This thesis presents the research results on the development of a microwave tomography imaging algorithm capable of reconstructing the dielectric properties of the unknown object. Our focus was on the theoretical aspects of the non-linear tomographic image reconstruction problem with particular emphasis on developing efficient numerical and non-linear optimization for solving the inverse scattering problem. A detailed description of a novel microwave tomography method based on frequency dependent finite difference time domain, a numerical method for solving Maxwell's equations and Genetic Algorithm (GA) as a global optimization technique is given. The proposed technique has the ability to deal with the heterogeneous and dispersive object with complex distribution of dielectric properties and to provide a quantitative image of permittivity and conductivity profile of the object. It is shown that the proposed technique is capable of using the multi-frequency, multi-view, and multi-incident planer techniques which provide useful information for the reconstruction of the dielectric properties profile and improve image quality. In addition, we show that when a-priori information about the object under test is known, it can be easily integrated with the inversion process. This provides realistic regularization of the solution and removes or reduces the possibility of non-true solutions. We further introduced application of the GA such as binary-coded GA, real-coded GA, hybrid binary and real coded GA, and neural-network/GA for solving the inverse scattering problem which improved the quality of the images as well as the conversion rate. The implications and possible advantages of each type of optimization are discussed, and synthetic inversion results are presented. The results showed that the proposed algorithm was capable of providing the quantitative images, although more research is still required to improve the image quality. In the proposed technique the computation time for solution convergence varies from a few hours to several days. Therefore, the parallel implementation of the algorithm was carried out to reduce the runtime. The proposed technique was evaluated for application in microwave breast cancer imaging as well as measurement data from university of Manitoba and Institut Frsenel's microwave tomography systems.

This thesis presents the research results on the development of a microwave tomography imaging algorithm capable of reconstructing the dielectric properties of the unknown object. Our focus was on the theoretical aspects of the non-linear tomographic image reconstruction problem with particular emphasis on developing efficient numerical and non-linear optimization for solving the inverse scattering problem. A detailed description of a novel microwave tomography method based on frequency dependent finite difference time domain, a numerical method for solving Maxwell's equations and Genetic Algorithm (GA) as a global optimization technique is given. The proposed technique has the ability to deal with the heterogeneous and dispersive object with complex distribution of dielectric properties and to provide a quantitative image of permittivity and conductivity profile of the object. It is shown that the proposed technique is capable of using the multi-frequency, multi-view, and multi-incident planer techniques which provide useful information for the reconstruction of the dielectric properties profile and improve image quality. In addition, we show that when a-priori information about the object under test is known, it can be easily integrated with the inversion process. This provides realistic regularization of the solution and removes or reduces the possibility of non-true solutions. We further introduced application of the GA such as binary-coded GA, real-coded GA, hybrid binary and real coded GA, and neural-network/GA for solving the inverse scattering problem which improved the quality of the images as well as the conversion rate. The implications and possible advantages of each type of optimization are discussed, and synthetic inversion results are presented. The results showed that the proposed algorithm was capable of providing the quantitative images, although more research is still required to improve the image quality. In the proposed technique the computation time for solution convergence varies from a few hours to several days. Therefore, the parallel implementation of the algorithm was carried out to reduce the runtime. The proposed technique was evaluated for application in microwave breast cancer imaging as well as measurement data from university of Manitoba and Institut Frsenel's microwave tomography systems.

Τα σύνθετα υλικά οργανικής μήτρας ενισχυμένα με ίνες γυαλιού είναι μια κατηγορία υλικών που έχει υψηλό τεχνολογικό ενδιαφέρον τις τελευταίες δεκαετίες με πληθώρα εφαρμογών στην αεροπορική και διαστημική βιομηχανία, στην αυτοκινητοβιομηχανία, στη formula 1, στα σπορ και γενικότερα όπου οι απαιτήσεις για υψηλή επίδοση των υλικών συνδυάζονται με την απαίτηση για χαμηλό βάρος. Στην κατεύθυνση αυτή έχει συντελέσει και το διαρκώς μειούμενο κόστος παραγωγής των υλικών αυτών μέσω της χρήσης καινοτόμων τεχνικών. Η συνεχής εξέλιξη των υλικών αυτών οδηγεί σε βελτιωμένα υλικά ενισχυτικής και μητρικής φάσης αλλά και εντελώς καινούρια υλικά και προσεγγίσεις όπως είναι ενισχυτικές φάσεις στη νανοκλίμακα (nanofibers, nanotubes). Η εισαγωγή τέτοιων υλικών στη μήτρα συνθέτων υλικών αλλάζει τις μηχανικές και φυσικές τους ιδιότητες με τρόπο πολλές φορές ολοκληρωτικό. Είναι προφανές ότι η τεκμηριωμένη γνώση και ανάπτυξη μεθόδων μη καταστροφικού ελέγχου της δομικής ακεραιότητας αλλά και η γνώση της μηχανικής συμπεριφοράς μέσω της διαδικασίας εξέλιξης της βλάβης σε μια κατηγορία υλικών με τόσο σημαντικές εφαρμογές είναι ζητούμενο από την ερευνητική κοινότητα παγκοσμίως. Προς αυτήν την κατεύθυνση είναι και η συμβολή της παρούσας διατριβής. Μη καταστροφικές μέθοδοι και δοκιμές εφαρμόζονται εδώ και πολλά χρόνια σε σύνθετα υλικά οργανικής μήτρας με επιτυχία παρά την εγγενή ανομοιογένεια και ανισοτροπία που παρουσιάζουν. Ωστόσο πάντα παραμένει ισχυρή η ζήτηση για μεθόδους που θα βοηθήσουν προς την κατεύθυνση της αύξησης της αξιόπιστης χρήσης των υλικών αυτών μέσω της διαρκούς αποτίμησης και γνώσης της φέρουσας ικανότητάς τους. Η συσσώρευση της βλάβης σε σύνθετα υλικά οργανικής μήτρας που υπόκεινται σε μηχανική φόρτιση είναι ένα ζήτημα που έχει διερευνηθεί εκτενώς μέχρι σήμερα. Ωστόσο, η εισαγωγή ενίσχυσης (carbon nanotubes, CNT) στη μήτρα αλλάζει τους μηχανισμούς δημιουργίας και εξέλιξής της. Επίσης προστίθεται η δυνατότητα της μέτρησης μιας ιδιότητας που εμφανίζεται ως αποτέλεσμα της εισαγωγής αυτής και η οποία είναι η ηλεκτρική αγωγιμότητα. Ο βασικός λοιπόν σκοπός της εργασίας αυτής είναι η μελέτη της χρήσης μη καταστροφικών ελέγχων κατά τη διάρκεια μηχανικών δοκιμών συσσώρευσης βλάβης στα υλικά αυτά, καθώς επίσης και η εισαγωγή της μέτρησης της ηλεκτρικής αντίστασης τους ως ικανής μεθόδου παρακολούθησης και ποσοτικοποίησης της βλάβης αυτής. Η διερεύνηση της επιβελτίωσης των μηχανικών ιδιοτήτων λόγω της εισαγωγής των CNT στα υλικά αυτά μέσω της σύγκρισης με τις ιδιότητες που έχουν χωρίς την προσθήκη αυτή. Αναλυτικότερα οι στόχοι που επιδιώξαμε να πετύχουμε στα πλαίσια της διατριβής είναι οι ακόλουθοι: • Μελέτη της διεθνούς βιβλιογραφίας στα συγκεκριμένα θέματα. • Εκτέλεση ειδικά επιλεγμένων μηχανικών δοκιμών σε σύνθετα υλικά Glass/vinylester και Glass/vinylester με CNT (κυκλικά πειράματα φόρτισης – αποφόρτισης – επαναφόρτισης). • Χρήση εξελιγμένων μη καταστροφικών μεθόδων όπως η χρήση δεδομένων ταχύτητας διάδοσης υπερηχητικών ελαστικών κυμάτων (UT) και η ακουστική εκπομπή (AE) για την παρακολούθηση της βλάβης κατά τη διάρκεια των μηχανικών δοκιμών. • Διερεύνηση καταγραφών ηλεκτρικής αντίστασης ως δείκτη βλάβης του υλικού. • Δοκιμές θραυστομηχανικής συμπεριφοράς για την εκτίμηση της βελτίωσης των επιδόσεων του υλικού παρουσία των CNT. / Multi wall carbon nanotubes were used as an additive in the matrix of glass / vinylester composites, in order to improve their damage tolerance and provide a means for their damage assessment at any stage of their loading history. The improvement of the damage tolerance is expected to stem from the incorporation of an additional interfacial area that activates energy dissipation mechanisms such as interfacial sliding, fibre pull out and bridging as well as crack bifurcation and arrest; all these mechanisms are active at the nanoscale. The life monitoring is performed via the electrical resistance changes in the conductive carbon nanotube network within the composite matrix; this network follows any deformation of the composite providing real time strain monitoring and, at the same time, pinpoints all loci of failure through the local breach of the conductive path that lead to a monotonic increase in the overall resistance. The experimental findings verify both the increased damage tolerance of the doped composites and the reliable damage assessment of the composite at all stages of its loading history. Other Non - Destructive Techniques were utilized in order to detect and quantify the accumulating damage. Inverse scattering theory and phase velocity data were used in order to determine the elastic constants of the stifness matrix of the anisotropic material. Fracture toughness and fatigue life behaviour were investigated for both the material systems.

Orientadores: Patricio A. Letelier Sotomayor e Marcelo Moraes Guzzo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-13T19:55:09Z (GMT). No. of bitstreams: 1 Castro_GianMachadode_D.pdf: 3217878 bytes, checksum: 48c026fc06d4c9e5db03014506ffc609 (MD5) Previous issue date: 2009 / Resumo: Nesta tese, estudamos o problema de um anel delgado de matéria de densidade constante com um buraco negro de Kerr em seu centro. Nosso objetivo foi resolver as equações de Einstein no vácuo com simetria axial para esse sistema gravitacional. Para fazer a sobreposição não-linear do anel com o buraco negro (BN), utilizamos o método de Belinsky e Zakharov (MBZ). Este método necessita de uma solução conhecida (solução semente) para gerar uma nova solução. Tomamos a aproximação da solução do anel em multipolos como solução semente. Como resultado, obtivemos a solução de um anel com o BN central. A expansão do anel em multipolos exige o truncamento da série. Esta aproximação introduz um erro em nossa solução. Realizamos o estudo do mesmo devido ao truncamento da série. Também estudamos a estabilidade de órbitas circulares equatoriais de partículas movendo-se ao redor do sistema anel-BN quanto a perturbações epicíclicas e verticais. Analisamos essas perturbações para os modelos de gravitação relativística e newtoniana. Como resultado, encon- tramos o efeito inesperado da duplicação das órbitas circulares de flotons para alguns valores de parâmetros relacionados com o anel e o BN, bem como zonas de estabilidade na região interna do anel. / Abstract: In this thesis, we will study the problem of a thin ring of matter of constant density with a central Kerr black hole. The aim of this work is to solve the Einstein equations in the vacuum with axial symmetry for that gravitational system. To do the nonlinear superposition of the ring with the black hole (BH), we used the Belinsky and Zakharov method (BZM). This method needs a known solution (called seed solution) to generate a new one. We took the Newtonian ring potential approximated by a multipolar expansion as seed solution. As result, we obtained the solution of a ring with a central BH. The ring multipolar expansion demands the truncation of the series. This approach introduces an error in our solution. Estimations of errors due to the truncation of the multipolar expansions are performed. We also studied the stability of equatorial circular orbits of particles moving around the system ring plus BH due to epicycle and vertical perturbations. We analyzed those perturbations for relativistic and Newtonian gravitational models. As result, we found the unexpected effect of the duplication of the photons circular orbits for certain values of parameters related with the ring and BH, as well as zones of stability in the inner area of the matter ring. / Doutorado / Relatividade e Gravitação / Doutor em Ciências

Ce travail thèse s’inscrit dans le cadre du projet FUI Tandem portant sur l’imagerie radar de mines enfouies dans un sol sec par des antennes héliportées. Les données d’antennes correspondent à des mesures de champ électromagnétique (composante tangentielle à l’antenne) en configuration « back-scattering » : une seule antenne émettrice-réceptrice. L’objectif premier de la thèse est de valider/modifier la méthodologie SAR (Synthetic Aperture Radar) proposée par les ingénieurs pour traiter les données d’antenne et imager les mines. La difficulté essentielle réside dans le fait que la méthode SAR repose sur le principe d’un milieu de référence homogène alors que le cas d’étude ne l’est pas. Nous avons étudié l’incorporation d’une approximation bicouche du milieu de référence pour corriger l’effet du sol et obtenir des images moins sensibles à l’effet de celui-ci. La première solution consiste à mimer la technique SAR pour construire une indicatrice de la géométrie via la rétro-propagation de la donnée dans le milieu bi-couche en utilisant la formule donnée par l’approximation de Born. La deuxième option, beaucoup plus coûteuse numériquement consiste à inverser le modèle de Born avec une technique de régularisation de type variation totale. Nous nous intéressons dans une deuxième partie à l’adaptation de méthodes d’inversion de type MUSIC (MUltiple SIgnal Classification) pour retrouver l’information « profondeur » non fournie par les méthodes SAR. S’inspirant de la problématique Tandem, nous avons proposé l’extension de ces méthodes au cas de données en configuration quasi-back-scattering : une antenne émettrice couplée à un réseau 1D d’antennes réceptrices. La méthodologie est complètement nouvelle et la justification de la méthode repose sur l’analyse asymptotique du problème de diffraction dans le régime petit obstacle et champ lointain. L’étude a également été étendue à des configurations cylindriques qui pourraient être adaptées à l’imagerie bio-médicale. / This work is part of the FUI Tandem project on radar imaging of mines buried in dry ground by heliborne antennas. The antenna data correspond to measurements of the electromagnetic field (component tangential to the antenna) in the back-scattering configuration: a single transmitter/transceiver antenna. The primary objective of the thesis is to validate / modify the SAR (Synthetic Aperture Radar) methodology proposed by engineers to process the antenna data and to image the mines. The main difficulty lies in the fact that the SAR method is based on the principle of a homogeneous background whereas the study case is not. We have studied the incorporation of a two-layer approximation of the reference medium to correct the effect of the soil and to obtain images that are less sensitive to the effect of the latter. The first solution consists in mimicking the SAR technique to construct an indicator of the geometry via the back propagation of the data in the bi-layer medium using the formula given by the Born approximation. The second option, much more costly numerically consists in inverting the Born model with a regularization technique of the total variation type. In a second part, we are interested in adapting MUSIC (MUltiple SIgnal Classification) methods to retrieve the "depth" information not provided by SAR methods. Based on the Tandem experiement, we proposed the extension of these methods to the case of data in quasi-back-scattering configuration: a transmitting antenna coupled to a 1D array of receiving antennas. The methodology is completely new and the justification of the method is based on the asymptotic analysis of the scattering problem in the small obstacle and far field regime. The study was also extended to cylindrical configurations that could be adapted to biomedical imaging.

No description available.

This thesis concerns the study, development and analysis of innovative artificial intelligence (AI)-driven optimization techniques within the System-by-Design (SbD) framework aimed at efficiently addressing the computational complexity inherent in advanced electromagnetic (EM) problems. By leveraging the available a-priori information as well as the proper integration of machine learning (ML) techniques with intelligent exploration strategies, the SbD paradigm enables the effective and reliable solution of the EM problem at hand, with user-defined performance and in a reasonable amount of time. The flexibility of the AI-driven SbD framework is demonstrated in practice with the implementation of two solution strategies to address the fully non-linear inverse scattering problem (ISP) for the detection and imaging of buried objects in ground penetrating radar (GPR)-based applications, and to address the design and optimization of mm-wave automotive radars that comply multiple challenging and contrasting requirements. A comprehensive set of numerical experiments is reported to demonstrate the efficacy and computational efficiency of the SbD-based optimization techniques in solving complex EM problems.

[EN] The aim of this work is to demonstrate theoretically and experimentally how acoustic wave propagation can be controlled by temperature gradients. Starting with the simplest case of two hot wires in air the study extends over periodic structures known as Sonic Crystals (SCs). The Finite Elements Method (FEM) has been employed to perform numerical simulations in order to demonstrate collimation and focusing effect of acoustic waves in two-dimensional (2D) SC whose filling fraction is adjusted by temperature gradients. As a part of the research, Bragg reflection and Fabry-Perot type of acoustic effects are investigated for the proposed type of SC. As example, a SC with desired transmittance can be tailored. Also, gradient index (GRIN) 2D sonic lenses are studied. Using parallel rows of heated wires whose temperatures vary according to a prefixed gradient index law a GRIN lens can be designed with a given performance. Moreover, by changing the temperature of the wires a change in the filling fraction inside the GRIN SC can be achieved. Thus, the local refraction index, which is directly related to the filling fraction, is changed too and an index gradient variation inside the GRIN SC is obtained. This GRIN SC is a direct analogy of gradient media observed in nature. Like their optical counterparts, the investigated 2D GRIN SC lenses have flat surfaces and are easier for fabrication than curved SC lenses. The bending of sound waves obtained by GRIN acoustics structures can be used to focusing and collimating acoustic waves. Another aspect of this work is about tuning some SC properties as effective refractive index, effective mass density, etc. in order to obtain a SC with prefixed properties. Since active tuning of the phononic band gaps is certainly desirable for future applications with enhanced functionalities, few attempts have been made to develop tunable SCs thus far. By controlling the incident angle or operating frequency, a GRIN SC can dynamically adjust the curved trajectory of acoustic wave propagation inside the SC structure. Among the last studies of tunable SCs, the filling fractions were tuned either by direct physical deformation of the structure or external stimuli. The former is impractical for most applications and the latter often requires very strong stimuli to produce only modest adjustment. In this work another way to tune the SC properties is proposed. Hot and cold media have different density, speed of sound, refractive index, etc. in comparison with the same properties at normal conditions, so inserting temperature gradients inside the medium can be used to tune the SC properties in certain limits. The proposed way to obtain temperature gradients inside SC is by wires made of Nicrom which are heated by electrical currents. There are some important advantages of this method. First, changing the electrical current intensity through the wires the SC properties can be changed dynamically. Second, it is relatively easier to change the filling fraction simply by adjusting the current intensity than physically changing the structure or applying strong electric or magnetic fields. In conclusion, the method proposed in this thesis allows us, in principle, to get materials and structures with dynamically adjustable acoustic properties using the temperature control through electric current in the wires, within certain limits. Thus, it is easy to carry out experiments of wave propagation phenomena in a macroscopic scale similar to those that occur in microscopic structures for the propagation of electromagnetic waves of high frequency (microwaves and light). / [ES] El objetivo de este trabajo es demostrar teoréticamente y experimentalmente como la propagación de ondas acústicas puede ser controlada por gradientes de temperatura. Empezando con el caso más simple de dos hilos calientes en aire, el estudio se extiende sobre estructuras periódicas conocidas como cristales sónicos (CS). Se ha utilizado el Método de Elementos Finitos (FEM) para realizar simulaciones numéricas con el objetivo de demonstrar la colimación y focalización de ondas acústicas en CS bidimensionales (2D) cuya fracción de llenado es ajustable mediante gradientes de temperatura. Como parte de la investigación se ha analizado la reflexión de Bragg y el efecto de tipo Fabry-Perot asociados con los CSs estudiados. Entre los ejemplos tratados figuran un CS con una transmitancia ajustable a voluntad, dentro de ciertos límites. También se han estudiado lentes acústicas bidimensionales de gradiente de índice, basadas en gradiente de temperatura. Utilizando cortinas paralelas de hilos calientes cuya temperatura varía según una ley dada se puede diseñar una lente GRIN con propiedades determinadas. Por otra parte, cambiando la temperatura de los hilos se puede lograr un cambio en la fracción de llenado dentro del GRIN CS. Así, el índice de refracción local, que está directamente relacionado con la fracción de llenado, se cambia también y se obtiene una variación de gradiente de índice dentro del GRIN CS. Este GRIN CS es una analogía directa de medios con gradiente, observados en la naturaleza. Otro aspecto de este trabajo trata sobre el ajuste de algunas propiedades de un SC como el índice de refracción efectivo o la densidad efectiva con el objetivo de obtener unas propiedades deseadas del cristal. Como el ajuste activo de los bandgaps fonónicos es ciertamente deseado para futuras aplicaciones con funcionalidades mejoradas, hasta ahora se han hecho varios intentos de desarrollar CSs de características ajustables. Controlando el ángulo de incidencia o la frecuencia de funcionamiento, un GRIN CS puede ajustar dinámicamente la curvatura de la trayectoria de propagación dentro de la estructura CS. Entre los últimos estudios de CSs las fracciones de llenado se ajustaron mediante una deformación física directa de la estructura o mediante estímulos externos (por ejemplo campos eléctricos o magnéticos). El primero es poco práctico para una gran parte de las aplicaciones y el segundo a menudo requiere estímulos muy fuertes para ajustes modestos. En este trabajo se propone otra forma de ajustar las propiedades de un CS. Las propiedades acústicas del medio de propagación (densidad, índice de refracción) dependen de la temperatura, por tanto, introduciendo gradientes de temperatura dentro de dicho medio pueden ajustarse a voluntad las propiedades del CS dentro de ciertos límites. La manera de obtener gradientes de temperatura dentro del CS, propuesta en este estudio, es mediante hilos de nicrom calentados con corrientes eléctricas. Hay algunas ventajas importantes de este método. En primer lugar, cambiando la intensidad de corriente eléctrica que circula por los hilos se puede conseguir cambiar dinámicamente las propiedades del CS. En segundo lugar, es relativamente más fácil de cambiar la fracción de llenado simplemente ajustando la intensidad de la corriente eléctrica que modificar físicamente la estructura o aplicar fuertes campos eléctricos o magnéticos. En conclusión, el método propuesto en esta tesis permite, en principio, conseguir materiales y estructuras con propiedades acústicas ajustables dinámicamente mediante el control de la temperatura a través de la corriente eléctrica en los hilos, dentro de ciertos límites. De esta forma se puede experimentar fácilmente a escala macroscópica fenómenos de propagación de ondas análogos a los que ocurren en estructuras microscópicas para la propagación de ondas electromagnéticas de alta frecuencia (microondas y l / [CA] L'objectiu d'este treball és demostrar teorèticament i experimentalment com la propagació d'ones acústiques pot ser controlada per gradients de temperatura. Començant amb el cas més simple de dos fils calents en aire, l'estudi s'estén sobre estructures periòdiques conegudes com a cristalls sónics (CS) . S'ha utilitzat el Mètode d'Elements Finits (FEM) per a realitzar simulacions numèriques amb l'objectiu de demonstrar la col¿limació i focalització d'ones acústiques en CS bidimensionals (2D) la fracció de omplit de la qual és ajustable per mitjà de gradients de temperatura. Com a part de la investigació s'ha analitzat la reflexió de Bragg i l'efecte de tipus Fabry-Perot associats amb els CSs estudiats. Entre els exemples tractats figuren un CS amb una transmitancia ajustable a voluntat, dins de certs límits. També s'han estudiat lents acústiques bidimensionals de gradient d'índex, basades en gradient de temperatura. Utilitzant cortines paral¿leles de fils calents la temperatura de la qual varia segons una llei donada es pot dissenyar una lent GRIN amb propietats determinades. D'altra banda, canviant la temperatura dels fils es pot aconseguir un canvi en la fracció d'ompliment dins del GRIN CS. Així, l'índex de refracció local, que està directament relacionat amb la fracció d'ompliment, es canvia també i s'obté una variació de gradient d'índex dins del GRIN CS. Este GRIN CS és una analogia directa de mitjans amb gradient, observats en la naturalesa. Com les seues analogies òptiques, les lents, estudiades en este treball, tenen les superfícies planes i són més fàcils de fabricar que les lents corbades. La deflexión de les ones acústiques obtinguda per mitjà d'una lent de gradient GRIN es pot utilitzar per a focalitzar o colimar feixos de so. Un altre aspecte d'este treball tracta sobre l'ajust d'algunes propietats d'un SC com l'índex de refracció efectiu o la densitat efectiva amb l'objectiu d'obtindre unes propietats desitjades del cristall. Com l'ajust actiu dels bandgaps fonónicos és certament desitjat per a futures aplicacions amb funcionalitats millorades, fins ara s'han fet diversos intents de desenrotllar CSs de característiques ajustables. Controlant l'angle d'incidència o la freqüència de funcionament, un GRIN CS pot ajustar dinàmicament la curvatura de la trajectòria de propagació dins de l'estructura CS. Entre els últims estudis de CSs les fraccions d'ompliment es van ajustar per mitjà d'una deformació física directa de l'estructura o per mitjà d'estímuls externs. El primer és poc pràctic per a una gran part de les aplicacions i el segon sovint requerix estímuls molt forts per a ajustos modestos. En este treball es proposa una altra forma d'ajustar les propietats d'un CS. Les propietats acústiques del mig de propagació (densitat, índex de refracció) depenen de la temperatura, per tant, introduint gradients de temperatura dins del dit mitjà poden ajustar-se a voluntat les propietats del CS dins de certs límits. La manera d'obtindre gradients de temperatura dins del CS, proposta en este estudi, és per mitjà de fils de Nicrom calfats amb corrents elèctrics. Hi ha alguns avantatges importants d'este mètode. En primer lloc, canviant la intensitat de corrent elèctric que circula pels fils es pot aconseguir canviar dinàmicament les propietats del CS. En segon lloc, és relativament més fàcil de canviar la fracció d'ompliment simplement ajustant la intensitat del corrent elèctric que modificar físicament l'estructura o aplicar forts camps elèctrics o magnètics. En conclusió, el mètode proposat en esta tesi permet, en principi, aconseguir materials i estructures amb propietats acústiques ajustables dinàmicament per mitjà del control de la temperatura a través del corrent elèctric en els fils, dins de certs límits. D'esta manera es pot experimentar fàcilment a escala macroscòpica fenòmens de propagació d'ones anàlegs a què ocorren e / Ivanov Angelov, M. (2016). Sound Scattering by Lattices of Heated Wires [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/63275

Inspiriert von den integrablen Strukturen der schwach gekoppelten planaren N=4 Super-Yang-Mills-Theorie studieren wir Q-Operatoren und Yangsche Invarianten. Wir geben eine Übersicht der Quanten-Inverse-Streumethode zusammen mit der Yang-Baxter Gleichung welche zentral für diesen systematischen Zugang zu integrablen Modellen ist. Den Fokus richten wir auf rationale integrable Spinketten und Vertexmodelle. Wir besprechen einige ihrer bekannten Gemeinsamkeiten und wie sie durch Bethe-Ansatz-Methoden mit Hilfe sogenannter Q-Funktionen gelöst werden können. Der Hauptteil basiert auf den ursprünglichen Publikationen des Autors. Zuerst konstruieren wir Q-Operatoren, deren Eigenwerte zu den Q-Funktionen rationaler homogener Spinketten führen. Die Q-Operatoren werden als Spuren gewisser Monodromien von R-Operatoren eingeführt. Unsere Konstruktion erlaubt es uns die Hierarchie der kommutierenden Q-Operatoren und ihre funktionalen Beziehungen herzuleiten. Wir studieren wie der nächste-Nachbarn Hamiltonoperator, sowie höhere lokale Ladungen direkt aus den Q-Operatoren extrahiert werden können. Danach widmen wir uns der Formulierung der Yangschen Invarianzbedingung, wie sie auch im Zusammenhang mit Baumgraphen die bei der Berechnung von Streuamplituden in der N=4 Super-Yang-Mills-Theorie auftreten, innerhalb der RTT-Realisierung. Dies erlaubt es uns den algebraischen Bethe-Ansatz anzuwenden und die dazugehörigen Bethe Gleichungen herzuleiten, welche für die Konstruktion der Eigenzustände die Yangsche Invarianz aufweisen, relevant sind. Die Komponenten dieser Eigenzustände der von uns betrachteten Spinketten können außerdem als Zustandssummen gewisser zweidimensionaler Vertexmodelle angesehen werden. Zudem analysieren wir die Verbindung zwischen den Eigenzuständen und den oben genannten Baumgraphen. Schlussendlich diskutieren wir die von uns vorgelegten Ergebnisse und deren Folgen im Hinblick auf die Erforschung der planaren N=4 Super-Yang-Mills-Theorie. / Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method QISM along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author''s original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the functional relations among them. We study how the nearest-neighbor Hamiltonian and in principle also higher local charges can be extracted from the Q-operators directly. Secondly, we formulate the Yangian invariance condition, also studied in relation to scattering amplitudes of N=4 super Yang-Mills theory, in the RTT-realization. We find that Yangian invariants can be interpreted as special eigenvectors of certain inhomogeneous spin chains. This allows us to apply the algebraic Bethe ansatz and derive the corresponding Bethe equations that are relevant to construct the invariants. We examine the connection between the Yangian invariant spin chain eigenstates whose components can be understood as partition functions of certain two-dimensional lattice models and tree-level scattering amplitudes of the four-dimensional gauge theory. Finally, we conclude and discuss some future directions and implications of our studies for planar N=4 super Yang-Mills theory.

Diese Arbeit untersucht die N = 4 super-Yang-Mills-Theorie bei schwacher Kopplung, mit dem Ziel eines tieferen Verständnisses von Größen der Theorie als Zustände des integrablen Modells dass der planaren Theorie zu Grunde liegt. Wir leiten On-Shell-Diagramme für Formfaktoren des chiralen Energie-Impuls-Tensor-Multipletts aus der BCFW-Rekursion her, und untersuchen deren Eigenschaften. Dies erlaubt die Herleitung eines Graßmannschen Integrals. Für NMHV-Formfaktoren bestimmen wir die Integrationskontur. Dies erlaubt es das Integral mit einer Twistor-String-Formulierung in Beziehung zu setzen. Mit Hilfe dieser Methoden zeigen wir dass Formfaktoren des chiralen Energie-Impuls-Tensor-Multipletts und On-Shell-Funktionen mit Einfügungen beliebiger Operatoren Eigenzustände integrabler Transfermatrizen sind. Diese Identitäten verallgemeinern die Yangsche Invarianz der On-Shell-Funktionen von Amplituden. Wir zeigen weiterhin dass ein Teil der Yangschen Symmetrien erhalten bleibt. Wir erweitern unsere Untersuchung auf nichtplanare On-Shell-Funktionen und zeigen dass sie ebenfalls solche Symmetrien besitzen. Weitere Identitäten mit Transfermatrizen werden hergeleitet, und zeigen insbesondere dass Diagramme auf Zylindern als Intertwiner fungieren. Als Schritt hin zur Berechnung der Eigenzustände des integrablen Modells zu höheren Schleifenordnungen untersuchen wir Einspuroperatoren. Hier erlaubt die Quantum Spectral Curve die nichtperturbative Berechnung ihres Spektrums, liefert jedoch keine Information zu den Zustände. Die QSC kann als Q-System verstanden werden, welches durch Baxter Q-Operatoren formulierbar sein sollte. Um darauf hinzuarbeiten untersuchen wir die Q-Operatoren nichtkompakter Superspinketten und entwickeln ein effiziente Methode zur Berechnung ihrer Matrixelemente. Dies erlaubt es das gesamte Q-System durch Matrizen für jeden Anregungssektor zu realisieren, und liefert die Grundlage für perturbative Rechnungungen mit der QSC in Operatorform. / This thesis investigates weakly coupled N = 4 super Yang-Mills theory, aiming at a better understanding of various quantities as states of the integrable model underlying the planar theory. We use the BCFW recursion relations to develop on-shell diagrams for form factors of the chiral stress-tensor multiplet, and investigate their properties. The diagrams allow to derive a Graßmannian integral for these form factors. We devise the contour of this integral for NMHV form factors, and use this knowledge to relate the integral to a twistor string formulation. Based on these methods, we show that both form factors of the chiral stress-tensor multiplet as well as on-shell functions with insertions of arbitrary operators are eigenstates of integrable transfer matrices. These identities can be seen as symmetries generalizing the Yangian invariance of amplitude on-shell functions. In addition, a part of these Yangian symmetries are unbroken. We furthermore consider nonplanar on-shell functions and prove that they exhibit a partial Yangian invariance. We also derive identities with transfer matrices, and show that on-shell diagrams on cylinders can be understood as intertwiners. To make progress towards the calculation of the higher loop eigenstates of the integrable model, we consider single trace operators, for which the Quantum Spectral Curve determines their spectrum non-perturbatively. This formulation however carries no information about the states. The QSC is an algebraic Q-system, for which an operatorial form in terms of Baxter Q-operators should exist. To initiate the development such a formulation we investigate the Q-operators of non-compact super spin chains and devise efficient methods to evaluate their matrix elements. This allows to obtain the entire Q-system in terms of matrices for each magnon sector. These can be used as input data for perturbative calculations using the QSC in operatorial form.