Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T12:28:21Z No. of bitstreams: 1 arquivototal.pdf: 2590482 bytes, checksum: a72ba5c8c44731f3cffe38777111a92d (MD5) / Made available in DSpace on 2017-09-18T12:28:21Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2590482 bytes, checksum: a72ba5c8c44731f3cffe38777111a92d (MD5) Previous issue date: 2011-04-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Aspects of the physics of nematic liquid crystals are studied in this thesis from the viewpoint of riemannian geometry through analogue models of gravitation. The topics chosen for study were: geometric and wave optics, elastic waves, hydrodynamics and heat conduction. The main analogue model used is based on the interpretation of Fermat’s principle as a process to obtain null geodesics, where the liquid crystalline material is seen as a riemannian manifold. This approach predicts that the metric effectively felt by the light ray depends on the configuration of molecules in the liquid crystal and on the parallel and perpendicular refractive indexes to the axis of symmetry of the liquid-cristal molecule. It is known that, for the particular case of the existence of topological defects within the material, effective metric similar to cosmological defects (like global monopoles and cosmic strings) are obtained. This thesis develops itself on the situation where there are topological defects of hedgehog type and (k = 1, c = 0) disclination type in the nematic phase of the liquid crystalline material. The first problem studied, as a review, deals with the wave optics, with respect to the light diffracted by the cited defects. Since plane waves of small wavelength have identical trajectories to light rays, the use of analog model is therefore justified. Thus, we show that light scattered by these defects generates a characteristic diffraction pattern, being the location given by an algebraic expression dependent on the parallel and perpendicular refractive indexes to the axis of symmetry of the molecule. We also show how theses patterns depend on the temperature of the material. The second studied problem deals with the geometrical optics and hydrodynamics of the nematic liquid crystals. From a molecular configuration similar to a (k = 1, c = 0) disclination, we let the material flow radially towards the axis of the defect. Then, using the hydrodynamic fact that velocity gradients in the material locally change the refractive index of the molecule, we find the velocity profile that must exist around the defect so that the metric actually experienced by light traveling in the plane perpendicular to the axis the defect is the Schwarzschild one in the equatorial plane, with the Schwarzschild radius interior to the object. We found that the absolute values of the velocity of liquid crystalline fluid can be order of a few meters per second, differing greatly from the values obtained by Gordon metric for an isotropic fluid under identical conditions. The third studied problem deals with the elastic oscillations in the presence of topological defects. Similarly to the first problem, the trajectory of the sound is obtained by an elastic version of Fermat’s principle and, then, compared with a null geodesic. We show how topological defects influence the sound trajectories and the sound diffracted by them. The fourth problem deals with the heat conduction in the vicinity of defects. Considering that the defects come from an addition or removal of portion of the material, letting the medium relaxes elastically, effective metric of the space disturbed by the defect are found, with expressions similar to those obtained by the analogous model based on Fermat’s principle. These metrics generate a modified thermal conductivity tensor, allowing the study of the temperature field in this situation. We show that, depending on the values of parallel and perpendicular thermal conductivity to the axis of symmetry of the molecule and on the defect in question, the temperature gradient can be accentuated or attenuated on the defect, allowing control of the response thermal temperature of the material, according to the presence of defects. Encouraging a greater understanding of the physics of liquid crystals and its use as a background in analogue models of gravity is the main theme of each analyzed problem. / Aspectos da física dos cristais líquidos nemáticos são estudados nesta tese do ponto de vista da geometria riemannina, por meio de modelos análogos de gravitação. Os tópicos escolhidos para estudo foram: óptica geométrica e ondulatória, ondas elásticas, hidrodinâmica e condução de calor. O principal modelo análogo empregado baseia-se na interpretação do princípio de Fermat como um processo de obtenção de geodésicas nulas, onde o material líquido-cristalino é visto como sendo uma variedade riemanniana. Esta abordagem prevê que a métrica efetivamente sentida pelo raio luminoso dependa da configuração das moléculas dentro do cristal líquido e dos índices de refração paralelo e perpendicular ao eixo de simetria da molécula líquido-cristalina. É sabido que, para o caso especial da existência de defeitos topológicos dentro do material, métricas efetivas semelhantes às de defeitos cosmológicos (como monopolos globais e cordas cósmicas) são obtidas. Esta tese desenrola-se sobre a situação onde existem defeitos topológicos do tipo ouriço e do tipo desclinação (k = 1, c = 0) na fase nemática do material líquido-cristalino. O primeiro problema estudado, em caráter de revisão, trata da óptica ondulatória, no que concerne a difração de luz pelos defeitos citados. Uma vez que ondas planas de comprimento de onda pequeno possuem trajetórias idênticas aos raios luminosos, o emprego do modelo análogo é justificado. Assim, mostramos que a luz espalhada por esses defeitos gera padrões de difração bem característicos, sendo a localização dada por expressão algébrica dependente dos índices de refração paralelo e perpendicular ao eixo de simetria da molécula líquido-cristalina. Também mostramos de que forma esses padrões dependem da temperatura do material. O segundo problema estudado trata da óptica geométrica e da hidrodinâmica dos cristais líquidos nemáticos. A partir de uma configuração de moléculas semelhantes à de uma desclinação (k = 1, c = 0), permitimos que o material flua radialmente na direção do eixo do defeito. Em seguida, fazendo uso do fato hidrodinâmico de que gradientes de velocidade no material modificam localmente os índices de refração da molécula, encontramos o perfil de velocidade que deve existir em torno do defeito para que a métrica efetivamente sentida pela luz, que viaja no plano perpendicular ao eixo do defeito, seja a de Schwarzschild no plano equatorial, com raio de Schwarzschild interior ao objeto. Encontramos que os valores absolutos da velocidade de fluido líquido-cristalino podem ser da ordem de alguns metros por segundo, diferindo enormemente dos valores obtidos pela métrica de Gordon para um fluido isotrópico em condições idênticas. O terceiro problema estudado aborda as oscilações elásticas na presença de defeitos. Semelhantemente ao primeiro problema, a trajetória do som é obtida por uma versão elástica do princípio de Fermat e, então, comparada com uma geodésica nula. Mostramos como defeitos topológicos influenciam nas trajetórias sonoras, assim como no som difratado por eles. O quarto problema trata da condução de calor na vizinhança de defeitos. Considerando que os defeitos são resultantes de uma adição ou remoção de porção de material, dando-se seguimento a uma relaxação elástica do meio, métricas efetivas do espaço perturbado pelo defeito são encontradas, com expressões semelhantes às obtidas pelo modelo análogo baseado no princípio de Fermat. Essas métricas geram um tensor condutividade térmica modificado, dando cabo ao estudo do campo de temperatura nessa situação. Mostramos que, dependendo dos valores da condutividade térmica perpendicular e paralela ao eixo de simetria da molécula líquido-cristalina e do defeito em questão, o gradiente de temperatura pode ser acentuado ou atenuado sobre o defeito, permitindo o controle da resposta térmica do material à temperatura, de acordo com a presença de defeitos. Suscitar um entendimento maior da física dos cristais líquidos e de seu emprego como background em modelos análogos de gravitação é o tema principal de cada um dos problemas analisados.

Une modélisation numérique des ondes poroélastiques, décrites par le modèle de Biot, est proposée dans le domaine temporel. La dissipation visqueuse à l'intérieur des pores est décrite par le modèle de perméabilité dynamique de Johnson-Koplik-Dashen (JKD). Certains coefficients du modèle de Biot-JKD sont proportionnels à la racine carrée de la fréquence, introduisant dans le domaine temporel des dérivées fractionnaires décalées d'ordre 1/2, revenant à un produit de convolution. Basé sur une représentation diffusive, le produit de convolution est remplacé par un nombre fini de variables de mémoire satisfaisant une équation différentielle ordinaire locale en temps, menant au modèle de Biot-DA (diffusive approximation). Les propriétés des deux modèles sont analysées : hyperbolicité, décroissance de l'énergie, dispersion. On montre que la meilleure méthode de détermination des coefficients de l'approximation diffusive - quadratures de Gauss, optimisation linéaire ou non-linéaire sur la plage de fréquence d'intérêt - est l'optimisation non-linéaire. Une méthode de splitting est utilisée numériquement : la partie propagative est discrétisée par un schéma aux différences finies ADER d'ordre 4, et la partie diffusive est intégrée exactement. Les conditions de saut aux interfaces sont discrétisées avec une méthode d'interface immergée. Des simulations numériques sont présentées pour des milieux isotropes et isotropes transverses. Des comparaisons avec des solutions analytiques montrent l'efficacité et la précision de cette approche. Des simulations numériques en milieux complexes sont réalisées : influence de la porosité d'os spongieux, diffusion multiple en milieu aléatoire. / A time-domain numerical modeling of Biot poroelastic waves is proposed. The viscous dissipation in the pores is described using the dynamic permeability model of Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce shifted fractional derivatives of order 1/2, involving a convolution product. Based on a diffusive representation, the convolution product is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations, resulting in the Biot-DA (diffusive approximation). The properties of the two models are analyzed: hyperbolicity, decrease of energy, dispersion. To determine the coefficients of the diffusive approximation, different methods of quadrature are analyzed: Gaussian quadratures, linear or nonlinear optimization procedures in the frequency range of interest. The nonlinear optimization is shown to be the best way of determination. A splitting strategy is applied numerically: the propagative part is discretized using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is solved exactly. An immersed interface method is implemented to discretize the jump conditions at interfaces. Numerical experiments are presented for isotropic and transversely isotropic media. Comparisons with analytical solutions show the efficiency and the accuracy of this approach. Some numerical experiments are performed in complex media: influence of the porosity of a cancellous bone, multiple scattering across a set of random scatterers.

L’imagerie du sous-sol par équations d’onde est une application de l’ingénierie pétrolière qui mobilise des ressources de calcul très importantes. On dispose aujourd’hui de calculateurs puissants qui rendent accessible l’imagerie de régions complexes mais des progrès sont encore nécessaires pour réduire les coûts de calcul et améliorer la qualité des simulations. Les méthodes utilisées aujourd’hui ne permettent toujours pas d’imager correctement des régions très hétérogènes 3D parce qu’elles sont trop coûteuses et /ou pas assez précises. Les méthodes d’éléments finis sont reconnues pour leur efficacité à produire des simulations de qualité dans des milieux hétérogènes. Dans cette thèse, on a fait le choix d’utiliser une méthode de Galerkine discontinue (DG) d’ordre élevé à flux centrés pour résoudre l’équation des ondes acoustiques et on développe un schéma d’ordre élevé pour l’intégration en temps qui peut se coupler avec la technique de discrétisation en espace, sans générer des coûts de calcul plus élevés qu’avec le schéma d’ordre deux Leap-Frog qui est le plus couramment employé. Le nouveau schéma est comparé au schéma d’ordre élevé ADER qui s’avère plus coûteux car il requiert un plus grand nombre d’opérations pour un niveau de précision fixé. De plus, le schéma ADER utilise plus de mémoire, ce qui joue aussi en faveur du nouveau schéma car la production d’images du sous-sol consomme beaucoup de mémoire et justifie de développer des méthodes numériques qui utilisent la mémoire au minimum. On analyse également la précision des deux schémas intégrés dans un code industriel et appliqués à des cas test réalistes. On met en évidence des phénomènes de pollution numériques liés à la mise en oeuvre d'une source ponctuelle dans le schéma DG et on montre qu'on peut éliminer ces ondes parasites en introduisant un terme de pénalisation non dissipatif dans la formulation DG. On finit cette thèse en discutant les difficultés engendrées par l'utilisation de schémas numériques dans un contexte industriel, et en particulier l'effet des calculs en simple précision. / Oil engineering uses a wide variety of technologies including imaging wave equation which involves very large computing resources. Very powerful computers are now available that make imaging of complex areas possible, but further progress is needed both to reduce the computational cost and improve the simulation accuracy. The current methods still do not allow to image properly heterogeneous 3D regions because they are too expensive and / or not accurate enough. Finite element methods turn out to be efficient for producing good simulations in heterogeneous media. In this thesis, we thus chose to use a high order Discontinuous Galerkin (DG) method based upon centered fluxes to solve the acoustic wave equation and developed a high-order scheme for time integration which can be coupled with the space discretization technique, without generating higher computational cost than the second-order Leap Frog scheme which is the most widely used . The new scheme is compared to the high order ADER scheme which is more expensive because it requires a larger number of computations for a fixed level of accuracy. In addition, the ADER scheme uses more memory, which also works in favor of the new scheme since producing subsurface images consumes lots of memory and justifies the development of low-memory numerical methods. The accuracy of both schemes is then analyzed when they are included in an industrial code and applied to realistic problems. The comparison highlights the phenomena of numerical pollution that occur when injecting a point source in the DG scheme and shows that spurious waves can be eliminated by introducing a non-dissipative penalty term in the DG formulation. This work ends by discussing the difficulties induced by using numerical methods in an industrial framework, and in particular the effect of single precision calculations.

Le contexte de cette thèse est la théorie de l'élasticité non linéaire, appelée également "élasticité finie". On y présente des résultats concernant la propagation d'ondes d'amplitude finie dans des matériaux élastiques non linéaires soumis à une grande déformation statique homogène. Bien que les matériaux considérés soient isotropes, lors de la propagation d'ondes un comportement anisotrope dû à la déformation statique se manifeste. <p><p>Après un rappel des équations de base de l'élasticité non linéaire (Chapitre 1), on considère tout d'abord la classe générale des matériaux incompressibles. Pour ces matériaux, on montre que la propagation d'ondes transversales polarisées linéairement est possible pour des choix appropriés des directions de polarisation et de propagation. De plus, on propose des généralisations des modèles classiques de "Mooney-Rivlin" et "néo-Hookéen" qui conduisent à de nouvelles solutions. Bien que le contexte soit tri-dimensionnel, il s'avère que toutes ces ondes sont régies par des équations d'ondes scalaires non linéaires uni-dimensionelles. Dans le cas de solutions du type ondes simples, on met en évidence une propriété remarquable du flux et de la densité d'énergie. <p><p>Dans les Chapitres 3 et 4, on se limite à un modèle particulier de matériaux compressibles appelé "modèle restreint de Blatz-Ko", qui est une version compressible du modèle néo-Hookéen. <p><p>En milieu infini (Chapitre 3), on montre que des ondes transversales polarisées linéairement, faisant intervenir deux variables spatiales, peuvent se propager. Bien que la théorie soit non linéaire, le champ de déplacement de ces ondes est régi par une version anisotrope de l'équation d'onde bi-dimensionnelle classique. En particulier, on présente des solutions à symétrie "cylindrique elliptique" analogues aux ondes cylindriques. Comme cas particulier, on obtient aussi des ondes planes inhomogènes atténuées à la fois dans l'espace et dans le temps. De plus, on montre que diverses superpositions appropriées de solutions sont possibles. Dans chaque cas, on étudie les propriétés du flux et de la densité d'énergie. En particulier, dans le cas de superpositions il s'avère que des termes d'interactions interviennent dans les expressions de la densité et du flux d'énergie. <p><p>Finalement (Chapitre 4), on présente une solution exacte qui constitue une généralisation non linéaire de l'onde de Love classique. On considère ici un espace semi-infini, appelé "substrat" recouvert par une couche. Le substrat et la couche sont constitués de deux matériaux restreints de Blatz-Ko pré-déformés. L'onde non linéaire de Love est constituée d'un mouvement non atténué dans la couche et d'une onde plane inhomogène dans le substrat, choisies de manière à satisfaire aux conditions aux limites. La relation de dispersion qui en résulte est analysée en détail. On présente de plus des propriétés générales du flux et de la densité d'énergie dans le substrat et dans la couche. <p><p><p>The context of this thesis is the non linear elasticity theory, also called "finite elasticity".<p>Results are obtained for finite-amplitude waves in non linear elastic materials which are first subjected to a large homogeneous static deformation. Although the materials are assumed to be isotropic, anisotropic behaviour for wave propagation is induced by the static deformation. <p><p>After recalling the basic equations of the non linear elasticity theory (Chapter 1), we first consider general incompressible materials. For such materials, linearly polarized transverse plane waves solutions are obtained for adequate choices of the polarization and propagation directions (Chapter 2). Also, extensions of the classical Mooney-Rivlin and neo-Hookean models are introduced, for which more solutions are obtained. Although we use the full three dimensional elasticity theory, it turns out that all these waves are governed by scalar one-dimensional non linear wave equations. In the case of simple wave solutions of these equations, a remarkable property of the energy flux and energy density is exhibited.<p><p>In Chapter 3 and 4, a special model of compressible material is considered: the special Blatz-Ko model, which is a compressible counterpart of the incompressible neo-Hookean model. <p><p>In unbounded media (Chapter 3), linearly polarized two-dimensional transverse waves are obtained. Although the theory is non linear, the displacement field of these waves is governed by a linear equation which may be seen as an anisotropic version of the classical two-dimensional wave equation. In particular, solutions analogous to cylindrical waves, but with an "elliptic cylindrical symmetry" are presented. Special solutions representing "damped inhomogeneous plane waves" are also derived: such waves are attenuated both in space and time. Moreover, various appropriate superpositions of solutions are shown to be possible. In each case, the properties of the energy density and the energy flux are investigated. In particular, in the case of superpositions, it is seen that interaction terms enter the expressions for the energy density and the energy flux. <p><p>Finally (Chapter 4), an exact finite-amplitude Love wave solution is presented. Here, an half-space, called "substrate", is assumed to be covered by a layer, both made of different prestrained special Blatz-Ko materials. The Love surface wave solution consists of an unattenuated wave motion in the layer and an inhomogeneous plane wave in the substrate, which are combined to satisfy the exact boundary conditions. A dispersion relation is obtained and analysed. General properties of the energy flux and the energy density in the substrate and the layer are exhibited. <p><p><p><p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Tesis por compendio / [EN] Phononic crystals are artificial materials formed by a periodic arrangement of inclusions embedded into a host medium, where each of them can be solid or fluid. By controlling the geometry and the impedance contrast of its constituent materials, one can control the dispersive properties of waves, giving rise to a huge variety of interesting and fundamental phenomena in the context of wave propagation. When a propagating wave encounters a medium with different physical properties it can be transmitted and reflected in lossless media, but also absorbed if dissipation is taken into account. These fundamental phenomena have been classically explained in the context of homogeneous media, but it has been a subject of increasing interest in the context of periodic structures in recent years as well. This thesis is devoted to the study of different effects found in sonic and phononic crystals associated with transmission, reflection and absorption of waves, as well as the development of a technique for the characterization of its dispersive properties, described by the band structure. We start discussing the control of wave propagation in transmission in conservative systems. Specifically, our interest is to show how sonic crystals can modify the spatial dispersion of propagating waves leading to control the diffractive broadening of sound beams. Making use of the spatial dispersion curves extracted from the analysis of the band structure, we first predict zero and negative diffraction of waves at frequencies close to the band-edge, resulting in collimation and focusing of sound beams in and behind a 3D sonic crystal, and later demonstrate it through experimental measurements. The focusing efficiency of a 3D sonic crystal is limited due to the strong scattering inside the crystal, characteristic of the diffraction regime. To overcome this limitation we consider axisymmetric structures working in the long wavelength regime, as a gradient index lens. In this regime, the scattering is strongly reduced and, in an axisymmetric configuration, the symmetry matching with acoustic sources radiating sound beams increase its efficiency dramatically. Moreover, the homogenization theory can be used to model the structure as an effective medium with effective physical properties, allowing the study of the wave front profile in terms of refraction. We will show the model, design and characterization of an efficient focusing device based on these concepts. Consider now a periodic structure in which one of the parameters of the lattice, such as the lattice constant or the filling fraction, gradually changes along the propagation direction. Chirped crystals represent this concept and are used here to demonstrate a novel mechanism of sound wave enhancement based on a phenomenon known as "soft" reflection. The enhancement is related to a progressive slowing down of the wave as it propagates along the material, which is associated with the group velocity of the local dispersion relation at the planes of the crystal. A model based on the coupled mode theory is proposed to predict and interpret this effect. Two different phenomena are observed here when dealing with dissipation in periodic structures. On one hand, when considering the propagation of in-plane sound waves in a periodic array of absorbing layers, an anomalous decrease in the absorption, combined with a simultaneous increase of reflection and transmission at Bragg frequencies is observed, in contrast to the usual decrease of transmission, characteristic in conservative periodic systems at these frequencies. For a similar layered media, backed now by a rigid reflector, out-of-plane waves impinging the structure from a homogeneous medium will increase dramatically the interaction strength. In other words, the time delay of sound waves inside the periodic system will be considerably increased resulting in an enhanced absorption, for a broadband spectral range. / [ES] Los cristales fonónicos son materiales artificiales formados por una disposición periódica de inclusiones en un medio, pudiendo ambos ser de carácter sólido o fluido. Controlando la geometría y el contraste de impedancias entre los materiales constituyentes se pueden controlar las propiedades dispersivas de las ondas. Cuando una onda propagante se encuentra un medio con diferentes propiedades físicas puede ser transmitida y reflejada, en medios sin pérdidas, pero también absorbida, si la disipación es tenida en cuenta. La presente tesis está dedicada al estudio de diferentes efectos presentes en cristales sónicos y fonónicos relacionados con la transmisión, reflexión y absorción de ondas, así como el desarrollo de una técnica para la caracterización de sus propiedades dispersivas, descritas por la estructura de bandas. En primer lugar, se estudia el control de la propagación de ondas en transmisión en sistemas conservativos. Específicamente, nuestro interés se centra en mostrar cómo los cristales sónicos son capaces de modificar la dispersión espacial de las ondas propagantes, dando lugar al control del ensanchamiento de haces de sonido. Haciendo uso de las curvas de dispersión espacial extraídas del análisis de la estructura de bandas, se predice primero la difracción nula y negativa de ondas a frecuencias cercanas al borde de la banda, resultando en la colimación y focalización de haces acústicos en el interior y detrás de un cristal sónico 3D, y posteriormente se demuestra mediante medidas experimentales. La eficiencia de focalización de un cristal sónico 3D está limitada debido a las múltiples reflexiones existentes en el interior del cristal. Para superar esta limitación se consideran estructuras axisimétricas trabajando en el régimen de longitud de onda larga, como lentes de gradiente de índice. En este régimen, las reflexiones internas se reducen fuertemente y, en configuración axisimétrica, la adaptación de simetría con fuentes acústicas radiando haces de sonido incrementa la eficiencia drásticamente. Además, la teoría de homogenización puede ser empleada para modelar la estructura como un medio efectivo con propiedades físicas efectivas, permitiendo el estudio del frente de ondas en términos refractivos. Se mostrará el modelado, diseño y caracterización de un dispositivo de focalización eficiente basado en los conceptos anteriores. Considérese ahora una estructura periódica en la que uno de los parámetros de la red, sea el paso de red o el factor de llenado, cambia gradualmente a lo largo de la dirección de propagación. Los cristales chirp representan este concepto y son empleados aquí para demostrar un mecanismo novedoso de incremento de la intensidad de la onda sonora basado en un fenómeno conocido como reflexión "suave". Este incremento está relacionado con una ralentización progresiva de la onda conforme se propaga a través del material, asociado con la velocidad de grupo de la relación de dispersión local en los planos del cristal. Un modelo basado en la teoría de modos acoplados es propuesto para predecir e interpretar este efecto. Se observan dos fenómenos diferentes al considerar pérdidas en estructuras periódicas. Por un lado, si se considera la propagación de ondas sonoras en un array periódico de capas absorbentes, cuyo frente de ondas es paralelo a los planos del cristal, se produce una reducción anómala en la absorción combinada con un incremento simultáneo de la reflexión y transmisión a las frecuencias de Bragg, de forma contraria a la habitual reducción de la transmisión, característica de sistemas periódicos conservativos a estas frecuencias. En el caso de la misma estructura laminada en la que se cubre uno de sus lados mediante un reflector rígido, la incidencia de ondas sonoras desde un medio homogéneo, cuyo frente de ondas es perpendicular a los planos del cristal, produce un gran incremento de la fuerza de / [CA] Els cristalls fonònics són materials artificials formats per una disposició d'inclusions en un medi, ambdós poden ser sòlids o fluids. Controlant la geometría i el contrast d'impedàncies dels seus materials constituents, és poden controlar les propietats dispersives de les ondes, permetent una gran varietatde fenòmens fonamentals interessants en el context de la propagació d'ones. Quan una ona propagant troba un medi amb pèrdues amb propietats físiques diferents es pot transmetre i reflectir, però també absorbida si la dissipació es té en compte. Aquests fenòmens fonamentals s'han explicat clàssicament en el context de medis homogenis, però també ha sigut un tema de creixent interés en el context d'estructures periòdiques en els últims anys. Aquesta tesi doctoral tracta de l'estudi de diferents efectes en cristalls fonònics i sònics lligats a la transmissió, reflexió i absorció d'ones, així com del desenvolupament d'una tècnica de caracterització de les propietats dispersives, descrites mitjançant la estructura de bandes. En primer lloc, s'estudia el control de la propagació ondulatori en transmissió en sistemes conservatius. Més específicament, el nostre interés és mostrar com els cristalls sonors poden modificar la dispersió espacial d'ones propagants donant lloc al control de l'amplària per difracció dels feixos sonors. Mitjançant les corbes dispersió espacial obtingudes de l'anàlisi de l'estructura de bandes, es prediu, en primer lloc, la difracció d'ones zero i negativa a freqüències próximes al final de banda. El resultat és la collimació i focalització de feixos sonors dins i darrere de cristalls de so. Després es mostra amb mesures experimentals. L'eficiència de focalització d'un cristall de so 3D està limitada per la gran dispersió d'ones dins del cristall, que és característic del règim difractiu. Per a superar aquesta limitació, estructures axisimètriques que treballen en el règim de llargues longituds d'ona, i es comporten com a lents de gradient d'índex. En aquest règim, la dispersió es redueix enormement i, en una configuració axisimètrica, a causa de l'acoblament de la simetría amb les fonts acústiques que radien feixos sonors, l'eficiència de radiació s'incrementa significativament. D'altra banda, la teoria d'homogeneïtzació es pot utilitzar per a modelar, dissenyar i caracteritzar un dispositiu eficient de focalització basat en aquests conceptes. Considerem ara una estructura periòdica en la qual un dels seus paràmetres de xarxa, com ara la constant de xarxa o el factor d'ompliment canvia gradualment al llarg de la direcció de propagació. Els cristalls chirped representen aquest concepte i s'utilitzen ací per a demostrar un mecanisme nou d'intensificació d'ones sonores basat en el fenòmen conegut com a reflexió "suau". La intensificació està relacionada amb la alentiment progressiva de l'ona conforme propaga al llarg del material, que està associada amb la velocitat de grup de la relació de dispersió local en els diferents plànols del cristall. Es proposa un model basat en la teoria de modes acoblats per a predir i interpretar este efecte. Dos fenòmens diferents cal destacar quan es tracta d'estructures periòdiques amb dissipació. Per un costat, al considerar la propagació d'ones sonores en el plànol en un array periòdic de capes absorbents, s'observa una disminució anòmala de l'absorció i es combina amb un augment simultani de reflexió i transmissió en les freqüències de Bragg que contrasta amb la usual disminució de transmissió, característica dels sistemes conservatius a eixes freqüències. Per a un medi similar de capes, amb un reflector rígid darrere, les ones fora del pla incidint l'estructura des de un medi homogeni, augmentaran considerablement la interacció. En altres paraules, el retràs temporal de les ones sonores dins del sistema periòdic augmentarà significativament produint un augmen / Cebrecos Ruiz, A. (2015). Transmission, reflection and absorption in Sonic and Phononic Crystals [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/56463 / TESIS / Premios Extraordinarios de tesis doctorales / Compendio