Free-form optical systems for nonimaging applications : Sistemas ópticos anamórficos para aplicaciones anidólicas

La óptica anidólica es una rama de la óptica cuyo desarrollo comenzó a mediados de la década de 1960. Este relativamente nuevo campo de la óptica se centra en la transferencia eficiente de la luz, algo necesario en muchas aplicaciones, entre las que destacamos los concentradores solares y los sistemas de iluminación. Las soluciones de la óptica clásica a los problemas de la transferencia de energía de la luz sólo son adecuadas cuando los rayos de luz son paraxiales. La condición paraxial no se cumple en la mayoría de las aplicaciones para concentración e iluminación. Esta tesis contiene varios diseños free-form (aquellos que no presentan ninguna simetría, ni de rotación ni lineal) cuyas aplicaciones van destinadas a estos dos campos. El término nonimaging viene del hecho de que estos sistemas ópticos no necesitan formar una imagen del objeto, aunque no formar la imagen no es una condición necesaria. Otra palabra que se utiliza a veces en lugar de nonimaging es la palabra anidólico, viene del griego "an+eidolon" y tiene el mismo significado. La mayoría de los sistemas ópticos diseñados para aplicaciones anidólicas no presentan ninguna simetría, es decir, son free-form (anamórficos). Los sistemas ópticos free-form están siendo especialmente relevantes durante los últimos años gracias al desarrollo de las herramientas para su fabricación como máquinas de moldeo por inyección y el mecanizado multieje. Sin embargo, solo recientemente se han desarrollado técnicas de diseño anidólicas capaces de cumplir con estos grados de libertad. En aplicaciones de iluminación el método SMS3D permite diseñar dos superficies free-form para controlar las fuentes de luz extensas. En los casos en que se requiere una elevada asimetría de la fuente, el objeto o las restricciones volumétricos, las superficies free-form permiten obtener soluciones de mayor eficiencia, o disponer de menos elementos en comparación con las soluciones de simetría de rotación, dado que las superficies free-form tienen más grados de libertad y pueden realizar múltiples funciones debido a su naturaleza anamórfica. Los concentradores anidólicos son muy adecuados para la captación de energía solar, ya que el objetivo no es la reproducción de una imagen exacta del sol, sino sencillamente la captura de su energía. En este momento, el campo de la concentración fotovoltaica (CPV) tiende hacia sistemas de alta concentración con el fin de compensar el gasto de las células solares multi-unión (MJ) utilizadas como receptores, reduciendo su área. El interés en el uso de células MJ radica en su alta eficiencia de conversión. Para obtener sistemas competitivos en aplicaciones terrestres se recurre a sistemas fotovoltaicos de alta concentración (HCPV), con factores de concentración geométrica por encima de 500x. Estos sistemas se componen de dos (o más) elementos ópticos (espejos y/o lentes). En los sistemas presentados a lo largo de este trabajo se presentan ejemplos de concentradores HCPV con elementos reflexivos como etapa primaria, así como concentradores con elementos refractivos (lente de Fresnel). Con la necesidad de aumentar la eficiencia de los sistemas HCPV reales y con el fin de proporcionar la división más eficiente del espectro solar, células conteniendo cuatro o más uniones (con un potencial de alcanzar eficiencias de más del 45% a una concentración de cientos de soles) se exploran hoy en día. En esta tesis se presenta una de las posibles arquitecturas de división del espectro (spectrum-splitting en la literatura anglosajona) que utilizan células de concentración comercial. Otro campo de aplicación de la óptica nonimaging es la iluminación, donde es necesario proporcionar un patrón de distribución de la iluminación específico. La iluminación de estado sólido (SSL), basada en la electroluminiscencia de materiales semiconductores, está proporcionando fuentes de luz para aplicaciones de iluminación general. En la última década, los diodos emisores de luz (LED) de alto brillo han comenzado a reemplazar a las fuentes de luz convencionales debido a la superioridad en la calidad de la luz emitida, elevado tiempo de vida, compacidad y ahorro de energía. Los colimadores utilizados con LEDs deben cumplir con requisitos tales como tener una alta eficiencia, un alto control del haz de luz, una mezcla de color espacial y una gran compacidad. Presentamos un colimador de luz free-form con microestructuras capaz de conseguir buena colimación y buena mezcla de colores con una fuente de LED RGGB. Una buena mezcla de luz es importante no sólo para simplificar el diseño óptico de la luminaria sino también para evitar hacer binning de los chips. La mezcla de luz óptica puede reducir los costes al evitar la modulación por ancho de pulso y otras soluciones electrónicas patentadas para regulación y ajuste de color. Esta tesis consta de cuatro capítulos. Los capítulos que contienen la obra original de esta tesis son precedidos por un capítulo introductorio donde se presentan los conceptos y definiciones básicas de la óptica geométrica y en el cual se engloba la óptica nonimaging. Contiene principios de la óptica no formadora de imagen junto con la descripción de sus problemas y métodos de diseño. Asimismo se describe el método de Superficies Múltiples Simultáneas (SMS), que destaca por su versatilidad y capacidad de controlar varios haces de rayos. Adicionalmente también se describe la integración Köhler y sus aplicaciones en el campo de la energía fotovoltaica. La concentración fotovoltaica y la iluminación de estado sólido son introducidas junto con la revisión de su estado actual. El Segundo y Tercer Capítulo contienen diseños ópticos avanzados con aplicación en la concentración solar principalmente, mientras que el Cuarto Capítulo describe el colimador free-form con surcos que presenta buena mezcla de colores para aplicaciones de iluminación. El Segundo Capítulo describe dos concentradores ópticos HCPV diseñados con el método SMS en tres dimensiones (SMS3D) que llevan a cabo integración Köhler en dos direcciones con el fin de proporcionar una distribución de irradiancia uniforme libre de aberraciones cromáticas sobre la célula solar. Uno de los diseños es el concentrador XXR free-form diseñado con el método SMS3D, donde el espejo primario (X) y la lente secundaria (R) se dividen en cuatro sectores simétricos y llevan a cabo la integración Köhler (proporcionando cuatro unidades del array Köhler), mientras que el espejo intermedio (X) presenta simetría rotacional. Otro concentrador HCPV presentado es el Fresnel-RXI (FRXI) con una lente de Fresnel funcionando como elemento primario (POE) y una lente RXI como elemento óptico secundario (SOE), que presenta configuración 4-fold con el fin de realizar la integración Köhler. Las lentes RXI son dispositivos nonimaging conocidos, pero su aplicación como elemento secundario es novedosa. Los concentradores XXR y FRXI Köhler son ejemplos académicos de muy alta concentración (más de 2,000x, mientras que los sistemas convencionales hoy en día no suelen llegar a 1,000x) preparados para las células solares N-unión (con N>3), que probablemente requerirán una mayor concentración y alta uniformidad espectral de irradiancia con el fin de obtener sistemas CPV terrestres eficientes y rentables. Ambos concentradores están diseñados maximizando funciones de mérito como la eficiencia óptica, el producto concentración-aceptancia (CAP) y la uniformidad de irradiancia sobre la célula libre de la aberración cromática (integración Köhler). El Tercer Capítulo presenta una arquitectura para la división del espectro solar basada en un módulo HCPV con alta concentración (500x) y ángulo de aceptancia alto (>1º) que tiene por objeto reducir ambas fuentes de pérdidas de las células triple unión (3J) comerciales: el uso eficiente del espectro solar y la luz reflejada de los contactos metálicos y de la superficie de semiconductor. El módulo para la división del espectro utiliza el espectro solar más eficiente debido a la combinación de una alta eficiencia de una célula de concentración 3J (GaInP/GaInAs/Ge) y una de contacto posterior (BPC) de concentración de silicio (Si), así como la técnica de confinamiento externo para la recuperación de la luz reflejada por la célula 3J con el fin de ser reabsorbida por la célula. En la arquitectura propuesta, la célula 3J opera con su ganancia de corriente optimizada (concentración geométrica de 500x), mientras que la célula de silicio trabaja cerca de su óptimo también (135x). El módulo de spectrum-splitting consta de una lente de Fresnel plana como POE y un concentrador RXI free-form como SOE con un filtro paso-banda integrado en él. Tanto POE como SOE realizan la integración Köhler para producir homogeneización de luz sobre la célula. El filtro paso banda envía los fotones IR en la banda 900-1,150nm a la célula de silicio. Hay varios aspectos prácticos de la arquitectura del módulo presentado que ayudan a reducir la complejidad de los sistemas spectrum-splitting (el filtro y el secundario forman una sola pieza sólida, ambas células son coplanarias simplificándose el cableado y la disipación de calor, etc.). Prototipos prueba-de-concepto han sido ensamblados y probados a fin de demostrar la fabricabilidad del filtro y su rendimiento cuando se combina con la técnica de reciclaje de luz externa. Los resultados obtenidos se ajustan bastante bien a los modelos y a las simulaciones e invitan al desarrollo de una versión más compleja de este prototipo en el futuro. Dos colimadores sólidos con surcos free-form se presentan en el Cuarto Capítulo. Ambos diseños ópticos están diseñados originalmente usando el método SMS3D. La segunda superficie ópticamente activa está diseñada a posteriori como una superficie con surcos. El diseño inicial de dos espejos (XX) está diseñado como prueba de concepto. En segundo lugar, el diseño RXI free-form es comparable con los colimadores RXI existentes. Se trata de un diseño muy compacto y eficiente que proporciona una muy buena mezcla de colores cuando funciona con LEDs RGB fuera del eje óptico como en los RGB LEDs convencionales. Estos dos diseños son dispositivos free-form diseñados con la intención de mejorar las propiedades de mezcla de colores de los dispositivos no aplanáticos RXI con simetría de revolución y la eficiencia de los aplanáticos, logrando una buena colimación y una buena mezcla de colores. La capacidad de mezcla de colores del dispositivo no-aplanático mejora añadiendo características de un aplanático a su homólogo simétrico sin pérdida de eficiencia. En el caso del diseño basado en RXI, su gran ventaja consiste en su menor coste de fabricación ya que el proceso de metalización puede evitarse. Aunque algunos de los componentes presentan formas muy complejas, los costes de fabricación son relativamente insensibles a la complejidad del molde, especialmente en el caso de la producción en masa (tales como inyección de plástico), ya que el coste del molde se reparte entre todas las piezas fabricadas. Por último, las últimas dos secciones son las conclusiones y futuras líneas de investigación. ABSTRACT Nonimaging optics is a branch of optics whose development began in the mid-1960s. This rather new field of optics focuses on the efficient light transfer necessary in many applications, among which we highlight solar concentrators and illumination systems. The classical optics solutions to the problems of light energy transfer are only appropriate when the light rays are paraxial. The paraxial condition is not met in most applications for the concentration and illumination. This thesis explores several free-form designs (with neither rotational nor linear symmetry) whose applications are intended to cover the above mentioned areas and more. The term nonimaging comes from the fact that these optical systems do not need to form an image of the object, although it is not a necessary condition not to form an image. Another word sometimes used instead of nonimaging is anidolic, and it comes from the Greek “an+eidolon” and has the same meaning. Most of the optical systems designed for nonimaging applications are without any symmetry, i.e. free-form. Free-form optical systems become especially relevant lately with the evolution of free-form tooling (injection molding machines, multi-axis machining techniques, etc.). Nevertheless, only recently there are nonimaging design techniques that are able to meet these degrees of freedom. In illumination applications, the SMS3D method allows designing two free-form surfaces to control very well extended sources. In cases when source, target or volumetric constrains have very asymmetric requirements free-form surfaces are offering solutions with higher efficiency or with fewer elements in comparison with rotationally symmetric solutions, as free-forms have more degrees of freedom and they can perform multiple functions due to their free-form nature. Anidolic concentrators are well suited for the collection of solar energy, because the goal is not the reproduction of an exact image of the sun, but instead the collection of its energy. At this time, Concentration Photovoltaics (CPV) field is turning to high concentration systems in order to compensate the expense of multi-junction (MJ) solar cells used as receivers by reducing its area. Interest in the use of MJ cells lies in their very high conversion efficiency. High Concentration Photovoltaic systems (HCPV) with geometric concentration of more than 500x are required in order to have competitive systems in terrestrial applications. These systems comprise two (or more) optical elements, mirrors and/or lenses. Systems presented in this thesis encompass both main types of HCPV architectures: concentrators with primary reflective element and concentrators with primary refractive element (Fresnel lens). Demand for the efficiency increase of the actual HCPV systems as well as feasible more efficient partitioning of the solar spectrum, leads to exploration of four or more junction solar cells or submodules. They have a potential of reaching over 45% efficiency at concentration of hundreds of suns. One possible architectures of spectrum splitting module using commercial concentration cells is presented in this thesis. Another field of application of nonimaging optics is illumination, where a specific illuminance distribution pattern is required. The Solid State Lighting (SSL) based on semiconductor electroluminescence provides light sources for general illumination applications. In the last decade high-brightness Light Emitting Diodes (LEDs) started replacing conventional light sources due to their superior output light quality, unsurpassed lifetime, compactness and energy savings. Collimators used with LEDs have to meet requirements like high efficiency, high beam control, color and position mixing, as well as a high compactness. We present a free-form collimator with microstructures that performs good collimation and good color mixing with RGGB LED source. Good light mixing is important not only for simplifying luminaire optical design but also for avoiding die binning. Optical light mixing may reduce costs by avoiding pulse-width modulation and other patented electronic solutions for dimming and color tuning. This thesis comprises four chapters. Chapters containing the original work of this thesis are preceded by the introductory chapter that addresses basic concepts and definitions of geometrical optics on which nonimaging is developed. It contains fundamentals of nonimaging optics together with the description of its design problems, principles and methods, and with the Simultaneous Multiple Surface (SMS) method standing out for its versatility and ability to control several bundles of rays. Köhler integration and its applications in the field of photovoltaics are described as well. CPV and SSL fields are introduced together with the review on their background and their current status. Chapter 2 and Chapter 3 contain advanced optical designs with primarily application in solar concentration; meanwhile Chapter 4 portrays the free-form V-groove collimator with good color mixing property for illumination application. Chapter 2 describes two HCPV optical concentrators designed with the SMS method in three dimensions (SMS3D). Both concentrators represent Köhler integrator arrays that provide uniform irradiance distribution free from chromatic aberrations on the solar cell. One of the systems is the XXR free-form concentrator designed with the SMS3D method. The primary mirror (X) of this concentrator and secondary lens (R) are divided in four symmetric sectors (folds) that perform Köhler integration; meanwhile the intermediate mirror (X) is rotationally symmetric. Second HCPV concentrator is the Fresnel-RXI (FRXI) with flat Fresnel lens as the Primary Optical Element (POE) and an RXI lens as the Secondary Optical Element (SOE). This architecture manifests 4-fold configuration for performing Köhler integration (4 array units), as well. The RXI lenses are well-known nonimaging devices, but their application as SOE is novel. Both XXR and FRXI Köhler HCPV concentrators are academic examples of very high concentration (more than 2,000x meanwhile conventional systems nowadays have up to 1,000x) prepared for the near future N-junction (N>3) solar cells. In order to have efficient and cost-effective terrestrial CPV systems, those cells will probably require higher concentrations and high spectral irradiance uniformity. Both concentrators are designed by maximizing merit functions: the optical efficiency, concentration-acceptance angle (CAP) and cell-irradiance uniformity free from chromatic aberrations (Köhler integration). Chapter 3 presents the spectrum splitting architecture based on a HCPV module with high concentration (500x) and high acceptance angle (>1º). This module aims to reduce both sources of losses of the actual commercial triple-junction (3J) solar cells with more efficient use of the solar spectrum and with recovering the light reflected from the 3J cells’ grid lines and semiconductor surface. The solar spectrum is used more efficiently due to the combination of a high efficiency 3J concentration cell (GaInP/GaInAs/Ge) and external Back-Point-Contact (BPC) concentration silicon (Si) cell. By employing external confinement techniques, the 3J cell’s reflections are recovered in order to be re-absorbed by the cell. In the proposed concentrator architecture, the 3J cell operates at its optimized current gain (at geometrical concentration of 500x), while the Si cell works near its optimum, as well (135x). The spectrum splitting module consists of a flat Fresnel lens (as the POE), and a free-form RXI-type concentrator with a band-pass filter embedded in it (as the SOE), both POE and SOE performing Köhler integration to produce light homogenization. The band-pass filter sends the IR photons in the 900-1,150nm band to the Si cell. There are several practical aspects of presented module architecture that help reducing the added complexity of the beam splitting systems: the filter and secondary are forming a single solid piece, both cells are coplanar so the heat management and wiring is simplified, etc. Two proof-of-concept prototypes are assembled and tested in order to prove filter manufacturability and performance, as well as the potential of external light recycling technique. Obtained measurement results agree quite well with models and simulations, and show an opened path to manufacturing of the Fresnel RXI-type secondary concentrator with spectrum splitting strategy. Two free-form solid V-groove collimators are presented in Chapter 4. Both free-form collimators are originally designed with the SMS3D method. The second mirrored optically active surface is converted in a grooved surface a posteriori. Initial two mirror (XX) design is presented as a proof-of-concept. Second, RXI free-form design is comparable with existing RXI collimators as it is a highly compact and a highly efficient design. It performs very good color mixing of the RGGB LED sources placed off-axis like in conventional RGB LEDs. Collimators described here improve color mixing property of the prior art rotationally symmetric no-aplanatic RXI devices, and the efficiency of the aplanatic ones, accomplishing both good collimation and good color mixing. Free-form V-groove collimators enhance the no-aplanatic device's blending capabilities by adding aplanatic features to its symmetric counterpart with no loss in efficiency. Big advantage of the RXI design is its potentially lower manufacturing cost, since the process of metallization may be avoided. Although some components are very complicated for shaping, the manufacturing costs are relatively insensitive to the complexity of the mold especially in the case of mass production (such as plastic injection), as the cost of the mold is spread in many parts. Finally, last two sections are conclusions and future lines of investigation.

Respuesta fisiológica, productiva y cualitativa del cultivar Syrah (Vitis vinifera L) con diferentes frecuencias de riego y densidad de goteros en suelos arcillosos

La disponibilidad hídrica es uno de los principales factores que determinan el rendimiento del viñedo en muchas regiones vitícolas, por lo que sus consecuencias han sido ampliamente estudiadas. Sin embargo, para una cantidad de agua de riego determinada, otros aspectos como la frecuencia de aplicación, o la combinación entre el caudal de los goteros y la distancia entre los mismos (es decir, el patrón de distribución de agua en el suelo), pueden jugar un papel relevante, pero estos factores han sido poco estudiados. El objetivo de este trabajo ha sido evaluar las implicaciones agronómicas y fisiológicas de dos frecuencias de riego (IrrF, cada 2 y 4 días) y dos patrones de distribución de agua (DisP, goteros de 2 L h-1 separados 0,6 m vs. goteros de 4 L h-1 separados 1,2 m). El experimento se llevó a cabo durante cuatro temporadas consecutivas en un viñedo cv. Syrah con un suelo arcilloso en el centro de España, y los dos factores fueron evaluados bajo dos condiciones de disponibilidad hídrica (Baja: 20% de ETo y Media: 40% de ETo). El efecto de la frecuencia de riego y el patrón de distribución de agua en la respuesta agronómica del cv. Syrah se ha estudiado en el capítulo 1. La frecuencia de riego y el patrón de distribución de agua en el suelo afectaron a algunos aspectos de los componentes de rendimiento y desarrollo vegetativo en las dos condiciones de disponibilidad hídrica, aunque los efectos observados no fueron los mismos todos los años. Los efectos fueron más evidentes para IrrF en condiciones de baja disponibilidad hídrica y para DisP en condiciones de disponibilidad hídrica media. Dos de los cuatro años del experimento, el pasar de frecuencia de riego de 2 días a 4 días causó un incremento medio de rendimiento del 20% para la situación de baja disponibilidad hídrica. La textura del suelo, sin duda ha condicionado los resultados obtenidos en los tratamientos regados con el 20% de la ETo, ya que regar cada dos días implicaba la aplicación de pequeñas cantidades de agua y se formaban bulbos de riego superficiales, probablemente favoreciendo las pérdidas por evaporación. En el capítulo 2, se ha analizado el efecto de la frecuencia de riego y del patrón de distribución de agua en el estado hídrico de la planta y el intercambio gaseoso a nivel de hoja con el fin de explicar las diferencias observadas en la respuesta agronómica. En lo que respecta a la frecuencia de riego, en condiciones de baja disponibilidad hídrica, las plantas regadas cada 4 días (plantas 4d), mostraron mayores tasas de asimilación neta y conductancia estomática que las plantas regadas cada 2 días (plantas 2d), lo que es consistente con la hipótesis de que con la frecuencia de riego de 2 días se produjo una pérdida de eficiencia del uso del agua, probablemente debido a una mayor evaporación como consecuencia del hecho de que el volumen de suelo mojado creado era pequeño y cerca de la superficie. En condiciones de disponibilidad hídrica media, las diferencias en el intercambio gaseoso a nivel de hoja fueron mucho más pequeñas. Al comienzo del verano cada frecuencia de riego se comportó mejor uno de los días de medida, compensando al final del ciclo de riego de 4 días. Sin embargo, a medida que avanzó el verano y el déficit de agua se hizo más alto, las diferencias significativas aparecieron sólo en el 'día 4' del ciclo de riego, cuando las plantas 2d se comportaron mejor que las plantas regadas 4d que llevaban tres días sin regarse. Estas diferencias fisiológicas fueron menores que en condiciones de baja disponibilidad hídrica y al parecer no suficientes para afectar el comportamiento agronómico. En cuanto al patrón de distribución de agua, el efecto fue poco significativo, pero la mayor densidad de goteros tendió a presentar un mayor intercambio gaseoso a nivel de hoja, especialmente a media mañana. El efecto fue más importante para las condiciones de disponibilidad hídrica media. En el capítulo 3, se han comparado las relaciones entre el intercambio gaseoso a nivel de hoja, el estado hídrico y la demanda atmosférica, con el fin de explicar los cambios en la intensidad de la respuesta fisiológica observados en el Capítulo 2. No se han encontrado diferencias en dichas relaciones para el patrón de distribución de agua, por lo que sólo se ha analizado el efecto de la frecuencia de riego. El estudio se ha centrado fundamentalmente en si las plantas mostraron una respuesta fisiológica diferente a los cambios en el estado hídrico y en la demanda atmosférica según el tiempo transcurrido desde el último riego. Las diferencias observadas explican los resultados obtenidos en los capítulos anteriores, y sugieren la existencia de procesos de aclimatación vinculados a la frecuencia de riego y a la disponibilidad hídrica. Las plantas bajo condiciones de baja disponibilidad hídrica se mostraron más aclimatadas al estrés hídrico que aquellas en condiciones de disponibilidad hídrica media. La frecuencia de riego afectó claramente la relación entre los parámetros de intercambio gaseoso a nivel de hoja, el estado hídrico de la planta y las condiciones atmosféricas, y junto con la cantidad de agua aplicada tuvo implicaciones en el desarrollo de mecanismos de aclimatación que afectaron a la respuesta fisiológica de la planta, afectando a la eficiencia del riego. ABSTRACT Water availability is one of the major factors that determine vineyard performance in many grape growing regions, so its implications have been widely studied before. However, for a given irrigation water amount, other aspects such as application frequency, or emitter spacing and flow rate (i.e., distribution pattern), may play a relevant role, but these factors have been scarcely studied. The aim of this work was to evaluate the agronomic and physiological implications of two irrigation frequencies (IrrF, every 2 and 4 days) and two water distribution patterns (DisP, 2 L h−1 emitters every 0.6 m vs. 4 L h−1 emitters every 1.2 m). The experiment was carried out during four consecutive seasons in a cv. Syrah vineyard with a clay soil in central Spain, and the two factors were evaluated under two water availability conditions (LOW WA: 20% of ETo and MEDIUM WA: 40% of ETo). The effect of irrigation frequency and water distribution pattern on the agronomical response of cv. Syrah was studied in Chapter 1. IrrF and DisP affected some aspects of vegetative development and yield components under both water availability conditions, although the effects observed were not the same every year. The effects were more evident for IrrF under low water availability and for DisP under medium water availability. Two out of the four years of the experiment, the change of irrigation frequency from 2 days to 4 days promoted an average yield increase of 20% for the LOW WA situation. Soil texture certainly conditioned the results obtained under LOW WA conditions, since high frequency irrigation implied applying small amounts of water that resulted in limited superficial water bulbs, which probably favored water evaporation. In Chapter 2, the effect of irrigation frequency and water distribution pattern on plant water status and leaf gas exchange was analyzed to explain the differences observed in the agronomical response. Concerning irrigation frequency, under LOW WA conditions, applying irrigation every 4 days, resulted in higher net assimilation rates and stomatal conductance than doing it every 2 days, supporting the hypothesis that the latter frequency resulted in a water use efficiency loss, probably due to higher evaporation as a consequence of the fact the wetted soil volume created was small and close to the surface. Under MEDIUM WA conditions, differences in leaf gas exchange were much smaller. At the beginning of the summer each irrigation frequency behaved better one of the measurements days, compensating at the end of the 4-day irrigation cycle. However, as the summer progressed and water deficit became higher, significant differences appeared only on ‘day 4’ of the irrigation cycle, when 2d plants behaved better than 4d plants. These physiological differences were smaller than under LOW WA conditions and apparently not sufficient to affect agronomical performance. Regarding water distribution pattern, the effect was less significant but the closest emitter spacing resulted in general terms in a higher leaf gas exchange, especially at midmorning. The effect was more noticeable for MEDIUM WA conditions. In Chapter 3, the relationships between leaf gas exchange and leaf water status and atmospheric demand were compared to explain the changes in the intensity of the physiological response observed in Chapter 2. No differences were found in the relationships for water distribution pattern, so only the effect of irrigation frequency was analyzed focusing on whether the plants have a different physiological response to changes in water status and atmospheric demand according to the time elapsed since the last irrigation. Differences observed in the relationships explained the results obtained in the previous chapters, and point at the occurrence of acclimation processes linked to irrigation frequency and to water availability. Plants under LOW WATER AVAILABILITY conditions seemed to be more acclimated to water stress than those under MEDIUM WATER AVAILABILITY conditions. Irrigation frequency clearly affected the relationship between leaf gas exchange parameters, plant water status and atmospheric conditions, and together with the amount of water applied had implications in the development of acclimation mechanisms that affected plant physiological response, thus affecting irrigation efficiency.

Three-dimensional distribution of cortical synapses: a replicated point pattern-based analysis

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500μm3 and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

Fine spatial pattern of an epiphytic lichen species is affected by habitat conditions in two forest types in the Iberian Mediterranean region

Persistence and abundance of species is determined by habitat availability and the ability to disperse and colonize habitats at contrasting spatial scales. Favourable habitat fragments are also heterogeneous in quality, providing differing opportunities for establishment and affecting the population dynamics of a species. Based on these principles, we suggest that the presence and abundance of epiphytes may reflect their dispersal ability, which is primarily determined by the spatial structure of host trees, but also by host quality. To our knowledge there has been no explicit test of the importance of host tree spatial pattern for epiphytes in Mediterranean forests. We hypothesized that performance and host occupancy in a favourable habitat depend on the spatial pattern of host trees, because this pattern affects the dispersal ability of each epiphyte and it also determines the availability of suitable sites for establishment. We tested this hypothesis using new point pattern analysis tools and generalized linear mixed models to investigate the spatial distribution and performance of the epiphytic lichen Lobaria pulmonaria, which inhabits two types of host trees (beeches and Iberian oaks). We tested the effects on L. pulmonaria distribution of tree size, spatial configuration, and host tree identity. We built a model including tree size, stand structure, and several neighbourhood predictors to understand the effect of host tree on L. pulmonaria. We also investigated the relative importance of spatial patterning on the presence and abundance of the species, independently of the host tree configuration. L. pulmonaria distribution was highly dependent on habitat quality for successful establishment, i.e., tree species identity, tree diameter, and several forest stand structure surrogates. For beech trees, tree diameter was the main factor influencing presence and cover of the lichen, although larger lichen-colonized trees were located close to focal trees, i.e., young trees. However, oak diameter was not an important factor, suggesting that bark roughness at all diameters favoured lichen establishment. Our results indicate that L. pulmonaria dispersal is not spatially restricted, but it is dependent on habitat quality. Furthermore, new spatial analysis tools suggested that L. pulmonaria cover exhibits a distinct pattern, although the spatial pattern of tree position and size was random.

On the Statistical Distribution of Object-Oriented System Properties

The statistical distributions of different software properties have been thoroughly studied in the past, including software size, complexity and the number of defects. In the case of object-oriented systems, these distributions have been found to obey a power law, a common statistical distribution also found in many other fields. However, we have found that for some statistical properties, the behavior does not entirely follow a power law, but a mixture between a lognormal and a power law distribution. Our study is based on the Qualitas Corpus, a large compendium of diverse Java-based software projects. We have measured the Chidamber and Kemerer metrics suite for every file of every Java project in the corpus. Our results show that the range of high values for the different metrics follows a power law distribution, whereas the rest of the range follows a lognormal distribution. This is a pattern typical of so-called double Pareto distributions, also found in empirical studies for other software properties.

Fine spatial pattern of an epiphytic lichen species is affected by habitat conditions in two forest types in the Iberian Mediterranean region

Persistence and abundance of species is determined by habitat availability and the ability to disperse and colonize habitats at contrasting spatial scales. Favourable habitat fragments are also heterogeneous in quality, providing differing opportunities for establishment and affecting the population dynamics of a species. Based on these principles, we suggest that the presence and abundance of epiphytes may reflect their dispersal ability, which is primarily determined by the spatial structure of host trees, but also by host quality. To our knowledge there has been no explicit test of the importance of host tree spatial pattern for epiphytes in Mediterranean forests. We hypothesized that performance and host occupancy in a favourable habitat depend on the spatial pattern of host trees, because this pattern affects the dispersal ability of each epiphyte and it also determines the availability of suitable sites for establishment. We tested this hypothesis using new point pattern analysis tools and generalized linear mixed models to investigate the spatial distribution and performance of the epiphytic lichen Lobaria pulmonaria, which inhabits two types of host trees (beeches and Iberian oaks). We tested the effects on L. pulmonaria distribution of tree size, spatial configuration, and host tree identity. We built a model including tree size, stand structure, and several neighbourhood predictors to understand the effect of host tree on L. pulmonaria. We also investigated the relative importance of spatial patterning on the presence and abundance of the species, independently of the host tree configuration. L. pulmonaria distribution was highly dependent on habitat quality for successful establishment, i.e., tree species identity, tree diameter, and several forest stand structure surrogates. For beech trees, tree diameter was the main factor influencing presence and cover of the lichen, although larger lichen-colonized trees were located close to focal trees, i.e., young trees. However, oak diameter was not an important factor, suggesting that bark roughness at all diameters favoured lichen establishment. Our results indicate that L. pulmonaria dispersal is not spatially restricted, but it is dependent on habitat quality. Furthermore, new spatial analysis tools suggested that L. pulmonaria cover exhibits a distinct pattern, although the spatial pattern of tree position and size was random.

On the spatial distribution of woody plant species in a tropical montane cloud forest

Abstract The cloud forest is a special type of forest ecosystem that depends on suitable conditions of humidity and temperature to exist; hence, it is a very fragile ecosystem. The cloud forest is also one of the richest ecosystems in terms of species diversity and rate of endemism. However, today, it is one of the most threatened ecosystems in the world. Little is known about tree species distribution and coexistence among cloud forest trees. Trees are essential to understanding ecosystem functioning and maintenance because they support the ecosystem in important ways. For this dissertation, an analysis of woody plant species distribution at a small scale in a north-Peruvian Andean cloud forest was performed, and some of the factors implicated in the observed patterns were identified. Towards that end, different natural factors acting on species distribution within the forest were investigated: (i) intra-specific arrangements, (ii) heterospecific spatial relationships and (iii) relationships with external environmental factors. These analyses were conducted first on standing woody plants and then on seedlings. The woody plants were found to be clumped in the forest, either considering all the species together or each species separately. However, each species presented a specific pattern and specific spatial relationship among different-age individuals. Dispersal mode, growth form and shade tolerance played roles in the final distribution of the species. Furthermore, spatial associations among species, either positive or negative, were observed. These associations were more numerous when considering individuals of the interacting species at different developmental stages, i.e., younger individuals from one species and older individuals from another. Accordingly, competition and facilitation are asymmetric processes and vary throughout the life of an individual. Moreover, some species appear to prefer certain habitat conditions and avoid other habitats. The habitat definition that best explains species distribution is that which includes both environmental and stand characteristics; thus, a combination of these factors is necessary to understanding species' niche preferences. Seedling distribution was also associated with habitat conditions, but these conditions explained less than the 30% of the spatial variation. The position of conspecific adult individuals also affected seedling distribution; although the seedlings of many tree species avoid the vicinity of conspecifics, a few species appeared to prefer the formation of cohorts around their parent trees. The importance of habitat conditions and distance dependence with conspecifics varied among regions within the forest as well as on the developmental stage of the stand. The results from this thesis suggest that different species can coexist within a given space, forming a “puzzle” of species as a result of the intra- and interspecific spatial relationships along with niche preferences and adaptations that operate at different scales. These factors not only affect each species in a different way, but specific preferences also vary throughout species' lifespans. Resumen Resumen El bosque de niebla es uno de los ecosistemas más amenazados del mundo además de ser uno de los más frágiles. Son formaciones azonales que dependen de la existencia de unas condiciones de humedad y temperatura que permitan la formación de nubes que cubran el bosque; lo que dificulta en gran medida su conservación. También es uno de los ecosistemas con mayor riqueza de especies además de tener uno de los mayores porcentajes de endemismos. Uno de los aspectos más importantes para entender el ecosistema, es identificar y entender los elementos que lo componen y los mecanismos que regulan las relaciones entre ellos. Los árboles son el soporte del ecosistema. Sin embargo, apenas hay información sobre la distribución y coexistencia de los árboles en los bosques de niebla. Esta tesis presenta un análisis de la distribución a pequeña escala de las plantas leñosas en un bosque de niebla situado en la cordillera andina del norte de Perú; así como el análisis de algunos de los factores que pueden estar implicados en que se origine la distribución observada. Para este propósito se estudia cómo influyen factores de diferente naturaleza en la distribución de las especies (i) organización intra-específica (ii) relaciones espaciales heterospecíficas y (iii) relación con factores ambientales externos. En estos análisis se estudiaron primero las plantas jóvenes y las adultas, y después las plántulas. Los árboles aparecieron agregados en el bosque, tanto considerando todos a la vez como cuando se estudió cada especie por separado. Sin embargo, cada especie mostró un patrón distinto así como una particular relación espacial entre individuos jóvenes y adultos. El modo de dispersión, la forma de vida y la tolerancia de la especies estuvieron relacionados con el patrón general observado. Se vio también que ciertas especies aparecían relacionadas con otras, tanto de forma positiva (compartiendo zonas) como negativa (apareciendo en áreas distintas). Las asociaciones fueron mucho más numerosas cuando se consideraron los pares de especies en diferente estado de desarrollo, es decir, individuos jóvenes de una especie e individuos mayores de la otra. Eso indicaría que los procesos de competencia y facilitación son asimétricos y además varían durante la vida de la planta. Por otro lado, algunas especies aparecen preferentemente bajo ciertas condiciones de hábitat y evitan otras. La definición de hábitat a la que mejor responden las especies es cuando se incluyen tanto variables ambientales como de masa; así que ambos tipos de variables son necesarias para entender la preferencia de las especies por ciertos nichos. La distribución de las plántulas también estuvo relacionada con condiciones de hábitat, pero eso sólo llegaba a explicar hasta un 30% de la variabilidad espacial. La posición de los adultos de la misma especie también afectó a la distribución de las plántulas. En bastantes especies las plántulas evitan la cercanía de adultos de su misma especie, padres potenciales, aunque algunas especies aisladas mostraron el patrón contrario y aparecieron preferentemente en las mismas áreas que sus padres. La importancia de las condiciones de hábitat y posición de los adultos en la disposición de las plántulas varía de una zona a otra del bosque y además también varía según el estado de desarrollo de la masa.

Modelling the spatio-temporal pattern of primary dispersal in stone pine (Pinus pinea L.) stands in the Northern Plateau (Spain)

Natural regeneration in stone pine (Pinus pinea L.) managed forests in the Spanish Northern Plateau is not achieved successfully under current silviculture practices, constituting a main concern for forest managers. We modelled spatio-temporal features of primary dispersal to test whether (a) present low stand densities constrain natural regeneration success and (b) seed release is a climate-controlled process. The present study is based on data collected from a 6 years seed trap experiment considering different regeneration felling intensities. From a spatial perspective, we attempted alternate established kernels under different data distribution assumptions to fit a spatial model able to predict P. pinea seed rain. Due to P. pinea umbrella-like crown, models were adapted to account for crown effect through correction of distances between potential seed arrival locations and seed sources. In addition, individual tree fecundity was assessed independently from existing models, improving parameter estimation stability. Seed rain simulation enabled to calculate seed dispersal indexes for diverse silvicultural regeneration treatments. The selected spatial model of best fit (Weibull, Poisson assumption) predicted a highly clumped dispersal pattern that resulted in a proportion of gaps where no seed arrival is expected (dispersal limitation) between 0.25 and 0.30 for intermediate intensity regeneration fellings and over 0.50 for intense fellings. To describe the temporal pattern, the proportion of seeds released during monthly intervals was modelled as a function of climate variables – rainfall events – through a linear model that considered temporal autocorrelation, whereas cone opening took place over a temperature threshold. Our findings suggest the application of less intensive regeneration fellings, to be carried out after years of successful seedling establishment and, seasonally, subsequent to the main rainfall period (late fall). This schedule would avoid dispersal limitation and would allow for a complete seed release. These modifications in present silviculture practices would produce a more efficient seed shadow in managed stands.

Application of active heat pulse method with fiber optic temperature sensing for estimation of wetting bulbs and water distribution in drip emitters.

Through the use of the Distributed Fiber Optic Temperature Measurement (DFOT) method, it is possible to measure the temperature in small intervals (on the order of centimeters) for long distances (on the order of kilometers) with a high temporal frequency and great accuracy. The heat pulse method consists of applying a known amount of heat to the soil and monitoring the temperature evolution, which is primarily dependent on the soil moisture content. The use of both methods, which is called the active heat pulse method with fiber optic temperature sensing (AHFO), allows accurate soil moisture content measurements. In order to experimentally study the wetting patterns, i.e. shape, size, and the water distribution, from a drip irrigation emitter, a soil column of 0.5 m of diameter and 0.6 m high was built. Inside the column, a fiber optic cable with a stainless steel sheath was placed forming three concentric helixes of diameters 0.2 m, 0.4 m and 0.6 m, leading to a 148 measurement point network. Before, during, and after the irrigation event, heat pulses were performed supplying electrical power of 20 W/m to the steel. The soil moisture content was measured with a capacitive sensor in one location at depths of 0.1 m, 0.2 m, 0.3 m and 0.4 m during the irrigation. It was also determined by the gravimetric method in several locations and depths before and right after the irrigation. The emitter bulb dimensions and shape evolution was satisfactorily measured during infiltration. Furthermore, some bulb's characteristics difficult to predict (e.g. preferential flow) were detected. The results point out that the AHFO is a useful tool to estimate the wetting pattern of drip irrigation emitters in soil columns and show a high potential for its use in the field.

Distribution of indole-3-acetic acid in Petunia hybrida shoot tip cuttings and relationship between auxin transport, carbohydrate metabolism and adventitious root formation.

To determine the contribution of polar auxin transport (PAT) to auxin accumulation and to adventitious root (AR) formation in the stem base of Petunia hybrida shoot tip cuttings, the level of indole-3-acetic acid (IAA) was monitored in non-treated cuttings and cuttings treated with the auxin transport blocker naphthylphthalamic acid (NPA) and was complemented with precise anatomical studies. The temporal course of carbohydrates, amino acids and activities of controlling enzymes was also investigated. Analysis of initial spatial IAA distribution in the cuttings revealed that approximately 40 and 10% of the total IAA pool was present in the leaves and the stem base as rooting zone, respectively. A negative correlation existed between leaf size and IAA concentration. After excision of cuttings, IAA showed an early increase in the stem base with two peaks at 2 and 24h post excision and, thereafter, a decline to low levels. This was mirrored by the expression pattern of the auxin-responsive GH3 gene. NPA treatment completely suppressed the 24-h peak of IAA and severely inhibited root formation. It also reduced activities of cell wall and vacuolar invertases in the early phase of AR formation and inhibited the rise of activities of glucose-6-phosphate dehydrogenase and phosphofructokinase during later stages. We propose a model in which spontaneous AR formation in Petunia cuttings is dependent on PAT and on the resulting 24-h peak of IAA in the rooting zone, where it induces early cellular events and also stimulates sink establishment. Subsequent root development stimulates glycolysis and the pentosephosphate pathway

Spatial distribution of the soil carbon pool in a Holm oak dehesa in Spain

Aims Dehesas are agroforestry systems characterized by scattered trees among pastures, crops and/or fallows. A study at a Spanish dehesa has been carried out to estimate the spatial distribution of the soil organic carbon stock and to assess the influence of the tree cover. Methods The soil organic carbon stock was estimated from the five uppermost cm of themineral soil with high spatial resolution at two plots with different grazing intensities. The Universal Kriging technique was used to assess the spatial distribution of the soil organic carbon stocks, using tree coverage within a buffering area as an auxiliary variable. Results A significant positive correlation between tree presence and soil organic carbon stocks up to distances of around 8 m from the trees was found. The tree crown cover within a buffer up to a distance similar to the crown radius around the point absorbed 30 % of the variance in the model for both grazing intensities, but residual variance showed stronger spatial autocorrelation under regular grazing conditions. Conclusions Tree cover increases soil organic carbon stocks, and can be satisfactorily estimated by means of crown parameters. However, other factors are involved in the spatial pattern of the soil organic carbon distribution. Livestock plays an interactive role together with tree presence in soil organic carbon distribution.

Two design methods for radial line slot antennas with arbitrary or beam pattern

Two design procedures for Radial Line Slot Antennas (RLSAs) with circular polarization and either maximum gain or an arbitrary shaped pattern are proposed. Firstly, a method to design a RLSA with any desired pattern is presented. It is based on an optimization algorithm and some measures to ensure its fast convergence and stability need to be taken. Secondly, a fast technique to calculate the length and the position of every slot in a high gain RLSA with uniform field distribution is described. Both procedures are vali dated with the design of three antennas with different characteristics.