An efficient numerical method for solving Schr&ouml / dinger&#039 / s and Poisson&#039 / s equations using a basis set of cubic B-splines is investigated. The method is applied to find both the wave functions and the corresponding eigenenergies of low-dimensional semiconductor structures. The computational efficiency of the method is explicitly shown by the multiresolution analysis, non-uniform grid construction and imposed boundary conditions by applying it to well-known single electron potentials. The method compares well with the results of analytical solutions and of the finite difference method.

[pt] As correntes de turbidez são fluxos gravitacionais que têm uma densidade mais elevada do que o seu entorno, sendo caracterizadas por terem uma aparência turbulenta e por moverem-se com uma alta velocidade, realizando um processo de transferência de sedimentos. O problema abordado nesta tese é a modelagem de depósitos turbidíticos baseada em um modelo deposicional com três lobos turbidíticos. A principal contribuição foi desenvolver um modelo baseado em objectos usando B-Splines univalorados para simular reservatórios de turbiditos em um grade cartesiana regular. / [en] Turbidity currents are gravitational flows that have higher density than its surroundings, and they are characterized by having a turbulent appearance and by moving at high speed carrying out a transfer process sediment. The problem addressed in this thesis is the modelling of turbidities deposits. It will be taken based on a depositional model that contains three turbidities lobes. Our contribution is to develop a object-based model using Single-valued B-Spline to simulate turbidities reservoirs in a regular Cartesian grid.

Paper A: In this paper, the development and implementation of a contact algorithm based on C2-continuous surface representations is discussed. In 3D contact simulations involving models with arbitrarily curved surfaces (as in the case of vessel walls), the discretization of the contact surfaces by means of facet-based techniques could lead to numerical instabilities and finally loss of quadratic convergence. These instabilities arise mainly due to the sliding of contractor (slave) nodes over the boundaries of target (master) contact facets, where jumps of the normal vector are experienced. The paper addresses successfully this problem, by discretization of the target surfaces by means of C2-continuous parameterization schemes. Initially, the uniform cubic B-spline surfaces are introduced. Next, in an attempt for more accurate representations of the geometric models of the contact surfaces, a new parameterization based on the expression of cubic B-splines is developed. The two approaches are implemented into a finite element framework and more specifically, into the multipurpose finite element analysis program FEAP. The special merits of the developed algorithms and the advantages of the smooth surfaces over facet-based approaches are exhibited through a classical contact mechanics problem, considering incompressibility, finite deformations and large slidings. Next, a simulation of balloon angioplasty with stenting is presented, where the contact between both medical devices (balloon and stent) with the arterial wall is modeled. The arterial wall is modeled in this first approach, as hyperelastic, homogeneous, isotropic, while a cylindrically orthotropic model is developed to capture the nonlinear, anisotropic behavior of the balloon catheter under pressure. Two stents with the same geometry but different strut thickness, are studied. Both are considered elasto-plastic. The performed simulations point out the outcome of the balloon angioplasty and stenting in terms of luminal gain and mechanical strains. Finally, a comparison between the two stent configurations is presented. Paper B: The second paper makes use of the contact tool developed in Paper A and focuses on the changes of the mechanical environment of the arterial wall due to stenting, as a function of a set of stent design parameters. In particular, Paper B presents a detailed geometric and material model of a postmortem human iliac artery, composed by distinct tissue components, each associated with specific mechanical properties. The constitutive formulation for the artery considers anisotropic, highly nonlinear mechanical characteristics under supraphysiological loadings. The material and structural parameters of the arterial model are obtained through uniaxial tensile tests on stripes extracted from the several arterial tissues that form the stenosis, axially and circumferentially oriented. Through cooperation with a well-established stent manufacturing company, an iliac stent was acquired. The dimensions of the stent are measured under a reflected-light microscope, while it is parameterized in such a way as to enable new designs to be simply generated through variations of its geometric parameters. The 3D balloon-stent-artery interaction is simulated by making use of the smooth contact surfaces with C2-continuity, as previously mentioned. Next, scalar quantities attempt to characterize the arterial wall changes after stenting, in form of contact forces induced by the stent struts, stresses within the individual components and luminal change. These numerically derived quantities allow the determination of the most appropriate stent configuration for an individual stenosis. Therefore, the proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures, stent material and geometries on a patient-specific level. / <p>QC 20101118</p>

Non-uniform rational B-splines (NURBS) methodology is presented, on which the isogeometric analysis is based. T-splines are also introduced as a surface design methodology, which are a generalization of NURBS and permit local refinement. Isogeometric analysis using NURBS and T-splines are applied separately to a structural mechanics problem. The results are compared with the closed-form solution. The desirable performance of isogeometric analysis using T-splines on engineering analysis is demonstrated.

No description available.

Ce travail est motivé par la spectroscopie de photoélectrons et l'étude de la cinématique des galaxies où les données correspondent respectivement à une séquence temporelle de spectres et à une image multispectrale. L'objectif est d'estimer les caractéristiques (amplitude, position spectrale et paramètre de forme) des raies présentes dans les spectres, ainsi que leur évolution au sein des données. Dans les applications considérées, cette évolution est lente puisque deux spectres voisins sont souvent très similaires : c'est une connaissance a priori qui sera prise en compte dans les méthodes développées. Ce problème inverse est abordé sous l'angle de la séparation de sources retardées, où les spectres et les raies sont attribués respectivement aux mélanges et aux sources. Les méthodes de l'état de l'art sont inadéquates car elles supposent la décorrélation ou l'indépendance des sources, ce qui n'est pas le cas. Nous tirons parti de la connaissance des sources pour les modéliser par une fonction paramétrique. Nous proposons une première méthode de moindres carrés alternés : les paramètres de formes sont estimés avec l'algorithme de Levenberg-Marquardt, tandis que les amplitudes et les positions sont estimées avec un algorithme inspiré d'Orthogonal Matching Pursuit. Une deuxième méthode introduit un terme de régularisation pour prendre en compte l'évolution lente des positions; un nouvel algorithme d'approximation parcimonieuse conjointe est alors proposée. Enfin, une troisième méthode contraint l'évolution des amplitudes, positions et paramètres de forme par des fonctions B-splines afin de garantir une évolution lente conforme au physique des phénomènes observés. Les points de contrôle des B-splines sont estimés par un algorithme de moindre carrés non-linéaires. Les résultats sur des données synthétiques et réelles montrent que les méthodes proposées sont plus efficaces que les méthodes de l'état de l'art et aussi efficaces qu'une méthode bayésienne adaptée au problème mais avec un temps de calcul sensiblement réduit. / This work is motivated by photoelectron spectroscopy and the study of galaxy kinematics where data respectively correspond to a temporal sequence of spectra and a multispectral image. The objective is to estimate the characteristics (amplitude, spectral position and shape) of peaks embedded in the spectra, but also their evolution within the data. In the considered applications, this evolution is slow since two neighbor spectra are often very similar: this a priori knowledge that will be taken into account in the developed methods. This inverse problem is approached as a delayed source separation problem where spectra and peaks are respectively associated with mixtures and sources. The state-of-the-art methods are inadequate because they suppose the source decorrelation and independence, which is not the case. We take advantage of the source knowledge in order to model them by a parameterized function. We first propose an alternating least squares method: the shape parameters are estimated with the Levenberg-Marquardt algorithm, whilst the amplitudes and positions are estimated with an algorithm inspired from Orthogonal Matching Pursuit. A second method introduces a regularization term to consider the delay slow evolution; a new joint sparse approximation algorithm is thus proposed. Finally, a third method constrains the evolution of the amplitudes, positions and shape parameters by B-spline functions to guarantee their slow evolution. The B-spline control points are estimated with a non-linear least squares algorithm. The results on synthetic and real data show that the proposed methods are more effective than state-of-the-art methods and as effective as a Bayesian method which is adapted to the problem. Moreover, the proposed methods are significantly faster.

Exploration is a fundamental problem in robotics that requires robots to navigate through unknown environments to autonomously gather information about their surroundings while executing collision-free paths. In this project, we propose a method for producing smooth paths during the exploration process in indoor environments using UAVs to improve battery efficiency and enhance the quality of pose estimation. The developed framework is built by merging two approaches that represent the state of the art in the field of autonomous exploration with UAVs. The overall exploration logic is given by GLocal, a paper that introduces a hybrid, i.e. both sampling-based and frontier-based, framework that is able to cope with the issue of odometry drift when exploring indoor environments due to the absence of absolute localization, e.g. through GNSS. The second approach is FUEL, which introduces a frontier-based exploration methodology which computes the ’drones path as an optimized non-uniform B-Spline. The framework described in this thesis borrows the optimized B-Spline trajectory generation from FUEL and implements it in GLocal. To do this, the original cost function defined by GLocal for each exploration viewpoint was modified and the resulting samples were used to select the initial control points of the B-Spline. Furthermore, we extended the underlying state machine governing the entire algorithm and we revisited the original re-planning logic. The presented system is evaluated in various simulated environments, showcasing the advantages and disadvantages of this method. These evaluations demonstrate its improved state estimation performance and absolute observed volume, albeit at the expense of longer traveled trajectories in big and complex environments. / Utforskning är ett grundläggande problem inom robotteknik som kräver att robotar navigerar genom okända miljöer för att autonomt samla in information om sin omgivning samtidigt som de utför kollisionsfria banor. I det här projektet föreslår vi en metod för att producera jämna banor under utforskningsprocessen i inomhusmiljöer med hjälp av UAV:er för att förbättra batterieffektiviteten och förbättra kvaliteten på posestimeringen. Det utvecklade ramverket bygger på en sammanslagning av två metoder som representerar den senaste tekniken inom autonom utforskning med UAV:er. Den övergripande utforskningslogiken ges av GLocal, en artikel som introducerar en hybrid, i.e. både samplingsbaserad och gränsbaserad, ram som kan hantera problemet med odometridrift vid utforskning av inomhusmiljöer på grund av frånvaron av absolut lokalisering, e.g. genom GNSS. Den andra metoden är FUEL, som introducerar en gränsbaserad utforskningsmetod som beräknar drönarens bana som en optimerad icke-uniform B-Spline. Ramverket som beskrivs i denna avhandling lånar den optimerade B-Spline-banegenereringen från FUEL och implementerar den i GLocal. För att göra detta modifierades den ursprungliga kostnadsfunktionen som definierades av GLocal för varje utforskningspunkt och de resulterande samplen användes för att välja de initiala kontrollpunkterna för B-Spline. Dessutom utökade vi den underliggande tillståndsmaskinen som styr hela algoritmen och vi reviderade den ursprungliga logiken för omplanering. Det presenterade systemet utvärderas i olika simulerade miljöer, vilket visar fördelarna och nackdelarna med denna metod. Dessa utvärderingar visar på förbättrad prestanda för tillståndsuppskattning och absolut observerad volym, om än på bekostnad av längre färdvägar i stora och komplexa miljöer.

Un nouvel point de vue est proposé pour la simulation des plasmas utilisant le modèle cinétique qui couple les équations de Vlasov pour la distribution des particules et les équations de Maxwell pour la contribution des champs électromagnétique. On part du principe que les équations de la Physique sont des objets mathématiques qui mettent en relation des objets géométriques. Afin de conserver les propriètés géométriques des différents objets intervenant dans une équation, on utilise, pour l'étude théorique et numérique, la géométrie différentielle. Il s'avère que toutes les équations de la Physique peuvent s'écrire à l'aide des formes différentielles et que sous ce point de vue celles-ci sont indépendantes du choix des coordonnées. On propose alors une discrétisation des formes différentielles en utilisant les B-splines comme fonctions d'interpolation. Afin d'être cohérent avec la théorie, on proposera également une discrétisation des différentes opérations de la géométrie différentielle agissant sur les formes différentielles. On teste notre schéma tout d'abord sur les équations de Maxwell avec plusieurs conditions aux bords et puisque ce schéma numérique obtenu est indépendant du système de coordonnées, on le teste également lorsque l'on effectue un changement de coordonnées. Enfin, on applique la même méthode sur les équations de Vlasov-Poisson 1D et on propose plusieurs schémas numériques.

Deformable image registration (DIR) is an essential tool in medical image processing. It provides a means to combine image datasets, allowing for intra-subject, inter-subject, multi-modality, and multi-instance analysis, as well as motion detection and compensation. One of the most popular DIR algorithms models the displacement vector field (DVF) as B-splines, a sum of piecewise polynomials with coefficients that enable local shape control. B-splines have many advantageous properties in the context of DIR, but they often struggle to adequately model steep local gradients and discontinuities. This dissertation addresses that limitation by proposing the replacement of conventional B-splines with a generalized formulation known as a Non-Uniform Rational B-Splines (NURBS). Beginning with the 1D fitting, heuristic rules are developed to determine the values of the additional free parameters introduced by NURBS. These rules are subsequently modified and extended to the 2D and 3D fitting of anonymized and publicly available patient DVFs. Based on the lessons learned from these increasingly complex test cases, a 2D DIR scheme is developed and tested on slices from a thoracic computed tomography (CT) scan. Finally, an automatic, non-uniform scheme is presented, and its registration performance is compared to the conventional uniform methods.

Devido à constante necessidade de construções de novas embarcações, quer seja pela demanda do mercado, quer seja pela renovação da frota, o desenvolvimento de programas computacionais que auxiliem na fase inicial de projeto torna-se bastante útil. Assim, o desenvolvimento de um procedimento de análise que permita obter formas de melhor desempenho vem a agregar valor nesta etapa de conceituação da geometria do navio. O trabalho aqui apresentado tem como objetivo discorrer sobre um método capaz de otimizar a geometria de um casco de deslocamento conhecido em relação a sua resistência ao avanço, sem perder, porém, as suas características principais, como corpo paralelo médio, por exemplo. Para tanto, dentro deste processo de otimização já estão inseridas algumas restrições que garantem a viabilidade da solução final, tais como variação máxima no comprimento, no volume total e na estabilidade do navio. A modelagem da embarcação pode ser feita através de funções B-Splines cúbicas de superfície, cujos pontos de controle (parâmetros inerentes à função) podem ser modificados de tal sorte a atingir um valor ótimo para a resistência ao avanço. Esta, por sua vez, será obtida através da soma de duas parcelas, sendo uma referente ao atrito e outra à geração de ondas pelo casco. Como a maior parte da resistência provém desta segunda parcela para a velocidade de projeto a ser considerada (alto número de Froude), a redução da resistência total pode ser assumida como conseqüência da diminuição da resistência devido à geração de ondas, a qual pode ser obtida através da formulação apresentada por Michell, em 1898. O cálculo das propriedades hidrostáticas como deslocamento, estabilidade ( KM transversal) e superfície molhada, usada para cálculo da resistência ao avanço, pode ser encontrado fazendo-se uso do cálculo vetorial. O procedimento a ser descrito foi desenvolvido em linguagem C++ (modelagem do casco) e com o auxílio do MATLAB® (método de otimização). Este trabalho foi realizado no Dep. de Eng. Naval e Oceânica da USP. / Due to an increasing necessity of building new vessels, whether by new orders or fleet renewal, the development of computational programs that could allow optimization of hull shapes is always helpful, saving project time and ensuring better performance at sea. Thus, the development of a synthesis procedure that allows obtaining shapes with better performance adds value to the initial phase of the ship geometry concept. The work to be presented herein objectives the presentation of a methodology to achieve optimal shapes for displacement hulls in relation to the total resistance, starting from an initial geometry given, describing hull form and applying specific constraints to optimization problem with the purpose of guarantee a reliable solution. Therefore, inside this optimization process there are included some constraints that ensure a feasible final solution, as maximum variation of ship length, total volume and stability. Hull geometry is described by using B-Spline surface functions and the ship wave resistance is calculated using Michell\'s formulation as a first approximation of the total resistance for high Froude numbers. Once vessel surface is well defined, B-Spline parameters are varied until an optimal form is attained and the minimum resistance is achieved. It can take a little time to calculate, depending on ship definition (number of buttocks and waterlines) and the problem complexity (number of constraints and variables). Ship displacement and other hydrostatic properties as stability, given by transversal KM , wetted surface, used for calculating ship resistance, can be obtained using the vectorial calculus. This work has been developed using C++ language, except the optimization process which makes use of a MATLAB® function called fmincon. This study has been held at the Department of Naval and Ocean Engineering of the University of São Paulo, Brazil.