Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.

On Fermat's principle for causal curves in time oriented Finsler spacetimes

In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the second variation of the time arrival functional along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765066]

Signal Transceiver Transit Times and Propagation Delay Corrections for Ranging and Georeferencing Applications

The accuracy of ranging measurements depends critically on the knowledge of time delays undergone by signals when retransmitted by a remote transponder and due to propagation effects. A new method determines these delays for every single pulsed signal transmission. It utilizes four ground-based reference stations, synchronized in time and installed at well-known geodesic coordinates and a repeater in space, carried by a satellite, balloon, aircraft, and so forth. Signal transmitted by one of the reference bases is retransmitted by the transponder, received back by the four bases, producing four ranging measurements which are processed to determine uniquely the time delays undergone in every retransmission process. A minimization function is derived comparing repeater's positions referred to at least two groups of three reference bases, providing the signal transit time at the repeater and propagation delays, providing the correct repeater position. The method is applicable to the transponder platform positioning and navigation, time synchronization of remote clocks, and location of targets. The algorithm has been demonstrated by simulations adopting a practical example with the transponder carried by an aircraft moving over bases on the ground.

High Resolution Image Correspondences for Video Post-Production

We present an algorithm for estimating dense image correspondences. Our versatile approach lends itself to various tasks typical for video post-processing, including image morphing, optical flow estimation, stereo rectification, disparity/depth reconstruction, and baseline adjustment. We incorporate recent advances in feature matching, energy minimization, stereo vision, and data clustering into our approach. At the core of our correspondence estimation we use Efficient Belief Propagation for energy minimization. While state-of-the-art algorithms only work on thumbnail-sized images, our novel feature downsampling scheme in combination with a simple, yet efficient data term compression, can cope with high-resolution data. The incorporation of SIFT (Scale-Invariant Feature Transform) features into data term computation further resolves matching ambiguities, making long-range correspondence estimation possible. We detect occluded areas by evaluating the correspondence symmetry, we further apply Geodesic matting to automatically determine plausible values in these regions.

Chemial and isotope compositions of rocks from the West Antarctic

The paper is devoted to a marine geophysical-geological research in the West Antarctic. This researche contributed to establishing the base geodesic network of the West Antarctic and supplemented geokinematic monitoring based on this network with geophysical and geologic information on structure and features of geomorphological and tectonic development of the South Ocean floor. Collected materials allow to conclude about the inhomogeneity of the Scotia Sea floor and about combination of fragments of a continental massif with young rift structures in conditions of the upwelling mantle. The ancient continental bridge, faunal connections between the South America and the West Antarctic has been destroyed by processes of destruction, taphrogeny and sea floor spreading. Structures of the Scotia and Caribbean Seas, North Fiji and Arctic Basins are similar.

Super-resolution for a point source using positive refraction

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a receptor called "perfect drain" (PD) located at the corresponding MFE image point. The PD has the property of absorbing the complete radiation without radiation or scattering and it has been claimed as necessary to obtain super-resolution (SR) in the MFE. However, a prototype using a "drain" different from the PD has shown λ/5 resolution for microwave frequencies (Ma et al, 2010). Recently, the SR properties of a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW) (Miñano et al, 2012) have been analyzed. The reported results show resolution up to λ /3000, for the SGW loaded with the perfect drain, and up to λ /500 f for the SGW without perfect drain. The perfect drain was realized as a coaxial probe loaded with properly calculated impedance. The SGW provides SR only in a narrow band of frequencies close to the resonance Schumann frequencies. Here we analyze the SGW loaded with a small "perfect drain region" (González et al, 2011). This drain is designed as a region made of a material with complex permittivity. The comparative results show that there is no significant difference in the SR properties for both perfect drain designs.

Surface Impedance Characterization for UTD Based Solution with IBC for Surface Fields on a Dielectric-Coated PEC Circular Cylinder

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green?s function between the original problem and the equivalent one with the IBC. This new approach requires small changes in the available UTD based solution with IBC to include the geodesic ray angle and length dependence in the surface impedance formulas. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green?s functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.

Latest developments in data analysis tools for disruption prediction and for the exploration of multimachine operational spaces.

In the last years significant efforts have been devoted to the development of advanced data analysis tools to both predict the occurrence of disruptions and to investigate the operational spaces of devices, with the long term goal of advancing the understanding of the physics of these events and to prepare for ITER. On JET the latest generation of the disruption predictor called APODIS has been deployed in the real time network during the last campaigns with the new metallic wall. Even if it was trained only with discharges with the carbon wall, it has reached very good performance, with both missed alarms and false alarms in the order of a few percent (and strategies to improve the performance have already been identified). Since for the optimisation of the mitigation measures, predicting also the type of disruption is considered to be also very important, a new clustering method, based on the geodesic distance on a probabilistic manifold, has been developed. This technique allows automatic classification of an incoming disruption with a success rate of better than 85%. Various other manifold learning tools, particularly Principal Component Analysis and Self Organised Maps, are also producing very interesting results in the comparative analysis of JET and ASDEX Upgrade (AUG) operational spaces, on the route to developing predictors capable of extrapolating from one device to another.

Perfect imaging of point sources with positive refraction

The capability of a device called the Spherical Geodesic Waveguide (SGW) to produce images with details below the classic Abbe diffraction limit (super-resolution) is analyzed here. The SGW is an optical system equivalent (by means of Transformation Optics) to the Maxwell Fish Eye (MFE) refractive index distribution. Recently, it has been claimed that the necessary condition to get super-resolution in the MFE and the SGW is the use of a Perfect Point Drain (PPD). The PPD is a punctual receptor placed in the focal point that absorbs the incident wave, without reflection or scattering. A microwave circuit comprising three elements, the SGW, the source and the drain (two coaxial lines loaded with specific impedances) is designed and simulated in COMSOL. The super-resolution properties have been analyzed for different position of the source and drain and for two different load impedances: the PPD and the characteristic line impedance. The results show that in both cases super-resolution occurs only for discrete number of frequencies. Out of these frequencies, the SGW does not show SR in the analysis carried out.

Caracterización de la impedancia de superficie para el cálculo del acoplo mutuo en un cilindro circular conductor cubierto por una dieléctrico multicapa

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green's function between the original problem and the equivalent one with the IBC. This new approach requires small changes in the available UTD based solution with IBC to include the geodesic ray angle and length dependence in the surface impedance formulas. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green's functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.

Higher-order regularization and morphological techniques for image segmentation

La segmentación de imágenes es un campo importante de la visión computacional y una de las áreas de investigación más activas, con aplicaciones en comprensión de imágenes, detección de objetos, reconocimiento facial, vigilancia de vídeo o procesamiento de imagen médica. La segmentación de imágenes es un problema difícil en general, pero especialmente en entornos científicos y biomédicos, donde las técnicas de adquisición imagen proporcionan imágenes ruidosas. Además, en muchos de estos casos se necesita una precisión casi perfecta. En esta tesis, revisamos y comparamos primero algunas de las técnicas ampliamente usadas para la segmentación de imágenes médicas. Estas técnicas usan clasificadores a nivel de pixel e introducen regularización sobre pares de píxeles que es normalmente insuficiente. Estudiamos las dificultades que presentan para capturar la información de alto nivel sobre los objetos a segmentar. Esta deficiencia da lugar a detecciones erróneas, bordes irregulares, configuraciones con topología errónea y formas inválidas. Para solucionar estos problemas, proponemos un nuevo método de regularización de alto nivel que aprende información topológica y de forma a partir de los datos de entrenamiento de una forma no paramétrica usando potenciales de orden superior. Los potenciales de orden superior se están popularizando en visión por computador, pero la representación exacta de un potencial de orden superior definido sobre muchas variables es computacionalmente inviable. Usamos una representación compacta de los potenciales basada en un conjunto finito de patrones aprendidos de los datos de entrenamiento que, a su vez, depende de las observaciones. Gracias a esta representación, los potenciales de orden superior pueden ser convertidos a potenciales de orden 2 con algunas variables auxiliares añadidas. Experimentos con imágenes reales y sintéticas confirman que nuestro modelo soluciona los errores de aproximaciones más débiles. Incluso con una regularización de alto nivel, una precisión exacta es inalcanzable, y se requeire de edición manual de los resultados de la segmentación automática. La edición manual es tediosa y pesada, y cualquier herramienta de ayuda es muy apreciada. Estas herramientas necesitan ser precisas, pero también lo suficientemente rápidas para ser usadas de forma interactiva. Los contornos activos son una buena solución: son buenos para detecciones precisas de fronteras y, en lugar de buscar una solución global, proporcionan un ajuste fino a resultados que ya existían previamente. Sin embargo, requieren una representación implícita que les permita trabajar con cambios topológicos del contorno, y esto da lugar a ecuaciones en derivadas parciales (EDP) que son costosas de resolver computacionalmente y pueden presentar problemas de estabilidad numérica. Presentamos una aproximación morfológica a la evolución de contornos basada en un nuevo operador morfológico de curvatura que es válido para superficies de cualquier dimensión. Aproximamos la solución numérica de la EDP de la evolución de contorno mediante la aplicación sucesiva de un conjunto de operadores morfológicos aplicados sobre una función de conjuntos de nivel. Estos operadores son muy rápidos, no sufren de problemas de estabilidad numérica y no degradan la función de los conjuntos de nivel, de modo que no hay necesidad de reinicializarlo. Además, su implementación es mucho más sencilla que la de las EDP, ya que no requieren usar sofisticados algoritmos numéricos. Desde un punto de vista teórico, profundizamos en las conexiones entre operadores morfológicos y diferenciales, e introducimos nuevos resultados en este área. Validamos nuestra aproximación proporcionando una implementación morfológica de los contornos geodésicos activos, los contornos activos sin bordes, y los turbopíxeles. En los experimentos realizados, las implementaciones morfológicas convergen a soluciones equivalentes a aquéllas logradas mediante soluciones numéricas tradicionales, pero con ganancias significativas en simplicidad, velocidad y estabilidad. ABSTRACT Image segmentation is an important field in computer vision and one of its most active research areas, with applications in image understanding, object detection, face recognition, video surveillance or medical image processing. Image segmentation is a challenging problem in general, but especially in the biological and medical image fields, where the imaging techniques usually produce cluttered and noisy images and near-perfect accuracy is required in many cases. In this thesis we first review and compare some standard techniques widely used for medical image segmentation. These techniques use pixel-wise classifiers and introduce weak pairwise regularization which is insufficient in many cases. We study their difficulties to capture high-level structural information about the objects to segment. This deficiency leads to many erroneous detections, ragged boundaries, incorrect topological configurations and wrong shapes. To deal with these problems, we propose a new regularization method that learns shape and topological information from training data in a nonparametric way using high-order potentials. High-order potentials are becoming increasingly popular in computer vision. However, the exact representation of a general higher order potential defined over many variables is computationally infeasible. We use a compact representation of the potentials based on a finite set of patterns learned fromtraining data that, in turn, depends on the observations. Thanks to this representation, high-order potentials can be converted into pairwise potentials with some added auxiliary variables and minimized with tree-reweighted message passing (TRW) and belief propagation (BP) techniques. Both synthetic and real experiments confirm that our model fixes the errors of weaker approaches. Even with high-level regularization, perfect accuracy is still unattainable, and human editing of the segmentation results is necessary. The manual edition is tedious and cumbersome, and tools that assist the user are greatly appreciated. These tools need to be precise, but also fast enough to be used in real-time. Active contours are a good solution: they are good for precise boundary detection and, instead of finding a global solution, they provide a fine tuning to previously existing results. However, they require an implicit representation to deal with topological changes of the contour, and this leads to PDEs that are computationally costly to solve and may present numerical stability issues. We present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension. We approximate the numerical solution of the contour evolution PDE by the successive application of a set of morphological operators defined on a binary level-set. These operators are very fast, do not suffer numerical stability issues, and do not degrade the level set function, so there is no need to reinitialize it. Moreover, their implementation is much easier than their PDE counterpart, since they do not require the use of sophisticated numerical algorithms. From a theoretical point of view, we delve into the connections between differential andmorphological operators, and introduce novel results in this area. We validate the approach providing amorphological implementation of the geodesic active contours, the active contours without borders, and turbopixels. In the experiments conducted, the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions, but with significant gains in simplicity, speed, and stability.

Contribution to active multi-beam reconfigurable antennas for L and S bands

La presente tesis doctoral con título "Contribution to Active Multi-Beam Reconfigurable Antennas for L and S Bands" ha sido desarrollada por el investigador ingeniero de telecomunicación estudiante de doctorado Javier García-Gasco Trujillo en el Grupo de Radiación del Departamento de Señales, Sistemas y Radiocomunicaciones de la ETSI de Telecomunicación de la Universidad Politécnica de Madrid bajo la dirección de los doctores Manuel Sierra Pérez y José Manuel Fernández González. Durante décadas, el desarrollo de antenas de apuntamiento electrónico ha estado limitado al área militar. Su alto coste y su gran complejidad eran los mayores obstáculos que frenaban la introducción de esta tecnología en aplicaciones comerciales de gran escala. La reciente aparición de componentes de estado sólido prácticos, fiables, y de bajo coste ha roto la barrera del coste y ha reducido la complejidad, haciendo que las antenas reconfigurables de apuntamiento electrónico sean una opción viable en un futuro cercano. De esta manera, las antenas phased array podrían llegar a ser la joya de la corona que permitan alcanzar los futuros retos presentes en los sistemas de comunicaciones tanto civiles como militares. Así pues, ahora es el momento de investigar en el desarrollo de antenas de apuntamiento electrónico de bajo coste, donde los nuevos componentes de estado sólido comerciales forman el núcleo duro de la arquitectura. De esta forma, el estudio e implementación de estos arrays de antenas activas de apuntamiento electrónico capaces de controlar la fase y amplitud de las distintas señales implicadas es uno de los grandes retos de nuestro tiempo. Esta tesis se enfrenta a este desafío, proponiendo novedosas redes de apuntamiento electrónico e innovadores módulos de transmisión/recepción (T/R) utilizando componentes de estado sólido de bajo coste, que podrán integrar asequibles antenas activas reconfigurables multihaz en bandas L y S. En la primera parte de la tesis se realiza una descripción del estado del arte de las antenas phased array, incluyendo su base teórica y sus ventajas competitivas. Debido a que las contribuciones obtenidas en la presente tesis han sido realizadas dentro de distintos proyectos de investigación, donde se han manejada antenas de simple/doble polarización circular y simple/doble banda de trabajo, se describen detenidamente los dos proyectos más relevantes de la investigación: el radar de basura espacial de la Agencia Espacial Europea (ESA), Space Situational Awareness (SSA); y la estación base de seguimiento y control de satélites de órbita baja, GEOdesic Dome Array (GEODA). Sin lugar a dudas, los dispositivos desfasadores son uno de los componentes clave en el diseño de antenas phased arrays. Recientemente se ha observado una gran variación en el precio final de estos dispositivos, llegando en ocasiones a límites inasequibles. Así pues, se han propuesto distintas técnicas de conformación de haz alternativas a la utilización de componentes desfasadores comerciales: el desfasador de líneas conmutadas, la red de haz conmutado, y una novedosa red desfasadora divisora/combinadora de potencia. Para mostrar un uso práctico de las mismas, se ha propuesto el uso de las tres alternativas para el caso práctico del subarray de cinco elementos de la celda GEODA-SARAS. Tras dicho estudio se obtiene que la novedosa red desfasadora divisora/combinadora de potencia propuesta es la que mejor relación comportamiento/coste presenta. Para verificar su correcto funcionamiento se construye y mide los dos bloques principales de los que está compuesta la red total, comprobando que en efecto la red responde según lo esperado. La estructura más simple que permite realizar un barrido plano es el array triangular de tres elementos. Se ha realizado el diseño de una nueva red multihaz que es capaz de proporcionar tres haces ortogonales en un ángulo de elevación _0 y un haz adicional en la dirección broadside utilizando el mencionado array triangular de tres elementos como antena. En primer lugar se realizar una breve introducción al estado del arte de las redes clásicas multihaz. Así mismo se comentan innovadores diseños de redes multihaz sin pérdidas. El estudio da paso a las redes disipativas, de tal forma que se analiza su base matemática y se muestran distintas aplicaciones en arrays triangulares de tres elementos. Finalmente, la novedosa red básica propuesta se presenta, mostrando simulaciones y medidas de la misma para el caso prácticoo de GEODA. También se ha diseñado, construido y medido una red compuesta por dos redes básicas complementarias capaz de proporcionar seis haces cuasi-ortogonales en una dirección _0 con dos haces superpuestos en broadside. La red propuesta queda totalmente validada con la fabricación y medida de estos con prototipos. Las cadenas de RF de los módulos T/R de la nueva antena GEODA-SARAS no son algo trivial. Con el fin de mostrar el desarrollo de una cadena compleja con una gran densidad de componentes de estado sólido, se presenta una descripción detallada de los distintos componentes que integran las cadenas de RF tanto en transmisión como en recepción de la nueva antena GEODA-SARAS. Tras presentar las especificaciones de la antena GEODA-SARA y su diagrama de bloques esquemático se describen los dos bloques principales de las cadenas de RF: la celda de cinco elementos, y el módulo de conversión de panel. De la misma manera también se presentará el módulo de calibración integrado dentro de los dos bloques principales. Para comprobar que el funcionamiento esperado de la placa es el adecuado, se realizará un análisis que tratará entre otros datos: la potencia máxima en la entrada del transmisor (comprobando la saturación de la cadena), señal de recepción mínima y máxima (verificando el rango de sensibilidad requerido), y el factor G/T (cumpliendo la especificación necesaria). Así mismo se mostrará un breve estudio del efecto de la cuantificación de la fase en el conformado de haz de RF. Los estudios muestran que la composición de las cadenas de RF permite el cumplimiento de las especificaciones necesarias. Finalmente la tesis muestra las conclusiones globales del trabajo realizado y las líneas futuras a seguir para continuar con esta línea de investigación. ABSTRACT This PhD thesis named "Contribution to Active Multi-Beam Reconfigurable Antennas for L and S Bands", has been written by the Electrical Engineer MSc. researcher Javier García-Gasco Trujillo in the Grupo de Radiación of the Departamento de Señales, Sistemas y Radiocomunicaciones from the ETSI de Telecomunicación of the Universidad Politécnica de Madrid. For decades, the implementation of electronically steerable phased array antennas was confined to the military area. Their high cost and complexity were the major obstacles to introduce this technology in large scale commercial applications. The recent emergence of new practical, low-cost, and highly reliable solid state devices; breaks the barrier of cost and reduces the complexity, making active phased arrays a viable future option. Thus, phased array antennas could be the crown jewel that allow to meet the future challenges in military and civilian communication systems. Now is time to deploy low-cost phased array antennas, where newly commercial components form the core of the architecture. Therefore, the study and implementation of these novel low-cost and highly efficient solid state phased array blocks capable of controlling signal phase/amplitude accurately is one of the great challenges of our time. This thesis faces this challenge, proposing innovative electronic beam steering networks and transmitter/ receiver (T/R) modules using affordable solid state components, which could integrate fair reconfigurable phased array antennas working in L and S bands. In the first part of the thesis, a description of the state of art of phased array antennas, including their fundamentals and their competitive advantages, is presented. Since thesis contributions have been carried out for different research projects, where antennas with single/double circular polarization and single/double working frequency bands have been examined, frameworks of the two more important projects are detailed: the Space Situational Awareness (SSA) programme from the European Space Agency (ESA), and the GEOdesic Dome Array (GEODA) project from ISDEFE-INSA and the ESA. Undoubtedly, phase shifter devices are one of the key components of phased array antennas. Recent years have witnessed wide fluctuations in commercial phase shifter prices, which sometimes led to unaffordable limit. Several RF steering technique alternatives to the commercial phase shifters are proposed, summarized, and compared: the switched line phase shifter, the switched-beam network, and the novel phase shifter power splitter/combiner network. In order to show a practical use of the three different techniques, the five element GEODA-SARAS subarray is proposed as a real case of study. Finally, a practical study of a newly phase shifter power splitter/combiner network for a subarray of five radiating elements with triangular distribution is shown. Measurements of the two different phase shifter power splitter/combiner prototypes integrating the whole network are also depicted, demonstrating their proper performance. A triangular cell of three radiating elements is the simplest way to obtain a planar scanner. A new multibeam network configuration that provides three orthogonal beams in a desired _0 elevation angle and an extra one in the broadside steering direction for a triangular array of three radiating elements is introduced. Firstly, a short introduction to the state of art of classical multi-beam networks is presented. Lossless network analysis, including original lossless network designs, are also commented. General dissipative network theory as well as applications for array antennas of three radiating elements are depicted. The proposed final basic multi-beam network are simulated, built and measured to the GEODA cell practical case. A combined network that provides six orthogonal beams in a desired _0 elevation angle and a double seventh one in the broadside direction by using two complementary proposed basic networks will be shown. Measurements of the whole system will be also depicted, verifying the expected behavior. GEODA-SARAS T/R module RF chains are not a trivial design. A thorough description of all the components compounding GEODA-SARAS T/R module RF chains is presented. After presenting the general specifications of the GEODA-SARAS antenna and its block diagrams; two main blocks of the RF chains, the five element cell and the panel conversion module, are depicted and analyzed. Calibration module integrated within the two main blocks are also depicted. Signal flow throw the system analyzing critical situations such as maximum transmitted power (testing the chain unsaturation), minimum and maximum receiving signal (verifying sensitivity range), maximum receiver interference signals (assuring a proper reception), and G/T factor (fulfilling the technical specification) are evaluated. Phase quantization error effects are also listed. Finally, the manuscript contains the conclusions drawn of the present research and the future work.

Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.

Experimental evidence of super-resolution better than lambda/105 with positive refraction

Super-resolution (SR) systems surpassing the Abbe diffraction limit have been theoretically and experimentally demonstrated using a number of different approaches and technologies: using materials with a negative refractive index, utilizing optical super-oscillation, using a resonant metalens, etc. However, recently it has been proved theoretically that in the Maxwell fish-eye lens (MFE), a device made of positive refractive index materials, the same phenomenon takes place. Moreover, using a simpler device equivalent to the MFE called the spherical geodesic waveguide (SGW), an SR of up to λ/3000 was simulated in COMSOL. Until now, only one piece of experimental evidence of SR with positive refraction has been reported (up to λ/5) for an MFE prototype working at microwave frequencies. Here, experimental results are presented for an SGW prototype showing an SR of up to λ/105. The SGW prototype consists of two concentric metallic spheres with an air space in between and two coaxial ports acting as an emitter and a receiver. The prototype has been analyzed in the range 1 GHz to 1.3 GHz.

Métodos diferenciales e interferométricos para la evaluación de deformaciones de la corteza terrestre mediante técnicas GNSS e InSAR = Differential and interferometric methods for evaluation of crustal deformation using GNSS and InSAR techniques

La actividad volcánica interviene en multitud de facetas de la propia actividad humana, no siempre negativas. Sin embargo, son más los motivos de peligrosidad y riesgo que incitan al estudio de la actividad volcánica. Existen razones de seguridad que inciden en el mantenimiento del seguimiento y monitorización de la actividad volcánica para garantizar la vida y la seguridad de los asentamientos antrópicos en las proximidades de los edificios volcánicos. En esta tesis se define e implementa un sistema de monitorización de movimientos de la corteza en las islas de Tenerife y La Palma, donde el impacto social que representa un aumento o variación de la actividad volcánica en las islas es muy severo. Aparte de la alta densidad demográfica del Archipiélago, esta población aumenta significativamente, en diferentes periodos a lo largo del año, debido a la actividad turística que representa la mayor fuente de ingresos de las islas. La población y los centros turísticos se diseminan predominantemente a lo largo de las costas y también a lo largo de los flancos de los edificios volcánicos. Quizá el mantenimiento de estas estructuras sociales y socio-económicas son los motivos más importantes que justifican una monitorización de la actividad volcánica en las Islas Canarias. Recientemente se ha venido trabajando cada vez más en el intento de predecir la actividad volcánica utilizando los nuevos sistemas de monitorización geodésica, puesto que la actividad volcánica se manifiesta anteriormente por deformación de la corteza terrestre y cambios en la fuerza de la gravedad en la zona donde más tarde se registran eventos volcánicos. Los nuevos dispositivos y sensores que se han desarrollado en los últimos años en materias como la geodesia, la observación de la Tierra desde el espacio y el posicionamiento por satélite, han permitido observar y medir tanto la deformación producida en el terreno como los cambios de la fuerza de la gravedad antes, durante y posteriormente a los eventos volcánicos que se producen. Estos nuevos dispositivos y sensores han cambiado las técnicas o metodologías geodésicas que se venían utilizando hasta la aparición de los mismos, renovando métodos clásicos y desarrollando otros nuevos que ya se están afianzando como metodologías probadas y reconocidas para ser usadas en la monitorización volcánica. Desde finales de la década de los noventa del siglo pasado se han venido desarrollando en las Islas Canarias varios proyectos que han tenido como objetivos principales el desarrollo de nuevas técnicas de observación y monitorización por un lado y el diseño de una metodología de monitorización volcánica adecuada, por otro. Se presenta aquí el estudio y desarrollo de técnicas GNSS para la monitorización de deformaciones corticales y su campo de velocidades para las islas de Tenerife y La Palma. En su implementación, se ha tenido en cuenta el uso de la infraestructura geodésica y de monitorización existente en el archipiélago a fin de optimizar costes, además de complementarla con nuevas estaciones para dar una cobertura total a las dos islas. Los resultados obtenidos en los proyectos, que se describen en esta memoria, han dado nuevas perspectivas en la monitorización geodésica de la actividad volcánica y nuevas zonas de interés que anteriormente no se conocían en el entorno de las Islas Canarias. Se ha tenido especial cuidado en el tratamiento y propagación de los errores durante todo el proceso de observación, medida y proceso de los datos registrados, todo ello en aras de cuantificar el grado de fiabilidad de los resultados obtenidos. También en este sentido, los resultados obtenidos han sido verificados con otros procedentes de sistemas de observación radar de satélite, incorporando además a este estudio las implicaciones que el uso conjunto de tecnologías radar y GNSS tendrán en un futuro en la monitorización de deformaciones de la corteza terrestre. ABSTRACT Volcanic activity occurs in many aspects of human activity, and not always in a negative manner. Nonetheless, research into volcanic activity is more likely to be motivated by its danger and risk. There are security reasons that influence the monitoring of volcanic activity in order to guarantee the life and safety of human settlements near volcanic edifices. This thesis defines and implements a monitoring system of movements in the Earth’s crust in the islands of Tenerife and La Palma, where the social impact of an increase (or variation) of volcanic activity is very severe. Aside from the high demographic density of the archipelago, the population increases significantly in different periods throughout the year due to tourism, which represents a major source of revenue for the islands. The population and the tourist centres are mainly spread along the coasts and also along the flanks of the volcanic edifices. Perhaps the preservation of these social and socio-economic structures is the most important reason that justifies monitoring volcanic activity in the Canary Islands. Recently more and more work has been done with the intention of predicting volcanic activity, using new geodesic monitoring systems, since volcanic activity is evident prior to eruption because of a deformation of the Earth’s crust and changes in the force of gravity in the zone where volcanic events will later be recorded. The new devices and sensors that have been developed in recent years in areas such as geodesy, the observation of the Earth from space, and satellite positioning have allowed us to observe and measure the deformation produced in the Earth as well as the changes in the force of gravity before, during, and after the volcanic events occur. The new devices and sensors have changed the geodetic techniques and methodologies that were used previously. The classic methods have been renovated and other newer ones developed that are now vouched for as proven recognised methodologies to be used for volcanic monitoring. Since the end of the 1990s, in the Canary Islands various projects have been developed whose principal aim has been the development of new observation and monitoring techniques on the one hand, and the design of an appropriate volcanic monitoring methodology on the other. The study and development of GNSS techniques for the monitoring of crustal deformations and their velocity field is presented here. To carry out the study, the use of geodetic infrastructure and existing monitoring in the archipelago have been taken into account in order to optimise costs, besides complementing it with new stations for total coverage on both islands. The results obtained in the projects, which are described below, have produced new perspectives in the geodetic monitoring of volcanic activity and new zones of interest which previously were unknown in the environment of the Canary Islands. Special care has been taken with the treatment and propagation of errors during the entire process of observing, measuring, and processing the recorded data. All of this was done in order to quantify the degree of trustworthiness of the results obtained. Also in this sense, the results obtained have been verified with others from satellite radar observation systems, incorporating as well in this study the implications that the joint use of radar technologies and GNSS will have for the future of monitoring deformations in the Earth’s crust.