In this dissertation the proper determination and allowable signs of the effective parameters of metamaterial structures will be examined. First, a method that was commonly used to determine the presence of a negative index of refraction will be discussed. It will be shown that this method, which relies on the appearance of transmission peaks in the region where the real parts of the effective permittivity and permeability are expected to be negative, does not provide sufficient evidence that a negative index exists. Two alternate methods will then be presented that can be used to properly determine the sign of the index. Then, the form of the index in media that exhibit backward wave propagation will be examined from a purely three dimensional wave propagation point of view. It will be shown that in an isotropic medium backward wave propagation requires that the index be negative and in an anisotropic medium it requires that the index be negative along at least one of the three principal axes. In short, the necessary and sufficient condition for the negative index of refraction is the existence of the backward wave. Next, a technique commonly used to retrieve the effective parameters in metamaterials from transmission and reflection data will be considered. It will be shown that this retrieval technique can lead to unphysical claims that the imaginary parts of the effective permittivity or permeability can be negative even though the medium remains passive. By comparing the effective parameters obtained analytically and from the retrieval technique it will be shown that these unphysical claims are the result of error in the numerical simulations. The concepts of causality and analyticity will also be discussed by considering the Lorentzian model and it will be shown that this model does not allow the imaginary parts of the permittivity or permeability to be negative in the metamaterials consisting of split ring resonators and split wires.

Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Sept. 9, 2009). Vita. Includes bibliographical references.

Οι χρονοσειρές των κλιματικών δεδομένων αποτελούν σημαντικό εργαλείο για τη μελέτη του κλίματος καθώς μπορούν να μας δώσουν χρήσιμες πληροφορίες για τις μεταβολές του. Για το λόγο αυτό θα πρέπει να είναι όσο το δυνατόν πιο πλήρης και ομογενείς έτσι ώστε οι οποιεσδήποτε μεταβολές που υπάρχουν σε αυτές να οφείλονται αποκλειστικά και μόνο σε μεταβολές του ίδιου του κλίματος. Υπάρχουν όμως αρκετοί παράγοντες που επηρεάζουν τις μετρήσεις των κλιματικών παραμέτρων και άρα τις αντίστοιχες χρονοσειρές τους. Έτσι έχουν αναπτυχθεί και εφαρμοστεί αρκετές μέθοδοι, που σκοπό έχουν την αποκάλυψη και διόρθωση των δεδομένων, με τελικό σκοπό την ομογενοποίηση των χρονοσειρών. Μία από αυτές είναι και η μέθοδος MASH (Multiple Analysis of Series for Homogenization), μία μέθοδος ομογενοποίησης κλιματικών χρονοσειρών που έχει αναπτυχθεί από την Ουγγρική Μετεωρολογική Υπηρεσία και τον κ. Szentimrey T. Η μέθοδος αυτή, αναλύεται και χρησιμοποιείται για την ομογενοποίηση μηνιαίων χρονοσειρών θερμοκρασίας από δίκτυο Ελληνικών μετεωρολογικών σταθμών, καθώς και για την επεξεργασία χρονοσειρών στα πλαίσια συμμετοχής στη δράση COST "Advances in homogenization methods of climatic time series". Τέλος παρουσιάζονται τα αποτελέσματα από την εφαρμογή της μεθόδου και τα συμπεράσματα που προκύπτουν. / Time series of climatic data consist an especial tool of climate research, as they may provide us with a lot of information about its changes. For that reason these series have to be as more complete and homogeneous as it can be, so that their variations are to caused only by variations in climate. But, there are a number of factors that affect measurements of climatic parameters and the corresponding time series as well, producing rapid or gradient shifts and trends. Owing to that, some methods have developed in order to detect and correct the data, aiming at the homogenization of time series. One such a method is MASH (Multiple Analysis of Series for Homogenization) which has been developed by Hungarian Weather Service and Mr. Szentimrey Σ. This method is analyzed and applied to monthly mean temperature time series from a network of Greek meteorological stations as well as to process time series in relation with the contribution on COST Action: ‟Advances in homogenization methods of climate series‟. Finally, the results and conclosions are presented.

L'estimation des pertes de précontrainte liées aux déformations différées des bétons est un sujet d'intérêt pour la maintenance à long terme d'ouvrages de génie civil tels que les enceintes de confinement des centrales nucléaires. L'objectif de ce travail de doctorat est d'améliorer la prise en compte des particularités morphologiques de la microstructure des bétons pour estimer le comportement à long terme des bétons précontraints. Cette étude est limitée au cadre de la mécanique des matériaux et à la théorie de l'homogénéisation : le béton y est décrit comme un matériau composite constitué de granulats élastiques enchâssés dans une matrice cimentaire viscoélastique linéaire vieillissante. Les outils novateurs mis en œuvre sont la tomographie par rayons X et la simulation numérique 3D.On distingue sur les images de tomographie les granulats, la matrice cimentaire et l'air occlus. Mais l'extraction de données morphologiques de ces images est une tâche difficile à systématiser. En revanche, la construction numérique de microstructures matrice-inclusions et la simulation numérique 3D en viscoélasticité linéaire se sont montrées assez robustes pour permettre l'étude de l'influence de paramètres morphologiques (fraction volumique, granulométrie et forme des inclusions) sur le comportement macroscopique estimé. Le schéma d'homogénéisation semi-analytique de Sanahuja dédié aux matériaux composites viscoélastiques linéaires vieillissants a été étendu aux cas d'inclusions ellipsoïdales pour étudier l'influence du rapport d'aspect des inclusions sur le comportement viscoélastique vieillissant d'un béton. Les estimations du comportement macroscopique par les simulations numériques 3D restent proches de celles obtenues par les schémas d'homogénéisation semi-analytiques. Ainsi, il reste difficile d'expliquer la dispersion des résultats expérimentaux de Granger par l'homogénéisation, dans la mesure où les bétons de Granger ont des formulations similaires. Enfin, les simulations numériques 3D permettent l'estimation des contraintes dans la matrice cimentaire lorsque l'on impose à un échantillon de béton une histoire de chargement similaire à celle rencontrée sur les ouvrages / Prestress losses due to creep of concrete is a matter of interest for long term operations of containment buildings. In the present study, the time-dependent strains of concretes are estimated starting from morphological details of the microstructure. X-ray tomography provide a new way to spot such details and 3D numerical simulations are performed to estimate the time-dependent strains. Concrete is described as a composite material made of aggregates embedded in a cementitious matrix. On X-ray tomography images, aggregates can be separated from the cementitious matrix and entrained air. But extracting morphological parameters remains a difficult task. Nevertheless, building numerical matrix-inclusion microstructures and performing 3D numerical simulations proved a reliable way to estimate the influence of morphological features such as a the volume fraction of aggregates or the sieve curve on the time-dependent strains of concretes. Moreover, the semi-analytic homogenization scheme of Sanahuja dedicated to linear aging viscoelastic composite materials has been extended to the case of ellipsoidal inclusions to study the influence of the aspect ratio of the aggregates on the time-dependent strains of concretes.3D numerical estimates of the overall time-dependent behavior of concrete are similar to the ones produced by semi-analytical homogenization schemes. Hence, explaining the differences between the experimental measurements of the time-dependent strains of concretes performed by Granger remains challenging given the similarities between their mix designs. Lastly, 3D numerical simulations are performed on a sample of concrete to estimate the local stress in the cementitious matrix, the history of loading being representative of the one experienced in a containment building

On étudie quelques problèmes singuliers d'homogénéisation en élasticité linéarisée ou électricté non-linéaire où, en plus de la période de distribution des hétérogénéités, apparaissent d'autres paramètres comme la très forte (ou faible) rigidité ou permittivité d'une des phases et la taille relative de celle-ci. Sont visés des milieux fibrés ou stratifiés et des maçonneries planes et minces. / We study some singular problems of homogenization in linearized elasticity or nonlinear electricty where, in addition to the period of distribution of heterogenities, other parameters do appear as the very high (or low) stiffness or permittivity of one phase and its the relative size. Fibered media, stratified media and flat and thin masonries are considered.

Neste trabalho foi estudada a influência da homogeneização a alta pressão na retenção de antocianinas e na inativação da atividade enzimática da peroxidase e polifenoloxidase presentes naturalmente na polpa de açaí. Este trabalho foi dividido em duas etapas. Na primeira, a polpa de açaí teve suas propriedades físicoquímicas e comportamento reológico determinados. Na segunda etapa, a polpa de açaí passou por um pré-tratamento de filtração e posteriormente, foi tratada por homogeneização a alta pressão, com pressões de (100, 200 e 300) MPa e temperaturas de entrada do produto de (20 e 30) °C. Amostras da polpa de açaí processada foram analisadas quanto às propriedades físico-químicas, composição centesimal, teor de antocianinas, atividade antioxidante, teor de fenólicos totais, atividade enzimática (peroxidase e polifenoloxidase) e análise de cor. Os dados experimentais reológicos das curvas com taxas de cisalhamento ascendente e decrescente foram bem ajustados ao modelo Herschel-Bulkley. Esses dados apresentaram uma curva de histerese em sentido anti-horário, denotando um comportamento anti-tixotrópico. A polpa de açaí, utilizada na segunda parte deste trabalho, apresentou teor de sólidos totais variando entre (11,44 e 14,63) %, teor de antocianinas monoméricas (Am) (2,20 e 2,54) mg/g extrato seco, atividade antioxidante (AA) (7,68 e 8,27) mol TE/g extrato seco; fenólicos totais (FT) (25,51 e 34,57) mg GAE/g extrato seco e atividade enzimática da peroxidase (POD) entre (1,02E-2 e 3,73E-2) U/s.oBrix.g extrato seco e da polifenoloxidase (PFO) (2,87E-2 e 7,59E-2) U/s.oBrix.g extrato seco. O tratamento de homogeneização a alta pressão preservou 97,5 % do teor de antocianinas monoméricas presentes na polpa de açaí tratada após filtração. A enzima PFO apresentou uma inativação máxima de 47 % para a polpa de açaí tratada a 300 MPa; a máxima inativação obtida para a POD foi de 43,7 %, para tratamento a 300 MPa e temperatura de entrada do produto de 20 °C. O tratamento de homogeneização a alta pressão é uma alternativa ao tratamento térmico por reter as antocianinas e reduzir a atividade enzimática da POD e PFO. / The effect of high pressure homogenization on the stability of anthocyanins and on the inactivation of enzymatic activity of peroxidase and polyphenoloxidase from açaí pulp was studied in this work. Experimental investigations were carried out in two steps. Firstly, açaí pulp had its physicochemical properties and rheological behavior determined. Secondly, açaí pulp was pretreated through filtration and processed through high pressure homogenization at pressures of (100, 200 and 300) MPa and inlet product temperatures of (20 and 30) °C. The processed açaí pulp had its composition and physicochemical properties determined: analyses such as anthocyanin content, antioxidant activity, content of phenolic compounds, enzymatic activity (peroxidase and polyphenoloxidase) and color analysis were carried out. The experimental rheological data for increasing and decreasing shear rates were well correlated by the Herschel-Bulkley model. These data showed a counterclockwise hysteretic loop that indicates an anti-thixotropic behavior. The açaí used in the second part of this work presented a total solid content ranging from (11.44 and 14.63) %, total monomeric anthocyanins (Am) (2.20 and 2.54) mg / g dry matter, antioxidant activity (AA) (7.68 and 8.27) mol TE / g dry matter, total phenolic content (FT) (25.51 and 34.57) mg GAE / g dry matter, enzymatic activity of peroxidase (POD) from (1.02 E-2 and 3.73 E-2) U/s.oBrix.g dry matter and enzymatic activity of polyphenoloxidase (PFO) from (2.87 E-2 and 7.59 E-2) U/s.oBrix.g dry matter. The use of high pressure homogenization allowed the recovery of 97.5% of monomeric anthocyanins present in filtered açaí pulp. The enzyme PFO underwent a maximum inactivation of 47% for açaí pulp treated at 300 MPa, regardless of inlet temperature of the product; the maximum inactivation achieved for POD was 43.7%, for the treatment at 300 MPa and inlet temperature of the product of 20 °C. The treatment of high pressure homogenization is an alternative to heat treatment because it retains the anthocyanins and inactivates the enzymatic activity of POD and PFO.

In dieser Arbeit wird für Strukturen, die im makroskopischen aufgrund unterschiedlicher Materialeigenschaften oder komplexer Geometrien eine hohe Netzfeinheit für Finite-Elemente-Berechnungen benötigen, eine neue Möglichkeit zur Berechnung effektiver Materialkennwerte vorgestellt. Durch einen modalen Ansatz, bei dem, je nach Struktur analytisch oder numerisch, mit Hilfe der modalen Kennwerte die Formänderungsenergie eines repräsentativen Volumens der Originalstruktur mit der Formänderungsenergie eines äquivalenten homogen Vergleichsvolumens verglichen wird, können effektive Materialkennwerte ermittelt und daran anschließend eine Finite-Elemente-Berechnung mit einem im Vergleich zum Originalmodell sehr viel gröberen Netz durchgeführt werden, was eine enorme Zeiteinsparung mit sich bringt. Weiterhin enthält die vorgestellte Methode die Möglichkeit, unsichere Eingabeparameter wie Geometrieabmessungen oder Materialkennwerte mit Hilfe der polynomialen Chaos Expansion zu approximieren, um Möglichkeiten zur Aussage bzgl. der daraus resultierenden Verteilungen modaler Kenngrößen auf eine schnelle und effektive Weise zu gewinnen.

Afin de retrouver un paramètre efficace de la structure périodique, on s'est efforcé de développer la théorie de l'homogénéisation, qui considère la structure périodique comme un milieu homogène. Cette thèse porte principalement sur la proposition et la validation de l'homogénéisation classique et de second ordre. Une méthode d'homogénéisation est appliquée pour obtenir des paramètres efficaces de structures multicouches. De plus, une homogénéisation classique est adoptée pour calculer les propriétés de transmission de structures diélectriques multicouches et la relation de dispersion d'un réseau de cylindres métalliques monté sur un plan de masse métallique lisse. D'après cette relation de dispersion, la propriété de coupe-bande à une certaine bande de fréquences est découverte et est appliquée sur la reformation du diagramme de rayonnement de l'antenne à plaque traditionnelle en supprimant l'onde de surface propageant sur le plan de masse. Nous avons publié cette partie dans [22]. Nous démontrons expérimentalement une limitation importante de l'homogénéisation classique lors du calcul de la propriété de transmission d'un réseau métallique ultra-fin. Le coefficient de transmission mesuré est beaucoup plus faible que celui calculé par homogénéisation classique, bien que les interférences qui peuvent être causées par l'installation d’expérience imparfaite sont éliminées. Nous proposons donc une nouvelle homogénéisation de second ordre, qui permet d'obtenir le coefficient de transmission correspondant aux résultats numériques. De plus, l'homogénéisation de second ordre a été validée expérimentalement par plusieurs grilles métalliques de même dimension sauf l'épaisseur. / In order to retrieve effective parameter of the periodic structure, people have made effort to develop the theory of homogenization, which regards the periodic structure as a homo- geneous medium. This thesis mainly focuses on the proposition and validation of classical and second order homogenization. A kind of method for homogenization is applied to ob- tain effective parameters of multilayer structures. Moreover, classical homogenization is adopted to calculate transmission properties of dielectric multilayer structures and the dis- persion relation of metallic cylinder array mounted on a smooth metallic ground plane. From the dispersion relation, its band gap property at a certain frequency band is revealed and is applied to reshape the radiation pattern of traditional patch antenna by suppressing the surface wave propagating on the ground plane. We have published his part of the work in [22]. We experimentally demonstrate one important limitation of classical homogenization when calculating the transmission property of an ultra-thin metallic grating. The mea- sured transmission coefficient is much smaller than that calculated by classical homoge- nization, although the interferences may be caused by the imperfect experiment facility are eliminated. Thus we propose a new second order homogenization, which is able to get the transmission coefficient correspondent to numerical results. Furthermore, second order homogenization has been experimentally validated by several metallic grating with the same dimension except for the thickness. This part of work will be included in a chapter of a book will be published by Intech Publisher.

In this thesis we are interested in the propagation of low-frequency linear elastic waves through composite materials. We use a variety of dynamic homogenization techniques to find the effective elastic properties of some composites. We consider composites with isotropic phases for ease of exposition but the theory could easily be extended to anisotropic inclusions or host.We use a Representative Volume Element approach with the Method of Asymptotic Homogenization to model a random fibre-reinforced composite. The fibres are all aligned in the same direction and are taken to be of infinite extent, so the composite is essentially two-dimensional. For a random composite we have considered the anti-plane case for SH wave propagation and the in-plane case for P and SV elastic wave propagation, extending the previous published work of Parnell and Abrahams (2006), (2008a), in which a periodic fibre-reinforced composite was studied. We also show, for a simple example, that it is possible to extend the Representative Volume Element method to a three-dimensional particulate composite.In this thesis an Integral Equation Method for homogenization is also studied, with application to periodic fibre-reinforced composites. We have extended the work of Parnell and Abrahams (2008b), which considered SH wave propagation only, to the case of P and SV wave propagation.

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