Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrodinger equation

The effective mass Schrodinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band which are similar to those originated in quantum wires and quantum wells coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.

Self-consistent relativistic band structure of the CH3NH3PbI3 perovskite

The electronic structure and properties of the orthorhombic phase of the CH 3 NH 3 PbI 3 perovskite are computed with density functional theory. The structure, optimized using a van der Waals functional, reproduces closely the unit cell volume. The experimental band gap is reproduced accurately by combining spin-orbit effects and a hybrid functional in which the fraction of exact exchange is tuned self-consistently to the optical dielectric constant. Including spin-orbit coupling strongly reduces the anisotropy of the effective mass tensor, predicting a low electron effective mass in all crystal directions. The computed binding energy of the unrelaxed exciton agrees with experimental data, and the values found imply a fast exciton dissociation at ambient temperature. Also polaron masses for the separated carriers are estimated. The values of all these parameters agree with recent indications that fast dynamics and large carrier diffusion lengths are key in the high photovoltaic efficiencies shown by these materials.

InN/GaN heterojunction electrical behavior

Indium nitride (InN) has been the subject of intense research in recent years. Some of its most attractive features are its excellent transport properties such as its small band edge electron effective mass, high electron mobilities and peak drift velocities, and high frequency transient drift velocity oscillations [1]. These suggest enormous potential applications for InN in high frequency electronic devices. But to date the high unintentional bulk electron concentration (n~1018 cm-3) of undoped InN samples and the surface electron accumulation layer make it a hard task to create a reliable metalsemiconductor Schottky barrier. Some attempts have been made to overcome this problem by means of material oxidation [2] or deposition of insulators [3]. In this work we present a way to obtain an electrical rectification behaviour by means of heterojunction growth. Due to the big band gap differences among nitride semiconductors, it’s possible to create a structure with high band offsets. In InN/GaN heterojunctions, depending on the GaN doping, the magnitude of conduction and valence band offset are critical parameters which allow distinguishing among different electrical behaviours. The earliest estimate of the valence band offset at an InN–GaN heterojunction in a wurtzite structure was measured to be ~0.85 eV [4], while the Schottky barrier heights were determined to be ~ 1,4 eV [5].We grew In-face InN layer with varying thickness (between 150 nm and 1 mm) by plasma assisted molecular beam epitaxy (PA-MBE) on GaNntemplates (GaN/Al2O3), with temperatures ranging between 300°C and 450°C. The different doping in GaN template (Si doping, Fe doping and Mg doping) results in differences in band alignments of the two semiconductors changing electrical barriers for carriers and consequently electrical conduction behaviour. The processing of the devices includes metallization of the ohmic contacts on InN and GaN, for which we used Ti/Al/Ni/Au. Whereas an ohmic contact on InN is straightforward, the main issue was the fabrication of the contact on GaN due to the very low decomposition temperature of InN. A standard ohmic contact on GaN is generally obtained by high temperature rapid thermal annealing (RTA), typically done between 500ºC and 900ºC[6]. In this case, the limitation due to the presence of In-face InN imposes an upper limit on the temperature for the thermal annealing process and ohmic contact formation of about 450°C. We will present results on the morphology of the InN layers by X-Ray diffraction and SEM, and electrical measurements, in particular current-voltage and capacitance-voltage characteristics.

Photon Management Structures for Absorption Enhancement in Intermediate Band Solar Cells and Crystalline Silicon Solar Cells

El objetivo de la tesis es investigar los beneficios que el atrapamiento de la luz mediante fenómenos difractivos puede suponer para las células solares de silicio cristalino y las de banda intermedia. Ambos tipos de células adolecen de una insuficiente absorción de fotones en alguna región del espectro solar. Las células solares de banda intermedia son teóricamente capaces de alcanzar eficiencias mucho mayores que los dispositivos convencionales (con una sola banda energética prohibida), pero los prototipos actuales se resienten de una absorción muy débil de los fotones con energías menores que la banda prohibida. Del mismo modo, las células solares de silicio cristalino absorben débilmente en el infrarrojo cercano debido al carácter indirecto de su banda prohibida. Se ha prestado mucha atención a este problema durante las últimas décadas, de modo que todas las células solares de silicio cristalino comerciales incorporan alguna forma de atrapamiento de luz. Por razones de economía, en la industria se persigue el uso de obleas cada vez más delgadas, con lo que el atrapamiento de la luz adquiere más importancia. Por tanto aumenta el interés en las estructuras difractivas, ya que podrían suponer una mejora sobre el estado del arte. Se comienza desarrollando un método de cálculo con el que simular células solares equipadas con redes de difracción. En este método, la red de difracción se analiza en el ámbito de la óptica física, mediante análisis riguroso con ondas acopladas (rigorous coupled wave analysis), y el sustrato de la célula solar, ópticamente grueso, se analiza en los términos de la óptica geométrica. El método se ha implementado en ordenador y se ha visto que es eficiente y da resultados en buen acuerdo con métodos diferentes descritos por otros autores. Utilizando el formalismo matricial así derivado, se calcula el límite teórico superior para el aumento de la absorción en células solares mediante el uso de redes de difracción. Este límite se compara con el llamado límite lambertiano del atrapamiento de la luz y con el límite absoluto en sustratos gruesos. Se encuentra que las redes biperiódicas (con geometría hexagonal o rectangular) pueden producir un atrapamiento mucho mejor que las redes uniperiódicas. El límite superior depende mucho del periodo de la red. Para periodos grandes, las redes son en teoría capaces de alcanzar el máximo atrapamiento, pero sólo si las eficiencias de difracción tienen una forma peculiar que parece inalcanzable con las herramientas actuales de diseño. Para periodos similares a la longitud de onda de la luz incidente, las redes de difracción pueden proporcionar atrapamiento por debajo del máximo teórico pero por encima del límite Lambertiano, sin imponer requisitos irrealizables a la forma de las eficiencias de difracción y en un margen de longitudes de onda razonablemente amplio. El método de cálculo desarrollado se usa también para diseñar y optimizar redes de difracción para el atrapamiento de la luz en células solares. La red propuesta consiste en un red hexagonal de pozos cilíndricos excavados en la cara posterior del sustrato absorbente de la célula solar. La red se encapsula en una capa dieléctrica y se cubre con un espejo posterior. Se simula esta estructura para una célula solar de silicio y para una de banda intermedia y puntos cuánticos. Numéricamente, se determinan los valores óptimos del periodo de la red y de la profundidad y las dimensiones laterales de los pozos para ambos tipos de células. Los valores se explican utilizando conceptos físicos sencillos, lo que nos permite extraer conclusiones generales que se pueden aplicar a células de otras tecnologías. Las texturas con redes de difracción se fabrican en sustratos de silicio cristalino mediante litografía por nanoimpresión y ataque con iones reactivos. De los cálculos precedentes, se conoce el periodo óptimo de la red que se toma como una constante de diseño. Los sustratos se procesan para obtener estructuras precursoras de células solares sobre las que se realizan medidas ópticas. Las medidas de reflexión en función de la longitud de onda confirman que las redes cuadradas biperiódicas consiguen mejor atrapamiento que las uniperiódicas. Las estructuras fabricadas se simulan con la herramienta de cálculo descrita en los párrafos precedentes y se obtiene un buen acuerdo entre la medida y los resultados de la simulación. Ésta revela que una fracción significativa de los fotones incidentes son absorbidos en el reflector posterior de aluminio, y por tanto desaprovechados, y que este efecto empeora por la rugosidad del espejo. Se desarrolla un método alternativo para crear la capa dieléctrica que consigue que el reflector se deposite sobre una superficie plana, encontrándose que en las muestras preparadas de esta manera la absorción parásita en el espejo es menor. La siguiente tarea descrita en la tesis es el estudio de la absorción de fotones en puntos cuánticos semiconductores. Con la aproximación de masa efectiva, se calculan los niveles de energía de los estados confinados en puntos cuánticos de InAs/GaAs. Se emplea un método de una y de cuatro bandas para el cálculo de la función de onda de electrones y huecos, respectivamente; en el último caso se utiliza un hamiltoniano empírico. La regla de oro de Fermi permite obtener la intensidad de las transiciones ópticas entre los estados confinados. Se investiga el efecto de las dimensiones del punto cuántico en los niveles de energía y la intensidad de las transiciones y se obtiene que, al disminuir la anchura del punto cuántico respecto a su valor en los prototipos actuales, se puede conseguir una transición más intensa entre el nivel intermedio fundamental y la banda de conducción. Tomando como datos de partida los niveles de energía y las intensidades de las transiciones calculados como se ha explicado, se desarrolla un modelo de equilibrio o balance detallado realista para células solares de puntos cuánticos. Con el modelo se calculan las diferentes corrientes debidas a transiciones ópticas entre los numerosos niveles intermedios y las bandas de conducción y de valencia bajo ciertas condiciones. Se distingue de modelos de equilibrio detallado previos, usados para calcular límites de eficiencia, en que se adoptan suposiciones realistas sobre la absorción de fotones para cada transición. Con este modelo se reproducen datos publicados de eficiencias cuánticas experimentales a diferentes temperaturas con un acuerdo muy bueno. Se muestra que el conocido fenómeno del escape térmico de los puntos cuánticos es de naturaleza fotónica; se debe a los fotones térmicos, que inducen transiciones entre los estados excitados que se encuentran escalonados en energía entre el estado intermedio fundamental y la banda de conducción. En el capítulo final, este modelo realista de equilibrio detallado se combina con el método de simulación de redes de difracción para predecir el efecto que tendría incorporar una red de difracción en una célula solar de banda intermedia y puntos cuánticos. Se ha de optimizar cuidadosamente el periodo de la red para equilibrar el aumento de las diferentes transiciones intermedias, que tienen lugar en serie. Debido a que la absorción en los puntos cuánticos es extremadamente débil, se deduce que el atrapamiento de la luz, por sí solo, no es suficiente para conseguir corrientes apreciables a partir de fotones con energía menor que la banda prohibida en las células con puntos cuánticos. Se requiere una combinación del atrapamiento de la luz con un incremento de la densidad de puntos cuánticos. En el límite radiativo y sin atrapamiento de la luz, se necesitaría que el número de puntos cuánticos de una célula solar se multiplicara por 1000 para superar la eficiencia de una célula de referencia con una sola banda prohibida. En cambio, una célula con red de difracción precisaría un incremento del número de puntos en un factor 10 a 100, dependiendo del nivel de la absorción parásita en el reflector posterior. Abstract The purpose of this thesis is to investigate the benefits that diffractive light trapping can offer to quantum dot intermediate band solar cells and crystalline silicon solar cells. Both solar cell technologies suffer from incomplete photon absorption in some part of the solar spectrum. Quantum dot intermediate band solar cells are theoretically capable of achieving much higher efficiencies than conventional single-gap devices. Present prototypes suffer from extremely weak absorption of subbandgap photons in the quantum dots. This problem has received little attention so far, yet it is a serious barrier to the technology approaching its theoretical efficiency limit. Crystalline silicon solar cells absorb weakly in the near infrared due to their indirect bandgap. This problem has received much attention over recent decades, and all commercial crystalline silicon solar cells employ some form of light trapping. With the industry moving toward thinner and thinner wafers, light trapping is becoming of greater importance and diffractive structures may offer an improvement over the state-of-the-art. We begin by constructing a computational method with which to simulate solar cells equipped with diffraction grating textures. The method employs a wave-optical treatment of the diffraction grating, via rigorous coupled wave analysis, with a geometric-optical treatment of the thick solar cell bulk. These are combined using a steady-state matrix formalism. The method has been implemented computationally, and is found to be efficient and to give results in good agreement with alternative methods from other authors. The theoretical upper limit to absorption enhancement in solar cells using diffractions gratings is calculated using the matrix formalism derived in the previous task. This limit is compared to the so-called Lambertian limit for light trapping with isotropic scatterers, and to the absolute upper limit to light trapping in bulk absorbers. It is found that bi-periodic gratings (square or hexagonal geometry) are capable of offering much better light trapping than uni-periodic line gratings. The upper limit depends strongly on the grating period. For large periods, diffraction gratings are theoretically able to offer light trapping at the absolute upper limit, but only if the scattering efficiencies have a particular form, which is deemed to be beyond present design capabilities. For periods similar to the incident wavelength, diffraction gratings can offer light trapping below the absolute limit but above the Lambertian limit without placing unrealistic demands on the exact form of the scattering efficiencies. This is possible for a reasonably broad wavelength range. The computational method is used to design and optimise diffraction gratings for light trapping in solar cells. The proposed diffraction grating consists of a hexagonal lattice of cylindrical wells etched into the rear of the bulk solar cell absorber. This is encapsulated in a dielectric buffer layer, and capped with a rear reflector. Simulations are made of this grating profile applied to a crystalline silicon solar cell and to a quantum dot intermediate band solar cell. The grating period, well depth, and lateral well dimensions are optimised numerically for both solar cell types. This yields the optimum parameters to be used in fabrication of grating equipped solar cells. The optimum parameters are explained using simple physical concepts, allowing us to make more general statements that can be applied to other solar cell technologies. Diffraction grating textures are fabricated on crystalline silicon substrates using nano-imprint lithography and reactive ion etching. The optimum grating period from the previous task has been used as a design parameter. The substrates have been processed into solar cell precursors for optical measurements. Reflection spectroscopy measurements confirm that bi-periodic square gratings offer better absorption enhancement than uni-periodic line gratings. The fabricated structures have been simulated with the previously developed computation tool, with good agreement between measurement and simulation results. The simulations reveal that a significant amount of the incident photons are absorbed parasitically in the rear reflector, and that this is exacerbated by the non-planarity of the rear reflector. An alternative method of depositing the dielectric buffer layer was developed, which leaves a planar surface onto which the reflector is deposited. It was found that samples prepared in this way suffered less from parasitic reflector absorption. The next task described in the thesis is the study of photon absorption in semiconductor quantum dots. The bound-state energy levels of in InAs/GaAs quantum dots is calculated using the effective mass approximation. A one- and four- band method is applied to the calculation of electron and hole wavefunctions respectively, with an empirical Hamiltonian being employed in the latter case. The strength of optical transitions between the bound states is calculated using the Fermi golden rule. The effect of the quantum dot dimensions on the energy levels and transition strengths is investigated. It is found that a strong direct transition between the ground intermediate state and the conduction band can be promoted by decreasing the quantum dot width from its value in present prototypes. This has the added benefit of reducing the ladder of excited states between the ground state and the conduction band, which may help to reduce thermal escape of electrons from quantum dots: an undesirable phenomenon from the point of view of the open circuit voltage of an intermediate band solar cell. A realistic detailed balance model is developed for quantum dot solar cells, which uses as input the energy levels and transition strengths calculated in the previous task. The model calculates the transition currents between the many intermediate levels and the valence and conduction bands under a given set of conditions. It is distinct from previous idealised detailed balance models, which are used to calculate limiting efficiencies, since it makes realistic assumptions about photon absorption by each transition. The model is used to reproduce published experimental quantum efficiency results at different temperatures, with quite good agreement. The much-studied phenomenon of thermal escape from quantum dots is found to be photonic; it is due to thermal photons, which induce transitions between the ladder of excited states between the ground intermediate state and the conduction band. In the final chapter, the realistic detailed balance model is combined with the diffraction grating simulation method to predict the effect of incorporating a diffraction grating into a quantum dot intermediate band solar cell. Careful optimisation of the grating period is made to balance the enhancement given to the different intermediate transitions, which occur in series. Due to the extremely weak absorption in the quantum dots, it is found that light trapping alone is not sufficient to achieve high subbandgap currents in quantum dot solar cells. Instead, a combination of light trapping and increased quantum dot density is required. Within the radiative limit, a quantum dot solar cell with no light trapping requires a 1000 fold increase in the number of quantum dots to supersede the efficiency of a single-gap reference cell. A quantum dot solar cell equipped with a diffraction grating requires between a 10 and 100 fold increase in the number of quantum dots, depending on the level of parasitic absorption in the rear reflector.

Advanced Fresnel Köhler concentrators for photovoltaic applications

La concentración fotovoltaica (CPV) es una de las formas más prometedoras de reducir el coste de la energía proveniente del sol. Esto es posible gracias a células solares de alta eficiencia y a una significativa reducción del tamaño de la misma, que está fabricada con costosos materiales semiconductores. Ambos aspectos están íntimamente ligados ya que las altas eficiencias solamente son posibles con materiales y tecnologías de célula caros, lo que forzosamente conlleva una reducción del tamaño de la célula si se quiere lograr un sistema rentable. La reducción en el tamaño de las células requiere que la luz proveniente del sol ha de ser redirigida (es decir, concentrada) hacia la posición de la célula. Esto se logra colocando un concentrador óptico encima de la célula. Estos concentradores para CPV están formados por diferentes elementos ópticos fabricados en materiales baratos, con el fin de reducir los costes de producción. El marco óptimo para el diseño de concentradores es la óptica anidólica u óptica nonimaging. La óptica nonimaging fue desarrollada por primera vez en la década de los años sesenta y ha ido evolucionando significativamente desde entonces. El objetivo de los diseños nonimaging es la transferencia eficiente de energía entre la fuente y el receptor (sol y célula respectivamente, en el caso de la CPV), sin tener en cuenta la formación de imagen. Los sistemas nonimaging suelen ser simples, están compuestos de un menor número de superficies que los sistemas formadores de imagen y son más tolerantes a errores de fabricación. Esto hace de los sistemas nonimaging una herramienta fundamental, no sólo en el diseño de concentradores fotovoltaicos, sino también en el diseño de otras aplicaciones como iluminación, proyección y comunicaciones inalámbricas ópticas. Los concentradores ópticos nonimaging son adecuados para aplicaciones CPV porque el objetivo no es la reproducción de una imagen exacta del sol (como sería el caso de las ópticas formadoras de imagen), sino simplemente la colección de su energía sobre la célula solar. Los concentradores para CPV pueden presentar muy diferentes arquitecturas y elementos ópticos, dando lugar a una gran variedad de posibles diseños. El primer elemento óptico que es atravesado por la luz del sol se llama Elemento Óptico Primario (POE en su nomenclatura anglosajona) y es el elemento más determinante a la hora de definir la forma y las propiedades del concentrador. El POE puede ser refractivo (lente) o reflexivo (espejo). Esta tesis se centra en los sistemas CPV que presentan lentes de Fresnel como POE, que son lentes refractivas delgadas y de bajo coste de producción que son capaces de concentrar la luz solar. El capítulo 1 expone una breve introducción a la óptica geométrica y no formadora de imagen (nonimaging), explicando sus fundamentos y conceptos básicos. Tras ello, la integración Köhler es presentada en detalle, explicando sus principios, válidos tanto para aplicaciones CPV como para iluminación. Una introducción a los conceptos fundamentales de CPV también ha sido incluida en este capítulo, donde se analizan las propiedades de las células solares multiunión y de los concentradores ópticos empleados en los sistemas CPV. El capítulo se cierra con una descripción de las tecnologías existentes empleadas para la fabricación de elementos ópticos que componen los concentradores. El capítulo 2 se centra principalmente en el diseño y desarrollo de los tres concentradores ópticos avanzados Fresnel Köhler que se presentan en esta tesis: Fresnel-Köhler (FK), Fresnel-Köhler curvo (DFK) y Fresnel-Köhler con cavidad (CFK). Todos ellos llevan a cabo integración Köhler y presentan una lente de Fresnel como su elemento óptico primario. Cada uno de estos concentradores CPV presenta sus propias propiedades y su propio procedimiento de diseño. Además, presentan todas las características que todo concentrador ha de tener: elevado factor de concentración, alta tolerancia de fabricación, alta eficiencia óptica, irradiancia uniforme sobre la superficie de la célula y bajo coste de producción. Los concentradores FK y DFK presentan una configuración de cuatro sectores para lograr la integración Köhler. Esto quiere decir que POE y SOE se dividen en cuatro sectores simétricos cada uno, y cada sector del POE trabaja conjuntamente con su correspondiente sector de SOE. La principal diferencia entre los dos concentradores es que el POE del FK es una lente de Fresnel plana, mientras que una lente curva de Fresnel es empleada como POE del DFK. El concentrador CFK incluye una cavidad de confinamiento externo integrada, que es un elemento óptico capaz de recuperar los rayos reflejados por la superficie de la célula con el fin de ser reabsorbidos por la misma. Por tanto, se aumenta la absorción de la luz, lo que implica un aumento en la eficiencia del módulo. Además, este capítulo también explica un método de diseño alternativo para los elementos faceteados, especialmente adecuado para las lentes curvas como el POE del DFK. El capítulo 3 se centra en la caracterización y medidas experimentales de los concentradores ópticos presentados en el capítulo 2, y describe sus procedimientos. Estos procedimientos son en general aplicables a cualquier concentrador basado en una lente de Fresnel, e incluyen tres tipos principales de medidas experimentales: eficiencia eléctrica, ángulo de aceptancia y uniformidad de la irradiancia en el plano de la célula. Los resultados que se muestran a lo largo de este capítulo validarán a través de medidas a sol real las características avanzadas que presentan los concentradores Köhler, y que se demuestran en el capítulo 2 mediante simulaciones de rayos. Cada concentrador (FK, DFK y CFK) está diseñado y optimizado teniendo en cuenta condiciones de operación realistas. Su rendimiento se modela de forma exhaustiva mediante el trazado de rayos en combinación con modelos distribuidos para la célula. La tolerancia es un asunto crítico de cara al proceso de fabricación, y ha de ser máxima para obtener sistemas de producción en masa rentables. Concentradores con tolerancias limitadas generan bajadas significativas de eficiencia a nivel de array, causadas por el desajuste de corrientes entre los diferentes módulos (principalmente debido a errores de alineación en la fabricación). En este sentido, la sección 3.5 presenta dos métodos matemáticos que estiman estas pérdidas por desajuste a nivel de array mediante un análisis de sus curvas I-V, y por tanto siendo innecesarias las medidas a nivel de mono-módulo. El capítulo 3 también describe la caracterización indoor de los elementos ópticos que componen los concentradores, es decir, de las lentes de Fresnel que actúan como POE y de los secundarios free-form. El objetivo de esta caracterización es el de evaluar los adecuados perfiles de las superficies y las transmisiones ópticas de los diferentes elementos analizados, y así hacer que el rendimiento del módulo sea el esperado. Esta tesis la cierra el capítulo 4, en el que la integración Köhler se presenta como una buena alternativa para obtener distribuciones uniformes en aplicaciones de iluminación de estado sólido (iluminación con LED), siendo particularmente eficaz cuando se requiere adicionalmente una buena mezcla de colores. En este capítulo esto se muestra a través del ejemplo particular de un concentrador DFK, el cual se ha utilizado para aplicaciones CPV en los capítulos anteriores. Otra alternativa para lograr mezclas cromáticas apropiadas está basada en un método ya conocido (deflexiones anómalas), y también se ha utilizado aquí para diseñar una lente TIR aplanética delgada. Esta lente cumple la conservación de étendue, asegurando así que no hay bloqueo ni dilución de luz simultáneamente. Ambos enfoques presentan claras ventajas sobre las técnicas clásicas empleadas en iluminación para obtener distribuciones de iluminación uniforme: difusores y mezcla caleidoscópica mediante guías de luz. ABSTRACT Concentrating Photovoltaics (CPV) is one of the most promising ways of reducing the cost of energy collected from the sun. This is possible thanks to both, very high-efficiency solar cells and a large decrease in the size of cells, which are made of costly semiconductor materials. Both issues are closely linked since high efficiency values are only possible with expensive cell materials and technologies, implying a compulsory area reduction if cost-effectiveness is desired. The reduction in the cell size requires that light coming from the sun must be redirected (i.e. concentrated) towards the cell position. This is achieved by placing an optical concentrator system on top of the cell. These CPV concentrators consist of different optical elements manufactured on cheap materials in order to maintain low production costs. The optimal framework for the design of concentrators is nonimaging optics. Nonimaging optics was first developed in the 60s decade and has been largely developed ever since. The aim of nonimaging devices is the efficient transfer of light power between the source and the receiver (sun and cell respectively in the case of CPV), disregarding image formation. Nonimaging systems are usually simple, comprised of fewer surfaces than imaging systems and are more tolerant to manufacturing errors. This renders nonimaging optics a fundamental tool, not only in the design of photovoltaic concentrators, but also in the design of other applications as illumination, projection and wireless optical communications. Nonimaging optical concentrators are well suited for CPV applications because the goal is not the reproduction of an exact image of the sun (as imaging optics would provide), but simply the collection of its energy on the solar cell. Concentrators for CPV may present very different architectures and optical elements, resulting in a vast variety of possible designs. The first optical element that sunlight goes through is called the Primary Optical Element (POE) and is the most determinant element in order to define the shape and properties of the whole concentrator. The POE can be either refractive (lens) or reflective (mirror). This thesis focuses on CPV systems based on Fresnel lenses as POE, which are thin and inexpensive refractive lenses able to concentrate sunlight. Chapter 1 exposes a short introduction to geometrical and nonimaging optics, explaining their fundamentals and basic concepts. Then, the Köhler integration is presented in detail, explaining its principles, valid for both applications: CPV and illumination. An introduction to CPV fundamental concepts is also included in this chapter, analyzing the properties of multijunction solar cells and optical concentrators employed in CPV systems. The chapter is closed with a description of the existing technologies employed for the manufacture of optical elements composing the concentrator. Chapter 2 is mainly devoted to the design and development of the three advanced Fresnel Köhler optical concentrators presented in this thesis work: Fresnel-Köhler (FK), Dome-shaped Fresnel-Köhler (DFK) and Cavity Fresnel-Köhler (CFK). They all perform Köhler integration and comprise a Fresnel lens as their Primary Optical Element. Each one of these CPV concentrators presents its own characteristics, properties and its own design procedure. Their performances include all the key issues in a concentrator: high concentration factor, large tolerances, high optical efficiency, uniform irradiance on the cell surface and low production cost. The FK and DFK concentrators present a 4-fold configuration in order to perform the Köhler integration. This means that POE and SOE are divided into four symmetric sectors each one, working each POE sector with its corresponding SOE sector by pairs. The main difference between both concentrators is that the POE of the FK is a flat Fresnel lens, while a dome-shaped (curved) Fresnel lens performs as the DFK’s POE. The CFK concentrator includes an integrated external confinement cavity, which is an optical element able to recover rays reflected by the cell surface in order to be re-absorbed by the cell. It increases the light absorption, entailing an increase in the efficiency of the module. Additionally, an alternative design method for faceted elements will also be explained, especially suitable for dome-shaped lenses as the POE of the DFK. Chapter 3 focuses on the characterization and experimental measurements of the optical concentrators presented in Chapter 2, describing their procedures. These procedures are in general applicable to any Fresnel-based concentrator as well and include three main types of experimental measurements: electrical efficiency, acceptance angle and irradiance uniformity at the solar cell plane. The results shown along this chapter will validate through outdoor measurements under real sun operation the advanced characteristics presented by the Köhler concentrators, which are demonstrated in Chapter 2 through raytrace simulation: high optical efficiency, large acceptance angle, insensitivity to manufacturing tolerances and very good irradiance uniformity on the cell surface. Each concentrator (FK, DFK and CFK) is designed and optimized looking at realistic performance characteristics. Their performances are modeled exhaustively using ray tracing combined with cell modeling, taking into account the major relevant factors. The tolerance is a critical issue when coming to the manufacturing process in order to obtain cost-effective mass-production systems. Concentrators with tight tolerances result in significant efficiency drops at array level caused by current mismatch among different modules (mainly due to manufacturing alignment errors). In this sense, Section 3.5 presents two mathematical methods that estimate these mismatch losses for a given array just by analyzing its full-array I-V curve, hence being unnecessary any single mono-module measurement. Chapter 3 also describes the indoor characterization of the optical elements composing the concentrators, i.e. the Fresnel lenses acting as POEs and the free-form SOEs. The aim of this characterization is to assess the proper surface profiles and optical transmissions of the different elements analyzed, so they will allow for the expected module performance. This thesis is closed by Chapter 4, in which Köhler integration is presented as a good approach to obtain uniform distributions in Solid State Lighting applications (i.e. illumination with LEDs), being particularly effective when dealing with color mixing requirements. This chapter shows it through the particular example of a DFK concentrator, which has been used for CPV applications in the previous chapters. An alternative known method for color mixing purposes (anomalous deflections) has also been used to design a thin aplanatic TIR lens. This lens fulfills conservation of étendue, thus ensuring no light blocking and no light dilution at the same time. Both approaches present clear advantages over the classical techniques employed in lighting to obtain uniform illumination distributions: diffusers and kaleidoscopic lightpipe mixing.

A level set approach for the analysis of flow and compaction during resin infusion in composite materials

Fluid flow and fabric compaction during vacuum assisted resin infusion (VARI) of composite materials was simulated using a level set-based approach. Fluid infusion through the fiber preform was modeled using Darcy’s equations for the fluid flow through a porous media. The stress partition between the fluid and the fiber bed was included by means of Terzaghi’s effective stress theory. Tracking the fluid front during infusion was introduced by means of the level set method. The resulting partial differential equations for the fluid infusion and the evolution of flow front were discretized and solved approximately using the finite differences method with a uniform grid discretization of the spatial domain. The model results were validated against uniaxial VARI experiments through an [0]8 E-glass plain woven preform. The physical parameters of the model were also independently measured. The model results (in terms of the fabric thickness, pressure and fluid front evolution during filling) were in good agreement with the numerical simulations, showing the potential of the level set method to simulate resin infusion

Nonhydrogenic exciton spectrum in perovskite CH3NH3PbI3

The excitons in the orthorhombic phase of the perovskite CH3NH3PbI3 are studied using the effective mass approximation. The electron–hole interaction is screened by a distance-dependent dielectric function, as described by the Haken potential or the Pollmann–Büttner potential. The energy spectrum and the eigenfunctions are calculated for both cases. The results show that the Pollmann–Büttner model, using the corresponding parameters obtained from ab initio calculations, provides better agreement with the experimental results.

Embryogenic suspensions of adult cork oak: the first step towards mass propagation.

Abstract Protocols have been established to clone adult cork oak trees by somatic embryogenesis using semisolid medium. However, for economically viable mass propagation, embryogenic cultures in liquid medium need to be developed. In this study, suspension cultures were initiated from embryo clusters obtained by secondary embryogenesis on a gelled medium lacking plant growth regulators. After 6 days of culture, these embryo clusters generated high cell density suspensions that also contained small organized structures (embryos and embryogenic clumps). As the culture duration increased, tissue necrosis and fewer embryogenic structures were observed and the establishment of suspension cultures failed. An alternative method was found adequate for initiation of embryogenic suspensions: embryo clusters from gelled medium were briefly shaken in liquid medium and detached cells and embryogenic masses of 41?800 lm were used as inoculum. Maintenance of embryogenic suspensions was achieved using a low-density inoculum (43 mg l-1) by subculturing four embryogenic clumps of 0.8?1.2 mm per 70 ml of medium. Proliferation ability was maintained for almost 1 year through ten consecutive subcultures. The initiation and maintenance protocols first developed for a single genotype were effective when tested on 11 cork oak genotypes.

Aircraft trajectory simulator using a three degrees of freedom aircraft point mass model

Aircraft Operators Companies (AOCs) are always willing to keep the cost of a flight as low as possible. These costs could be modelled using a function of the fuel consumption, time of flight and fixed cost (over flight cost, maintenance, etc.). These are strongly dependant on the atmospheric conditions, the presence of winds and the aircraft performance. For this reason, much research effort is being put in the development of numerical and graphical techniques for defining the optimal trajectory. This paper presents a different approach to accommodate AOCs preferences, adding value to their activities, through the development of a tool, called aircraft trajectory simulator. This tool is able to simulate the actual flight of an aircraft with the constraints imposed. The simulator is based on a point mass model of the aircraft. The aim of this paper is to evaluate 3DoF aircraft model errors with BADA data through real data from Flight Data Recorder FDR. Therefore, to validate the proposed simulation tool a comparative analysis of the state variables vector is made between an actual flight and the same flight using the simulator. Finally, an example of a cruise phase is presented, where a conventional levelled flight is compared with a continuous climb flight. The comparison results show the potential benefits of following user-preferred routes for commercial flights.

HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality. This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox. Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis.

Electron temperature versus laser intensity times wavelength squared: a comparison of theory and experiments

The peak temperature in the corona of plasma ejected by a laser-irradiated slab is discussed in terms of a one-electron-temperature model. Both heat-flux saturation and pulse rise-time effects are considered;the intensity in the rising half of the pulse is approximated by a linear function of time, I(t) = Iot/r. The temperature is found to be proportional to (IQX2)273 and a function of I0X4/r. Above a certain value of I0X4/T, the plasma presents two characteristic temperatures (at saturation and at the critical surface) which can be identified with experimentally observed cold- and hot-electron temperatures. The results are compared with extensive experimental data available for both nd and CO2 lasers, I0(W'cnf2) X2 (/um) starting around 1012. The agreement is good if substantial flux inhibition is assumed (flux-limit factor f = 0.03), and fails for I0X2 above 1O1S. Results for both ablation pressure and mass ablation rate are also given.

Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder

Con esta tesis ”Desarrollo de una Teoría Uniforme de la Difracción para el Análisis de los Campos Electromagnéticos Dispersados y Superficiales sobre un Cilindro” hemos iniciado una nueva línea de investigación que trata de responder a la siguiente pregunta: ¿cuál es la impedancia de superficie que describe una estructura de conductor eléctrico perfecto (PEC) convexa recubierta por un material no conductor? Este tipo de estudios tienen interés hoy en día porque ayudan a predecir el campo electromagnético incidente, radiado o que se propaga sobre estructuras metálicas y localmente convexas que se encuentran recubiertas de algún material dieléctrico, o sobre estructuras metálicas con pérdidas, como por ejemplo se necesita en determinadas aplicaciones aeroespaciales, marítimas o automovilísticas. Además, desde un punto de vista teórico, la caracterización de la impedancia de superficie de una estructura PEC recubierta o no por un dieléctrico es una generalización de varias soluciones que tratan ambos tipos de problemas por separado. En esta tesis se desarrolla una teoría uniforme de la difracción (UTD) para analizar el problema canónico del campo electromagnético dispersado y superficial en un cilindro circular eléctricamente grande con una condición de contorno de impedancia (IBC) para frecuencias altas. Construir una solución basada en UTD para este problema canónico es crucial en el desarrollo de un método UTD para el caso más general de una superficie arbitrariamente convexa, mediante el uso del principio de localización de los campos electromagnéticos a altas frecuencias. Esta tesis doctoral se ha llevado a cabo a través de una serie de hitos que se enumeran a continuación, enfatizando las contribuciones a las que ha dado lugar. Inicialmente se realiza una revisión en profundidad del estado del arte de los métodos asintóticos con numerosas referencias. As í, cualquier lector novel puede llegar a conocer la historia de la óptica geométrica (GO) y la teoría geométrica de la difracción (GTD), que dieron lugar al desarrollo de la UTD. Después, se investiga ampliamente la UTD y los trabajos más importantes que pueden encontrarse en la literatura. As í, este capítulo, nos coloca en la posición de afirmar que, hasta donde nosotros conocemos, nadie ha intentado antes llevar a cabo una investigación rigurosa sobre la caracterización de la impedancia de superficie de una estructura PEC recubierta por un material dieléctrico, utilizando para ello la UTD. Primero, se desarrolla una UTD para el problema canónico de la dispersión electromagnética de un cilindro circular eléctricamente grande con una IBC uniforme, cuando es iluminado por una onda plana con incidencia oblicua a frecuencias altas. La solución a este problema canónico se construye a partir de una solución exacta mediante una expansión de autofunciones de propagación radial. Entonces, ésta se convierte en una nueva expansión de autofunciones de propagación circunferencial muy apropiada para cilindros grandes, a través de la transformación de Watson. De esta forma, la expresión del campo se reduce a una integral que se evalúa asintóticamente, para altas frecuencias, de manera uniforme. El resultado se expresa según el trazado de rayos descrito en la UTD. La solución es uniforme porque tiene la importante propiedad de mantenerse continua a lo largo de la región de transición, a ambos lados de la superficie del contorno de sombra. Fuera de la región de transición la solución se reduce al campo incidente y reflejado puramente ópticos en la región iluminada del cilindro, y al campo superficial difractado en la región de sombra. Debido a la IBC el campo dispersado contiene una componente contrapolar a causa de un acoplamiento entre las ondas TEz y TMz (donde z es el eje del cilindro). Esta componente contrapolar desaparece cuando la incidencia es normal al cilindro, y también en la región iluminada cuando la incidencia es oblicua donde el campo se reduce a la solución de GO. La solución UTD presenta una muy buena exactitud cuando se compara numéricamente con una solución de referencia exacta. A continuación, se desarrolla una IBC efectiva para el cálculo del campo electromagnético dispersado en un cilindro circular PEC recubierto por un dieléctrico e iluminado por una onda plana incidiendo oblicuamente. Para ello se derivan dos impedancias de superficie en relación directa con las ondas creeping y de superficie TM y TE que se excitan en un cilindro recubierto por un material no conductor. Las impedancias de superficie TM y TE están acopladas cuando la incidencia es oblicua, y dependen de la geometría del problema y de los números de onda. Además, se ha derivado una impedancia de superficie constante, aunque con diferente valor cuando el observador se encuentra en la zona iluminada o en la zona de sombra. Después, se presenta una solución UTD para el cálculo de la dispersión de una onda plana con incidencia oblicua sobre un cilindro eléctricamente grande y convexo, mediante la generalización del problema canónico correspondiente al cilindro circular. La solución asintótica es uniforme porque se mantiene continua a lo largo de la región de transición, en las inmediaciones del contorno de sombra, y se reduce a la solución de rayos ópticos en la zona iluminada y a la contribución de las ondas de superficie dentro de la zona de sombra, lejos de la región de transición. Cuando se usa cualquier material no conductor se excita una componente contrapolar que tiende a desaparecer cuando la incidencia es normal al cilindro y en la región iluminada. Se discuten ampliamente las limitaciones de las fórmulas para la impedancia de superficie efectiva, y se compara la solución UTD con otras soluciones de referencia, donde se observa una muy buena concordancia. Y en tercer lugar, se presenta una aproximación para una impedancia de superficie efectiva para el cálculo de los campos superficiales en un cilindro circular conductor recubierto por un dieléctrico. Se discuten las principales diferencias que existen entre un cilindro PEC recubierto por un dieléctrico desde un punto de vista riguroso y un cilindro con una IBC. Mientras para un cilindro de impedancia se considera una impedancia de superficie constante o uniforme, para un cilindro conductor recubierto por un dieléctrico se derivan dos impedancias de superficie. Estas impedancias de superficie están asociadas a los modos de ondas creeping TM y TE excitadas en un cilindro, y dependen de la posición y de la orientación del observador y de la fuente. Con esto en mente, se deriva una solución UTD con IBC para los campos superficiales teniendo en cuenta las dependencias de la impedancia de superficie. La expansión asintótica se realiza, mediante la transformación de Watson, sobre la representación en serie de las funciones de Green correspondientes, evitando as í calcular las derivadas de orden superior de las integrales de tipo Fock, y dando lugar a una solución rápida y precisa. En los ejemplos numéricos realizados se observa una muy buena precisión cuando el cilindro y la separación entre el observador y la fuente son grandes. Esta solución, junto con el método de los momentos (MoM), se puede aplicar para el cálculo eficiente del acoplamiento mutuo de grandes arrays conformados de antenas de parches. Los métodos propuestos basados en UTD para el cálculo del campo electromagnético dispersado y superficial sobre un cilindro PEC recubierto de dieléctrico con una IBC efectiva suponen un primer paso hacia la generalización de una solución UTD para superficies metálicas convexas arbitrarias cubiertas por un material no conductor e iluminadas por una fuente electromagnética arbitraria. ABSTRACT With this thesis ”Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder” we have initiated a line of investigation whose goal is to answer the following question: what is the surface impedance which describes a perfect electric conductor (PEC) convex structure covered by a material coating? These studies are of current and future interest for predicting the electromagnetic (EM) fields incident, radiating or propagating on locally smooth convex parts of highly metallic structures with a material coating, or by a lossy metallic surfaces, as for example in aerospace, maritime and automotive applications. Moreover, from a theoretical point of view, the surface impedance characterization of PEC surfaces with or without a material coating represents a generalization of independent solutions for both type of problems. A uniform geometrical theory of diffraction (UTD) is developed in this thesis for analyzing the canonical problem of EM scattered and surface field by an electrically large circular cylinder with an impedance boundary condition (IBC) in the high frequency regime, by means of a surface impedance characterization. The construction of a UTD solution for this canonical problem is crucial for the development of the corresponding UTD solution for the more general case of an arbitrary smooth convex surface, via the principle of the localization of high frequency EM fields. The development of the present doctoral thesis has been carried out through a series of landmarks that are enumerated as follows, emphasizing the main contributions that this work has given rise to. Initially, a profound revision is made in the state of art of asymptotic methods where numerous references are given. Thus, any reader may know the history of geometrical optics (GO) and geometrical theory of diffraction (GTD), which led to the development of UTD. Then, the UTD is deeply investigated and the main studies which are found in the literature are shown. This chapter situates us in the position to state that, as far as we know, nobody has attempted before to perform a rigorous research about the surface impedance characterization for material-coated PEC convex structures via UTD. First, a UTD solution is developed for the canonical problem of the EM scattering by an electrically large circular cylinder with a uniform IBC, when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transformation, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the GO or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution. Then, an effective IBC is developed for the EM scattered field on a coated PEC circular cylinder illuminated by an obliquely incident plane wave. Two surface impedances are derived in a direct relation with the TM and TE surface and creeping wave modes excited on a coated cylinder. The TM and TE surface impedances are coupled at oblique incidence, and depend on the geometry of the problem and the wave numbers. Nevertheless, a constant surface impedance is found, although with a different value when the observation point lays in the lit or in the shadow region. Then, a UTD solution for the scattering of an obliquely incident plane wave on an electrically large smooth convex coated PEC cylinder is introduced, via a generalization of the canonical circular cylinder problem. The asymptotic solution is uniform because it remains continuous across the transition region, in the vicinity of the shadow boundary, and it recovers the ray optical solution in the deep lit region and the creeping wave formulation within the deep shadow region. When a coating is present a cross-polar field term is excited, which vanishes at normal incidence and in the deep lit region. The limitations of the effective surface impedance formulas are discussed, and the UTD solution is compared with some reference solutions where a very good agreement is met. And in third place, an effective surface impedance approach is introduced for determining surface fields on an electrically large coated metallic circular cylinder. Differences in analysis of rigorouslytreated coated metallic cylinders and cylinders with an IBC are discussed. While for the impedance cylinder case a single constant or uniform surface impedance is considered, for the coated metallic cylinder case two surface impedances are derived. These are associated with the TM and TE creeping wave modes excited on a cylinder and depend on observation and source positions and orientations. With this in mind, a UTD based method with IBC is derived for the surface fields by taking into account the surface impedance variation. The asymptotic expansion is performed, via the Watson transformation, over the appropriate series representation of the Green’s functions, thus avoiding higher-order derivatives of Fock-type integrals, and yielding a fast and an accurate solution. Numerical examples reveal a very good accuracy for large cylinders when the separation between the observation and the source point is large. Thus, this solution could be efficiently applied in mutual coupling analysis, along with the method of moments (MoM), of large conformal microstrip array antennas. The proposed UTD methods for scattered and surface EM field analysis on a coated PEC cylinder with an effective IBC are considered the first steps toward the generalization of a UTD solution for large arbitrarily convex smooth metallic surfaces covered by a material coating and illuminated by an arbitrary EM source.

Functional and effective connectivity in MEG. Application to the study of epilepsy

Nuestro cerebro contiene cerca de 1014 sinapsis neuronales. Esta enorme cantidad de conexiones proporciona un entorno ideal donde distintos grupos de neuronas se sincronizan transitoriamente para provocar la aparición de funciones cognitivas, como la percepción, el aprendizaje o el pensamiento. Comprender la organización de esta compleja red cerebral en base a datos neurofisiológicos, representa uno de los desafíos más importantes y emocionantes en el campo de la neurociencia. Se han propuesto recientemente varias medidas para evaluar cómo se comunican las diferentes partes del cerebro a diversas escalas (células individuales, columnas corticales, o áreas cerebrales). Podemos clasificarlos, según su simetría, en dos grupos: por una parte, la medidas simétricas, como la correlación, la coherencia o la sincronización de fase, que evalúan la conectividad funcional (FC); mientras que las medidas asimétricas, como la causalidad de Granger o transferencia de entropía, son capaces de detectar la dirección de la interacción, lo que denominamos conectividad efectiva (EC). En la neurociencia moderna ha aumentado el interés por el estudio de las redes funcionales cerebrales, en gran medida debido a la aparición de estos nuevos algoritmos que permiten analizar la interdependencia entre señales temporales, además de la emergente teoría de redes complejas y la introducción de técnicas novedosas, como la magnetoencefalografía (MEG), para registrar datos neurofisiológicos con gran resolución. Sin embargo, nos hallamos ante un campo novedoso que presenta aun varias cuestiones metodológicas sin resolver, algunas de las cuales trataran de abordarse en esta tesis. En primer lugar, el creciente número de aproximaciones para determinar la existencia de FC/EC entre dos o más señales temporales, junto con la complejidad matemática de las herramientas de análisis, hacen deseable organizarlas todas en un paquete software intuitivo y fácil de usar. Aquí presento HERMES (http://hermes.ctb.upm.es), una toolbox en MatlabR, diseñada precisamente con este fin. Creo que esta herramienta será de gran ayuda para todos aquellos investigadores que trabajen en el campo emergente del análisis de conectividad cerebral y supondrá un gran valor para la comunidad científica. La segunda cuestión practica que se aborda es el estudio de la sensibilidad a las fuentes cerebrales profundas a través de dos tipos de sensores MEG: gradiómetros planares y magnetómetros, esta aproximación además se combina con un enfoque metodológico, utilizando dos índices de sincronización de fase: phase locking value (PLV) y phase lag index (PLI), este ultimo menos sensible a efecto la conducción volumen. Por lo tanto, se compara su comportamiento al estudiar las redes cerebrales, obteniendo que magnetómetros y PLV presentan, respectivamente, redes más densamente conectadas que gradiómetros planares y PLI, por los valores artificiales que crea el problema de la conducción de volumen. Sin embargo, cuando se trata de caracterizar redes epilépticas, el PLV ofrece mejores resultados, debido a la gran dispersión de las redes obtenidas con PLI. El análisis de redes complejas ha proporcionado nuevos conceptos que mejoran caracterización de la interacción de sistemas dinámicos. Se considera que una red está compuesta por nodos, que simbolizan sistemas, cuyas interacciones se representan por enlaces, y su comportamiento y topología puede caracterizarse por un elevado número de medidas. Existe evidencia teórica y empírica de que muchas de ellas están fuertemente correlacionadas entre sí. Por lo tanto, se ha conseguido seleccionar un pequeño grupo que caracteriza eficazmente estas redes, y condensa la información redundante. Para el análisis de redes funcionales, la selección de un umbral adecuado para decidir si un determinado valor de conectividad de la matriz de FC es significativo y debe ser incluido para un análisis posterior, se convierte en un paso crucial. En esta tesis, se han obtenido resultados más precisos al utilizar un test de subrogadas, basado en los datos, para evaluar individualmente cada uno de los enlaces, que al establecer a priori un umbral fijo para la densidad de conexiones. Finalmente, todas estas cuestiones se han aplicado al estudio de la epilepsia, caso práctico en el que se analizan las redes funcionales MEG, en estado de reposo, de dos grupos de pacientes epilépticos (generalizada idiopática y focal frontal) en comparación con sujetos control sanos. La epilepsia es uno de los trastornos neurológicos más comunes, con más de 55 millones de afectados en el mundo. Esta enfermedad se caracteriza por la predisposición a generar ataques epilépticos de actividad neuronal anormal y excesiva o bien síncrona, y por tanto, es el escenario perfecto para este tipo de análisis al tiempo que presenta un gran interés tanto desde el punto de vista clínico como de investigación. Los resultados manifiestan alteraciones especificas en la conectividad y un cambio en la topología de las redes en cerebros epilépticos, desplazando la importancia del ‘foco’ a la ‘red’, enfoque que va adquiriendo relevancia en las investigaciones recientes sobre epilepsia. ABSTRACT There are about 1014 neuronal synapses in the human brain. This huge number of connections provides the substrate for neuronal ensembles to become transiently synchronized, producing the emergence of cognitive functions such as perception, learning or thinking. Understanding the complex brain network organization on the basis of neuroimaging data represents one of the most important and exciting challenges for systems neuroscience. Several measures have been recently proposed to evaluate at various scales (single cells, cortical columns, or brain areas) how the different parts of the brain communicate. We can classify them, according to their symmetry, into two groups: symmetric measures, such as correlation, coherence or phase synchronization indexes, evaluate functional connectivity (FC); and on the other hand, the asymmetric ones, such as Granger causality or transfer entropy, are able to detect effective connectivity (EC) revealing the direction of the interaction. In modern neurosciences, the interest in functional brain networks has increased strongly with the onset of new algorithms to study interdependence between time series, the advent of modern complex network theory and the introduction of powerful techniques to record neurophysiological data, such as magnetoencephalography (MEG). However, when analyzing neurophysiological data with this approach several questions arise. In this thesis, I intend to tackle some of the practical open problems in the field. First of all, the increase in the number of time series analysis algorithms to study brain FC/EC, along with their mathematical complexity, creates the necessity of arranging them into a single, unified toolbox that allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of them. I developed such a toolbox for this aim, it is named HERMES (http://hermes.ctb.upm.es), and encompasses several of the most common indexes for the assessment of FC and EC running for MatlabR environment. I believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis and will entail a great value for the scientific community. The second important practical issue tackled in this thesis is the evaluation of the sensitivity to deep brain sources of two different MEG sensors: planar gradiometers and magnetometers, in combination with the related methodological approach, using two phase synchronization indexes: phase locking value (PLV) y phase lag index (PLI), the latter one being less sensitive to volume conduction effect. Thus, I compared their performance when studying brain networks, obtaining that magnetometer sensors and PLV presented higher artificial values as compared with planar gradiometers and PLI respectively. However, when it came to characterize epileptic networks it was the PLV which gives better results, as PLI FC networks where very sparse. Complex network analysis has provided new concepts which improved characterization of interacting dynamical systems. With this background, networks could be considered composed of nodes, symbolizing systems, whose interactions with each other are represented by edges. A growing number of network measures is been applied in network analysis. However, there is theoretical and empirical evidence that many of these indexes are strongly correlated with each other. Therefore, in this thesis I reduced them to a small set, which could more efficiently characterize networks. Within this framework, selecting an appropriate threshold to decide whether a certain connectivity value of the FC matrix is significant and should be included in the network analysis becomes a crucial step, in this thesis, I used the surrogate data tests to make an individual data-driven evaluation of each of the edges significance and confirmed more accurate results than when just setting to a fixed value the density of connections. All these methodologies were applied to the study of epilepsy, analysing resting state MEG functional networks, in two groups of epileptic patients (generalized and focal epilepsy) that were compared to matching control subjects. Epilepsy is one of the most common neurological disorders, with more than 55 million people affected worldwide, characterized by its predisposition to generate epileptic seizures of abnormal excessive or synchronous neuronal activity, and thus, this scenario and analysis, present a great interest from both the clinical and the research perspective. Results revealed specific disruptions in connectivity and network topology and evidenced that networks’ topology is changed in epileptic brains, supporting the shift from ‘focus’ to ‘networks’ which is gaining importance in modern epilepsy research.

Potential theory

In this chapter we will introduce the reader to the techniques of the Boundary Element Method applied to simple Laplacian problems. Most classical applications refer to electrostatic and magnetic fields, but the Laplacian operator also governs problems such as Saint-Venant torsion, irrotational flow, fluid flow through porous media and the added fluid mass in fluidstructure interaction problems. This short list, to which it would be possible to add many other physical problems governed by the same equation, is an indication of the importance of the numerical treatment of the Laplacian operator. Potential theory has pioneered the use of BEM since the papers of Jaswon and Hess. An interesting introduction to the topic is given by Cruse. In the last five years a renaissance of integral methods has been detected. This can be followed in the books by Jaswon and Symm and by Brebbia or Brebbia and Walker.In this chapter we shall maintain an elementary level and follow a classical scheme in order to make the content accessible to the reader who has just started to study the technique. The whole emphasis has been put on the socalled "direct" method because it is the one which appears to offer more advantages. In this section we recall the classical concepts of potential theory and establish the basic equations of the method. Later on we discuss the discretization philosophy, the implementation of different kinds of elements and the advantages of substructuring which is unavoidable when dealing with heterogeneous materials.

A theory of electron collection by a grid sphere

Use of a spherical grid as electron collector at the anodic end of a tether, as recently proposed, is considered. The standard analysis of space-charge limited current to a solid sphere (with neither magnetic nor plasma-motion effects), which has been shown to best fit TSS1R in-orbit results at very high bias, is used to determine effects from grid transparency on current collected; the analysis is first reformulated in the formalism recently introduced in the two-dimensional analysis of bare-tethers. A discussion of the electric potential created by a spherical grid in vacuum is then carried out; it is shown that each grid-wire collects current well below its maximum OML current, the effective grid transparency being close to its optical value. Formulae for the current to a spherical grid, showing the effects of grid transparency, is determined. A fully consistent analysis of electric potential and electron density, outside and inside the grid, is completed.