perpendicular direction to support the vertical forces. In addition, piles should be able to withstand corrosive environments near the surface of the ground and maintain their performance during the lifespan of the bridge. Fiber Reinforced Polymer (FRP) piles are a new type of pile that can not only accommodate large displacements, but can also resist corrosion significantly better than traditional steel or concrete piles. The use of FRP piles extends the life of the pile which in turn extends the life of the bridge. This dissertation studies FRP piles with elliptical shapes. The elliptical shapes can simultaneously provide flexibility and stiffness in two perpendicular axes. The elliptical shapes can be made using the filament winding method which is a less expensive method of manufacturing compared to the pultrusion or other manufacturing methods. In this dissertation a new way is introduced to construct the desired elliptical shapes with the filament winding method. Pile specifications such as dimensions, number of layers, fiber orientation angles, material, and soil stiffness are defined as parameters and the effects of each parameter on the pile stresses and pile failure have been studied. The ANSYS software has been used to model the composite materials. More than 14,000 nonlinear finite element pile models have been created, each slightly different from the others. The outputs of analyses have been used to draw curves. Optimum values of the parameters have been defined using generated curves. The best approaches to find optimum shape, angle of fibers and types of composite material have been discussed.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular we are able to treat "patchy'" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs. Article published and (c) American Physical Society 2007

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Endoscopic sleeve gastroplasty (the Apollo method): a new approach to obesity management

Background: Many obese patients cannot lose weight or reject conventional obesity management. Endoscopic sleeve gastroplasty (the Apollo method) is a pioneering coadjuvant, interventionist technique for the integral management of obesity. Objectives: The goals of this study were to report safety and efficacy results obtained at 6 months in patients undergoing endoscopic sleeve gastroplasty. Material and methods: A prospective study was performed in 55 patients (13 males, 42 females) who were subjected to the Apollo technique; mean age was 43.5 years (range 25-60) and mean BMI was 37.7 kg/m² (range 30-48). All received multidisciplinary follow-up for weight loss. Weight changes and presence of complications were assessed. Through the endoscope a triangular pattern suture is performed consisting of approximately 3-6 transmural (mucosa to serosa) stitches, using a cinch device to bring them nearer and form a plication. Results: A total of 6-8 plications are used to provide a tubular or sleeve-shaped restriction to the gastric cavity. No major complications developed and patients were discharged at 24 hours following the procedure. Endoscopic and radiographic follow-up at 6 months post-procedure showed a well preserved tubular form to the stomach. After 6 months patients had lost 18.9 kg and 55.3% of excess weight. Conclusions: Endoscopic sleeve gastroplasty, together with dietary and psycho-behavioral changes, is a safe, effective technique in the coadjuvant management of obese patients.

Solução semi-analítica para modelagem das condições inicial e de contorno aplicáveis ao ensaio de difusão pura

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2015.

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.

Modelagem univariada e regressão múltipla na análise da oferta e do preço do boi gordo no mercado brasileiro

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Agronomia e Medicina Veterinária, Programa de Pós-Graduação em Agronegócios, 2016.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Modelo de Medición de la Gestión Estratégica Mediante el Empleo de una Estructura de Cuadro de Mando Integral Dirigido a las Empresas Pertenecientes al Sector Manufacturero de Artículos de Talabartería y Guarnicionería en Venezuela

En éste artículo se analiza las características y dimensiones de los indicadores de las Estrategias Genéricas (Porter, 1980) y de los Cuadro de Mando Integral (Kaplan y Norton, 1992), para posteriormente integrarlas y conjugarlas con el propósito de conformar un “Modelo de Medición de la Gestión Estrategia mediante una Estructura del Cuadro de Mando Integral para el Sector Manufacturero de Talabartería y Guarnicionería de Venezuela” (CMI-EGP). Los datos fueron recolectados con dos cuestionarios basados en dimensiones de éstas dos teorías, relacionadas con la alineación entre el recurso humano y la gestión organizacional. Es decir, donde cada dependencia busca alinear los enfoques estratégicos propios de la organización, para así convertirse en un factor de éxito. La metodología empírica empleada esta basada en la técnica de reducción de datos o análisis factorial y por un análisis confirmatorio mediante la técnica Structural Equation Models (SEM), que es una herramienta integral de modelización multiecuacional que fusiona la econometría con los principios de medición de la psicología y la sociología. Esta técnica estadística de análisis multivariante tiene como objetivos primordiales, el aumentar la capacidad explicativa del investigador y la eficacia estadística. La investigación proporciona una modelización confirmatoria que correlaciona las variables latentes y manifiestas, que determinan el grado de relación y alineación entre las cuatro perspectivas de cuadro de mando integral (procesos internos, financieros, del cliente y aprendizaje y crecimiento) y las estrategias genéricas de Porter. Para el procesamiento se emplea el software LISREL versión más reciente 8.8 del año 2009, que es un programa usado en el análisis de ecuaciones estructurales, que fue desarrollado en los años setenta por Karl Jöreskog y Dag Sörbom, ambos profesores de la Universidad de Upsala, Suecia.

Muito além da tecnologia : o impacto dos mecanismos não operacionais na efetividade da governança de TI na administração pública

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Economia, Administração e Contabilidade, Programa de Pós-Graduação em Administração, 2016.

Otimização evolucionária para problemas de transferência de calor em PCI usando MEC

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Programa de Pós-graduação em Integridade de Materiais da Engenharia, 2015.

Projeto conceitual de um instrumento para avaliar o estado de compactação do solo

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2016.

Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model

We predict macroscopic fracture related material parameters of fully exfoliated clay/epoxy nano- composites based on their fine scale features. Fracture is modeled by a phase field approach which is implemented as user subroutines UEL and UMAT in the commercial finite element software Abaqus. The phase field model replaces the sharp discontinuities with a scalar damage field representing the diffuse crack topology through controlling the amount of diffusion by a regularization parameter. Two different constitutive models for the matrix and the clay platelets are used; the nonlinear coupled system con- sisting of the equilibrium equation and a diffusion-type equation governing the phase field evolution are solved via a NewtoneRaphson approach. In order to predict the tensile strength and fracture toughness of the clay/epoxy composites we evaluated the J integral for different specimens with varying cracks. The effect of different geometry and material parameters, such as the clay weight ratio (wt.%) and the aspect ratio of clay platelets are studied.