Nesta dissertação vamos estudar alguns importantes resultados acerca da resolubilidade local de operadores lineares de primeira ordem. Mais especificamente, seja o campo vetorial singular L em \'R POT. n\' e dado por: L = \'\\SIGMA SUP. m\' . INF. j=1\' a IND. j\' (x) \'SUP. \\PARTIAL\' INF. \\PARTIAL x INF. j\'. Esta trabalho dirige-se ao estudo da resolubilidade local de L, isto é, dada f \'PERTENCE A\' \' C POT. INFINITO\' (\'R POT. n\') e dado \'x IND. 0\' \'PERTENCE A\' \'R POT. n queremos encontrar u \'PERTENCE A\' D\'(\'R POT.n \') tal que Lu = f numa vizinhança de \'x INF. 0\'. Será dada atenção especial ao caso em que os coeficientes \'a IND. j\'(x) de L são função lineares. Também, serão apresentados resultados sobre a resolubilidade local da equação Lu = cu + f, sendo c \'PERTENCE A\' \'C POT. INFINITO\' (\'R POT. n\') / This dissertation aims to study some important results about local solvability of first order differential operators. Specifically, let L be a singular vector field on \'R POT. n\' given by L = \' \\SIGMA SUP. m INF.j=1\' \'a IND. j(x) \'\\PARTIAL SUP. INF. \\PARTIAL x INF. j\'. This work explore the local solvability of L, that is, given f \'IT BELONGS\' \'C POT. INFINITY\' (\'R POT. n\' and \'x INF. 0\' \'IT BELONGS\' \'R POT. n\' we want to find u \'IT BELONGS\' 2 D\'(\'R POT. n) such that Lu = f in a neighborhood of \'x INF. 0\'. We give special attention to the case where the coefficients \'a IND. j\'(x) are linear. We also present some results about local solvability of the equation Lu = cu + f for c \'IT BELONGS\' \'C POT. INFINITY\' (\'R POT. n\')

Orientador: Eleri Cardozo / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-26T06:38:13Z (GMT). No. of bitstreams: 1 Olivi_LeonardoRocha_D.pdf: 17712423 bytes, checksum: a9b0ec521405e93735844f7ce8b3b968 (MD5) Previous issue date: 2014 / Resumo: A mobilidade é uma competência humana extremamente valiosa, e pode ser perdida por diversas razões, tais como traumas na coluna vertebral, acidentes vasculares cerebrais, dentre outras. Algumas tecnologias desenvolvidas para as áreas médicas, como eletroencefalografia e eletromiografia, podem ser empregadas no desenvolvimento de Interfaces Humano-Máquina (Human-Machine Interface, ou, HMI) com o objetivo de permitir que pessoas com capacidades motoras severamente comprometidas possam comunicar e operar os mais diversos equipamentos. Assim, esses usuários podem conduzir robôs móveis por meio de uma HMI adaptada para suas capacidades motoras e cognitivas. Entretanto, essas interfaces apresentam erros na identificação da ação pretendida pelo usuário, os quais comprometem sobremaneira a experiência desse usuário na interação com o mundo exterior. Para o caso dos robôs móveis assistivos, o conceito de controle compartilhado (shared control) foi concebido para compensar as taxas de erros das HMIs, e a responsabilidade pela navegação do robô é dividida entre o usuário e um sistema supervisor automático. As abordagens mais populares na literatura comutam poucos modos de comportamentos específicos para situações individualizadas, como passagens estreitas e desvio de obstáculos. Esta tese propõe uma nova técnica de controle compartilhado, denominada de navegação assistida por campos vetoriais, a qual não possui modos de operação chaveados, evitando quaisquer instabilidades e abrangendo as configurações do ambiente de maneira ilimitada, além de minimizar significativamente os erros gerados pelas HMIs e facilitar a navegação do usuário. Os campos vetoriais oferecem as navegações manual e autônoma, ampliando a interação do usuário com o ambiente. Nessa nova técnica, o sistema de controle embarcado irá executar a ação identificada pela HMI em função dos estados do robô e do ambiente, com o objetivo de maximizar a segurança e capacidade de controle do usuário. Os resultados mostrados neste trabalho evidenciam uma nova forma de tratar o problema, obtendo ganhos significativos com relação ao estado da arte, com baixa complexidade computacional, alta flexibilidade a ambientes e usuários e otimização efetiva de erros, contribuindo para a recuperação da mobilidade dos usuários / Abstract: Human mobility is an extremely valued skill that can be lost due to various reasons, such as spinal cord injuries, strokes, amputations, among others. Technologies developed for the medical areas, such as electroencephalography and electromyography, can be employed in the development of Human-Machine Interfaces (HMI) with the objective of allowing people with severe mobility impairments to communicate and to operate a wide range of equipments. Therefore, these users are allowed to conduct assistive robots allow through a HMI designed according to the user's mobility and cognitive skills. However, these interfaces still present low performance in the correct identification of the intended action by the user, which severely compromise the experience of the user when interacting with external world. In the specific case of assistive mobile robots, a shared control concept was developed in order to compensate the high error rates produced by the HMIs, where the responsibility for the navigation of the mobile robot is shared among the user and an autonomous supervisor system. The mainly approaches shown in literature switch a few modes of specific behavior for individualized situations, such as narrow corridors and obstacle avoidance. This work presents a novel shared control technique, named assistive navigation by vector fields, which does not employ switching modes, avoiding any instabilities and covering the unlimited environment configurations, significantly minimizing the HMI errors, facilitating the user's navigation. The vector fields offer both manual and autonomous navigation, increasing the user's interaction with the environment. In this novel technique, the embedded control system incorporates the HMI command with the robot and environment states, aiming the maximization of user's security and control capabilities. Results shown a novel manner for treating the problem, obtaining substantial gains over the state of art works, with low computational complexity, high flexibility concerning environments and users and effective optimization of errors, contributing for the user's mobility retrieval / Doutorado / Automação / Doutor em Engenharia Elétrica

Context. Particle systems and particle effects are used to simulate a realistic and appealing atmosphere in many virtual environments. However, they do occupy a significant amount of computational resources. The demand for more advanced graphics increases by each generation, likewise does particle systems need to become increasingly more detailed. Objectives. This thesis proposes a texture-based 3D vector field particle system, computed on the Graphics Processing Unit, and compares it to an equation-based particle system. Methods. Several tests were conducted comparing different situations and parameters for the methods. All of the tests measured the computational time needed to execute the different methods. Results. We show that the texture-based method was effective in very specific situations where it was expected to outperform the equation-based. Otherwise, the equation-based particle system is still the most efficient. Conclusions. Generally the equation-based method is preferred, except for in very specific cases. The texture-based is most efficient to use for static particle systems and when a huge number of forces is applied to a particle system. Texture-based vector fields is hardly useful otherwise.

Orientador: Fabiano Borges da Silva / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T12:59:08Z (GMT). No. of bitstreams: 1 Fernandes_AristonLopes_M.pdf: 1807643 bytes, checksum: 1b8f6422f12372fd95aefa1b55d12fc7 (MD5) Previous issue date: 2011 / Resumo: Este trabalho tem como propósito estudar trajetórias geradas por sistemas hamiltonianos no plano. Para isso, são analisados os diversos tipos de retratos de fase dos sistemas lineares planares e a classificação destes. Sistemas hamiltonianos surgiram na mecânica clássica e seus pontos de equilíbrio são classificados em selas ou centros, conforme os sinais dos autovalores da matriz do sistema linearizado. Além disso, é apresentada a relação entre campos de vetores hamiltonianos e espaços vetoriais simpléticos / Abstract: This work has the objective of studing trajectories generated by Hamiltonian systems on the plane. For this, we analyse the various types of phase portraits of planar and linear systems. Hamiltonian systems have emerged in the mechanical and their classical equilibrium points are classified into saddles or centers, as the signs of the eigenvalues of linearized system matrix. We have also illustrated the connection between Hamiltonian vector fields and symplectic spaces / Mestrado / Matemática Universitária / Mestre em Matemática Universitária

We describe the space of polynomial fields tangent to a given an algebraic curve. / Se da una descripción del espacio de campos polinomiales tangentes a una curva algebraica dada.

Vortex detection has been a long-standing and challenging topic in fluid analysis. Recent state-of-the-art extraction and visualization of vortices in unsteady fluid flow employ objective vortex criteria, which makes feature extraction independent of reference frames or observers. However, even objectivity can only guarantee that different observers reach the same conclusions, but not necessarily guarantee that these conclusions are the only physically meaningful or relevant ones. Moreover, a significant challenge is that a single observer is often not sufficient to accurately observe multiple vortices that follow different motions. This thesis presents a novel mathematical framework that represents physically realizable observers as the Lie algebra of the Killing fields on the underlying manifold, together with a software system that enables the exploration and use of an interactively chosen set of observers, resulting in relative velocity fields and objective vortex structures in real-time. Based on our mathematical framework, our system facilitates the objective detection and visualization of vortices relative to well-adapted reference frame motions, while at the same time guaranteeing that these observers are physically realizable. We show how our framework speeds up the exploration of objective vortices in unsteady 2D flow, on planar as well as on spherical domains.

It is a challenging task to visualize the behavior of time-dependent 3D vector fields. Most of the time an overview of unsteady fields is provided via animations, but, unfortunately, animations provide only transient impressions of momentary flow. In this paper we present two approaches to visualize time varying fields with fixed geometry. Path lines and streak lines represent such a steady visualization of unsteady vector fields, but because of occlusion and visual clutter it is useless to draw them all over the spatial domain. A selection is needed. We show how bundles of streak lines and path lines, running at different times through one point in space, like through an eyelet, yield an insightful visualization of flow structure ('eyelet lines'). To provide a more intuitive and appealing visualization we also explain how to construct a surface from these lines. As second approach, we use a simple measurement of local changes of a field over time to determine regions with strong changes. We visualize these regions with isosurfaces to give an overview of the activity in the dataset. Finally we use the regions as a guide for placing eyelets.

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The superline has one even and one odd coordinate. We consider the Lie superalgebra of contact vector fields on the superline. Its tensor density modules are a one-parameter family of deformations of the natural action on the ring of polynomials on the superline. They are parameterized by a complex number, and they are irreducible when this parameter is not zero. In this dissertation, we describe the annihilating ideals of these representations in the universal enveloping algebra of this Lie superalgebra by providing their generators. We also describe the intersection of all such ideals: the annihilator of the direct sum of the tensor density modules. The annihilating ideal of an irreducible non-zero left module is called a primitive ideal, and the space of all such ideals in the universal enveloping algebra is its primitive spectrum. The primitive spectrum is endowed with the Jacobson topology, which induces a topology on the annihilators of the tensor density modules. We conclude our discussion with a description of the annihilators as a topological space.