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.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

Ecología política y economía de la visibilidad de los dispositivos tecnológicos de escala urbana durante el siglo XX Abriendo la caja negra

En paralelo a la superficie cotidiana de la ciudad moderna, discurre otra "ciudad invisible" o "caja negra" tecnológica, que opera, de manera silenciosa e imperceptible, al servicio de los ciudadanos. Paradójicamente, en este espacio invisible, se toman decisiones de la máxima relevancia para la ciudad: en la "caja negra", las ciudades pactan sus relaciones con la naturaleza; a través de ella, se produce la administración y distribución de los recursos que componen su metabolismo urbano. En definitiva, la "caja negra" es el conjunto de las arquitecturas donde se urbaniza la naturaleza, donde ésta pasa a ser ciudad. Y, sin embargo, ha tendido a permanecer invisible. No obstante, en el último tercio del siglo XX, se ha "abierto la caja negra" urbana y lo que era invisible ha dejado de serlo o, al menos, ha alterado su estatuto de visibilidad. El objetivo de esta tesis doctoral es evaluar las repercusiones arquitectónicas, urbanísticas y ecológicas, que conlleva este reciente fenómeno urbano que, desde hace unas décadas, está teniendo lugar en muchas de las ciudades herederas de las grandes reformas urbanas acometidas en las metrópolis europeas durante el siglo XIX, bajo el paradigma simbólico de un proyecto moderno "prometeico" y emancipador. Para abordar dicho análisis, se pondrán en relación dos parámetros urbanos elementales que han tendido a ser estudiados por separado. Por un lado, la "ecología política urbana", es decir, la red de relaciones socio-ecológicas que acontecen en la ciudad. Por otro lado, la "economía de la visibilidad", es decir, las formas de articular lo visible y lo invisible, en relación a los marcos de gobernanza. La intersección entre la "ecología política urbana" y la "economía de la visibilidad" proporciona un marco de análisis efectivo para comprender el fenómeno de la "apertura de la caja negra" y conlleva un cuestionamiento de algunas nociones dominantes en la teoría urbana y arquitectónica clásicas, como la segregación de la naturaleza, las infraestructuras y la sociedad o como las formas tradicionales de explotación ecológica del medio. Además, ofrece un criterio de análisis privilegiado para la comprensión del proceso de deslegitimación (filosófica, arquitectónica, económica, así como desde perspectivas ecológicas, sociales, de género o queer) de los modelos urbanísticos integrales modernos, herederos de los marcos antropocéntricos del siglo XIX. Por último, proporciona algunas herramientas arquitectónicas para afrontar los desafíos ecosistémicos del siglo XXI. A través del estudio de autores relevantes que han analizado esta problemática para la arquitectura, así como del estudio de casos arquitectónicos que han marcado hitos fundamentales en la consolidación urbana de los procesos asociados a la "caja negra", se concluirá que, en términos ecológicos, la ciudad moderna ha movilizado una "ecología política urbana" basada en fórmulas de sometimiento del entorno, a partir de operaciones arquitectónicas y tecnológicas invisibles. En esta tesis doctoral se estudiará la organización arquitectónica de las arquitecturas de la "caja negra" y se evaluará si el fenómeno de la "apertura de la caja negra" puede ser considerado como un síntoma de la alteración en la "ecología política urbana". 'Abriremos la caja negra" para estudiar cómo se integran en el espacio urbano los dispositivos tecnológicos de escala urbana, toda vez éstos han dejado de ser invisibles. Cómo participan, como un actor más, en la configuración de otros marcos de cohabitación, dentro de la ciudad contemporánea. ABSTRACT An 'invisible city' or technological 'black box' runs parallel to the day-to-day surface of modern cities, remaining silent, unnoticed, at the service of the citizenry. Paradoxically, this invisible space is where some of the most relevant decisions concerning the city are made: the 'black box' is where cities agree on their relationships with nature; it is used to manage and distribute the resources that form its urban metabolism. In short, the 'black box' is the collection of architectures where nature is urbanised, where it becomes a city. And in spite of all this, it has mostly remained invisible. Nevertheless, this urban 'black box' was opened during the last third of the 20th century, so what used to be invisible is invisible no more, or at least the laws governing its visibility have been altered. The purpose of this doctoral thesis is to evaluate the architectural, urban planning and ecological repercussions of this recent urban phenomenon that has been taking place for several decades in many of the cities that followed in the footsteps of the large European metropolises of the 19th century, under the symbolic paradigm of a modern 'prometheic' and emancipating project. This analysis shall be done by juxtaposing two basic urban parameters that in general have been studied separately: frstly the ‘urban political ecology', that is, the network of socio-ecological relationships within the city. Secondly, the 'economy of visibility', that is, the way the visible and invisible spheres are structured in relation with the governance frameworks. The intersection between the 'urban political ecology' and the 'economy of visibility' provides an effective analysis framework to understand the phenomenon of the 'opening of the black box'. It entails calling into question some of the predominant notions in classical urban and architectural theory, such as the segregation of nature, infrastructures and society, or the traditional forms of ecological usage of the environment. It also offers an exceptional analysis criterion to understand the discrediting process (from a philosophical, architectural, economic perspective, but also from the point of view of ecology, society, gender or queerness) of modern all-encompassing urban models that draw from the anthropocentric frameworks of the 19th century. Finally, it provides some architectural tools to tackle 21st-century ecosystemic challenges. The study of relevant authors that have analysed these problems for architecture, as well as the study of milestone architectural cases for the urban consolidation of processes associated to the 'black box', shall serve to reach the conclusion that, in ecological terms, modern cities have mobilised an 'urban political ecology' based on formulas of subjugation of the environment, through invisible architectural and technological operations. This thesis shall present an evaluation of whether the phenomenon of the 'opening of the black box' can be considered a symptom of the alteration of the 'urban political ecology'. We shall 'open the black box' to study the integration of the various urbanscale technological devices within the urban landscape, now that they have ceased to be invisible. We shall see how they participate, like any other actor, in the confguration of other cohabitation frameworks within today's cities.

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

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.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.

Theory of intermittency applied to classical pathological cases

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Though it works fine in some model systems, there exist a number of so-called pathological cases characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. Recently, we reported on how the reinjection probability density (RPD) can be generalized. Here, we extend this methodology and apply it to different dynamical systems exhibiting anomalous type-II and type-III intermittencies. Estimation of the universal RPD is based on fitting a linear function to experimental data and requires no a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets (dozens of points). Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. We show that the method copes well with dynamical systems exhibiting significantly different statistics reported in the literature. We also derive and classify characteristic relations between the mean laminar length and main controlling parameter in perfect agreement with data provided by numerical simulations

Analysis and suppression of reflections in far-field antenna measurement ranges

This paper presents the analysis of the reflections in two kind of spherical far field ranges: one if the classical acquisition where the AUT is rotated and the second one corresponds to the systems where the AUT is fixed and the antenna probe is rotated. In large far field systems this is not possible, but this can be used to the measurement of small antennas, for instance, with the SATIMO StarGate system. In both cases, it is assumed that only one frequency is acquired and the results should be improved cut by cut, in order not to lose the advantages or far field measurements. Finally, some practical results are studied using measurements of one antenna in the outdoor far field facility of LIT INPE in Brazil.

Diagnostics of classical and dusty plasmas w ith collecting and emissive langmuir probes = Diagnosis de plasmas clásicos y granulares mediante sondas colectoras y emisoras de Langmuir

Las sondas eléctricas se emplean habitualmente en la diagnosis de plasmas. La presente tesis aborda la operación de las sondas colectoras y emisoras de Langmuir en plasmas fríos de baja densidad. El estudio se ha centrado en la determinación del potencial de plasma, Vsp, mediante el potencial flotante de una sonda emisora. Esta técnica consiste en la medida del potencial de la sonda correspondiente a la condición de corriente neta igual a cero, el cual se denomina potencial flotante, VF. Este potencial se desplaza hacia el potencial del plasma según aumenta la emisión termoiónica de la sonda, hasta que se satura cerca de Vsp. Los experimentos llevados a cabo en la pluma de plasma de un motor iónico y en un plasma de descarga de glow muestran que la corriente de electrones termoiónicos es mayor que la corriente de electrones recogidos para una sonda polarizada por debajo del potencial del plasma, resultado inconsistente con la teoría tradicionalmente aceptada. Para investigar estos resultados se ha introducido el parámetro R, definido como el cociente entre la corriente de electrones emitidos y recogidos por la sonda. Este parámetro, que está relacionado con la diferencia de potencial VF - Vsp, también es útil para la descripción de los modos de operación de la sonda emisora (débil, fuerte y más allá del fuerte). Los resultados experimentales evidencian que, al contrario de lo que indica la teoría, R es mayor que la unidad. Esta discrepancia se puede solucionar introduciendo una población efectiva de electrones. Con dicha población, el nuevo modelo para la corriente total de la sonda reproduce los datos experimentales. El origen de este grupo electrónico es todavía una cuestión abierta, pero podría estar originada por una nueva estructura de potencial cerca de la sonda cuando ésta trabaja en el régimen de emisión fuerte. Para explicar dicha estructura de potencial, se propone un modelo unidimensional compuesto por un mínimo de potencial cerca de la superficie de la sonda. El análisis numérico indica que este pozo de potencial aparece para muy altas temperaturas de la sonda, reduciendo la cantidad de electrones emitidos que alcanzan el plasma y evitando así cualquier posible perturbación de éste. Los aspectos experimentales involucrados en el método del potencial flotante también se han estudiado, incluyendo cuestiones como las diferentes técnicas de obtención del VF, el cociente señal-ruido, el acoplamiento de la señal de los equipos utilizados para la obtención de las curvas I-V o la evidencia experimental de los diferentes modos de operación de la sonda. Estas evidencias empíricas se encuentran en todos los aspectos de operación de la sonda: la recolección de electrones, el potencial flotante, la precisión en las curvas I-V y la emisión electrónica. Ésta última también se estudia en la tesis, debido a que un fenómeno de super emisión tiene lugar en el régimen de emisión fuerte. En este modo de operación, las medidas experimentales indican que las corrientes termoiónicas de electrones son mayores que aquéllas predichas por la ecuación de Richardson-Dushman clásica. Por último, la diagnosis de plasmas usando sondas eléctrica bajo presencia de granos de polvo (plasmas granulares) en plasmas fríos de baja densidad también se ha estudiado, mediante la aplicación numérica de la técnica del potencial flotante de la sonda emisora en un plasma no convencional. Los resultados apuntan a que el potencial flotante de una sonda emisora se vería afectado por altas densidades de polvo o grandes partículas. ABSTRACT Electric probes are widely employed for plasma diagnostics. This dissertation concerns the operation of collecting and emissive Langmuir probes in low density cold plasmas. The study is focused on the determination of the plasma potential, Vsp, by means of the floating potential of emissive probes. This technique consists of the measurement of the probe potential, corresponding to the zero net probe current, which is the so-called floating potential, VF . This potential displaces towards the plasma potential as the thermionic electron emission increases, until it saturates near Vsp. Experiments carried out in the plasma plume of an ion thruster and in a glow discharge plasma show the thermionic electron current of the emissive Langmuir probe is higher than the collected electron current, for a probe with a bias potential below Vsp, which is inconsistent with the traditional accepted theory. To investigate these results, a parameter R is introduced as the ratio between the emitted and the collected electron current. This parameter, which is related to the difference VF - Vsp, is also useful for the description of the operation modes of the emissive Langmuir probe (weak, strong and beyond strong). The experimental results give an inconsistency of R > 1, which is solved by a modification of the theory for emissive probes, with the introduction of an effective electron population. With this new electron group, the new model for the total probe current agrees with the experimental data. The origin of this electron group remains an open question, but it might be originated by a new potential structure near the emissive probe when it operates in the strong emission regime. A simple one-dimension model composed by a minimum of potential near the probe surface is discussed for strongly emitting emissive probes. The results indicate that this complex potential structure appears for very high probe temperatures and the potential well might reduce the emitted electrons population reaching the plasma bulk. The experimental issues involved in the floating potential method are also studied, as the different obtaining techniques of VF, the signal-to-noise ratio, the signal coupling of the I-V curve measurement system or the experimental evidence of the probe operation modes. These empirical proofs concern all the probe operation aspects: the electron collection, the floating potential, the I-V curve accuracy as well as the electron emission. This last issue is also investigated in this dissertation, because a super emission takes place in the strong emission regime. In this operation mode, the experimental results indicate that the thermionic electron currents might be higher than those predicted by the classical Richardson-Dushman equation. Finally, plasma diagnosis using electric probes in the presence of dust grains (dusty plasmas) in low density cold plasmas is also addressed. The application of the floating potential technique of the emissive probe in a non-conventional complex plasma is numerically investigated, whose results point out the floating potential of the emissive probe might be shifted for high dust density or large dust particles.

On sonic anemometer measurement theory

In this paper a model for the measuring process of sonic anemometers (ultrasound pulse based) is presented. The differential equations that describe the travel of ultrasound pulses are solved in the general case of non-steady, non-uniform atmospheric flow field. The concepts of instantaneous line-average and travelling pulse-referenced average are established and employed to explain and calculate the differences between the measured turbulent speed (travelling pulse-referenced average) and the line-averaged one. The limit k1l=1 established by Kaimal in 1968, as the maximum value which permits the neglect of the influence of the sonic measuring process on the measurement of turbulent components is reviewed here. Three particular measurement cases are analysed: A non-steady, uniform flow speed field, a steady, non-uniform flow speed field and finally an atmospheric flow speed field. In the first case, for a harmonic time-dependent flow field, Mach number, M (flow speed to sound speed ratio) and time delay between pulses have revealed themselves to be important parameters in the behaviour of sonic anemometers, within the range of operation. The second case demonstrates how the spatial non-uniformity of the flow speed field leads to an influence of the finite transit time of the pulses (M≠0) even in the absence of non-steady behaviour of the wind speed. In the last case, a model of the influence of the sonic anemometer processes on the measurement of wind speed spectral characteristics is presented. The new solution is compared to the line-averaging models existing in the literature. Mach number and time delay significantly distort the measurement in the normal operational range. Classical line averaging solutions are recovered when Mach number and time delay between pulses go to zero in the new proposed model. The results obtained from the mathematical model have been applied to the calculation of errors in different configurations of practical interest, such as an anemometer located on a meteorological mast and the transfer function of a sensor in an atmospheric wind. The expressions obtained can be also applied to determine the quality requirements of the flow in a wind tunnel used for ultrasonic anemometer calibrations.