Orientador: Cleonice Fátima Bracciali / Banca: Rosana Sueli da Motta Jafelice / Banca: Alagacone Sri Ranga / Resumo: O objetivo deste trabalho é estudar os polinômios de Szegõ, que são ortogonais no círculo unitário, e suas relações com certas frações contínuas de Perron-Carathéodory e quadratura no círculo unitário, afim de resolver o problema de momento trigonométrico. Além disso, estudar a utilização dos polinômios de Szegõ na determinação das freqüências de um sinal trigonométrico em tempo discreto xN(m). Para isso, investigamos os polinômios de Szegõ gerados por uma medida N definida através do sinal trigonométrico xN(m), para m = 0, 1, 2, ...N -1, e o comportamento dos zeros desses polinômios quando N_8. / Abstract: The purpose here is to study the orthogonal polynomials on the unit circle, known as Szegõ polynomials, and the relations to Perron- Carathéodory continued fractions, and quadratures on the unit circle in order to solve the trigonometric moment problem. Another purpose is to study how the Szegõ polynomials can be used to determine the frequencies from a discrete time trigonometric signal xN(m). We investigate the Szegõ polynomials associated with a measure N defined by the trigonometric sinal xN(m), m = 0, 1, 2, ...N -1. We study the behaviour of zeros of these polynomials when N 8. / Mestre

abstract: Nonregular screening designs can be an economical alternative to traditional resolution IV 2^(k-p) fractional factorials. Recently 16-run nonregular designs, referred to as no-confounding designs, were introduced in the literature. These designs have the property that no pair of main effect (ME) and two-factor interaction (2FI) estimates are completely confounded. In this dissertation, orthogonal arrays were evaluated with many popular design-ranking criteria in order to identify optimal 20-run and 24-run no-confounding designs. Monte Carlo simulation was used to empirically assess the model fitting effectiveness of the recommended no-confounding designs. The results of the simulation demonstrated that these new designs, particularly the 24-run designs, are successful at detecting active effects over 95% of the time given sufficient model effect sparsity. The final chapter presents a screening design selection methodology, based on decision trees, to aid in the selection of a screening design from a list of published options. The methodology determines which of a candidate set of screening designs has the lowest expected experimental cost. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

Cette thèse traite de la réduction d’ordre de modèle du phénomène communément rencontré dans la modélisation de microsystèmes, à savoir, dans la littérature anglaise, le « squeeze-film damping ». Dans un premier chapitre sont présentées les différentes méthodes de réduction d’ordre de modèle. Dans le cas des systèmes linéaires, elles ont un cadre théorique bien établi. Ces méthodes peuvent être adaptées pour les systèmes non-linéaires. La validité des modèles réduits résultants sera alors réduite à un certain espace des phases, leur établissement faisant intervenir certaines trajectoires particulières servant d’apprentissage. On présente finalement la méthode des modes normaux non-linéaires dont les modèles résultants ne dépendent pas d’une trajectoire d’apprentissage. Au chapitre 2, on s’intéresse plus particulièrement au phénomène de « squeeze-film damping » régi par l’équation de Reynolds. Après avoir détaillé son établissement à partir de certaines hypothèses, on décrit les différentes méthodes de résolution de l’équation linéaire puis non-linéaire de la littérature. On compare ensuite les résultats d’un modèle de l’équation de Reynolds à des simulations éléments finis de l’équation de Navier-Stokes afin de valider les hypothèses faites pour la dérivation de l’équation de Reynolds. On propose ensuite une résolution originale par changement de variable. On étudie aussi plusieurs autres résolutions possibles ainsi que plusieurs bases de projection parmi celles décrites dans le premier chapitre. Le chapitre 3 est consacré à la modélisation du problème couplé que constitue le micro-interrupteur MEMS qui est un candidat au remplacement des interrupteurs à base de transistors dans les communications RF. Sa modélisation fait intervenir trois domaines, la mécanique, l’électrostatique, et la fluidique à travers l’équation de Reynolds. Après voir décrit les différents modèles de la littérature, on propose un modèle réduit couplé dont le modèle fluidique est basé sur le modèle établi au chapitre 2. Ce modèle est validé par rapport à des modèles différences finies et à des résultats expérimentaux de la littérature.Enfin le quatrième chapitre traite de la réduction du coût d’évaluation du modèle réduit couplé de micro-interrupteur du chapitre 3. La première méthode proposée consiste à trouver une fonction d’approximation de la projection de la force fluidique sur le premier mode mécanique, fonction des coordonnées modales mécaniques position et vitesse. Cette méthode ne se révèle valable que dans le cas incompressible. Dans le cas compressible, la résolution de l’équation de Reynolds restant obligatoire, on utilise la méthode de Rewienski et al. qui consiste à linéariser par morceaux les fonctions régissant la dynamique. Une autre méthode de linéarisation par morceaux, tirant parti d’une particularité du modèle du chapitre 2 et permettant de s’affranchir d’une trajectoire d’apprentissage, est également proposée. / This thesis deals with reduced-order modelling of squeeze-film damping, a fluidic phenomenon that is commonly encountered in MEMS. In the first chapter, reduced-order modelling methods are presented. For linear systems, well-established theories exist. They can be adapted to nonlinear systems. However, the resulting reduced-order models are valid in a certain region of the state-space only, depending on the training trajectory. The method of nonlinear normal modes, which does not depend on a training trajectory is also introduced. Chapter two is focused on the squeeze-film damping phenomenon governed by the Reynolds equation. We first establish the equation from appropriate hypotheses, and then present the different resolutions of its linear and nonlinear form found in literature. The results from a model based on the Reynolds equation are then compared to results from a finite element Navier-Stokes model, in order to validate the various hypotheses made. An original method of resolution based on a change of variable is then proposed. Several other method of resolution are studied as well as different projection bases amongst those presented in chapter one.Chapter three is dedicated to the modelling a micro-switch, a candidate to the replacement of switches based on transistors in RF communications. Its modelling implies the coupling of three domains: mechanics, electrostatics, and fluidics with Reynolds equation. Following a description of the models from literature, a coupled model is proposed, the fluidic model being the one presented in chapter two. This model is validated compared to finite difference models as well as experimental data from the literature.Finally, the fourth chapter aims at reducing the evaluation cost of the coupled micro-switch model established in chapter three. The first method consists in finding an approximation function of the projection of the fluidic force on the first linear mechanical mode as a function of the mechanical modal coordinates, position and speed. This method is applicable in the incompressible case only. In the compressible case, the Reynolds equation has to be solved. The method of Rewienski and al., which consists in piecewise-linearizing the functions governing the dynamics, is used. Another method based on a piecewise-linear approach, taking advantage of the particular structure of the model presented in chapter two, thus not depending on a training trajectory, is proposed.

Orientadores: Sergio Antonio Tozoni, Alexander Kushpel / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T21:23:04Z (GMT). No. of bitstreams: 1 Oliveira_FernandaMourade_M.pdf: 1054228 bytes, checksum: 75fe14a8c8e718328bbee826a80d14ae (MD5) Previous issue date: 2005 / Resumo: O objetivo da dissertação e desenvolver um texto em português sobre Análise Harmônica na esfera d-dimensional real e aplicar os resultados deste texto no estudo de um teorema de multiplicadores. Nos dois primeiros capítulos e realizado um estudo sobre funções harmônicas em um domínio do espaço euclidiano Rd+1, harmônicos esféricos, representações de SO(d+1), harmônicos zonais, polinômios ultraesféricos e sobre o operador de Laplace Beltrami para a esfera. Finalmente, no terceiro capítulo é estudado um teorema de multiplicadores recente, o qual fornece condições suficientes para que um operador multiplicador seja limitado de Lp(Sd) em Lq(Sd), para quaisquer p e q, 1=p, q=8. Como aplicação deste teorema são obtidas estimativas superiores para n-larguras de Kolmogorov de classes de Sobolev nos espaços Lq(Sd), 1=p, q= 8, g > 0 / Abstract: The purpose of this work is to develop a text in Portuguese about Harmonic Analysis on the d-dimensional real sphere Sd and to apply the results of the text to study a multiplier theorem. In the first two chapters it is made a study about harmonic functions in a domain of the euclidian space Rd+1, spherics harmonics, representations of SO(d+1), zonal harmonics, ultraspherics polynomials and about the Laplace Beltrami operator on the sphere. Finally, in the third chapter it is studied a recent multiplier theorem which gives sufficient conditions for a multiplier operator be bounded from Lp(Sd) to Lq(Sd), for 1=p, q=8. As application of this theorem are obtained upper bounds for n-widths of Kolmogorov type of Sobolev classes in the spaces Lq(Sd), 1=p, q= 8, g > 0 / Mestrado / Matematica / Mestre em Matemática

Orientadores: Dimitar Kolev Dimitrov, Roberto Andreani / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-23T19:23:17Z (GMT). No. of bitstreams: 1 Yen_ChiLun_D.pdf: 3950162 bytes, checksum: 1812f3dd736abbe2d4ff070c7877fdff (MD5) Previous issue date: 2013 / Resumo: O objetivo deste trabalho é apresentar uma nova formulação do Teorema de comparação de Sturm e suas aplicações na teoria dos zeros de polinômios ortogonais, que são: monotonicidade dos zeros dos polinômios ortogonais X1-Jacobi, desigualdades de Gautschi sobre os zeros dos polinômios ortogonais de Jacobi e o comportamento assintótico dos zeros dos polinômios ultrasféricos / Abstract: In this thesis we state a new formulation of the Sturm comparison Theorem and its applications to the zeros of orthogonal polynomials. Specifically, these applications deal with the monotonicity of zeros of X1-Jacobi orthogonal polynomials, Gautschi's conjectures about inequalities of zeros of Jacobi polynomials and the asymptotic of zeros of ultrasphricals polynomials / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Dans le cadre de l’avion plus électrique, les avionneurs cherchent à remplacer les commandes de vol hydrauliques par des commandes de vol électriques, avec pour intérêt de diminuer le poids, et d’améliorer la flexibilité des équipements aéronautiques. Sachant que sur un A380, la distance cumulée pour les câbles peut atteindre plus de 500 km, la solution consistant à faire cohabiter les transmissions de données et de puissances au sein de mêmes câbles grâce à la technologie CPL pourrait contribuer à réduire la masse de câble dans un avion. Cependant les câbles de puissance n’ont pas été dimensionnés pour transmettre un signal informationnel, et les équipements présents sur le réseau sont source de bruits. Dans ce contexte nous souhaitons montrer la faisabilité d’une transmission CPL soumise aux contraintes avioniques tout en respectant les normes aéronautiques. La première partie des travaux a consisté à mesurer le canal de propagation sur un banc de test représentatif d’un environnement aéronautique. Le canal de propagation est composé de deux coupleurs de type inductif ou capacitif dont le but est de connecter les câbles de télécommunication au réseau de puissance et d’une paire bifilaire torsadée de puissance d’une longueur de 32 m représentative d’un réseau HVDC ±270 V. Nous avons alors testé trois architectures différentes : l’architecture point-À-Point avec coupleur capacitif, l’architecture point-À-Point avec coupleur inductif et l’architecture point-À-Multipoints avec coupleur inductif. Le but de ces mesures a été d’évaluer la fonction de transfert du canal sur la bande [1 ; 100] MHz. Nous avons alors calculé les éléments caractéristiques du canal comme la bande de cohérence et l’étalement des retards. Après la caractérisation du canal de propagation, nous avons choisi et dimensionné les algorithmes de traitement du signal au regard des spécifications aéronautiques à savoir : un débit utile de 10 Mbit/s, un temps de latence de 167-334 μs, un TEB de 10-12 et le respect du gabarit de la DO-160 en émission conduite. Au regard de la fonction de transfert du canal, nous avons choisi d’utiliser l’OFDM comme technique de transmission. Ainsi, à l’aide de la caractérisation du canal de propagation nous avons au cours d’une étude paramétrique défini les paramètres de la transmission OFDM au regard des spécifications de débit et de temps réel. Dans un second temps, nous avons implanté les paramètres OFDM ainsi que la modélisation du canal de propagation dans une chaine de transmission Matlab. Cette chaine nous a alors permis de vérifier les paramètres issues de l’étude paramétrique ainsi que de définir le système de codage de canal (Reed-Solomon et code convolutif) pour respecter les spécifications aéronautiques. La dernière partie de cette thèse a consisté en l’étude du système de synchronisation. Du fait de la stabilité du canal de propagation, nous avons considéré une synchronisation fine du système lors d’une phase d’initialisation puis nous nous somme focalisé sur le dimensionnement d’un système de suivi dans le but de corriger le décalage de fenêtre FFT dû au défaut de fréquence d’échantillonnage. Pour limiter les pertes de débit lors de la phase de suivi, nous avons proposé une estimation de l’erreur de fréquence d’échantillonnage sur la phase des données reçues sur une période de 20 symboles OFDM. / In the new aircrafts, hydraulic flight control systems are replaced by electric flight control systems. The main interests are a better flexibility of the aeronautical equipments and a decrease in maintenance costs and construction costs, but the major problem is the increasing of the wires length. In order to decrease this length, it has been proposed to use power line communications (PLC) technology for flight control systems. The decrease of wire will first decrease aircraft weight and therefore the consumption of kerosene and on the other hand will simplify maintenance and construction. The first part of this work is the measurement and the characterisation of the propagation channel on an aeronautic test bench (with HVDC supply and loads). This channel is composed of two couplers (inductive or capacitive) in order to connect the telecommunication system on the power wires with galvanic isolation and one twisted pair of 32 m longs. We have tested three architectures: the point-To-Point architecture with capacitive coupler, the point-To-Point architecture with inductive coupler and the point-To-Multipoint architecture with inductive coupler. The purpose of these measurements is to measured the transfer function on the [1 ; 100] MHz bandwidth. Then, we have computed the channel parameters like the coherence bandwidth and the delay spread. The second step was the design of the signal processing algorithm in order to satisfy the aeronautical specifications: a useful bite rate of 10 Mbit/s, a latency of 167- 334 μs, a BER of 10-12 and the respect of the DO-160 gauge in conducted emissions. For the transmissions, we have chosen the OFDM technology which has been use with success in other PLC systems. With the channel characterization, we have proposed a parametric study in order to define the OFDM parameters to satisfy the bite rate and the real time constraints. After, we compute digital simulations with Matlab to check the OFDM parameters. With these simulations, we have also defined the channel coding parameters (Reed-Solomon and convolutional coding) to satisfy the aeronautical specifications. The last part of this study was the design of the synchronisation system. Because of the channel stability, we considered a precise synchronisation after an initialisation period. Then, we focus on the estimation of the FFT shift, due to the sampling frequency shift, during a following-Up period. In order to avoid the decrease of the latency and the bitrate due to the pilot symbols or pilot sub-Carriers insertion, we proposed to correct the FFT shift with the receive data thanks to the maximal likelihood algorithm.

In this thesis we present some fundamental results regarding orthogonal polynomials and biorthogonal polynomials, the latter defined as in the article "Cauchy Biorthogonal Polynomials", authored by Bertola, Gekhtman, and Szmigielski. We show that total positivity of the kernel can be weakened and how this implies that interlacement for biorthogonal polynomials holds in general. A counterexample is provided showing that in general there does not exist a four-term recurrence relation such as the one found for the Cauchy kernel. As a direct consequence we show that biorthogonal polynomial sequences cannot be considered orthogonal polynomial sequences by an appropriate choice of orthogonality measure. Furthermore, we motivate a conjecture stating that the more general form of interlacement that exists for orthogonal polynomials also exists for biorthogonal polynomials. We end with suggesting some further work that could be of interest.

The integrable Schrödinger operators often have a singularity on the real line, which creates problems for their spectral analysis. In several particular cases we show that all closed gaps lie on the infinite spectral arc. In the second part we develop a theory of complex exceptional orthogonal polynomials corresponding to integrable rational and trigonometric Schrödinger operators, which may have a singularity on the real line. In particular, we study the properties of the corresponding complex exceptional Hermite polynomials related to Darboux transformations of the harmonic oscillator, and exceptional Laurent orthogonal polynomials related to trigonometric monodromy-free operators.

[pt] O trabalho desenvolveu uma metodologia de solução numérica de escoamentos em geometrias complexas, numa formulação incompressível e bi-dimensional. As equações de conservação são discretizas com o emprego da técnica de volumes finitos em coordenadas não ortogonais. Esta técnica mapeia o espaço real num espaço transformado, no qual as fronteiras do domínio de cálculo coincidem com as fronteiras do domínio físico. Os componentes contravariantes da velocidade foram empregados como variáveis dependentes nas equações de conservação de quantidade de movimento. Estas equações foram obtidas em coordenadas não ortogonais pela manipulação algébrica das equações discretizadas para os componentes cartesianos. Este procedimento, que emprega um sistema de coordenadas auxiliar fixo localmente, evita o surgimento dos diversos termos oriundos da curvutura e da não ortogonalidade da malha, que seriam obtidos caso fosse empregada a análise tensorial para a derivação destas equações. O ocoplamento pressão-velocidade é feito utilizando SIMPLEC. O conjunto de equações algébricas resultante é resolvido por um esquema de solução segregado, no qual é empregado um esquema de solução linha-a-a linha(TDMA), com um processo de correção por blocos para acelerar a convergência. A metodologia desenvolvida foi utilizada para solução de diversos problemas visando analisar o seu desempenho. Foram estudados os seguintes casos-escoamento laminar entre dois cilindros, convecção natural entre dois cilidros excêntricos, escoamento induzido numa cavidade trapezoidal pelo movimento de suas bases, escoamento laminar num canal, escoamento axi-simétrico num duto com estrangulamento.Tendo em vista os bons resultados obtidos para testes, pode-se concluir que as opções realizadas para a confeção do esquema desenvolvido foram corretas, pois geraram um algoritimo efeciente e versátil. / [en] A solution method for bi-dimensional incompressibible fluid flow problems in complex geometrics is developed in this work. The method solves the conservation equations in nonorthogonal coordinate system using the finite volumes technique. The contravariant velocities are kept as dependent variables in the momentum equations. These equations are obtained by an algebric manipulation of the discretization equations written in locally fixed coordinate system. This producedure avoids the treatment of the extra terms if the discretization equations for the curvilinear velocities are obtained in the conventional manner. The coupling of pressure and velocities are performed by the SIMPLEC algorithm. The set of algebric equations are solved using an iterative method in conjunction with coefficient update for linerization. In the computer implementation of the proposed scheme a line-by-line algorithm (TDMA) has been employed with a block corretion procedure to enhance the convergence. The method is tested by solving a variety of problems. The problems include-flow between two concentric rotating cylinders, natural convection in an eccentric annuli, driven flow in a trapezoidal cavity with moving lids, laminar flow in a channel, exismetric flow in duct with reduced cross section and laminar and turbulent flow through a tube with an axisimetric constriction. The objetive of these tests is to establish the validity of the proposed scheme and demonstrate its applicability to a wide variety of problems.

To maximize the effectiveness of the rapidly increasing capacity of installed wind energy resources, new models must be developed that are capable of more nuanced control of each wind turbine so that each device is more responsive to inflow events. Models used to plan wind turbine arrays and control behavior of devices within the farm currently make questionable estimates of the incoming atmospheric flow and update turbine configurations infrequently. As a result, wind turbines often operate at diminished capacities, especially in arrays where wind turbine wakes interact and inflow conditions are far from ideal. New turbine control and wake prediction models must be developed to tune individual devices and make accurate power predictions. To that end, wind tunnel experiments are conducted detailing the turbulent flow in the wake of a wind turbine in a model-scale array. The proper orthogonal decomposition (POD) is applied to characterize the spatial evolution of structures in the wake. Mode bases from distinct downstream locations are reconciled through a secondary decomposition, called double proper orthogonal decomposition (DPOD), indicating that modes of common rank in the wake share an ordered set of sub-modal projections whose organization delineates underlying wake structures and spatial evolution. The doubly truncated basis of sub-modal structures represents a reduction to 0.015% of the total degrees of freedom of the wind turbine wake. Low-order representations of the Reynolds stress tensor are made using only the most dominant DPOD modes, corrected to account for energy excluded from the truncated basis with a tensor of constant coefficients defined to rescale the low-order representation of the stresses to match the original statistics. Data from the wind turbine wake are contrasted against simulation data from a fully-developed channel flow, illuminating a range of anisotropic states of turbulence. Complexity of flow descriptions resulting from truncated POD bases is suppressed in severe basis truncations, exaggerating anisotropy of the modeled flow and, in extreme cases, can lead to the loss of three dimensionality. Constant corrections to the low-order descriptions of the Reynolds stress tensor reduce the root-mean-square error between low-order descriptions of the flow and the full statistics as much as 40% and, in some cases, reintroduce three-dimensionality to severe truncations of POD bases. Low-dimensional models are constructed by coupling the evolution of the dynamic mode coefficients through their respective time derivatives and successfully account for non-linear mode interaction. Deviation between time derivatives of mode coefficients and their least-squares fit is amplified in numerical integration of the system, leading to unstable long-time solutions. Periodic recalibration of the dynamical system is undertaken by limiting the integration time and using a virtual sensor upstream of the wind turbine actuator disk in to read the effective inflow velocity. A series of open-loop transfer functions are designed to inform the low-order dynamical system of the flow incident to the wind turbine rotor. Validation data shows that the model tuned to the inflow reproduces dynamic mode coefficients with little to no error given a sufficiently small interval between instances of recalibration. The reduced-order model makes accurate predictions of the wake when informed of turbulent inflow events. The modeling scheme represents a viable path for continuous time feedback and control that may be used to selectively tune a wind turbine in the effort to maximize power output of large wind farms.