Thesis (M. Sc.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 125-133). Also available via the World Wide Web.

Proefschrift Rijksuniversiteit Groningen. / Datum laatste update: 22-06-1998. Met lit. opg., index en een samenvatting in het Nederlands.

Στην παρούσα εργασία θα παρουσιαστούν διάφορα προβλήματα, με την επίλυσή τους, τα οποία ανήκουν στο πεδίο των Διακριτών Μαθηματικών. Πιο συγκεκριμένα στο πρώτο κεφάλαιο θα δούμε διάφορα προβλήματα αναδρομής όπου κάποια από αυτά θα είναι παραλλαγές γνωστών προβλημάτων (π.χ.: Ο ΠΥΡΓΟΣ ΤΟΥ HANOI) των οποίων οι (γνωστές) λύσεις θα μας βοηθάνε για να αποδεικνύουμε κάθε φορά αυτό που θέλουμε. Στο δεύτερο κεφάλαιο θα ασχοληθούμε με προβλήματα και ασκήσεις αθροισμάτων, τα οποία είναι παντού στα μαθηματικά, γι'αυτό χρησιμοποιούμε βασικά εργαλεία για να τα λύσουμε, αναπτύσσοντας γενικές τεχνικές έτσι ώστε η διαδικασία να είναι φιλική προς τον αναγνώστη. Στη συνέχεια στο τρίτο κεφάλαιο θα συναντήσουμε ασκήσεις οι οποίες αφορούν τις ακέραιες συναρτήσεις. Οι ακέραιοι αριθμοί αποτελούν τη ραχοκοκαλιά των Διακριτών Μαθηματικών, και εμείς συχνά χρειάζεται να μετατρέπουμε κλάσματα ή αυθαίρετους πραγματικούς αριθμούς σε ακέραιους. Ο στόχος λοιπόν αυτού του κεφαλαίου είναι να αποκτήσουμε οικειότητα και άνεση με τέτοιου είδους μετατροπές μέσα από τις ασκήσεις και να μάθουμε μερικές από τις αξιοσημείωτες ιδιότητες τους. Μέσα από τις ασκήσεις του τέταρτου κεφαλαίου γίνεται μια εισαγωγή στη θεωρία αριθμών ένα σημαντικό κλάδο των μαθηματικών που ασχολείται με τις ιδιότητες των ακεραίων. Τέλος στο κεφάλαιο 5 θα συναντήσουμε ασκήσεις και προβλήματα τα οποία βασίζονται στη μελέτη των διωνυμικών συντελεστών οι οποίοι είναι πολύ σημαντικοί στις εφαρμογές και επίσης πιo εύκολοι να τους χειριστούμε σε σύγκριση με άλλες ποσότητες των προηγούμενων κεφαλαίων. / -

A thorough review of the literature on the model reduction of linear, time-invariant, dynamical systems in both the frequency and time domains is presented. Particular attention is paid to the least-squares extension of the classical method of Padé approximation. An account is given of the development of apparently different approaches of least-squares parameter- matching Padé model reduction applied to continuous-time and discrete-time systems. These approaches are shown to be related via a unifying theory. From the formulation it is possible to show several interesting features of the least-squares approach which lead to a fuller understanding of exactly how the reduced model approximates the full system. An error index is derived in the general continuous-time case and it is shown that a range of system parameter preservation options are available. Using the theory developed in the continuous-time case a non-uniqueness property of the method is proven. An ‘optimal’ least-squares method based on the approach and the introduction of weighting for the system parameters are both investigated. The unifying theory is extended to the discrete-time case where an important new stability preservation property is proved and is shown to provide the basis for a new least- squares Padé method. This method uses transformations between the z- and 5-planes to guarantee stable reduced order models approximating stable high order continuous-time systems. The application of least-squares Padé approximation is further extended to the multivariable case with particular attention given to the factors affecting the levels of order reduction achieved. Appropriate numerical examples are used to illustrate the main points of the thesis and graphs of the impulse and step responses are used throughout to visually highlight the accuracy of approximation.

Les silices nanostructurées sont des matériaux ultra-poreux (plus de 80% de porosité) utilisés pour la confection de Panneaux Isolants sous Vides (PIV). Elles possèdent des propriétés thermiques exceptionnelles, mais de piètres propriétés mécaniques.L’enjeu de cette thèse est d’étudier ces matériaux aux échelles de la particule (quelques nm), de l’agrégat de particules (quelques dizaines de nm) et de l’agglomérat d’agrégats (quelques centaines de nm), afin de mieux comprendre les comportements mécanique et thermique à l’aide de simulations, et de proposer des pistes pour améliorer le compromis thermique / mécanique. La nature particulaire du matériau et son caractère multi-échelle justifient l’utilisation de méthodes de simulations discrètes (DEM : Discrete Element Method). Un modèle original permettant de générer des agrégats à morphologiecontrôlée (dimension fractale, rayon de giration, porosité) est proposé. Le comportement à la compaction des agrégats est ensuite étudié par simulations DEM. Une approche par cyclage à faible densité a été développée pour obtenir des arrangements initiaux réalistes d’agrégats. La prépondérance des phénomènes adhésifs dans le système rend en effet celui-ci très sensible à l’arrangement initial. La réponse en traction des structures générées par compaction est également évaluée.L’influence de la morphologie des agrégats, de l’adhésion et du frottement ont été étudiées. L’accent est mis sur la comparaison de deux types de silices (pyrogénées et précipitées) présentant des morphologies différentes et pour lesquelles des données expérimentales permettent une confrontation avec les simulations. Les simulations présentées permettent d’apporter des réponses sur l’origine des différences de comportement mécanique observées expérimentalement pour ces deux types de silice.Une modélisation de la conductivité thermique du matériau, avec une focalisation sur la conductivité solide, est également proposée. / Nanostructured silicas are ultra-porous materials (more than 80 % porosity) used to make Vacuum Insulation Panels (VIP).They have exceptional thermal properties, but poor mechanical properties. The goal of this thesis is to study these materials at the scale of the particle (a few nm), the aggregate of particles (a few tens of nm) and the agglomerate of aggregates (a few hundred nm), in order to better understand mechanical and thermal behaviour using simulations, and to propose ways to improve the thermal / mechanical compromise. The particulate nature of the material and its multi-scale naturejustify the use of Discrete Element Methods (DEM). An original model allowing to generate aggregates with controlledmorphology (fractal dimension, radius of gyration, porosity) is proposed. The compaction behaviour of the aggregates is then studied by DEM. A low-density cycling approach has been developed to obtain realistic initial aggregate arrangements.The preponderance of adhesive phenomena in the system makes it very sensitive to the initial arrangement. The tensile response of structures generated by compaction is also evaluated. The influence of aggregate morphology, adhesion and friction were studied. Emphasis is placed on the comparison of two types of silica (pyrogenic and precipitated) with different morphologies and for which experimental data allow a comparison with simulations. The simulations presented allow us to provide answers on the origin of the differences in mechanical behaviour observed experimentally for these two types of silica.A modeling of the thermal conductivity of the material, with a focus on solid conductivity, is also proposed.

No description available.

Orientador: José Paulo Fernandes Garcia / Banca: Haroldo Rodrigues de Azevedo / Banca: Marcelo Carvalho M. Teixeira / Resumo: Este trabalho apresenta uma nova estratégia de controle discreto. A técnica é baseada em Modos Deslizantes Discretos, utilizando uma lei de controle suave. Quando um algoritmo de controle é implementado em um computador digital, existe um atraso no tempo de computação, devido ao tempo de execução das instruções. Neste trabalho, vamos assumir que estes atrasos são constantes e menores que um período de amostragem. A presença do atraso no tempo de computação não apenas reduz a estabilidade e robustez, mas também degrada a performance de controle. O novo controlador proposto é projetado para atuar na presença destes atrasos, melhorando substancialmente o desempenho do controle. Outra propriedade importante deste controlador é a possibilidade de trabalhar com períodos de amostragem mais altos, garantindo o uso de freqüências mais baixas de processamento, ou seja, proporcionando uma economia do hardware de atuação. A nova lei de controle proposta foi aplicada na estabilização de quatro sistemas incertos e de natureza instável: Sistema Bola e Viga, Sistema Pêndulo Invertido Linear, Sistema Pêndulo Invertido Rotacional e Sistema Pêndulo Invertido Rotacional Duplo. Resultados das simulações são apresentados e comparados com resultados de outro controlador de Modo Deslizante, proposto na literatura, caracterizando um estudo comparativo, onde a eficácia do novo controlador projetado se mostra evidente, devido a seu algoritmo de fácil elaboração prática. Para melhor visualização do comportamento dos sistemas estudados e visando a contribuição no aprendizado de sistemas de controle, modelos de animação em três dimensões foram utilizados. / Abstract: This work presents a new strategy of discrete-time control. The technique is based on Discrete-Time Sliding Modes, using a smooth control law. When a control algorithm is implemented in a digital computer, there is a computation time delay, due the execution time of the instructions. In this work, we go to assume that these delays are constant and smaller than a sampling period. The presence of the computation time delay not only reduces the stability and robustness, but also degrades the control performance. The new considered controller is projected to work in the presence of these delays, improving substantially the performance of the control. Another important property of this controller is the possibility to work with higher sampling periods, guaranteeing the use of lower frequencies of processing, providing an economy of the actuation hardware. The new control law proposal was applied in the stabilization of four uncertain systems with unstable nature: Ball and Beam System, Linear Inverted Pendulum System, Rotational Inverted Pendulum System and Double Rotational Inverted Pendulum System. Simulations results are presented and compared with results of other Sliding Mode controller, proposed in the literature, characterizing a comparative study, where the effectiveness of the new designed controller shows evident, due your algorithm of easy practical elaboration. For better visualization of the behavior of the systems studied and aiming at the contribution in the learning of control systems, models of animation in three dimensions had been used. / Mestre

abstract: Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations. The map which encapsulates the population development from one year to the next is approximated at the origin (the extinction state) by a linear or homogeneous map. The (cone) spectral radius of this approximating map is the threshold between extinction and persistence. General persistence results are applied to three particular models: a size-structured plant population model, a diffusion model (with both Neumann and Dirichlet boundary conditions) for a dispersing population of males and females that only mate and reproduce once during a very short season, and a rank-structured model for a population of males and females. / Dissertation/Thesis / Ph.D. Mathematics 2014

abstract: This thesis focuses on sequencing questions in a way that provides students with manageable steps to understand some of the fundamental concepts in discrete mathematics. The questions are aimed at younger students (middle and high school aged) with the goal of helping young students, who have likely never seen discrete mathematics, to learn through guided discovery. Chapter 2 is the bulk of this thesis as it provides questions, hints, solutions, as well as a brief discussion of each question. In the discussions following the questions, I have attempted to illustrate some relationships between the current question and previous questions, explain the learning goals of that question, as well as point out possible flaws in students' thinking or point out ways to explore this topic further. Chapter 3 provides additional questions with hints and solutions, but no discussion. Many of the questions in Chapter 3 contain ideas similar to questions in Chapter 2, but also illustrate how versatile discrete mathematics topics are. Chapter 4 focuses on possible future directions. The overall framework for the questions is that a student is hosting a birthday party, and all of the questions are ones that might actually come up in party planning. The purpose of putting it in this setting is to make the questions seem more coherent and less arbitrary or forced. / Dissertation/Thesis / Masters Thesis Mathematics 2014

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