Instabilities In hybrid optical bistable devices with nonlinear feedback

As we have shown,several output conditions can be obtained from a hybrid optical bistable device when twisted nematic liquid crystal cells are employed as nonlinear elements.

Morphological Functions to Quantify Three-Dimensional Tomograms of Macropore Structure in a Vineyard Soil with Two Different Management Regimes

Soil tomography and morphological functions built over Minkowski functionals were used to describe the impact on pore structure of two soil management practices in a Mediterranean vineyard. Soil structure controls important physical and biological processes in soil–plant–microbial systems. Those processes are dominated by the geometry of soil pore structure, and a correct model of this geometry is critical for understanding them. Soil tomography has been shown to provide rich three-dimensional digital information on soil pore geometry. Recently, mathematical morphological techniques have been proposed as powerful tools to analyze and quantify the geometrical features of porous media. Minkowski functionals and morphological functions built over Minkowski functionals provide computationally efficient means to measure four fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. We used the threshold and the dilation and erosion of three-dimensional images to generate morphological functions and explore the evolution of Minkowski functionals as the threshold and as the degree of dilation and erosion changes. We analyzed the three-dimensional geometry of soil pore space with X-ray computed tomography (CT) of intact soil columns from a Spanish Mediterranean vineyard by using two different management practices (conventional tillage versus permanent cover crop of resident vegetation). Our results suggested that morphological functions built over Minkowski functionals provide promising tools to characterize soil macropore structure and that the evolution of morphological features with dilation and erosion is more informative as an indicator of structure than moving threshold for both soil managements studied.

Comparative study about the use of two and three-dimensional methods in surface finishing characterization

The increasing number of works related to the surface texture characterization based on 3D information, makes convenient rethinking traditional methods based on two-dimensional measurements from profiles. This work compares results between measurements obtained using two and three-dimensional methods. It uses three kinds of data sources: reference surfaces, randomly generated surfaces and measured. Preliminary results are presented. These results must be completed trying to cover a wider number of possibilities according to the manufacturing process and the measurement instrumentation since results can vary quite significantly between them.

Optimum high temperature strength of two-dimensional nanocomposites

High-temperature nanoindentation was used to reveal nano-layer size effects on the hardness of two-dimensional metallic nanocomposites. We report the existence of a critical layer thickness at which strength achieves optimal thermal stability. Transmission electron microscopy and theoretical bicrystal calculations show that this optimum arises due to a transition from thermally activated glide within the layers to dislocation transmission across the layers. We demonstrate experimentally that the atomic-scale properties of the interfaces profoundly affect this critical transition. The strong implications are that interfaces can be tuned to achieve an optimum in high temperature strength in layered nanocomposite structures.

Advances in global instability computations: from incompressible to hypersonic flow

Esta tesis constituye un gran avance en el conocimiento del estudio y análisis de inestabilidades hidrodinámicas desde un punto de vista físico y teórico, como consecuencia de haber desarrollado innovadoras técnicas para la resolución computacional eficiente y precisa de la parte principal del espectro correspondiente a los problemas de autovalores (EVP) multidimensionales que gobiernan la inestabilidad de flujos con dos o tres direcciones espaciales inhomogéneas, denominados problemas de estabilidad global lineal. En el contexto del trabajo de desarrollo de herramientas computacionales presentado en la tesis, la discretización mediante métodos de diferencias finitas estables de alto orden de los EVP bidimensionales y tridimensionales que se derivan de las ecuaciones de Navier-Stokes linealizadas sobre flujos con dos o tres direcciones espaciales inhomogéneas, ha permitido una aceleración de cuatro órdenes de magnitud en su resolución. Esta mejora de eficiencia numérica se ha conseguido gracias al hecho de que usando estos esquemas de diferencias finitas, técnicas eficientes de resolución de problemas lineales son utilizables, explotando el alto nivel de dispersión o alto número de elementos nulos en las matrices involucradas en los problemas tratados. Como más notable consecuencia cabe destacar que la resolución de EVPs multidimensionales de inestabilidad global, que hasta la fecha necesitaban de superordenadores, se ha podido realizar en ordenadores de sobremesa. Además de la solución de problemas de estabilidad global lineal, el mencionado desarrollo numérico facilitó la extensión de las ecuaciones de estabilidad parabolizadas (PSE) lineales y no lineales para analizar la inestabilidad de flujos que dependen fuertemente en dos direcciones espaciales y suavemente en la tercera con las ecuaciones de estabilidad parabolizadas tridimensionales (PSE-3D). Precisamente la capacidad de extensión del novedoso algoritmo PSE-3D para el estudio de interacciones no lineales de los modos de estabilidad, desarrollado íntegramente en esta tesis, permite la predicción de transición en flujos complejos de gran interés industrial y por lo tanto extiende el concepto clásico de PSE, el cuál ha sido empleado exitosamente durante las pasadas tres décadas en el mismo contexto para problemas de capa límite bidimensional. Típicos ejemplos de flujos incompresibles se han analizado en este trabajo sin la necesidad de recurrir a restrictivas presuposiciones usadas en el pasado. Se han estudiado problemas vorticales como es el caso de un vórtice aislado o sistemas de vórtices simulando la estela de alas, en los que la homogeneidad axial no se impone y así se puede considerar la difusión viscosa del flujo. Además, se ha estudiado el chorro giratorio turbulento, cuya inestabilidad se utiliza para mejorar las características de funcionamiento de combustores. En la tesis se abarcan adicionalmente problemas de flujos compresibles. Se presenta el estudio de inestabilidad de flujos de borde de ataque a diferentes velocidades de vuelo. También se analiza la estela formada por un elemento rugoso aislado en capa límite supersónica e hipersónica, mostrando excelentes comparaciones con resultados obtenidos mediante simulación numérica directa. Finalmente, nuevas inestabilidades se han identificado en el flujo hipersónico a Mach 7 alrededor de un cono elíptico que modela el vehículo de pruebas en vuelo HIFiRE-5. Los resultados comparan favorablemente con experimentos en vuelo, lo que subraya aún más el potencial de las metodologías de análisis de estabilidad desarrolladas en esta tesis. ABSTRACT The present thesis constitutes a step forward in advancing the frontiers of knowledge of fluid flow instability from a physical point of view, as a consequence of having been successful in developing groundbreaking methodologies for the efficient and accurate computation of the leading part of the spectrum pertinent to multi-dimensional eigenvalue problems (EVP) governing instability of flows with two or three inhomogeneous spatial directions. In the context of the numerical work presented in this thesis, the discretization of the spatial operator resulting from linearization of the Navier-Stokes equations around flows with two or three inhomogeneous spatial directions by variable-high-order stable finite-difference methods has permitted a speedup of four orders of magnitude in the solution of the corresponding two- and three-dimensional EVPs. This improvement of numerical performance has been achieved thanks to the high-sparsity level offered by the high-order finite-difference schemes employed for the discretization of the operators. This permitted use of efficient sparse linear algebra techniques without sacrificing accuracy and, consequently, solutions being obtained on typical workstations, as opposed to the previously employed supercomputers. Besides solution of the two- and three-dimensional EVPs of global linear instability, this development paved the way for the extension of the (linear and nonlinear) Parabolized Stability Equations (PSE) to analyze instability of flows which depend in a strongly-coupled inhomogeneous manner on two spatial directions and weakly on the third. Precisely the extensibility of the novel PSE-3D algorithm developed in the framework of the present thesis to study nonlinear flow instability permits transition prediction in flows of industrial interest, thus extending the classic PSE concept which has been successfully employed in the same context to boundary-layer type of flows over the last three decades. Typical examples of incompressible flows, the instability of which was analyzed in the present thesis without the need to resort to the restrictive assumptions used in the past, range from isolated vortices, and systems thereof, in which axial homogeneity is relaxed to consider viscous diffusion, as well as turbulent swirling jets, the instability of which is exploited in order to improve flame-holding properties of combustors. The instability of compressible subsonic and supersonic leading edge flows has been solved, and the wake of an isolated roughness element in a supersonic and hypersonic boundary-layer has also been analyzed with respect to its instability: excellent agreement with direct numerical simulation results has been obtained in all cases. Finally, instability analysis of Mach number 7 ow around an elliptic cone modeling the HIFiRE-5 flight test vehicle has unraveled flow instabilities near the minor-axis centerline, results comparing favorably with flight test predictions.

Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer

The linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach 2:5, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average 17% faster tan the most unstable sinuous mode and 30 times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growthrates registered in the presence of the roughness element, an amplification factor of N D 9 is reached within 50 roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

Análisis constructivo y dimensional de fachadas de la Gran Vía madrileña

ANÁLISIS CONSTRUCTIVO Y DIMENSIONAL DE FACHADAS DE LA GRAN VÍA MADRILEÑA

P-adaptive boundary elements for three-dimensional potential problems

This paper deals with the boundary element method (BEM) p-convergence approach applied to three-dimensional problems governed by Laplace's equation. The advantages derived from the boundary discretization and hierarchical interpolation functions are collated in order to minimize human effort in preparation of input data and improve numerical results.

The p-Adaptive Biem Approach for Two-Dimensional Elasticity Analysis

This paper presents the development and application of the p-adaptive BIEM version in elastostatics. The basic concepts underlying the p-adaptive technique are summarized and discussed. Some Pascal pseudocodes which show the way how such a technique can be implemented easily in microcomputers are also provided. Both the applicability and the accuracy of the method proposed here are illustrated through a numerical example.

Instability Analysis of Incompressible Open Cavity Flows

El problema del flujo sobre una cavidad abierta ha sido estudiado en profundidad en la literatura, tanto por el interés académico del problema como por sus aplicaciones prácticas en gran variedad de problemas ingenieriles, como puede ser el alojamiento del tren de aterrizaje de aeronaves, o el depósito de agua de aviones contraincendios. Desde hace muchos a˜nos se estudian los distintos tipos de inestabilidades asociadas a este problema: los modos bidimensionales en la capa de cortadura, y los modos tridimensionales en el torbellino de recirculación principal dentro de la cavidad. En esta tesis se presenta un estudio paramétrico completo del límite incompresible del problema, empleando la herramienta de estabilidad lineal conocida como BiGlobal. Esta aproximación permite contemplar la estabilidad global del flujo, y obtener tanto la forma como las características de los modos propios del problema físico, sean estables o inestables. El estudio realizado permite caracterizar con gran detalle todos los modos relevantes, así como la envolvente de estabilidad en el espacio paramétrico del problema incompresible (Mach nulo, variación de Reynolds, espesor de capa límite incidente, relación altura/profundidad de la cavidad, y longitud característica de la perturbación en la dirección transversal). A la luz de los resultados obtenidos se proponen una serie de relaciones entre los parámetros y características de los modos principales, como por ejemplo entre el Reynolds crítico de un modo, y la longitud característica del mismo. Los resultados numéricos se contrastan con una campaña experimental, siendo la principal conclusión de dicha comparación que los modos lineales están presentes en el flujo real saturado, pero que existen diferencias notables en frecuencia entre las predicciones teóricas y los experimentos. Para intentar determinar la naturaleza de dichas diferencias se realiza una simulación numérica directa tridimensional, y se utiliza un algoritmo de DMD (descomposición dinámica de modos) para describir el proceso de saturación. ABSTRACT The problem of the flow over an open cavity has been studied in depth in the literature, both for being an interesting academical problem and due to the multitude of industrial applications, like the landing gear of aircraft, or the water deposit of firefighter airplanes. The different types of instabilities appearing in this flow studied in the literature are two: the two-dimensional shear layer modes, and the three-dimensional modes that appear in the main recirculating vortex inside the cavity. In this thesis a parametric study in the incompressible limit of the problem is presented, using the linear stability analysis known as BiGlobal. This approximation allows to obtain the global stability behaviour of the flow, and to capture both the morphological features and the characteristics of the eigenmodes of the physical problem, whether they are stable or unstable. The study presented here characterizes with great detail all the relevant eigenmodes, as well as the hypersurface of instability on the parameter space of the incompressible problem (Mach equal to zero, and variation of the Reynolds number, the incoming boundary layer thickness, the length to depth aspect ratio of the cavity and the spanwise length of the perturbation). The results allow to construct parametric relations between the characteristics of the leading eigenmodes and the parameters of the problem, like for example the one existing between the critical Reynolds number and its characteristic length. The numerical results presented here are compared with those of an experimental campaign, with the main conclusion of said comparison being that the linear eigenmode are present in the real saturated flow, albeit with some significant differences in the frequencies of the experiments and those predicted by the theory. To try to determine the nature of those differences a three-dimensional direct numerical simulation, analyzed with Dynamic Mode Decomposition algorithm, was used to describe the process of saturation.

Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given.

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

Técnicas avanzadas de metrología dimensional indirecta mediante el empleo de máquinas de medición por visión en entornos industriales. Modelo para la estimación de incertidumbres

Esta tesis contiene una investigación detallada sobre las características y funcionamiento de las máquinas de medición por visión. El objetivo fundamental es modelar su comportamiento y dotarlas de trazabilidad metrológica bajo cualquier condición de medida. Al efecto, se ha realizado un exhaustivo análisis de los elementos que conforman su cadena de medición, a saber: sistema de iluminación, estructura, lentes y objetivos, cámara, software de tratamiento de imágenes y software de cálculo. Se han definido modelos físico-matemáticos, de desarrollo propio, capaces de simular con fiabilidad el comportamiento de los elementos citados, agrupados, a efectos de análisis numérico, en dos subsistemas denominados: de visión y mecánico. Se han implementado procedimientos de calibración genuinos para ambos subsistemas mediante el empleo de patrones ópticos. En todos los casos se ha podido determinar la incertidumbre asociada a los diferentes parámetros involucrados, garantizando la trazabilidad metrológica de los resultados. Los distintos modelos desarrollados han sido implementados en Matlab®. Se ha verificado su validez empleando valores sintéticos obtenidos a partir de simulaciones informáticas y también con imágenes reales capturadas en el laboratorio. El estudio experimental y validación definitiva de los resultados se ha realizado en el Laboratorio de Longitud del Centro Español de Metrología y en el Laboratorio de Metrología Dimensional de la ETS de Ingeniería y Diseño Industrial de la UPM. Los modelos desarrollados se han aplicado a dos máquinas de medición por visión de diferentes características constructivas y metrológicas. Empleando dichas máquinas se han medido distintas piezas, pertenecientes a los ámbitos mecánico y oftalmológico. Los resultados obtenidos han permitido la completa caracterización dimensional de dichas piezas y la determinación del cumplimiento de las especificaciones metrológicas en todos los casos, incluyendo longitudes, formas y ángulos. ABSTRACT This PhD thesis contains a detailed investigation of characteristics and performance of the optical coordinate measurement machines. The main goal is to model their behaviour and provide metrological traceability to them under any measurement conditions. In fact, a thorough analysis of the elements which form the measuring chain, i.e.: lighting system, structure, lenses and objectives, camera, image processing software and coordinate metrology software has conducted. Physical-mathematical models, of self-developed, able to simulate with reliability the behavior of the above elements, grouped, for the purpose of numerical analysis, in two subsystems called: “vision subsystem” and “mechanical subsystem”, have been defined. Genuine calibration procedures for both subsystems have been implemented by use of optical standards. In all cases, it has been possible to determine the uncertainty associated with the different parameters involved, ensuring metrological traceability of results. Different developed models have been implemented in Matlab®. Their validity has been verified using synthetic values obtained from computer simulations and also with real images captured in laboratory. The experimental study and final validation of the results was carried out in the Length Laboratory of “Centro Español de Metrología” and Dimensional Metrology Laboratory of the “Escuela Técnica Superior de Ingeniería y Diseño Industrial” of the UPM. The developed models have been applied to two optical coordinate measurement machines with different construction and metrological characteristics. Using such machines, different parts, belonging to the mechanical and ophthalmologist areas, have been measured. The obtained results allow the full dimensional characterization of such parts and determination of compliance with metrological specifications in all cases, including lengths, shapes and angles.

Influencia del viento transversal en sistemas ferroviarios = Cross-wind effects on railway infrastructure

El viento, como factor medio-ambiental, ha sido objeto de numerosos estudios por los efectos que induce tanto en vehículos como en estructuras. Dentro del ámbito ferroviario, las cargas aerodinámicas debidas a la acción del viento transversal pueden poner en compromiso la seguridad de los vehículos en circulación, pudiendo llegar a ocasionar el vuelco del mismo. Incluso el sistema de cables encargado de realizar el suministro eléctrico necesario para la tracción del tren, conocido como catenaria, es sensible a la acción del viento. De hecho, al igual que ocurre en ciertas estructuras de cables, la interacción entre las fuerzas aerodinámicas no estacionarias y la catenaria puede ocasionar la aparición de oscilaciones de gran amplitud debido al fenómeno de galope. Una forma sencilla de reducir los efectos no deseados de la acción del viento, es la instalación de barreras cortavientos aguas arriba de la zona que se desea proteger. La instalación de estos dispositivos, reduce la velocidad en la estela generada, pero también modifica las propiedades del flujo dentro de la misma. Esta alteración de las condiciones del flujo puede contribuir a la aparición del fenómeno de galope en estructuras caracterizadas por su gran flexibilidad, como la catenaria ferroviaria. Estos dos efectos contrapuestos hacen evidente la importancia de mantener cierta visión global del efecto introducido por la instalación de barreras cortavientos en la plataforma ferroviaria. A lo largo de este documento, se evalúa desde un enfoque multidisciplinar el efecto inducido por las barreras cortavientos en varios subsistemas ferroviarios. Por un lado se analizan las mejoras en la estabilidad lateral del vehículo mediante una serie de ensayos en túnel de viento. La medición de la distribución de presiones en la superficie de un modelo bidimensional de vehículo ferroviario proporciona una buena estimación del nivel de protección que se consigue en función de la altura de una barrera cortavientos. Por otra parte, se analiza la influencia del mismo juego de barreras cortavientos en las características del flujo situado sobre la plataforma ferroviaria, mediante la utilización de anemometría de hilo caliente (HWA) y velocimetría de imágenes de párticulas (PIV). En particular se centra la atención en las características en la posición correspondiente a los hilos conductores de la catenaria. En la última parte del documento, se realiza un análisis simplificado de la aparición oscilaciones en la catenaria, por el efecto de la inestabilidad de galope. La información obtenida sobre las características del flujo se combinan con las propiedades aerodinámicas del hilo de contacto, obtenidas en mediante una serie de ensayos en túnel de viento. De esta manera se realiza una evaluación del riesgo a la aparición de este tipo de inestabilidad aeroeslástica aplicada a una catenaria ferroviaria situada sobre un viaducto tipo. ABSTRACT Wind as an environmental factor may induce undesirable effects on vehicles and structures. The analysis of those effects has caught the attention of several researchers. Concerning the railway system, cross-wind induces aerodynamic loads on rolling stock that may increase the overturning risk of the vehicle, threatening its safe operation. Even the cable system responsible to provide the electric current required for the train traction, known as the railway overhead or catenary, is sensitive to the wind action. In fact, the interaction between the unsteady aerodynamic forces and the railway overhead may trigger the development of undamped oscillations due to galloping phenomena. The inclusion of windbreaks upstream the area that needs wind protection is a simple mean to palliate the undesirable effects caused by the wind action. Although the presence of this wind protection devices reduces the wind speed downstream, they also modify the flow properties inside their wake. This modification on the flow characteristics may ease the apparition of the galloping phenomena on flexible structures, such as the railway overhead. This two opposite effects require to maintain a global perspective on the analysis of the influence of the windbreak presence. In the present document, a multidisciplinary analysis on the effect induced by windbreaks on several railways subsystems is conducted. On the one hand, a set of wind tunnel tests is conducted to assess the improvement on the rolling stock lateral stability. The qualitative estimation of the shelter effect, as function of the windbreak height, is established through the pressure distribution measured on the surface of a two-dimensional train model. On the other hand, the flow properties above the railway platform are assessed using the same set of windbreaks. Two experimental techniques are used to measure the flow properties, hot-wire anemometry (HWA) and particle image velocimetry (PIV). In particular, the attention is focused on the flow characteristics on the contact wire location. A simplified analysis on the catenary oscillations due to galloping phenomena is conducted in the last part of the document. Both, the flow characterization performed via PIV and the aerodynamic properties of the contact wire cross-section are combined. In this manner, the risk of the aeroelastic instabilities on a railway overhead placed on a railway bridge is assessed through a practical application.

One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.