Elastostatics

In this chapter, we are going to describe the main features as well as the basic steps of the Boundary Element Method (BEM) as applied to elastostatic problems and to compare them with other numerical procedures. As we shall show, it is easy to appreciate the adventages of the BEM, but it is also advisable to refrain from a possible unrestrained enthusiasm, as there are also limitations to its usefulness in certain types of problems. The number of these problems, nevertheless, is sufficient to justify the interest and activity that the new procedure has aroused among researchers all over the world. Briefly speaking, the most frequently used version of the BEM as applied to elastostatics works with the fundamental solution, i.e. the singular solution of the governing equations, as an influence function and tries to satisfy the boundary conditions of the problem with the aid of a discretization scheme which consists exclusively of boundary elements. As in other numerical methods, the BEM was developed thanks to the computational possibilities offered by modern computers on totally "classical" basis. That is, the theoretical grounds are based on linear elasticity theory, incorporated long ago into the curricula of most engineering schools. Its delay in gaining popularity is probably due to the enormous momentum with which Finite Element Method (FEM) penetrated the professional and academic media. Nevertheless, the fact that these methods were developed before the BEM has been beneficial because de BEM successfully uses those results and techniques studied in past decades. Some authors even consider the BEM as a particular case of the FEM while others view both methods as special cases of the general weighted residual technique. The first paper usually cited in connection with the BEM as applied to elastostatics is that of Rizzo, even though the works of Jaswon et al., Massonet and Oliveira were published at about the same time, the reason probably being the attractiveness of the "direct" approach over the "indirect" one. The work of Tizzo and the subssequent work of Cruse initiated a fruitful period with applicatons of the direct BEM to problems of elastostacs, elastodynamics, fracture, etc. The next key contribution was that of Lachat and Watson incorporating all the FEM discretization philosophy in what is sometimes called the "second BEM generation". This has no doubt, led directly to the current developments. Among the various researchers who worked on elastostatics by employing the direct BEM, one can additionallly mention Rizzo and Shippy, Cruse et al., Lachat and Watson, Alarcón et al., Brebbia el al, Howell and Doyle, Kuhn and Möhrmann and Patterson and Sheikh, and among those who used the indirect BEM, one can additionally mention Benjumea and Sikarskie, Butterfield, Banerjee et al., Niwa et al., and Altiero and Gavazza. An interesting version of the indirct method, called the Displacement Discontinuity Method (DDM) has been developed by Crounh. A comprehensive study on various special aspects of the elastostatic BEM has been done by Heisse, while review-type articles on the subject have been reported by Watson and Hartmann. At the present time, the method is well established and is being used for the solution of variety of problems in engineering mechanics. Numerous introductory and advanced books have been published as well as research-orientated ones. In this sense, it is worth noting the series of conferences promoted by Brebbia since 1978, wich have provoked a continuous research effort all over the world in relation to the BEM. In the following sections, we shall concentrate on developing the direct BEM as applied to elastostatics.

Interpretation of the pressuremeter test using numerical models based on deformation tensor equations

The pressuremeter test in boreholes has proven itself as a useful tool in geotechnical explorations, especially comparing its results with those obtained from a mathematical model ruled by a soil representative constitutive equation. The numerical model shown in this paper is aimed to be the reference framework for the interpretation of this test. The model analyses variables such as: the type of response, the initial state, the drainage regime and the constitutive equations. It is a model of finite elements able to work with a mesh without deformation or one adapted to it.

On the generative equations of fractal self-similarity in granular media and the related PSD models

The physical appearance of granular media suggests the existence of geometrical scale invariance. The paper discuss how this physico-empirical property can be mathematically encoded leading to different generative models: a smooth one encoded by a differential equation and another encoded by an equation coming from a measure theoretical property.

A self-timed multipurpose delay sensor for field programmable gate arrays (FPGAs)

This paper presents a novel self-timed multi-purpose sensor especially conceived for Field Programmable Gate Arrays (FPGAs). The aim of the sensor is to measure performance variations during the life-cycle of the device, such as process variability, critical path timing and temperature variations. The proposed topology, through the use of both combinational and sequential FPGA elements, amplifies the time of a signal traversing a delay chain to produce a pulse whose width is the sensor’s measurement. The sensor is fully self-timed, avoiding the need for clock distribution networks and eliminating the limitations imposed by the system clock. One single off- or on-chip time-to-digital converter is able to perform digitization of several sensors in a single operation. These features allow for a simplified approach for designers wanting to intertwine a multi-purpose sensor network with their application logic. Employed as a temperature sensor, it has been measured to have an error of ±0.67 °C, over the range of 20–100 °C, employing 20 logic elements with a 2-point calibration.

A framework for the analysis and optimization of delay in multiview video coding schemes

Esta tesis presenta un novedoso marco de referencia para el análisis y optimización del retardo de codificación y descodificación para vídeo multivista. El objetivo de este marco de referencia es proporcionar una metodología sistemática para el análisis del retardo en codificadores y descodificadores multivista y herramientas útiles en el diseño de codificadores/descodificadores para aplicaciones con requisitos de bajo retardo. El marco de referencia propuesto caracteriza primero los elementos que tienen influencia en el comportamiento del retardo: i) la estructura de predicción multivista, ii) el modelo hardware del codificador/descodificador y iii) los tiempos de proceso de cuadro. En segundo lugar, proporciona algoritmos para el cálculo del retardo de codificación/ descodificación de cualquier estructura arbitraria de predicción multivista. El núcleo de este marco de referencia consiste en una metodología para el análisis del retardo de codificación/descodificación multivista que es independiente de la arquitectura hardware del codificador/descodificador, completada con un conjunto de modelos que particularizan este análisis del retardo con las características de la arquitectura hardware del codificador/descodificador. Entre estos modelos, aquellos basados en teoría de grafos adquieren especial relevancia debido a su capacidad de desacoplar la influencia de los diferentes elementos en el comportamiento del retardo en el codificador/ descodificador, mediante una abstracción de su capacidad de proceso. Para revelar las posibles aplicaciones de este marco de referencia, esta tesis presenta algunos ejemplos de su utilización en problemas de diseño que afectan a codificadores y descodificadores multivista. Este escenario de aplicación cubre los siguientes casos: estrategias para el diseño de estructuras de predicción que tengan en consideración requisitos de retardo además del comportamiento tasa-distorsión; diseño del número de procesadores y análisis de los requisitos de velocidad de proceso en codificadores/ descodificadores multivista dado un retardo objetivo; y el análisis comparativo del comportamiento del retardo en codificadores multivista con diferentes capacidades de proceso e implementaciones hardware. ABSTRACT This thesis presents a novel framework for the analysis and optimization of the encoding and decoding delay for multiview video. The objective of this framework is to provide a systematic methodology for the analysis of the delay in multiview encoders and decoders and useful tools in the design of multiview encoders/decoders for applications with low delay requirements. The proposed framework characterizes firstly the elements that have an influence in the delay performance: i) the multiview prediction structure ii) the hardware model of the encoder/decoder and iii) frame processing times. Secondly, it provides algorithms for the computation of the encoding/decoding delay of any arbitrary multiview prediction structure. The core of this framework consists in a methodology for the analysis of the multiview encoding/decoding delay that is independent of the hardware architecture of the encoder/decoder, which is completed with a set of models that particularize this delay analysis with the characteristics of the hardware architecture of the encoder/decoder. Among these models, the ones based in graph theory acquire special relevance due to their capacity to detach the influence of the different elements in the delay performance of the encoder/decoder, by means of an abstraction of its processing capacity. To reveal possible applications of this framework, this thesis presents some examples of its utilization in design problems that affect multiview encoders and decoders. This application scenario covers the following cases: strategies for the design of prediction structures that take into consideration delay requirements in addition to the rate-distortion performance; design of number of processors and analysis of processor speed requirements in multiview encoders/decoders given a target delay; and comparative analysis of the encoding delay performance of multiview encoders with different processing capabilities and hardware implementations.

Systematic analysis of the decoding delay on MVC decoders

We present a framework for the analysis of the decoding delay and communication latency in Multiview Video Coding. The application of this framework on MVC decoders allows minimizing the overall delay in immersive video-conference systems.

Chaos in non lineal Alfven waves using the DNLS equations

The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.

Large aperture antenna arrays with subband delay compensation for reception of wideband satellite signals

Con esta disertación se pretenden resolver algunos de los problemas encontrados actualmente en la recepción de señales de satélites bajo dos escenarios particularmente exigentes: comunicaciones de Espacio Profundo y en banda Ka. Las comunicaciones con sondas de Espacio Profundo necesitan grandes aperturas en tierra para poder incrementar la velocidad de datos. La opción de usar antennas con diámetro mayor de 35 metros tiene serios problemas, pues antenas tan grandes son caras de mantener, difíciles de apuntar, pueden tener largos tiempo de reparación y además tienen una efeciencia decreciente a medida que se utilizan bandas más altas. Soluciones basadas en agrupaciones de antenas de menor tamaño (12 ó 35 metros) son mas ecónomicas y factibles técnicamente. Las comunicaciones en banda Ka tambien pueden beneficiarse de la combinación de múltiples antennas. Las antenas de menor tamaño son más fáciles de apuntar y además tienen un campo de visión mayor. Además, las técnicas de diversidad espacial pueden ser reemplazadas por una combinación de antenas para así incrementar el margen del enlace. La combinación de antenas muy alejadas sobre grandes anchos de banda, bien por recibir una señal de banda ancha o múltiples de banda estrecha, es complicada técnicamente. En esta disertación se demostrará que el uso de conformador de haz en el dominio de la frecuencia puede ayudar a relajar los requisitos de calibración y, al mismo tiempo, proporcionar un mayor campo de visión y mayores capacidades de ecualización. Para llevar esto a cabo, el trabajo ha girado en torno a tres aspectos fundamentales. El primero es la investigación bibliográfica del trabajo existente en este campo. El segundo es el modelado matemático del proceso de combinación y el desarrollo de nuevos algoritmos de estimación de fase y retardo. Y el tercero es la propuesta de nuevas aplicaciones en las que usar estas técnicas. La investigación bibliográfica se centra principalmente en los capítulos 1, 2, 4 y 5. El capítulo 1 da una breve introducción a la teoría de combinación de antenas de gran apertura. En este capítulo, los principales campos de aplicación son descritos y además se establece la necesidad de compensar retardos en subbandas. La teoría de bancos de filtros se expone en el capítulo 2; se selecciona y simula un banco de filtros modulado uniformemente con fase lineal. Las propiedades de convergencia de varios filtros adaptativos se muestran en el capítulo 4. Y finalmente, las técnicas de estimación de retardo son estudiadas y resumidas en el capítulo 5. Desde el punto de vista matemático, las principales contribución de esta disertación han sido: • Sección 3.1.4. Cálculo de la desviación de haz de un conformador de haz con compensación de retardo en pasos discretos en frecuencia intermedia. • Sección 3.2. Modelo matemático de un conformador de haz en subbandas. • Sección 3.2.2. Cálculo de la desviación de haz de un conformador de haz en subbandas con un buffer de retardo grueso. • Sección 3.2.4. Análisis de la influencia de los alias internos en la compensación en subbandas de retardo y fase. • Sección 3.2.4.2. Cálculo de la desviación de haz de un conformador de haz con compensación de retardo en subbandas. • Sección 3.2.6. Cálculo de la ganancia de relación señal a ruido de la agrupación de antenas en cada una de las subbandas. • Sección 3.3.2. Modelado de la función de transferencia de la agrupación de antenas bajo errores de estimación de retardo. • Sección 3.3.3. Modelado de los efectos de derivas de fase y retardo entre actualizaciones de las estimaciones. • Sección 3.4. Cálculo de la directividad de la agrupación de antenas con y sin compensación de retardos en subbandas. • Sección 5.2.6. Desarrollo de un algorimo para estimar la fase y el retardo entre dos señales a partir de su descomposición de subbandas bajo entornos estacionarios. • Sección 5.5.1. Desarrollo de un algorimo para estimar la fase, el retardo y la deriva de retardo entre dos señales a partir de su descomposición de subbandas bajo entornos no estacionarios. Las aplicaciones que se pueden beneficiar de estas técnicas son descritas en el capítulo 7: • Sección 6.2. Agrupaciones de antenas para comunicaciones de Espacio Profundo con capacidad multihaz y sin requisitos de calibración geométrica o de retardo de grupo. • Sección 6.2.6. Combinación en banda ancha de antenas con separaciones de miles de kilómetros, para recepción de sondas de espacio profundo. • Secciones 6.4 and 6.3. Combinación de estaciones remotas en banda Ka en escenarios de diversidad espacial, para recepción de satélites LEO o GEO. • Sección 6.3. Recepción de satélites GEO colocados con arrays de antenas multihaz. Las publicaciones a las que ha dado lugar esta tesis son las siguientes • A. Torre. Wideband antenna arraying over long distances. Interplanetary Progress Report, 42-194:1–18, 2013. En esta pulicación se resumen los resultados de las secciones 3.2, 3.2.2, 3.3.2, los algoritmos en las secciones 5.2.6, 5.5.1 y la aplicación destacada en 6.2.6. • A. Torre. Reception of wideband signals from geostationary collocated satellites with antenna arrays. IET Communications, Vol. 8, Issue 13:2229–2237, September, 2014. En esta segunda se muestran los resultados de la sección 3.2.4, el algoritmo en la sección 5.2.6.1 , y la aplicación mostrada en 6.3. ABSTRACT This dissertation is an attempt to solve some of the problems found nowadays in the reception of satellite signals under two particular challenging scenarios: Deep Space and Ka-band communications. Deep Space communications require from larger apertures on ground in order to increase the data rate. The option of using single dishes with diameters larger than 35 meters has severe drawbacks. Such antennas are expensive to maintain, prone to long downtimes, difficult to point and have a degraded performance in high frequency bands. The array solution, either with 12 meter or 35 meter antennas is deemed to be the most economically and technically feasible solution. Ka-band communications can also benefit from antenna arraying technology. The smaller aperture antennas that make up the array are easier to point and have a wider field of view allowing multiple simultaneous beams. Besides, site diversity techniques can be replaced by pure combination in order to increase link margin. Combination of far away antennas over a large bandwidth, either because a wideband signal or multiple narrowband signals are received, is a demanding task. This dissertation will show that the use of frequency domain beamformers with subband delay compensation can help to ease calibration requirements and, at the same time, provide with a wider field of view and enhanced equalization capabilities. In order to do so, the work has been focused on three main aspects. The first one is the bibliographic research of previous work on this subject. The second one is the mathematical modeling of the array combination process and the development of new phase/delay estimation algorithms. And the third one is the proposal of new applications in which these techniques can be used. Bibliographic research is mainly done in chapters 1, 2, 4 and 5. Chapter 1 gives a brief introduction to previous work in the field of large aperture antenna arraying. In this chapter, the main fields of application are described and the need for subband delay compensation is established. Filter bank theory is shown in chapter 2; a linear phase uniform modulated filter bank is selected and simulated under diverse conditions. The convergence properties of several adaptive filters are shown in chapter 4. Finally, delay estimation techniques are studied and summarized in chapter 5. From a mathematical point of view, the main contributions of this dissertation have been: • Section 3.1.4. Calculation of beam squint of an IF beamformer with delay compensation at discrete time steps. • Section 3.2. Establishment of a mathematical model of a subband beamformer. • Section 3.2.2. Calculation of beam squint in a subband beamformer with a coarse delay buffer. • Section 3.2.4. Analysis of the influence of internal aliasing on phase and delay subband compensation. • Section 3.2.4.2. Calculation of beam squint of a beamformer with subband delay compensation. • Section 3.2.6. Calculation of the array SNR gain at each of the subbands. • Section 3.3.2. Modeling of the transfer function of an array subject to delay estimation errors. • Section 3.3.3. Modeling of the effects of phase and delay drifts between estimation updates. • Section 3.4. Calculation of array directivity with and without subband delay compensation. • Section 5.2.6. Development of an algorithm to estimate relative delay and phase between two signals from their subband decomposition in stationary environments. • Section 5.5.1. Development of an algorithm to estimate relative delay rate, delay and phase between two signals from their subband decomposition in non stationary environments. The applications that can benefit from these techniques are described in chapter 7: • Section 6.2. Arrays of antennas for Deep Space communications with multibeam capacity and without geometric or group delay calibration requirement. • Section 6.2.6. Wideband antenna arraying over long distances, in the range of thousands of kilometers, for reception of Deep Space probes. • Sections 6.4 y 6.3. Combination of remote stations in Ka-band site diversity scenarios for reception of LEO or GEO satellites. • Section 6.3. Reception of GEO collocated satellites with multibeam antenna arrays. The publications that have been made from the work in this dissertation are • A. Torre. Wideband antenna arraying over long distances. Interplanetary Progress Report, 42-194:1–18, 2013. This article shows the results in sections 3.2, 3.2.2, 3.3.2, the algorithms in sections 5.2.6, 5.5.1 and the application in section 6.2.6. • A. Torre. Reception of wideband signals from geostationary collocated satellites with antenna arrays. IET Communications, Vol. 8, Issue 13:2229–2237, September, 2014. This second article shows among others the results in section 3.2.4, the algorithm in section 5.2.6.1 , and the application in section 6.3.

A dynamic programming approach to the formulation and solution of finite element equations

A method for formulating and algorithmically solving the equations of finite element problems is presented. The method starts with a parametric partition of the domain in juxtaposed strips that permits sweeping the whole region by a sequential addition (or removal) of adjacent strips. The solution of the difference equations constructed over that grid proceeds along with the addition removal of strips in a manner resembling the transfer matrix approach, except that different rules of composition that lead to numerically stable algorithms are used for the stiffness matrices of the strips. Dynamic programming and invariant imbedding ideas underlie the construction of such rules of composition. Among other features of interest, the present methodology provides to some extent the analyst's control over the type and quantity of data to be computed. In particular, the one-sweep method presented in Section 9, with no apparent counterpart in standard methods, appears to be very efficient insofar as time and storage is concerned. The paper ends with the presentation of a numerical example

Control of a Teleoperation System by State Convergence with Variable Time Delay

In this paper, we propose a novel control scheme for bilateral teleoperation of n degree-of-freedom (DOF) nonlinear robotic systems with time-varying communication delay. We consider that the human operator contains a constant force on the local manipulator. The local and remote manipulators are coupled using state convergence control scheme. By choosing a Lyapunov-Krasovskii functional, we show that the local-remote teleoperation system is asymptotically stable. It is also shown that, in the case of reliable communication protocols, the proposed scheme guarantees that the remote manipulator tracks the delayed trajectory of the local manipulator. The time delay of communication channel is assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known.

Stability Analysis of Teleoperation System by State Convergence with Variable Time Delay

We propose a novel control scheme for bilateral teleoperation of n degree-of-freedom (DOF) nonlinear robotic systems with time-varying communication delay. A major contribution from this work lies in the demonstration that the structure of a state convergence algorithm can be also applied to nth-order nonlinear teleoperation systems. By choosing a Lyapunov Krasovskii functional, we show that the local-remote teleoperation system is asymptotically stable. The time delay of communication channel is assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known.

Development of AMREM: a Maxwell's equations solver with Adaptive Mesh Refinement

El principal objetivo de la presente tesis es el de desarrollar y probar un código capaz de resolver las ecuaciones de Maxwell en el dominio del tiempo con Malla Refinada Adaptativa (AMR por sus siglas en inglés). AMR es una técnica de cálculo basada en dividir el dominio físico del problema en distintas mallas rectangulares paralelas a las direcciones cartesianas. Cada una de las mallas tendrá distinta resolución y aquellas con mayor resolución se sitúan allí dónde las ondas electromagnéticas se propagan o interaccionan con los materiales, es decir, dónde mayor precisión es requerida. Como las ondas van desplazándose por todo el dominio, las mayas deberán seguirlas. El principal problema al utilizar esta metodología se puede encontrar en las fronteras internas, dónde las distintas mallas se unen. Ya que el método más corrientemente utilizado para resolver las ecuaciones de Maxwell es el de las diferencias finitas en el dominio del tiempo (FDTD por sus siglas en inglés) , el trabajo comenzó tratando de adaptar AMR a FDTD. Tras descubrirse que esta interacción resultaba en problemas de inestabilidades en las fronteras internas antes citadas, se decidió cambiar a un método basado en volúmenes finitos en el dominio del tiempo (FVTD por sus siglas en inglés). Este se basa en considerar la forma en ecuaciones de conservación de las ecuaciones de Maxwell y aplicar a su resolución un esquema de Godunov. Se ha probado que es clave para el correcto funcionamiento del código la elección de un limitador de flujo que proteja los extremos de la onda de la disipación típica de los métodos de este tipo. Otro problema clásico a la hora de resolver las ecuaciones de Maxwell es el de tratar con las condiciones de frontera física cuando se simulan dominios no acotados, es decir, dónde las ondas deben salir del sistema sin producir ninguna reflexión. Normalmente la solución es la de disponer una banda absorbente en las fronteras físicas. En AMREM se ha desarrollado un nuevo método basado en los campos característicos que con menor requisito de CPU funcina suficientemente bien incluso en los casos más desfaborables. El código ha sido contrastado con soluciones analíticas de diferentes problemas y también su velocidad ha sido comparada con la de Meep, uno de los programas más conocidos del ámbito. También algunas aplicaciones han sido simuladas con el fin de demostrar el amplio espectro de campos en los que AMREM puede funcionar como una útil herramienta.

Systematic analysis of the decoding delay in multiview video

We present a framework for the analysis of the decoding delay in multiview video coding (MVC). We show that in real-time applications, an accurate estimation of the decoding delay is essential to achieve a minimum communication latency. As opposed to single-view codecs, the complexity of the multiview prediction structure and the parallel decoding of several views requires a systematic analysis of this decoding delay, which we solve using graph theory and a model of the decoder hardware architecture. Our framework assumes a decoder implementation in general purpose multi-core processors with multi-threading capabilities. For this hardware model, we show that frame processing times depend on the computational load of the decoder and we provide an iterative algorithm to compute jointly frame processing times and decoding delay. Finally, we show that decoding delay analysis can be applied to design decoders with the objective of minimizing the communication latency of the MVC system.

Overtopping of harbour breakwaters: a comparison of semi-empirical equations, neural networks, and physical model tests

This paper reports extensive tests of empirical equations developed by different authors for harbour breakwater overtopping. First, the existing equations are compiled and evaluated as tools for estimating the overtopping rates on sloping and vertical breakwaters. These equations are then tested using the data obtained in a number of laboratory studies performed in the Centre for Harbours and Coastal Studies of the CEDEX, Spain. It was found that the recommended application ranges of the empirical equations typically deviate from those revealed in the experimental tests. In addition, a neural network model developed within the European CLASH Project is tested. The wind effects on overtopping are also assessed using a reduced scale physical model

Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.