Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Physiological effects of mechanical pain stimulation at the lower back measured by functional near-infrared spectroscopy and capnography

The aim was to investigate the effect of mechanical pain stimulation at the lower back on hemodynamic and oxygenation changes in the prefrontal cortex (PFC) assessed by functional near-infrared spectroscopy (fNIRS) and on the partial pressure of end-tidal carbon dioxide ( PetCO 2) measured by capnography. 13 healthy subjects underwent three measurements (M) during pain stimulation using pressure pain threshold (PPT) at three locations, i.e., the processus spinosus at the level of L4 (M1) and the lumbar paravertebral muscles at the level of L1 on the left (M2) and the right (M3) side. Results showed that only in the M2 condition the pain stimulation elicited characteristic patterns consisting of (1) a fNIRS-derived decrease in oxy- and total hemoglobin concentration and tissue oxygen saturation, an increase in deoxy-hemoglobin concentration, (2) a decrease in the PetCO 2 response and (3) a decrease in coherence between fNIRS parameters and PetCO 2 responses in the respiratory frequency band (0.2-0.5 Hz). We discuss the comparison between M2 vs. M1 and M3, suggesting that the non-significant findings in the two latter measurements were most likely subject to effects of the different stimulated tissues, the stimulated locations and the stimulation order. We highlight that PetCO 2 is a crucial parameter for proper interpretation of fNIRS data in experimental protocols involving pain stimulation. Together, our data suggest that the combined fNIRS-capnography approach has potential for further development as pain monitoring method, such as for evaluating clinical pain treatment.

Pulse-shaping assisted multidimensional coherent electronic spectroscopy

Understanding nuclear and electronic dynamics of molecular systems has advanced considerably by probing their nonlinear responses with a suitable sequence of pulses. Moreover, the ability to control crucial parameters of the excitation pulses, such as duration, sequence, frequency, polarization, slowly varying envelope, or carrier phase, has led to a variety of advanced time-resolved spectroscopic methodologies. Recently, two-dimensional electronic spectroscopy with ultrashort pulses has become a more and more popular tool since it allows to obtain information on energy and coherence transfer phenomena, line broadening mechanisms, or the presence of quantum coherences in molecular complexes. Here, we present a high fidelity two-dimensional electronic spectroscopy setup designed for molecular systems in solution. It incorporates the versatility of pulse-shaping methods to achieve full control on the amplitude and phase of the individual exciting and probing pulses. Selective and precise amplitude- and phase-modulation is shown and applied to investigate electronic dynamics in several reference molecular systems.

Probing the Structure, Pseudorotation, and Radial Vibrations of Cyclopentane by Femtosecond Rotational Raman Coherence Spectroscopy

Femtosecond time-resolved Raman rotational coherence spectroscopy (RCS) is employed to determine accurate rotational, vibration–rotation coupling constants, and centrifugal distortion constants of cyclopentane (C⁵H¹⁰). Its lowest-frequency vibration is a pseudorotating ring deformation that interconverts 10 permutationally distinct but energetically degenerate “twist” minima interspersed by 10 “bent” conformers. While the individual twist and bent structures are polar asymmetric tops, the pseudorotation is fast on the time scale of external rotation, rendering cyclopentane a fluxionally nonpolar symmetric top molecule. The pseudorotational level pattern corresponds to a one-dimensional internal rotor with a pseudorotation constant Bps ≈ 2.8 cm⁻¹. The pseudorotational levels are significantly populated up to l = ± 13 at 298 K; <10% of the molecules are in the l = 0 level. The next-higher vibration is the “radial” ν²³ ring deformation mode at 273 cm⁻¹, which is far above the pseudorotational fundamental. Femtosecond Raman RCS measurements were performed in a gas cell at T = 293 K and in a pulsed supersonic jet at T ≈ 90 K. The jet cooling reduces the pseudorotational distribution to l < ±8 and eliminates the population of ν²³, allowing one to determine the rotational constant as A0 = B0 = 6484.930(11) MHz. This value is ∼300 times more precise than the previous value. The fit of the RCS transients reveals that the rotation–pseudorotation coupling constant αe,psB = −0.00070(1) MHz is diminutive, implying that excitation of the pseudorotation has virtually no effect on the B0 rotational constant of cyclopentane. The smallness of αe,psB can be realized when comparing to the vibration–rotation coupling constant of the ν²³ vibration, αe,23B = −9.547(1) MHz, which is about 10⁴ times larger.

Does superficial fat affect metabolite concentrations determined by MR spectroscopy with water referencing?

It has recently been reported in this journal that local fat depots produce a sizable frequency-dependent signal attenuation in magnetic resonance spectroscopy (MRS) of the brain. If of a general nature, this effect would question the use of internal reference signals for quantification of MRS and the quantitative use of MRS as a whole. Here, it was attempted to verify this effect and pinpoint the potential causes by acquiring data with various acquisition settings, including two field strengths, two MR scanners from different vendors, different water suppression sequences, RF coils, localization sequences, echo times, and lipid/metabolite phantoms. With all settings tested, the reported effect could not be reproduced, and it is concluded that water referencing and quantitative MRS per se remain valid tools under common acquisition conditions.

Gradient-domain Path Tracing

We introduce gradient-domain rendering for Monte Carlo image synthesis.While previous gradient-domain Metropolis Light Transport sought to distribute more samples in areas of high gradients, we show, in contrast, that estimating image gradients is also possible using standard (non-Metropolis) Monte Carlo algorithms, and furthermore, that even without changing the sample distribution, this often leads to significant error reduction. This broadens the applicability of gradient rendering considerably. To gain insight into the conditions under which gradient-domain sampling is beneficial, we present a frequency analysis that compares Monte Carlo sampling of gradients followed by Poisson reconstruction to traditional Monte Carlo sampling. Finally, we describe Gradient-Domain Path Tracing (G-PT), a relatively simple modification of the standard path tracing algorithm that can yield far superior results.

Efficient algorithms for dynamic probabilistic safety assessment. An application to convex damage domain.

The design of nuclear power plant has to follow a number of regulations aimed at limiting the risks inherent in this type of installation. The goal is to prevent and to limit the consequences of any possible incident that might threaten the public or the environment. To verify that the safety requirements are met a safety assessment process is followed. Safety analysis is as key component of a safety assessment, which incorporates both probabilistic and deterministic approaches. The deterministic approach attempts to ensure that the various situations, and in particular accidents, that are considered to be plausible, have been taken into account, and that the monitoring systems and engineered safety and safeguard systems will be capable of ensuring the safety goals. On the other hand, probabilistic safety analysis tries to demonstrate that the safety requirements are met for potential accidents both within and beyond the design basis, thus identifying vulnerabilities not necessarily accessible through deterministic safety analysis alone. Probabilistic safety assessment (PSA) methodology is widely used in the nuclear industry and is especially effective in comprehensive assessment of the measures needed to prevent accidents with small probability but severe consequences. Still, the trend towards a risk informed regulation (RIR) demanded a more extended use of risk assessment techniques with a significant need to further extend PSA’s scope and quality. Here is where the theory of stimulated dynamics (TSD) intervenes, as it is the mathematical foundation of the integrated safety assessment (ISA) methodology developed by the CSN(Consejo de Seguridad Nuclear) branch of Modelling and Simulation (MOSI). Such methodology attempts to extend classical PSA including accident dynamic analysis, an assessment of the damage associated to the transients and a computation of the damage frequency. The application of this ISA methodology requires a computational framework called SCAIS (Simulation Code System for Integrated Safety Assessment). SCAIS provides accident dynamic analysis support through simulation of nuclear accident sequences and operating procedures. Furthermore, it includes probabilistic quantification of fault trees and sequences; and integration and statistic treatment of risk metrics. SCAIS comprehensively implies an intensive use of code coupling techniques to join typical thermal hydraulic analysis, severe accident and probability calculation codes. The integration of accident simulation in the risk assessment process and thus requiring the use of complex nuclear plant models is what makes it so powerful, yet at the cost of an enormous increase in complexity. As the complexity of the process is primarily focused on such accident simulation codes, the question of whether it is possible to reduce the number of required simulation arises, which will be the focus of the present work. This document presents the work done on the investigation of more efficient techniques applied to the process of risk assessment inside the mentioned ISA methodology. Therefore such techniques will have the primary goal of decreasing the number of simulation needed for an adequate estimation of the damage probability. As the methodology and tools are relatively recent, there is not much work done inside this line of investigation, making it a quite difficult but necessary task, and because of time limitations the scope of the work had to be reduced. Therefore, some assumptions were made to work in simplified scenarios best suited for an initial approximation to the problem. The following section tries to explain in detail the process followed to design and test the developed techniques. Then, the next section introduces the general concepts and formulae of the TSD theory which are at the core of the risk assessment process. Afterwards a description of the simulation framework requirements and design is given. Followed by an introduction to the developed techniques, giving full detail of its mathematical background and its procedures. Later, the test case used is described and result from the application of the techniques is shown. Finally the conclusions are presented and future lines of work are exposed.

In situ control of the GE(100)surface domain structure for III-V multijunction solar cells

Vicinal Ge(100) is the common substrate for state of the art multi-junction solar cells grown by metal-organic vapor phase epitaxy (MOVPE). While triple junction solar cells based on Ge(100) present efficiencies mayor que 40%, little is known about the microscopic III-V/Ge(100) nucleation and its interface formation. A suitable Ge(100) surface preparation prior to heteroepitaxy is crucial to achieve low defect densities in the III-V epilayers. Formation of single domain surfaces with double layer steps is required to avoid anti-phase domains in the III-V films. The step formation processes in MOVPE environment strongly depends on the major process parameters such as substrate temperature, H2 partial pressure, group V precursors [1], and reactor conditions. Detailed investigation of these processes on the Ge(100) surface by ultrahigh vacuum (UHV) based standard surface science tools are complicated due to the presence of H2 process gas. However, in situ surface characterization by reflection anisotropy spectroscopy (RAS) allowed us to study the MOVPE preparation of Ge(100) surfaces directly in dependence on the relevant process parameters [2, 3, 4]. A contamination free MOVPE to UHV transfer system [5] enabled correlation of the RA spectra to results from UHV-based surface science tools. In this paper, we established the characteristic RA spectra of vicinal Ge(100) surfaces terminated with monohydrides, arsenic and phosphorous. RAS enabled in situ control of oxide removal, H2 interaction and domain formation during MOVPE preparation.

Contribution to the analysis and design of reflectarray antennas for reconfigurable beam applications at frequencies above 100 GHz using liquid crystal technology

El trabajo contenido en esta tesis doctoral está encuadrado en el desarrollo de antenas reconfigurables electrónicamente capaces de proporcionar prestaciones competitivas a las aplicaciones cada vez más comunes que operan a frecuencias superiores a 60 GHz. En concreto, esta tesis se centra en el estudio, diseño, e implementación de las antenas reflectarray, a las que se introduce la tecnología de cristal líquido como elemento característico con el que se consigue reconfigurabilidad de haz de forma electrónica. Desde un punto de vista muy general, se puede describir un cristal líquido como un material cuya permitividad eléctrica es variable y controlada por una excitación externa, que generalmente suele corresponderse con un campo eléctrico quasi-estático (AC). Las antenas reflectarray de cristal líquido se han escogido como objeto de estudio por varias razones. La primera de ellas tiene que ver con las ventajas que los reflectarrays, y en especial aquellos realizados en configuración planar, proporcionan con respecto a otras antenas de alta ganancia como los reflectores o los “phased-arrays”. En los reflectarrays, la alimentación a través de una fuente primaria común (característica de reflectores) y el elevado número de grados de libertad de las celdas que los componen (característica de arrays) hacen que estas antenas puedan proporcionar prestaciones eléctricas iguales o mejores que las anteriores, a un coste más reducido y con estructuras de antena más compactas. La segunda razón radica en la flexibilidad que ofrece el cristal líquido a ser confinado y polarizado en recintos de geometría variada, como consecuencia de su fluidez (propiedad de los líquidos). Por ello, la tecnología de cristal líquido permite que el propio elemento reconfigurable en las celdas de reflectarray se adapte a la configuración planar de manera que en sí mismo, el cristal líquido sea una o varias de las capas características de esta configuración. Esto simplifica de forma drástica la estructura y la fabricación de este tipo de antenas, incluso si se comparan con reflectarrays reconfigurables basados en otras tecnologías como diodos, MEMS, etc. Por tanto, su coste y desarrollo es muy reducido, lo que hace que se puedan fabricar reflectarrays reconfigurables eléctricamente grandes, a bajo coste, y en producción elevada. Un ejemplo claro de una estructura similar, y que ha tenido éxito comercial, son las pantallas de cristal líquido. La tercera razón reside en el hecho de que el cristal líquido es, hasta la fecha, de las pocas tecnologías capaces de ofrecer reconfigurabilidad del haz a frecuencias superiores a 60 GHz. De hecho, el cristal líquido permite reconfigurabilidad en un amplio margen de frecuencias, que va desde DC a frecuencias del espectro visible, incluyendo las microondas y los THz. Otras tecnologías, como los materiales ferroeléctricos, el grafeno o la tecnología CMOS “on chip” permiten también conmutar el haz en estas frecuencias. Sin embargo, la tecnología CMOS tiene un elevado coste y actualmente está limitada a frecuencias inferiores a 150 GHz, y aunque los materiales ferroeléctricos o el grafeno puedan conmutar a frecuencias más altas y en un rango más amplio, tienen serias dificultades que los hacen aún inmaduros. En el caso de los materiales ferroeléctricos, los elevados voltajes para conmutar el material los hacen poco atractivos, mientras que en el caso del grafeno, su modelado aún está en discusión, y todavía no se han arrojado resultados experimentales que validen su idoneidad. Estas tres razones hacen que los reflectarrays basados en cristal líquido sean atractivos para multitud de aplicaciones de haz reconfigurable a frecuencias superiores a 60 GHz. Aplicaciones como radar de escaneo de imágenes de alta resolución, espectroscopia molecular, radiómetros para observación atmosférica, o comunicaciones inalámbricas de alta frecuencia (WiGig) son algunas de ellas. La tesis está estructurada en tres partes. En la primera de ellas se describen las características más comunes de los cristales líquidos, centrándonos en detalle en aquellas propiedades ofrecidas por este material en fase nemática. En concreto, se estudiará la anisotropía dieléctrica (Ae) de los cristales líquidos uniaxiales, que son los que se emplean en esta tesis, definida como la diferencia entre la permitividad paralela (£//) y la perpendicular (e±): Ae = e,, - e±. También se estudiará la variación de este parámetro (Ae) con la frecuencia, y el modelado electromagnético macroscópico más general que, extraído a partir de aquella, permite describir el cristal líquido para cada tensión de polarización en celdas de geometría planar. Este modelo es de suma importancia para garantizar precisión en el desfasaje proporcionado por las diferentes celdas reconfigurables para reflectarrays que se describirán en la siguiente parte de la tesis. La segunda parte de la tesis se centra en el diseño de celdas reflectarray resonantes basadas en cristal líquido. La razón por la que se escogen estos tipos de celdas reside en el hecho de que son las únicas capaces de proporcionar rangos de fase elevados ante la reducida anisotropía dieléctrica que ofrecen los cristales líquidos. El objetivo de esta parte trata, por tanto, de obtener estructuras de celdas reflectarray que sean capaces de proporcionar buenas prestaciones eléctricas a nivel de antena, mejorando sustancialmente las prestaciones de las celdas reportadas en el estado del arte, así como de desarrollar una herramienta de diseño general para aquellas. Para ello, se estudian las prestaciones eléctricas de diferentes tipos de elementos resonantes de cristal líquido que van, desde el más sencillo, que ha limitado el estado de la técnica hasta el desarrollo de esta tesis y que está formado por un sólo resonador, a elementos que constan de varios resonadores (multi-resonantes) y que pueden ser monocapa o multicapa. En un primer paso, el procedimiento de diseño de estas estructuras hace uso de un modelo convencional de cristal líquido que ha venido siendo usado en el estado del arte para este tipo de celdas, y que considera el cristal líquido como un material homogéneo e isótropo cuya permitividad varía entre (e/7) y (e±). Sin embargo, en esta parte de la tesis se demuestra que dicho modelado no es suficiente para describir de forma genérica el comportamiento del cristal líquido en las celdas tipo reflectarray. En la tesis se proponen procedimientos más exactos para el análisis y diseño basados en un modelo más general que define el cristal líquido como un material anisótropo e inhomogeneo en tres dimensiones, y se ha implementado una técnica que permite optimizar celdas multi-resonantes de forma eficiente para conseguir elevadas prestaciones en cuanto a ancho de banda, rango de fase, pérdidas, o sensibilidad al ángulo de incidencia. Los errores cometidos en el uso del modelado convencional a nivel de celda (amplitud y fase) se han analizado para varias geometrías, usando medidas de varios prototipos de antena que usan un cristal líquido real a frecuencias superiores a 100 GHz. Las medidas se han realizado en entorno periódico mediante un banco cuasi-óptico, que ha sido diseñado especialmente para este fin. Uno de estos prototipos se ha optimizado a 100 GHz para conseguir un ancho de banda relativamente elevado (10%), pérdidas reducidas, un rango de fase mayor de 360º, baja sensibilidad al ángulo de incidencia, y baja influencia de la inhomogeneidad transversal del cristal líquido en la celda. Estas prestaciones a nivel de celda superan de forma clara aquellas conseguidas por otros elementos que se han reportado en la literatura, de manera que dicho prototipo se ha usado en la última parte de la tesis para realizar diversas antenas de barrido. Finalmente, en esta parte se presenta una estrategia de caracterización de la anisotropía macroscópica a partir de medidas de los elementos de reflectarray diseñados en banco cuasi-óptico, obteniendo resultados tanto en las frecuencias de interés en RF como en AC, y comparándolas con aquellas obtenidas mediante otros métodos. La tercera parte de la tesis consiste en el estudio, diseño, fabricación y medida de antenas reconfigurables basadas en cristal líquido en configuraciones complejas. En reflectarrays pasivos, el procedimiento de diseño de la antena se limita únicamente al ajuste en cada celda de la antena de las dimensiones de las metalizaciones que se emplean para el control de fase, mediante procesos de optimización bien conocidos. Sin embargo, en el caso de reflectarrays reconfigurables basados en cristal líquido, resulta necesario un paso adicional, que consiste en calcular de forma adecuada las tensiones de control en cada celda del reflectarray para configurar la fase requerida en cada una de ellas, así como diseñar la estructura y los circuitos de control que permitan direccionar a cada elemento su tensión correspondiente. La síntesis de tensiones es por tanto igual o más importante que el diseño de la geometría de las celdas, puesto que éstas son las que están directamente relacionadas con la fase. En el estado del arte, existen varias estrategias de síntesis de tensiones que se basan en la caracterización experimental de la curva de fase respecto al voltaje. Sin embargo, esta caracterización sólo puede hacerse a un solo ángulo de incidencia y para unas determinadas dimensiones de celda, lo que produce que las tensiones sintetizadas sean diferentes de las adecuadas, y en definitiva que se alcancen errores de fase mayores de 70º. De esta forma, hasta la fecha, las prestaciones a nivel de antena que se han conseguido son reducidas en cuanto a ancho de banda, rango de escaneo o nivel de lóbulos secundarios. En esta última parte de la tesis, se introduce una nueva estrategia de síntesis de tensiones que es capaz de predecir mediante simulaciones, y con alta precisión, las tensiones que deben introducirse en cada celda teniendo en cuenta su ángulo de incidencia, sus dimensiones, la frecuencia, así como la señal de polarización definida por su frecuencia y forma de onda AC. Esta estrategia se basa en modelar cada uno de los estados de permitividad del cristal líquido como un sustrato anisótropo con inhomogeneidad longitudinal (1D), o en ciertos casos, como un tensor equivalente homogéneo. La precisión de ambos modelos electromagnéticos también se discute. Con el objetivo de obtener una herramienta eficiente de cálculo de tensiones, también se ha escrito e implementado una herramienta de análisis basada en el Método de los Momentos en el Dominio Espectral (SD-MoM) para sustratos estratificados anisótropos, que se usa en cada iteración del procedimiento de síntesis para analizar cada una de las celdas de la antena. La síntesis de tensiones se ha diseñado además para reducir al máximo el efecto del rizado de amplitud en el diagrama de radiación, que es característico en los reflectarrays que están formados por celdas con pérdidas elevadas, lo que en sí, supone un avance adicional para la obtención de mejores prestaciones de antena. Para el cálculo de los diagramas de radiación empleados en el procedimiento de síntesis, se asume un análisis elemento a elemento considerando periodicidad local, y se propone el uso de un método capaz de modelar el campo incidente de forma que se elimine la limitación de la periodicidad local en la excitación. Una vez definida la estrategia adecuada de cálculo de las tensiones a aplicar al cristal líquido en cada celda, la estructura de direccionamiento de las mismas en la antena, y diseñados los circuitos de control, se diseñan, fabrican y miden dos prototipos diferentes de antena de barrido electrónico a 100 GHz usando las celdas anteriormente presentadas. El primero de estos prototipos es un reflectarray en configuración “single offset” con capacidad de escaneo en un plano (elevación o azimut). Aunque previamente se realizan diseños de antenas de barrido en 2D a varias frecuencias en el rango de milimétricas y sub-milimétricas, y se proponen ciertas estrategias de direccionamiento que permiten conseguir este objetivo, se desarrolla el prototipo con direccionamiento en una dimensión con el fin de reducir el número de controles y posibles errores de fabricación, y así también validar la herramienta de diseño. Para un tamaño medio de apertura (con un numero de filas y columnas entre 30 y 50 elementos, lo que significa un reflectarray con un número de elementos superior a 900), la configuración “single offset” proporciona rangos de escaneo elevados, y ganancias que pueden oscilar entre los 20 y 30 dBi. En concreto, el prototipo medido proporciona un haz de barrido en un rango angular de 55º, en el que el nivel de lóbulos secundarios (SLL) permanece mejor de -13 dB en un ancho de banda de un 8%. La ganancia máxima es de 19.4 dBi. Estas prestaciones superan de forma clara aquellas conseguidas por otros autores. El segundo prototipo se corresponde con una antena de doble reflector que usa el reflectarray de cristal líquido como sub-reflector para escanear el haz en un plano (elevación o azimut). El objetivo básico de esta geometría es obtener mayores ganancias que en el reflectarray “single offset” con una estructura más compacta, aunque a expensas de reducir el rango de barrido. En concreto, se obtiene una ganancia máxima de 35 dBi, y un rango de barrido de 12º. Los procedimientos de síntesis de tensiones y de diseño de las estructuras de las celdas forman, en su conjunto, una herramienta completa de diseño precisa y eficiente de antenas reflectarray reconfigurables basados en cristales líquidos. Dicha herramienta se ha validado mediante el diseño, la fabricación y la medida de los prototipos anteriormente citados a 100 GHz, que consiguen algo nunca alcanzado anteriormente en la investigación de este tipo de antenas: unas prestaciones competitivas y una predicción excelente de los resultados. El procedimiento es general, y por tanto se puede usar a cualquier frecuencia en la que el cristal líquido ofrezca anisotropía dieléctrica, incluidos los THz. Los prototipos desarrollados en esta tesis doctoral suponen también unas de las primeras antenas de barrido real a frecuencias superiores a 100 GHz. En concreto, la antena de doble reflector para escaneo de haz es la primera antena reconfigurable electrónicamente a frecuencias superiores a 60 GHz que superan los 25 dBi de ganancia, siendo a su vez la primera antena de doble reflector que contiene un reflectarray reconfigurable como sub-reflector. Finalmente, se proponen ciertas mejoras que aún deben se deben realizar para hacer que estas antenas puedan ser un producto completamente desarrollado y competitivo en el mercado. ABSTRACT The work presented in this thesis is focused on the development of electronically reconfigurable antennas that are able to provide competitive electrical performance to the increasingly common applications operating at frequencies above 60 GHz. Specifically, this thesis presents the study, design, and implementation of reflectarray antennas, which incorporate liquid crystal (LC) materials to scan or reconfigure the beam electronically. From a general point of view, a liquid crystal can be defined as a material whose dielectric permittivity is variable and can be controlled with an external excitation, which usually corresponds with a quasi-static electric field (AC). By changing the dielectric permittivity at each cell that makes up the reflectarray, the phase shift on the aperture is controlled, so that a prescribed radiation pattern can be configured. Liquid Crystal-based reflectarrays have been chosen for several reasons. The first has to do with the advantages provided by the reflectarray antenna with respect to other high gain antennas, such as reflectors or phased arrays. The RF feeding in reflectarrays is achieved by using a common primary source (as in reflectors). This arrangement and the large number of degrees of freedom provided by the cells that make up the reflectarray (as in arrays), allow these antennas to provide a similar or even better electrical performance than other low profile antennas (reflectors and arrays), but assuming a more reduced cost and compactness. The second reason is the flexibility of the liquid crystal to be confined in an arbitrary geometry due to its fluidity (property of liquids). Therefore, the liquid crystal is able to adapt to a planar geometry so that it is one or more of the typical layers of this configuration. This simplifies drastically both the structure and manufacture of this type of antenna, even when compared with reconfigurable reflectarrays based on other technologies, such as diodes MEMS, etc. Therefore, the cost of developing this type of antenna is very small, which means that electrically large reconfigurable reflectarrays could be manufactured assuming low cost and greater productions. A paradigmatic example of a similar structure is the liquid crystal panel, which has already been commercialized successfully. The third reason lies in the fact that, at present, the liquid crystal is one of the few technologies capable of providing switching capabilities at frequencies above 60 GHz. In fact, the liquid crystal allows its permittivity to be switched in a wide range of frequencies, which are from DC to the visible spectrum, including microwaves and THz. Other technologies, such as ferroelectric materials, graphene or CMOS "on chip" technology also allow the beam to be switched at these frequencies. However, CMOS technology is expensive and is currently limited to frequencies below 150 GHz, and although ferroelectric materials or graphene can switch at higher frequencies and in a wider range, they have serious difficulties that make them immature. Ferroelectric materials involve the use of very high voltages to switch the material, making them unattractive, whereas the electromagnetic modelling of the graphene is still under discussion, so that the experimental results of devices based on this latter technology have not been reported yet. These three reasons make LC-based reflectarrays attractive for many applications that involve the use of electronically reconfigurable beams at frequencies beyond 60 GHz. Applications such as high resolution imaging radars, molecular spectroscopy, radiometers for atmospheric observation, or high frequency wireless communications (WiGig) are just some of them. This thesis is divided into three parts. In the first part, the most common properties of the liquid crystal materials are described, especially those exhibited in the nematic phase. The study is focused on the dielectric anisotropy (Ac) of uniaxial liquid crystals, which is defined as the difference between the parallel (e/7) and perpendicular (e±) permittivities: Ae = e,, - e±. This parameter allows the permittivity of a LC confined in an arbitrary volume at a certain biasing voltage to be described by solving a variational problem that involves both the electrostatic and elastic energies. Thus, the frequency dependence of (Ae) is also described and characterised. Note that an appropriate LC modelling is quite important to ensure enough accuracy in the phase shift provided by each cell that makes up the reflectarray, and therefore to achieve a good electrical performance at the antenna level. The second part of the thesis is focused on the design of resonant reflectarray cells based on liquid crystal. The reason why resonant cells have been chosen lies in the fact that they are able to provide enough phase range using the values of the dielectric anisotropy of the liquid crystals, which are typically small. Thus, the aim of this part is to investigate several reflectarray cell architectures capable of providing good electrical performance at the antenna level, which significantly improve the electrical performance of the cells reported in the literature. Similarly, another of the objectives is to develop a general tool to design these cells. To fulfill these objectives, the electrical yields of different types of resonant reflectarray elements are investigated, beginning from the simplest, which is made up of a single resonator and limits the state of the art. To overcome the electrical limitations of the single resonant cell, several elements consisting of multiple resonators are considered, which can be single-layer or multilayer. In a first step, the design procedure of these structures makes use of a conventional electromagnetic model which has been used in the literature, which considers that the liquid crystal behaves as homogeneous and isotropic materials whose permittivity varies between (e/7) y (e±). However, in this part of the thesis it is shown that the conventional modelling is not enough to describe the physical behaviour of the liquid crystal in reflectarray cells accurately. Therefore, a more accurate analysis and design procedure based on a more general model is proposed and developed, which defines the liquid crystal as an anisotropic three-dimensional inhomogeneous material. The design procedure is able to optimize multi-resonant cells efficiently to achieve good electrical performance in terms of bandwidth, phase range, losses, or sensitivity to the angle of incidence. The errors made when the conventional modelling (amplitude and phase) is considered have been also analysed for various cell geometries, by using measured results from several antenna prototypes made up of real liquid crystals at frequencies above 100 GHz. The measurements have been performed in a periodic environment using a quasi-optical bench, which has been designed especially for this purpose. One of these prototypes has been optimized to achieve a relatively large bandwidth (10%) at 100 GHz, low losses, a phase range of more than 360º, a low sensitivity to angle of incidence, and a low influence of the transversal inhomogeneity of the liquid crystal in the cell. The electrical yields of this prototype at the cell level improve those achieved by other elements reported in the literature, so that this prototype has been used in the last part of the thesis to perform several complete antennas for beam scanning applications. Finally, in this second part of the thesis, a novel strategy to characterise the macroscopic anisotropy using reflectarray cells is presented. The results in both RF and AC frequencies are compared with those obtained by other methods. The third part of the thesis consists on the study, design, manufacture and testing of LCbased reflectarray antennas in complex configurations. Note that the design procedure of a passive reflectarray antenna just consists on finding out the dimensions of the metallisations of each cell (which are used for phase control), using well-known optimization processes. However, in the case of reconfigurable reflectarrays based on liquid crystals, an additional step must be taken into account, which consists of accurately calculating the control voltages to be applied to each cell to configure the required phase-shift distribution on the surface of the antenna. Similarly, the structure to address the voltages at each cell and the control circuitry must be also considered. Therefore, the voltage synthesis is even more important than the design of the cell geometries (dimensions), since the voltages are directly related to the phase-shift. Several voltage synthesis procedures have been proposed in the state of the art, which are based on the experimental characterization of the phase/voltage curve. However, this characterization can be only carried out at a single angle of incidence and at certain cell dimensions, so that the synthesized voltages are different from those needed, thus giving rise to phase errors of more than 70°. Thus, the electrical yields of the LCreflectarrays reported in the literature are limited in terms of bandwidth, scanning range or side lobes level. In this last part of the thesis, a new voltage synthesis procedure has been defined and developed, which allows the required voltage to be calculated at each cell using simulations that take into account the particular dimensions of the cells, their angles of incidence, the frequency, and the AC biasing signal (frequency and waveform). The strategy is based on the modelling of each one of the permittivity states of the liquid crystal as an anisotropic substrate with longitudinal inhomogeneity (1D), or in certain cases, as an equivalent homogeneous tensor. The accuracy of both electromagnetic models is also discussed. The phase errors made by using the proposed voltage synthesis are better than 7º. In order to obtain an efficient tool to analyse and design the reflectarray, an electromagnetic analysis tool based on the Method of Moments in the spectral domain (SD-MoM) has also written and developed for anisotropic stratified media, which is used at each iteration of the voltage synthesis procedure. The voltage synthesis is also designed to minimize the effect of amplitude ripple on the radiation pattern, which is typical of reflectarrays made up of cells exhibiting high losses and represents a further advance in achieving a better antenna performance. To calculate the radiation patterns used in the synthesis procedure, an element-by-element analysis is assumed, which considers the local periodicity approach. Under this consideration, the use of a novel method is proposed, which avoids the limitation that the local periodicity imposes on the excitation. Once the appropriate strategy to calculate the voltages to be applied at each cell is developed, and once it is designed and manufactured both the structure to address the voltages to the antenna and the control circuits, two complete LC-based reflectarray antennas that operate at 100 GHz have been designed, manufactured and tested using the previously presented cells. The first prototype consists of a single offset reflectarray with beam scanning capabilities on one plane (elevation and azimuth). Although several LC-reflectarray antennas that provide 2-D scanning capabilities are also designed, and certain strategies to achieve the 2-D addressing of the voltage are proposed, the manufactured prototype addresses the voltages in one dimension in order to reduce the number of controls and manufacturing errors, and thereby validating the design tool. For an average aperture size (with a number of rows and columns of between 30 and 50 elements, which means a reflectarray with more than 900 cells), the single offset configuration provides an antenna gain of between 20 and 30 dBi and a large scanning range. The prototype tested at 100 GHz exhibits an electronically scanned beam in an angular range of 55º and 8% of bandwidth, in which the side lobe level (SLL) remains better than -13 dB. The maximum gain is 19.4 dBi. The electrical performance of the antenna is clearly an improvement on those achieved by other authors in the state of the art. The second prototype corresponds to a dual reflector antenna with a liquid crystal-based reflectarray used as a sub-reflector for beam scanning in one plane (azimuth or elevation). The main objective is to obtain a higher gain than that provided by the single offset configuration, but using a more compact architecture. In this case, a maximum gain of 35 dBi is achieved, although at the expense of reducing the scanning range to 12°, which is inherent in this type of structure. As a general statement, the voltage synthesis and the design procedure of the cells, jointly make up a complete, accurate and efficient design tool of reconfigurable reflectarray antennas based on liquid crystals. The tool has been validated by testing the previously mentioned prototypes at 100 GHz, which achieve something never reached before for this type of antenna: a competitive electrical performance, and an excellent prediction of the results. The design procedure is general and therefore can be used at any frequency for which the liquid crystal exhibits dielectric anisotropy. The two prototypes designed, manufactured and tested in this thesis are also some of the first antennas that currently operate at frequencies above 100 GHz. In fact, the dual reflector antenna is the first electronically scanned dual reflector antenna at frequencies above 60 GHz (the operation frequency is 100 GHz) with a gain greater than 25 dBi, being in turn the first dual-reflector antenna with a real reconfigurable sub-reflectarray. Finally, some improvements that should be still investigated to make these antennas commercially competitive are proposed.

The peculiar electrical response of liquid crystal-carbon nanotube systems as seen by impedance spectroscopy

Conductive nanoparticles, especially elongated ones such as carbon nanotubes, dramatically modify the electrical behavior of liquid crystal cells. These nanoparticles are known to reorient with liquid crystals in electric fields, causing significant variations of conductivity at minute concentrations of tens or hundreds ppm. The above notwithstanding, impedance spectroscopy of doped cells in the frequency range customarily employed by liquid crystal devices, 100 Hz?10 kHz, shows a relatively simple resistor/capacitor response where the components of the cell can be univocally assigned to single components of the electrical equivalent circuit. However, widening the frequency range up to 1 MHz or beyond reveals a complex behavior that cannot be explained with the same simple EEC. Moreover, the system impedance varies with the application of electric fields, their effect remaining after removing the field. Carbon nanotubes are reoriented together with liquid crystal reorientation when applying voltage, but barely reoriented back upon liquid crystal relaxation once the voltage is removed. Results demonstrate a remarkable variation in the impedance of the dielectric blend formed by liquid crystal and carbon nanotubes, the irreversible orientation of the carbon nanotubes and possible permanent contacts between electrodes.

The N-terminal domain of PsaF: Precise recognition site for binding and fast electron transfer from cytochrome c6 and plastocyanin to photosystem I of Chlamydomonas reinhardtii

The PsaF-deficient mutant 3bF of Chlamydomonas reinhardtii was used to modify PsaF by nuclear transformation and site-directed mutagenesis. Four lysine residues in the N-terminal domain of PsaF, which have been postulated to form the positively charged face of a putative amphipathic α-helical structure were altered to K12P, K16Q, K23Q, and K30Q. The interactions between plastocyanin (pc) or cytochrome c6 (cyt c6) and photosystem I (PSI) isolated from wild type and the different mutants were analyzed using crosslinking techniques and flash absorption spectroscopy. The K23Q change drastically affected crosslinking of pc to PSI and electron transfer from pc and cyt c6 to PSI. The corresponding second order rate constants for binding of pc and cyt c6 were reduced by a factor of 13 and 7, respectively. Smaller effects were observed for mutations K16Q and K30Q, whereas in K12P the binding was not changed relative to wild type. None of the mutations affected the half-life of the microsecond electron transfer performed within the intermolecular complex between the donors and PSI. The fact that these single amino acid changes within the N-terminal domain of PsaF have different effects on the electron transfer rate constants and dissociation constants for both electron donors suggests the existence of a rather precise recognition site for pc and cyt c6 that leads to the stabilization of the final electron transfer complex through electrostatic interactions.

Low frequency vibrational modes in proteins: Changes induced by point-mutations in the protein-cofactor matrix of bacterial reaction centers

As a step toward understanding their functional role, the low frequency vibrational motions (<300 cm−1) that are coupled to optical excitation of the primary donor bacteriochlorophyll cofactors in the reaction center from Rhodobacter sphaeroides were investigated. The pattern of hydrogen-bonding interaction between these bacteriochlorophylls and the surrounding protein was altered in several ways by mutation of single amino acids. The spectrum of low frequency vibrational modes identified by femtosecond coherence spectroscopy varied strongly between the different reaction center complexes, including between different mutants where the pattern of hydrogen bonds was the same. It is argued that these variations are primarily due to changes in the nature of the individual modes, rather than to changes in the charge distribution in the electronic states involved in the optical excitation. Pronounced effects of point mutations on the low frequency vibrational modes active in a protein-cofactor system have not been reported previously. The changes in frequency observed indicate a strong involvement of the protein in these nuclear motions and demonstrate that the protein matrix can increase or decrease the fluctuations of the cofactor along specific directions.

The solution structure of the N-terminal domain of α2-macroglobulin receptor-associated protein

The three-dimensional structure of the N-terminal domain (residues 18–112) of α2-macroglobulin receptor-associated protein (RAP) has been determined by NMR spectroscopy. The structure consists of three helices composed of residues 23–34, 39–65, and 73–88. The three helices are arranged in an up-down-up antiparallel topology. The C-terminal 20 residues were shown not to be in a well defined conformation. A structural model for the binding of RAP to the family of low-density lipoprotein receptors is proposed. It defines a role in binding for both the unordered C terminus and the structural scaffold of the core structure. Pathogenic epitopes for the rat disease Heymann nephritis, an experimental model of human membranous glomerulonephritis, have been identified in RAP and in the large endocytic receptor gp330/megalin. Here we provide the three-dimensional structure of the pathogenic epitope in RAP. The amino acid residues known to form the epitope are in a helix–loop–helix conformation, and from the structure it is possible to rationalize the published results obtained from studies of fragments of the N-terminal domain.

Semirational design of active tumor suppressor p53 DNA binding domain with enhanced stability

We have designed a p53 DNA binding domain that has virtually the same binding affinity for the gadd45 promoter as does wild-type protein but is considerably more stable. The design strategy was based on molecular evolution of the protein domain. Naturally occurring amino acid substitutions were identified by comparing the sequences of p53 homologues from 23 species, introducing them into wild-type human p53, and measuring the changes in stability. The most stable substitutions were combined in a multiple mutant. The advantage of this strategy is that, by substituting with naturally occurring residues, the function is likely to be unimpaired. All point mutants bind the consensus DNA sequence. The changes in stability ranged from +1.27 (less stable Q165K) to −1.49 (more stable N239Y) kcal mol−1, respectively. The changes in free energy of unfolding on mutation are additive. Of interest, the two most stable mutants (N239Y and N268D) have been known to act as suppressors and restored the activity of two of the most common tumorigenic mutants. Of the 20 single mutants, 10 are cancer-associated, though their frequency of occurrence is extremely low: A129D, Q165K, Q167E, and D148E are less stable and M133L, V203A and N239Y are more stable whereas the rest are neutral. The quadruple mutant (M133LV203AN239YN268D), which is stabilized by 2.65 kcal mol−1 and Tm raised by 5.6°C is of potential interest for trials in vivo.

Crystal structure of the ribosomal RNA domain essential for binding elongation factors

The structure of a 29-nucleotide RNA containing the sarcin/ricin loop (SRL) of rat 28 S rRNA has been determined at 2.1 Å resolution. Recognition of the SRL by elongation factors and by the ribotoxins, sarcin and ricin, requires a nearly universal dodecamer sequence that folds into a G-bulged cross-strand A stack and a GAGA tetraloop. The juxtaposition of these two motifs forms a distorted hairpin structure that allows direct recognition of bases in both grooves as well as recognition of nonhelical backbone geometry and two 5′-unstacked purines. Comparisons with other RNA crystal structures establish the cross-strand A stack and the GNRA tetraloop as defined and modular RNA structural elements. The conserved region at the top is connected to the base of the domain by a region presumed to be flexible because of the sparsity of stabilizing contacts. Although the conformation of the SRL RNA previously determined by NMR spectroscopy is similar to the structure determined by x-ray crystallography, significant differences are observed in the “flexible” region and to a lesser extent in the G-bulged cross-strand A stack.