We propose an efficient wideband theory for adjoint variable sensitivity analysis of problems with general anisotropic materials. The method is formulated based on the transmission line numerical modeling technique. The anisotropic material properties of potential interest are the full tensors of permittivity, permeability, electrical conductivity, magnetic resistivity, magnetoelectric coupling, and electromagnetic coupling. The tensors may contain non-diagonal elements. Our method estimates the gradients of the desired response with respect to all designable parameters using at most one extra simulation, regardless of their number. In contrast, in the conventional sensitivity analysis method using central finite differences, the number of the required simulations scales linearly with the number of designable parameters. The theory has been implemented for sensitivity analysis of the two and three-dimensional structures. The available adjoint variable method (AVM) sensitivities enable the optimization-based design of anisotropic and dispersive anisotropic structures. We apply our AVM technique to optimization-based wideband invisibility cloak design of arbitrary-shape objects. Our method optimizes the voxel-by-voxel constitutive parameters of an anisotropic cloak. This results in a large number of optimizable parameters. The associated sensitivities of a wideband cloaking objective function are efficiently estimated using our anisotropic adjoint variable method technique. A gradient-based optimization algorithm utilizes the available sensitivity information to iteratively minimize the visibility objective function and to determine the constitutive parameters of the optimal cloak. / Thesis / Doctor of Philosophy (PhD)

Dans le cadre de certaines applications militaires ou méthodologiques, on peut chercher à rendre un objet « invisible » vis-à-vis des ondes acoustiques. Différentes méthodes passives ont été proposées ces dernières années pour éviter ou atténuer la diffraction d'ondes acoustiques sur des obstacles rigides. Ces techniques reposent sur des phénomènes purement acoustiques, avec par exemple la présence de multiples résonateurs ou d'objets diffractants. L'étude présentée ici s'intéresse pour sa part aux effets que l'on pourrait obtenir au moyen d'un revêtement multicouche élastique fixé à un cylindre que l'on souhaite rendre indétectable. Le comportement vibro-acoustique d'un tel revêtement est d'abord modélisé. Par optimisation, on détermine les caractéristiques mécaniques et dimensionnelles des couches permettant une atténuation omnidirectionnelle de la diffraction. Des configurations réalistes de revêtements composés d'une couche orthotrope et d'une couche isotrope sont dégagées dans le cas d'un milieu extérieur constitué d'air. On montre que de tels dispositifs permettent d'atténuer la diffraction à une fréquence donnée ou sur une bande de fréquence. Le problème de la caractérisation expérimentale de ces revêtements est également abordé. Dans un second temps, le cas d'un milieu extérieur constitué d'eau est étudié. On met alors en évidence une réduction de la diffraction avec des revêtements composés de deux couches isotropes. L'influence des différents paramètres de la couche intérieure est analysée. Enfin, des exemples montrent que la bande de fréquence sur laquelle a lieu l'atténuation de la diffraction peut être élargie en augmentant le nombre de couches. / Making an object invisible to acoustic waves could prove useful for military applications or measurements in confined space. Different passive methods have been proposed in recent years to avoid acoustic scattering from rigid obstacles.These techniques are exclusively based on acoustic phenomena, and use for instance multiple resonators or scatterers. This thesis deals with a different method and studies the effects in terms of scattering reduction of an elastic multi-layered coating fixed to the object to conceal. Vibrations of the coating subject to acoustic waves are first modelled to compute the scattered pressure in the external fluid. Mechanical and dimensional properties of the layers leading to omnidirectional scattering reduction are optimised. Considering an external fluid consisting of air, realistic configurations of coatings emerge, composed of a thick internal orthotopic layer and a thin external isotropic layer. These coatings are shown to enable scattering reduction at a precise frequency or on a larger frequency band. The problem of experimental characterisation is also addressed.The study then focuses on a cylinder immersed in water. Bi-layer isotropic coatings can be used in such configuration. A parametric study is led on the characteristics of the internal layer. Finally, significant scattering reduction is achieved for alarger frequency range by increasing the number of layers. Examples of four-layer isotropic coatings are presented to highlight this result.

Cette thèse porte sur l’étude numérique et expérimentale de l’utilisation de métamatériaux pour le contrôle des ondes à la surface de l’eau. Dans la première partie, nous avons montré comment focaliser les ondes à la surface de l’eau en utilisant une analogie existant avec des métamatériaux électromagnétiques de permittivité diélectrique quasi nulle qualifiés de ”epsilon-near-zero”. Cela a permis d’adapter le motif de phase à l’interface circulaire entre deux domaines présentant un contraste élevé de profondeur d’eau. L’analogie a donné lieu a un comportement fortement non linéaire des ondes, qui se manifeste par la génération d’une cascade de points focaux associés à des sous-multiples de longueurs d’onde par rapport à l’onde incidente. La deuxième application envisagée des métamatériaux pour les ondes à la surface est de rendre invisible les défauts géométriques d’un guide pour un observateur situé en champ lointain. Dans le premier projet lié au cloaking, des guides d’onde possédant différentes sections transverses ont été analysés. L’efficacité de la bathymétrie, donnée par la cartographie conformationnelle, a été evaluée numériquement en termes de propriétés de diffusion. Dans le second projet, nous avons montré numériquement comment rendre invisible un cylindre qui est décalé de l’axe d’un guide d’onde. Utiliser une bathymétrie de cloaking lisse autour du cylindre permet de reduire de manière significative la dispersion dans une large gamme de frequences. Des experiences réalisées avec des bathymétries conformes aux simulations ont confirmé une augmentation de la transmission par rapport à un scenario de référence avec fond plat. / This thesis presents numerical and experimental results concerning usage of metamaterials for water waves control. Two applications were considered. Firstly, we showed how to focus water waves using analogy to a group of metamaterials called epsilon-near-zero. This allowed to tailor phase pattern at the circular interface between two domains with high contrast in water depth. The analogy resulted in highly nonlinear behaviour of waves, manifested by sub-wavelength cascade of focal spots with respect to the incident wave. The second considered application of metamaterials for water waves was hiding (cloaking) defects in a waveguide from the far-field observer. In the first project, related to cloaking, waveguide with varying cross-sections was analyzed. The efficiency of bathymetry, rendered by conformal mapping, was evaluated in terms of scattering properties. The influence of water waves dispersivity on the cancellation of scattering was also determined. Cloaking properties of the obtained bathymetry were experimentally confirmed using a wave packet characterized by broadband spectrum. In the second project, we showed how to cloak a cylinder that is shifted from the centreline of a waveguide. Smooth cloaking bathymetry surrounding a cylinder was able to significantly reduce the scattering in broad range of frequencies. The experimental counterparts confirmed increase in transmission with respect to a reference case with flat bathymetry. The remainder of the thesis presents novel method for the analysis of fringe profilometry images. Performance of the new method was compared to the Fourier Transform Profilometry. We obtained significant enhancement in spectral capabilities.

[EN] The aim of this work is to design new acoustic devices based on arrangements of scattering units. First, the use of sonic crystals as noise barriers for traffic noise control is comprehensively analyzed. Due to the limitations of the conventional structures based on rigid scatterers, the inclusion of absorbing elements is proposed. Two different types of absorbers are here considered: porous materials and microperforated plates. In the first case, the attenuation characteristics of barriers made with cylinders containing rubber crumb is analyzed. The second proposal is based on the construction of cylindrical microperforated shells. Analytical approaches modelling the behavior of the barriers have been developed in both cases. These models show a satisfactory agreement with the corresponding experimental realizations. Finally, it is performed an optimization process in order to obtain efficient sound barriers intended to attenuate traffic noise. Another application considered in this work is the construction of cloaks to render objects acoustically invisible. In particular, cloaks made with rigid inclusions are designed to operate with airborne sound. The first proposal consists of a cloak that utilizes the temperature of the background to control the properties of the effective medium. In addition, two and three-dimensional cloaks have been developed through the scattering cancellation technique. These devices have been designed by means of an optimization procedure and their performance has been experimentally demonstrated. / [ES] El objetivo de este trabajo es el diseño de nuevos dispositivos acústicos basados en disposiciones de centros de dispersión. En primer lugar, el uso de cristales sónicos como barreras acústicas para el control de ruido de tráfico es analizado en detalle. Debido a las limitaciones que presentan las estructuras convencionales basadas en centros de dispersión rígidos, se propone la inclusión de elementos absorbentes en los mismos. Se han considerado dos tipos distintos de absorbente: materiales porosos y placas microperforadas. En el primer caso se analizan las propiedades atenuadoras de barreras formadas por cilindros que contienen granza de caucho. La segunda solución se basa en la construcción de coronas microperforadas. En ambos casos se han desarrollado modelos analíticos que permiten determinar el comportamiento de las barreras. Dichos modelos muestran un acuerdo satisfactorio con las correspondientes realizaciones experimentales. Finalmente se ha realizado un proceso de optimización con objeto de obtener barreras eficientes para la atenuación de ruido de tráfico. Otra aplicación considerada en este trabajo es el desarrollo de dispositivos de invisibilidad acústica. Concretamente se pretenden diseñar mantos constituidos con elementos rígidos para ondas acústicas en aire. La primera propuesta consiste en un manto que utiliza la temperatura del medio externo para controlar sus propiedades efectivas. Además se han desarrollado mantos en dos y tres dimensiones a través de la técnica de cancelación de la dispersión. Los diseños han sido realizados por medio de un proceso de optimización y su funcionamiento ha sido demostrado experimentalmente. / [CA] L'objectiu d'aquest treball és el disseny de nous dispositius acústics basats en disposicions de centres de dispersió. En primer lloc, l'ús de vidres sònics com barreres acústiques per al control de soroll de trànsit és analitzat en detall. A causa de les limitacions que presenten les estructures convencionals basades en centres de dispersió rígids, es proposa la inclusió d'elements absorbents en els mateixos. S'han considerat dos tipus diferents de absorbent: materials porosos i plaques microperforades. En el primer cas s'analitzen les propietats atenuadores de barreres formades per cilindres que contenen gransa de cautxú. La segona solució es basa en la construcció de corones microperforades. En tots dos casos s'han desenvolupat models analítics que permeten determinar el comportament de les barreres. Aquests models mostren un acord satisfactori amb les corresponents realitzacions experimentals. Finalment s'ha realitzat un procés d'optimització per tal d'obtenir barreres eficients per l'atenuació de soroll de trànsit. Una altra aplicació considerada en aquest treball és el desenvolupament de dispositius d'invisibilitat acústica. Concretament es pretenen dissenyar mantells constituïts amb elements rígids per ones acústiques en aire. La primera proposta consisteix en un mantell que utilitza la temperatura del medi extern per controlar les seves propietats efectives. A més s'han desenvolupat mantells en dues i tres dimensions a través de la tècnica de cancel·lació de la dispersió. Els dissenys han estat realitzats per mitjà d'un procés d'optimització i el seu funcionament ha estat demostrat experimentalment. / García Chocano, VM. (2015). New devices for noise control and acoustic cloaking [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/53026 / TESIS / Premios Extraordinarios de tesis doctorales

[pt] Invisibilidade sempre mexeu com a imaginação de crianças e adultos. Quem nunca imaginou ser capaz de tornar-se invisível em certas ocasiões? Recentemente essa ideia da ficção científica tomou forma na vida real, e um dos objetivos do presente texto é explicar de uma maneira acessível as principais ideias físicas e matemáticas por trás do conceito de invisibilidade. Pedimos do leitor somente uma modesta familiaridade com Cálculo Vetorial, Séries de Fourier e Álgebra Linear. O objetivo da capa de invisibilidade é tornar um objeto não detectável por meio de energia eletromagnética. A capa é fisicamente realizada por um metamaterial especialmente projetado para redirecionar certas ondas eletromagnéticas irradiadas sobre o objeto. Nesta exposição, usaremos como exemplo a tomografia de impedância elétrica (TIE) como método de detecção e explicaremos como criar uma capa invisível à TIE. Cabe ressaltar que o processamento de imagem através da TIE diz respeito a um problema inverso e, no contexto das equações diferenciais, esse problema envolve, a partir de determinadas simplificações, a equação de Laplace com condições de contorno. Despretensiosamente, optamos pelo caso bidimensional para facilitar a exposição das idéias principais, embora todos os nossos resultados possam ser generalizados em 3 dimensões. / [en] Invisibility has always instigated children and adult s imagination. Who never thought of occasionally being able to turn yourself invisible? Recently, this science fiction idea has taken shape in real life, and one of the objectives of this text is explain the main physical and mathematical ideas behind the invisibility concept, on a comprehensible way. We only require the reader has a modest familiarity with Vectorial Calculus, Fourier Series and Linear Algebra. Invisibility cloak aims to turn an object imperceptible to electromagnetic energy detection. The cloak is made of an especially projected metamaterial that redirects certain electromagnetic waves irradiated over the object. Here we will take as an example electrical impedance tomography (EIT) as a detection method and we will explain how to create an invisible cloak for EIT. It is worth mentioning that image processing through EIT is an inverse problem. Thereby, in the context of differential equations, this problem involves a few simplifications in the Laplace s problem with contours conditions. Unpretentiously, we chose the two-dimensional case to simplify the exposition of the main ideas, although all of our results may be generalized in three-dimensional case.

El objetivo de este trabajo ha sido obtener expresiones matemáticas para los parámetros elásticos y acústicos efectivos de sistemas heterogéneos en el límite de homogeneización, lo que ha permitido el diseño de nuevos dispositivos acústicos y elásticos funcionales en un amplio rango de longitudes de onda. Los sistemas heterogéneos estudiados han sido, principalmente, estructuras de cilindros elásticos inmersos en un medio fluido no-viscoso, aunque otras geometrías han sido comentadas. La periodicidad de estas estructuras permite reducir el problema al estudio de la "celda unidad"; es decir, a la región del espacio que se repite. Sin embargo, el método desarrollado en el presente trabajo ha permitido analizar el comportamiento cuando la periodicidad se ve alterada por defectos estructurales. Matemáticamente este problema ha sido tratado mediante la teoría de dispersión múltiple, ya que las geometrías del problema son principalmente circulares y dicha teoría ha demostrado ser la más adecuada en ese caso. Se ha utilizado la citada teoría de dispersión múltiple para analizar el comportamiento de un sólo cilindro y de un conjunto de cilindros. Este conjunto de cilindros ha sido ordenado, por un lado, en filas infinitas, dando lugar a expresiones para la reflectancia y transmitancia. Por otro lado, la extensión a todo el plano de las redes de cilindros ha permitido obtener resultados para la estructura de bandas. Para obtener los parámetros efectivos se han desarrollado dos métodos de homogeneización que, si bien coinciden en resultados para los casos elementales, han demostrado ser complementarios para calcular situaciones más complejas. El primero se basa en la propagación de ondas elásticas a través de medios periódicos. Se ha demostrado que, en el límite de baja frecuencia, la propagación de estas ondas presenta una relación de dispersión lineal, de cuya pendiente se ha podido obtener la velocidad de propagación efectiva del medio uniforme asociado. El segundo / Torrent Martí, D. (2008). Towards the full control of sound with sonic crystals and acoustic metamaterials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/3061 / Palancia

High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time. / text

Abnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.

Abnormal electromagnetic wave propagation characterized by negative group velocity and consequently negative group delay (NGD) has been observed in certain materials as well as in artificially built structures. Within finite frequency intervals where an NGD phenomenon is observed, higher frequency components of the applied waveform are propagated with phase advancement, not delay, relative to the lower frequency components. These media have found use in many applications that require positive delay compensation and an engineered phase characteristic, such as eliminating phase variation with frequency in phase shifters, beam-squint minimization in phased array antenna systems, size reduction of feed-forward amplifiers and others. The three principal questions this thesis addresses are: can a generic formulation for artificial NGD structures based on electric circuit resonators be developed; is it possible to derive a quantitative functional relationship (asymptotic limit) between the maximum achievable NGD and the identified trade-off quantity (out-of-band gain); and, can a microwave circuit exhibiting a fully loss-compensated NGD propagation in both directions be designed and implemented? A generic frequency-domain formulation of artificial NGD structures based on electric circuit resonators is developed and characterized by three parameters, namely center frequency, bandwidth and the out-of-band gain. The developed formulation is validated through several topologies reported in the literature. The trade-off relationship between the achievable NGD on one hand, and the out-of-band gain on the other, is identified. The out-of-band gain is shown to be proportional to transient amplitudes when waveforms with defined “turn on/off” times are propagated through an NGD medium. An asymptotic limit for achievable NGD as a function of the out-of-band gain is derived for multi-stage resonator-based NGD circuits as well as for an optimally engineered linear causal NGD medium. Passive NGD media exhibit loss which can be compensated for via active elements. However, active elements are unilateral in nature and therefore do not allow propagation in both directions. A bilateral gain-compensated circuit is designed and implemented, which overcomes this problem by employing a dual-amplifier configuration while preserving the overall circuit stability.