Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

Near-infrared integral field spectroscopy of the Homunculus nebula around eta Carinae using Gemini/CIRPASS

This work presents the first integral field spectroscopy of the Homunculus nebula around eta Carinae in the near-infrared spectral region (J band). We confirmed the presence of a hole on the polar region of each lobe, as indicated by previous near-IR long-slit spectra and mid-IR images. The holes can be described as a cylinder of height (i.e. the thickness of the lobe) and diameter of 6.5 and 6.0 x 10(16) cm, respectively. We also mapped the blue-shifted component of He I lambda 10830 seen towards the NW lobe. Contrary to previous works, we suggested that this blue-shifted component is not related to the Paddle but it is indeed in the equatorial disc. We confirmed the claim of N. Smith and showed that the spatial extent of the Little Homunculus matches remarkably well the radio continuum emission at 3 cm, indicating that the Little Homunculus can be regarded as a small H II region. Therefore, we used the optically thin 1.3 mm radio flux to derive a lower limit for the number of Lyman-continuum photons of the central source in eta Car. In the context of a binary system, and assuming that the ionizing flux comes entirely from the hot companion star, the lower limit for its spectral type and luminosity class ranges from O5.5 III to O7 I. Moreover, we showed that the radio peak at 1.7 arcsec NW from the central star is in the same line-of-sight of the `Sr-filament` but they are obviously spatially separated, while the blue-shifted component of He I lambda 10830 may be related to the radio peak and can be explained by the ultraviolet radiation from the companion star.

Mapping low- and high-density clouds in astrophysical nebulae by imaging forbidden line emission

Emission line ratios have been essential for determining physical parameters such as gas temperature and density in astrophysical gaseous nebulae. With the advent of panoramic spectroscopic devices, images of regions with emission lines related to these physical parameters can, in principle, also be produced. We show that, with observations from modern instruments, it is possible to transform images taken from density-sensitive forbidden lines into images of emission from high- and low-density clouds by applying a transformation matrix. In order to achieve this, images of the pairs of density-sensitive lines as well as the adjacent continuum have to be observed and combined. We have computed the critical densities for a series of pairs of lines in the infrared, optical, ultraviolet and X-rays bands, and calculated the pair line intensity ratios in the high- and low-density limit using a four- and five-level atom approximation. In order to illustrate the method, we applied it to Gemini Multi-Object Spectrograph (GMOS) Integral Field Unit (GMOS-IFU) data of two galactic nuclei. We conclude that this method provides new information of astrophysical interest, especially for mapping low- and high-density clouds; for this reason, we call it `the ld/hd imaging method`.

Non-transposed three-phase line analyses with a single real transformation matrix

In transmission line transient analyses, a single real transformation matrix can obtain exact modes when the analyzed line is transposed. For non-transposed lines, the results are not exact. In this paper, non-symmetrical and non transposed three-phase line samples are analyzed with a single real transformation matrix application (Clarke's matrix). Some interesting characteristics of this matrix application are: single, real, frequency independent, line parameter independent, identical for voltage and current determination. With Clarke's matrix use, mathematical simplifications are obtained and the developed model can be applied directly in programs based on time domain. This model works without convolution procedures to deal with phase-mode transformation. In EMTP programs, Clarke's matrix can be represented by ideal transformers and the frequency dependent line parameters can be represented by modified-circuits. With these representations, the electrical values at any line point can be accessed for phase domain or mode domain using the Clarke matrix or its inverse matrix. For symmetrical and non-transposed lines, the model originates quite small errors. In addition, the application of the proposed model to the non-symmetrical and non-transposed three phase transmission lines is investigated. ©2005 IEEE.

Estudo comparativo das técnicas de elementos finitos e equação integral na modelagem eletromagnética bidimensional

Os métodos numéricos de Elementos Finitos e Equação Integral são comumente utilizados para investigações eletromagnéticas na Geofísica, e, para essas modelagens é importante saber qual algoritmo é mais rápido num certo modelo geofísico. Neste trabalho são feitas comparações nos resultados de tempo computacional desses dois métodos em modelos bidimensionais com heterogeneidades condutivas num semiespaço resistivo energizados por uma linha infinita de corrente (com 1000Hz de freqüência) e situada na superfície paralelamente ao "strike" das heterogeneidades. Após a validação e otimização dos programas analisamos o comportamento dos tempos de processamento nos modelos de corpos retangulares variandose o tamanho, o número e a inclinação dos corpos. Além disso, investigamos nesses métodos as etapas que demandam maior custo computacional. Em nossos modelos, o método de Elementos Finitos foi mais vantajoso que o de Equação Integral, com exceção na situação de corpos com baixa condutividade ou com geometria inclinada.

Representation of transmission lines: comparison of models and parameters distributed discrete parameters

A transmission line is characterized by the fact that its parameters are distributed along its length. This fact makes the voltages and currents along the line to behave like waves and these are described by differential equations. In general, the differential equations mentioned are difficult to solve in the time domain, due to the convolution integral, but in the frequency domain these equations become simpler and their solutions are known. The transmission line can be represented by a cascade of π circuits. This model has the advantage of being developed directly in the time domain, but there is a need to apply numerical integration methods. In this work a comparison of the model that considers the fact that the parameters are distributed (Universal Line Model) and the fact that the parameters considered concentrated along the line (π circuit model) using the trapezoidal integration method, and Simpson's rule Runge-Kutta in a single-phase transmission line length of 100 km subjected to an operation power. © 2003-2012 IEEE.

Algorithms for on-line image registration from multiple views

Images of a scene, static or dynamic, are generally acquired at different epochs from different viewpoints. They potentially gather information about the whole scene and its relative motion with respect to the acquisition device. Data from different (in the spatial or temporal domain) visual sources can be fused together to provide a unique consistent representation of the whole scene, even recovering the third dimension, permitting a more complete understanding of the scene content. Moreover, the pose of the acquisition device can be achieved by estimating the relative motion parameters linking different views, thus providing localization information for automatic guidance purposes. Image registration is based on the use of pattern recognition techniques to match among corresponding parts of different views of the acquired scene. Depending on hypotheses or prior information about the sensor model, the motion model and/or the scene model, this information can be used to estimate global or local geometrical mapping functions between different images or different parts of them. These mapping functions contain relative motion parameters between the scene and the sensor(s) and can be used to integrate accordingly informations coming from the different sources to build a wider or even augmented representation of the scene. Accordingly, for their scene reconstruction and pose estimation capabilities, nowadays image registration techniques from multiple views are increasingly stirring up the interest of the scientific and industrial community. Depending on the applicative domain, accuracy, robustness, and computational payload of the algorithms represent important issues to be addressed and generally a trade-off among them has to be reached. Moreover, on-line performance is desirable in order to guarantee the direct interaction of the vision device with human actors or control systems. This thesis follows a general research approach to cope with these issues, almost independently from the scene content, under the constraint of rigid motions. This approach has been motivated by the portability to very different domains as a very desirable property to achieve. A general image registration approach suitable for on-line applications has been devised and assessed through two challenging case studies in different applicative domains. The first case study regards scene reconstruction through on-line mosaicing of optical microscopy cell images acquired with non automated equipment, while moving manually the microscope holder. By registering the images the field of view of the microscope can be widened, preserving the resolution while reconstructing the whole cell culture and permitting the microscopist to interactively explore the cell culture. In the second case study, the registration of terrestrial satellite images acquired by a camera integral with the satellite is utilized to estimate its three-dimensional orientation from visual data, for automatic guidance purposes. Critical aspects of these applications are emphasized and the choices adopted are motivated accordingly. Results are discussed in view of promising future developments.

In-situ measurement and characterization of cloud particles using digital in-line holography

Satellite measurement validations, climate models, atmospheric radiative transfer models and cloud models, all depend on accurate measurements of cloud particle size distributions, number densities, spatial distributions, and other parameters relevant to cloud microphysical processes. And many airborne instruments designed to measure size distributions and concentrations of cloud particles have large uncertainties in measuring number densities and size distributions of small ice crystals. HOLODEC (Holographic Detector for Clouds) is a new instrument that does not have many of these uncertainties and makes possible measurements that other probes have never made. The advantages of HOLODEC are inherent to the holographic method. In this dissertation, I describe HOLODEC, its in-situ measurements of cloud particles, and the results of its test flights. I present a hologram reconstruction algorithm that has a sample spacing that does not vary with reconstruction distance. This reconstruction algorithm accurately reconstructs the field to all distances inside a typical holographic measurement volume as proven by comparison with analytical solutions to the Huygens-Fresnel diffraction integral. It is fast to compute, and has diffraction limited resolution. Further, described herein is an algorithm that can find the position along the optical axis of small particles as well as large complex-shaped particles. I explain an implementation of these algorithms that is an efficient, robust, automated program that allows us to process holograms on a computer cluster in a reasonable time. I show size distributions and number densities of cloud particles, and show that they are within the uncertainty of independent measurements made with another measurement method. The feasibility of another cloud particle instrument that has advantages over new standard instruments is proven. These advantages include a unique ability to detect shattered particles using three-dimensional positions, and a sample volume size that does not vary with particle size or airspeed. It also is able to yield two-dimensional particle profiles using the same measurements.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

An Integral View of Fast Shocks Around Supernova 1006

Supernova remnants are among the most spectacular examples of astrophysical pistons in our cosmic neighborhood. The gas expelled by the supernova explosion is launched with velocities ~1000 kilometers per second into the ambient, tenuous interstellar medium, producing shocks that excite hydrogen lines. We have used an optical integral-field spectrograph to obtain high-resolution spatial-spectral maps that allow us to study in detail the shocks in the northwestern rim of supernova 1006. The two-component Hα line is detected at 133 sky locations. Variations in the broad line widths and the broad-to-narrow line intensity ratios across tens of atomic mean free paths suggest the presence of suprathermal protons, the potential seed particles for generating high-energy cosmic rays.

Orientación geográfica : La geoperspectiva integral

La propuesta presenta la perspectiva integral y natural desde la Orientación en sí misma, ofreciendo el sustento para promover el debate sobre el manejo y el dominio de perspectivas físicas y geográficas. Toma al ser humano como el sujeto, en este caso como el observador terrestre. Se ha desarrollado un marco teórico sustentado por axiomas, los cuales permiten la discusión sobre el uso de perspectivas, su aplicación en el conocimiento, la educación, el replanteamiento epistemológico y la definición de una identidad global. Este planteamiento busca generar una nueva línea de discusión, una propuesta científicamente cuestionadora de la hegemonía del pensamiento geográfico y que brinde nuevas matrices de racionalidad geográfica

Orientación geográfica : La geoperspectiva integral

La propuesta presenta la perspectiva integral y natural desde la Orientación en sí misma, ofreciendo el sustento para promover el debate sobre el manejo y el dominio de perspectivas físicas y geográficas. Toma al ser humano como el sujeto, en este caso como el observador terrestre. Se ha desarrollado un marco teórico sustentado por axiomas, los cuales permiten la discusión sobre el uso de perspectivas, su aplicación en el conocimiento, la educación, el replanteamiento epistemológico y la definición de una identidad global. Este planteamiento busca generar una nueva línea de discusión, una propuesta científicamente cuestionadora de la hegemonía del pensamiento geográfico y que brinde nuevas matrices de racionalidad geográfica

Orientación geográfica : La geoperspectiva integral

La propuesta presenta la perspectiva integral y natural desde la Orientación en sí misma, ofreciendo el sustento para promover el debate sobre el manejo y el dominio de perspectivas físicas y geográficas. Toma al ser humano como el sujeto, en este caso como el observador terrestre. Se ha desarrollado un marco teórico sustentado por axiomas, los cuales permiten la discusión sobre el uso de perspectivas, su aplicación en el conocimiento, la educación, el replanteamiento epistemológico y la definición de una identidad global. Este planteamiento busca generar una nueva línea de discusión, una propuesta científicamente cuestionadora de la hegemonía del pensamiento geográfico y que brinde nuevas matrices de racionalidad geográfica

Indicadores de sostenibilidad de la gestión integral de las aguas de lluvia en los entornos urbanos : aplicación a la ciudad de Zaragoza

En un contexto de rápido crecimiento de la población urbana y de cambio climático global, la consecución de un modelo de desarrollo sostenible pasa inevitablemente por construir ciudades más sostenibles. Basado en una intensiva impermeabilización de los suelos, el modelo actual de desarrollo urbano modifica profundamente el ciclo natural del agua en las ciudades. La drástica reducción de la capacidad de infiltración del terreno hace que gran parte de la precipitación se transforme en escorrentía superficial, que se concentra rápidamente originando grandes caudales punta. Además, el lavado de las superficies urbanas aporta altas cargas de contaminación a la escorrentía que producen importantes impactos en los medios receptores. Esta realidad motiva la realización de la presente tesis doctoral cuyo objetivo general es contribuir a la consecución de ciudades sostenibles a través de la gestión integral de las aguas de lluvia en los entornos urbanos. Con el objetivo prioritario de minimizar los riesgos de inundación, el enfoque convencional del drenaje urbano desarrolló las primeras soluciones en relación a los caudales punta, centralizando su gestión en el sistema de saneamiento e incorporando la escorrentía al mismo tan rápido como fuera posible. Pero en episodios de lluvias intensas la sobrecarga tanto hidráulica como de contaminación del sistema provoca un incremento de la vulnerabilidad de la población a las inundaciones, una falta de garantía de salud pública y graves impactos sobre los medios receptores. La aprobación en 1987 del CleanWaterAct en Estados Unidos, en el que se reconoció por primera vez el problema de la contaminación aportada por la escorrentía urbana, fue el punto de partida de un nuevo enfoque que promueve un conjunto de técnicas de drenaje que integran aspectos como cantidad de agua, calidad de agua y servicio a la sociedad. Estas técnicas, conocidas como Sistemas de Drenaje Sostenible (SUDS), son consideradas como las técnicas más apropiadas para gestionar los riesgos resultantes de la escorrentía urbana así como para contribuir a la mejora medioambiental de la cuenca y de los ecosistemas receptores. La experiencia internacional apunta a que la efectiva incorporación de los SUDS como sistemas habituales en el desarrollo urbano debe basarse en tres elementos clave: El desarrollo de un marco normativo, la aplicación de instrumentos económicos y la participación ciudadana activa en el proceso. Además se identifica como una de las líneas estratégicas para avanzar en la resolución de la problemática el desarrollo y aplicación de metodologías que apoyen el proceso de toma de decisiones basadas en indicadores cuantificables. Convergiendo con esta línea estratégica la presente tesis doctoral define unos indicadores de sostenibilidad focalizados en una temática no desarrollada hasta el momento, la gestión integral de las aguas de lluvia. Para ello, se aplica el marco analítico Presión-Estado–Respuesta bajo un enfoque que rebasa el sistema de saneamiento, enmarcando la gestión de las aguas de lluvia en las múltiples y complejas interrelaciones del sistema urbano. Así se determinan indicadores de presión, de estado y de respuesta para cada elemento del sistema urbano (Medio Receptor – Cuenca Urbana – Sistema de Saneamiento), definiendo para cada indicador el objetivo específico, la unidad de medición, la tendencia deseada de evolución y la periodicidad de seguimiento recomendada. La validez de la metodología propuesta se comprueba en el estudio de caso de la ciudad de Zaragoza. La determinación de los indicadores permite realizar un diagnóstico y definir unas líneas estratégicas de actuación que contemplan mejoras no sólo en el sistema de saneamiento y drenaje urbano, sino también en el marco normativo, urbanístico, económico, social y ambiental. Finalmente, se concluye que la integración de la gestión de las aguas de lluvia en las políticas de ordenación del territorio, el desarrollo de mecanismos de coordinación institucional, la mejora del marco normativo y la aplicación de instrumentos económicos son elementos clave para la gestión integral de las aguas de lluvia y el consecuente desarrollo de ciudades más sostenibles en España. In a context of rapid urbanization and global climate change, coping with sustainable development challenges requires the development of sustainable cities. Based on an intensive soil permeability reduction, the current development model deeply modifies the natural water cycle in the urban environment. Reduction of soil infiltration capacity turns most of the rainwater into surface runoff, rapidly leading to heavy peak flows which are highly contaminated due to the flushing of the urban surface. This is the central motivation for this thesis, which aspires to contribute to the attainment of more sustainable cities through an integrated management of rainwater in urban environments. With the main objective of minimizing floods, the conventional approach of drainage systems focused on peak flows, centralizing their management on the sewage system and incorporating flows as fast as possible. But during heavy rains the hydraulic and contamination overcharge of the sewage system leads to an increase in the vulnerability of the population, in regards to floods and lack of public health, as well as to severe impacts in receiving waters. In 1987, the United States’Clean Water Act Declaration, which firstly recognized the problem of runoff contamination, was the starting point of a new approach that promotes a set of techniques known as Sustainable Drainage Systems (SUDS)that integrates issues such as quantity of water, quality of water and service to society. SUDS are considered the most suitable set of techniques to manage the risks resulting from urban runoff, as well as to contribute to the environmental enhancement of urban basins and of the aquatic ecosystems. International experience points out that the effective adoption of SUDS as usual systems in urban development must be based on three key elements: The enhancement of the legal frame, the application of economic tools and the active public participation throughout the process. Additionally, one of the strategic actions to advance in the resolution of the problem is the development and application of methodologies based in measurable indicators that support the decision making process. In that line, this thesis defines a set of sustainability indicators focused in integrated management of rainwater. To that end, the present document applies the analytical frame Pressure – State – Response under an approach that goes beyond the sewage system and considers the multiple and complex interrelations within urban systems. Thus, for the three basic elements that interact in the issue (Receiving Water Bodies – Urban Basin – Sewage System) a set of Pressure – State – Response indicators are proposed, and the specific aim, the measurement unit, the desired evolution trend and the regularity of monitoring are defined for each of the indicators. The application of the proposed indicators to the case study of the city of Zaragoza acknowledged their suitability for the definition of lines of action that encompass not only the enhancement of the performance of sewage and drainage systems during rain events, but also the legal, urban, economic, social and environmental framework. Finally, this thesis concludes that the inclusion of urban rainwater management issues in the definition of regional planning policies, the development of mechanisms to attain an effective institutional coordination, the enhancement of the legal framework and the application of economic tools are key elements in order to achieve an integrated rainwater management and the subsequent sustainability of urban development in Spain.

Lugares adecuados para la utilización de nuevos materiales y formas con geotextiles en la gestión integral de la zona litoral como protección ambiental

La erosión costera es un fenómeno que ha cobrado importancia durante los últimos años, debido a sus repercusiones tanto en el turismo, como en el incremento de riesgo para las infraestructuras y para la población allí ubicada. Se define como el retroceso progresivo de la línea de costa cuyas causas pueden ser de origen natural o antropogénicas. La costa merece la máxima protección, y su gestión debe asegurar su integridad física y su libre acceso, al igual que un uso público por parte de todos. En este horizonte, la reducción de costes, la facilidad de construcción y velocidad de realización, las obras de geotextil se han mostrado como una alternativa muy seria a las obras duras u obras clásicas, tradicionalmente realizadas a lo largo de las costas. Pero esta alternativa de uso conlleva un mayor conocimiento en el comportamiento de éstas, su diseño y durabilidad. Las obras de geotextil, como su nombre indica, se realizan con elementos tridimensionales de geotextil (cosidos o no cosidos) rellenos de arena. Estos elementos se pueden considerar innovadores, económicos, ecológicos y alternativos frente a los tradicionales. Se distinguen tres tipos denominados: sacos, tubos y contenedores. El principal objetivo de esta tesis se centra en la determinación de las zonas de la costa apropiados para la utilización de estructuras compuestas de elementos de geotextil rellenos de arena, como obras de defensa de costas, con el fin de facilitar su uso en la ingeniería de costas. Para ello se ha clasificado tanto las distintas zonas del perfil longitudinal de una playa, como los tipos de costa en función de la variable altura de ola significante. Se han determinado las limitaciones de esta variable en las distintas fórmulas de estabilidad de estas estructuras. Y finalmente, en función de la máxima limitación de altura de ola significante y de sus posibles valores en las zonas y tipos de costa, se han determinado las zonas más apropiadas para el uso de las estructuras compuestas por elementos de geotextil. Finalmente se han redactado las conclusiones de la investigación y se han propuesto nuevas líneas de investigación relacionadas con esta Tesis Doctoral. Coastal erosion is a phenomenon that has become more important in recent years because of its impact on both on tourism, and increased risk to infrastructure and the population located there. It is defined as the gradual decline in the coastline whose causes may be natural or anthropogenic origin. The coast deserves maximum protection, and management should ensure their physical integrity and their free access, as well as public use by all. In this line, cost reduction, ease of construction and completion rate, geotextile works have been shown as a very serious to hard works or classics alternative, traditionally performed along the coasts. But this alternative use entails greater insight into the behaviour of these, design and durability. Works of geotextile, as its name suggests, are made with three-dimensional elements of geotextile (sewn or stitched) filled with sand. These items can be considered innovative, economic, and ecological alternative compared to traditional. Bags, tubes and containers, three known types are distinguished. The main objective of this thesis focuses on determining the appropriate areas of the coast for the use of composite structures of elements filled geotextile sand as coastal defence works, in order to facilitate their use, in coastal engineering. For it, has been classified by both the different areas of the longitudinal profile of a beach as the shoreline types depending on the variable significant wave height. We have determined the limitations of this variable in the different formulas stability of these structures. And finally, depending on the maximum limitation of significant wave height and its possible values in the areas and types of coastline, have determined the most appropriate for use in structures composed of elements of geotextile areas. Finally, the conclusions of the research have been addressed and the proposal of new lines of work related to the topic has been made.