Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

Evaluation and improvement of empirical models of global solar irradiation: Case study northern Spain

This paper presents a new methodology to build parametric models to estimate global solar irradiation adjusted to specific on-site characteristics based on the evaluation of variable im- portance. Thus, those variables higly correlated to solar irradiation on a site are implemented in the model and therefore, different models might be proposed under different climates. This methodology is applied in a study case in La Rioja region (northern Spain). A new model is proposed and evaluated on stability and accuracy against a review of twenty-two already exist- ing parametric models based on temperatures and rainfall in seventeen meteorological stations in La Rioja. The methodology of model evaluation is based on bootstrapping, which leads to achieve a high level of confidence in model calibration and validation from short time series (in this case five years, from 2007 to 2011). The model proposed improves the estimates of the other twenty-two models with average mean absolute error (MAE) of 2.195 MJ/m2 day and average confidence interval width (95% C.I., n=100) of 0.261 MJ/m2 day. 41.65% of the daily residuals in the case of SIAR and 20.12% in that of SOS Rioja fall within the uncertainty tolerance of the pyranometers of the two networks (10% and 5%, respectively). Relative differences between measured and estimated irradiation on an annual cumulative basis are below 4.82%. Thus, the proposed model might be useful to estimate annual sums of global solar irradiation, reaching insignificant differences between measurements from pyranometers.

Model-to-Code transformation from product-line architecture models to aspectJ

Software Product Line Engineering has significant advantages in family-based software development. The common and variable structure for all products of a family is defined through a Product-Line Architecture (PLA) that consists of a common set of reusable components and connectors which can be configured to build the different products. The design of PLA requires solutions for capturing such configuration (variability). The Flexible-PLA Model is a solution that supports the specification of external variability of the PLA configuration, as well as internal variability of components. However, a complete support for product-line development requires translating architecture specifications into code. This complex task needs automation to avoid human error. Since Model-Driven Development allows automatic code generation from models, this paper presents a solution to automatically generate AspectJ code from Flexible-PLA models previously configured to derive specific products. This solution is supported by a modeling framework and validated in a software factory.

Numerical model for the study of hydrodynamics on bays and estuaries

A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow water equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric, Lagrangian elements. To obtain the different element matrices, Simpson numerical integration has been applied. For time integration of the model, several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step Δt; however, central differences time integration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally, an application to the Bay of Santander is also presented.

CCD image sensor induced error in PIV applications

The readout procedure of charge-coupled device (CCD) cameras is known to generate some image degradation in different scientific imaging fields, especially in astrophysics. In the particular field of particle image velocimetry (PIV), widely extended in the scientific community, the readout procedure of the interline CCD sensor induces a bias in the registered position of particle images. This work proposes simple procedures to predict the magnitude of the associated measurement error. Generally, there are differences in the position bias for the different images of a certain particle at each PIV frame. This leads to a substantial bias error in the PIV velocity measurement (~0.1 pixels). This is the order of magnitude that other typical PIV errors such as peak-locking may reach. Based on modern CCD technology and architecture, this work offers a description of the readout phenomenon and proposes a modeling for the CCD readout bias error magnitude. This bias, in turn, generates a velocity measurement bias error when there is an illumination difference between two successive PIV exposures. The model predictions match the experiments performed with two 12-bit-depth interline CCD cameras (MegaPlus ES 4.0/E incorporating the Kodak KAI-4000M CCD sensor with 4 megapixels). For different cameras, only two constant values are needed to fit the proposed calibration model and predict the error from the readout procedure. Tests by different researchers using different cameras would allow verification of the model, that can be used to optimize acquisition setups. Simple procedures to obtain these two calibration values are also described.

Communication Middleware for Distributed Hard Real-Time Systems in Java

Distributed real-time embedded systems are becoming increasingly important to society. More demands will be made on them and greater reliance will be placed on the delivery of their services. A relevant subset of them is high-integrity or hard real-time systems, where failure can cause loss of life, environmental harm, or significant financial loss. Additionally, the evolution of communication networks and paradigms as well as the necessity of demanding processing power and fault tolerance, motivated the interconnection between electronic devices; many of the communications have the possibility of transferring data at a high speed. The concept of distributed systems emerged as systems where different parts are executed on several nodes that interact with each other via a communication network. Java’s popularity, facilities and platform independence have made it an interesting language for the real-time and embedded community. This was the motivation for the development of RTSJ (Real-Time Specification for Java), which is a language extension intended to allow the development of real-time systems. The use of Java in the development of high-integrity systems requires strict development and testing techniques. However, RTJS includes a number of language features that are forbidden in such systems. In the context of the HIJA project, the HRTJ (Hard Real-Time Java) profile was developed to define a robust subset of the language that is amenable to static analysis for high-integrity system certification. Currently, a specification under the Java community process (JSR- 302) is being developed. Its purpose is to define those capabilities needed to create safety critical applications with Java technology called Safety Critical Java (SCJ). However, neither RTSJ nor its profiles provide facilities to develop distributed realtime applications. This is an important issue, as most of the current and future systems will be distributed. The Distributed RTSJ (DRTSJ) Expert Group was created under the Java community process (JSR-50) in order to define appropriate abstractions to overcome this problem. Currently there is no formal specification. The aim of this thesis is to develop a communication middleware that is suitable for the development of distributed hard real-time systems in Java, based on the integration between the RMI (Remote Method Invocation) model and the HRTJ profile. It has been designed and implemented keeping in mind the main requirements such as the predictability and reliability in the timing behavior and the resource usage. iThe design starts with the definition of a computational model which identifies among other things: the communication model, most appropriate underlying network protocols, the analysis model, and a subset of Java for hard real-time systems. In the design, the remote references are the basic means for building distributed applications which are associated with all non-functional parameters and resources needed to implement synchronous or asynchronous remote invocations with real-time attributes. The proposed middleware separates the resource allocation from the execution itself by defining two phases and a specific threading mechanism that guarantees a suitable timing behavior. It also includes mechanisms to monitor the functional and the timing behavior. It provides independence from network protocol defining a network interface and modules. The JRMP protocol was modified to include two phases, non-functional parameters, and message size optimizations. Although serialization is one of the fundamental operations to ensure proper data transmission, current implementations are not suitable for hard real-time systems and there are no alternatives. This thesis proposes a predictable serialization that introduces a new compiler to generate optimized code according to the computational model. The proposed solution has the advantage of allowing us to schedule the communications and to adjust the memory usage at compilation time. In order to validate the design and the implementation a demanding validation process was carried out with emphasis in the functional behavior, the memory usage, the processor usage (the end-to-end response time and the response time in each functional block) and the network usage (real consumption according to the calculated consumption). The results obtained in an industrial application developed by Thales Avionics (a Flight Management System) and in exhaustive tests show that the design and the prototype are reliable for industrial applications with strict timing requirements. Los sistemas empotrados y distribuidos de tiempo real son cada vez más importantes para la sociedad. Su demanda aumenta y cada vez más dependemos de los servicios que proporcionan. Los sistemas de alta integridad constituyen un subconjunto de gran importancia. Se caracterizan por que un fallo en su funcionamiento puede causar pérdida de vidas humanas, daños en el medio ambiente o cuantiosas pérdidas económicas. La necesidad de satisfacer requisitos temporales estrictos, hace más complejo su desarrollo. Mientras que los sistemas empotrados se sigan expandiendo en nuestra sociedad, es necesario garantizar un coste de desarrollo ajustado mediante el uso técnicas adecuadas en su diseño, mantenimiento y certificación. En concreto, se requiere una tecnología flexible e independiente del hardware. La evolución de las redes y paradigmas de comunicación, así como la necesidad de mayor potencia de cómputo y de tolerancia a fallos, ha motivado la interconexión de dispositivos electrónicos. Los mecanismos de comunicación permiten la transferencia de datos con alta velocidad de transmisión. En este contexto, el concepto de sistema distribuido ha emergido como sistemas donde sus componentes se ejecutan en varios nodos en paralelo y que interactúan entre ellos mediante redes de comunicaciones. Un concepto interesante son los sistemas de tiempo real neutrales respecto a la plataforma de ejecución. Se caracterizan por la falta de conocimiento de esta plataforma durante su diseño. Esta propiedad es relevante, por que conviene que se ejecuten en la mayor variedad de arquitecturas, tienen una vida media mayor de diez anos y el lugar ˜ donde se ejecutan puede variar. El lenguaje de programación Java es una buena base para el desarrollo de este tipo de sistemas. Por este motivo se ha creado RTSJ (Real-Time Specification for Java), que es una extensión del lenguaje para permitir el desarrollo de sistemas de tiempo real. Sin embargo, RTSJ no proporciona facilidades para el desarrollo de aplicaciones distribuidas de tiempo real. Es una limitación importante dado que la mayoría de los actuales y futuros sistemas serán distribuidos. El grupo DRTSJ (DistributedRTSJ) fue creado bajo el proceso de la comunidad de Java (JSR-50) con el fin de definir las abstracciones que aborden dicha limitación, pero en la actualidad aun no existe una especificacion formal. El objetivo de esta tesis es desarrollar un middleware de comunicaciones para el desarrollo de sistemas distribuidos de tiempo real en Java, basado en la integración entre el modelo de RMI (Remote Method Invocation) y el perfil HRTJ. Ha sido diseñado e implementado teniendo en cuenta los requisitos principales, como la predecibilidad y la confiabilidad del comportamiento temporal y el uso de recursos. El diseño parte de la definición de un modelo computacional el cual identifica entre otras cosas: el modelo de comunicaciones, los protocolos de red subyacentes más adecuados, el modelo de análisis, y un subconjunto de Java para sistemas de tiempo real crítico. En el diseño, las referencias remotas son el medio básico para construcción de aplicaciones distribuidas las cuales son asociadas a todos los parámetros no funcionales y los recursos necesarios para la ejecución de invocaciones remotas síncronas o asíncronas con atributos de tiempo real. El middleware propuesto separa la asignación de recursos de la propia ejecución definiendo dos fases y un mecanismo de hebras especifico que garantiza un comportamiento temporal adecuado. Además se ha incluido mecanismos para supervisar el comportamiento funcional y temporal. Se ha buscado independencia del protocolo de red definiendo una interfaz de red y módulos específicos. También se ha modificado el protocolo JRMP para incluir diferentes fases, parámetros no funcionales y optimizaciones de los tamaños de los mensajes. Aunque la serialización es una de las operaciones fundamentales para asegurar la adecuada transmisión de datos, las actuales implementaciones no son adecuadas para sistemas críticos y no hay alternativas. Este trabajo propone una serialización predecible que ha implicado el desarrollo de un nuevo compilador para la generación de código optimizado acorde al modelo computacional. La solución propuesta tiene la ventaja que en tiempo de compilación nos permite planificar las comunicaciones y ajustar el uso de memoria. Con el objetivo de validar el diseño e implementación se ha llevado a cabo un exigente proceso de validación con énfasis en: el comportamiento funcional, el uso de memoria, el uso del procesador (tiempo de respuesta de extremo a extremo y en cada uno de los bloques funcionales) y el uso de la red (consumo real conforme al estimado). Los buenos resultados obtenidos en una aplicación industrial desarrollada por Thales Avionics (un sistema de gestión de vuelo) y en las pruebas exhaustivas han demostrado que el diseño y el prototipo son fiables para aplicaciones industriales con estrictos requisitos temporales.

Facing the climate change challenges in the mining and mineral industry as providers of a sustainable manufacturing process

A sustainable manufacturing process must rely on an also sustainable raw materials and energy supply. This paper is intended to show the results of the studies developed on sustainable business models for the minerals industry as a fundamental previous part of a sustainable manufacturing process. As it has happened in other economic activities, the mining and minerals industry has come under tremendous pressure to improve its social, developmental, and environmental performance. Mining, refining, and the use and disposal of minerals have in some instances led to significant local environmental and social damage. Nowadays, like in other parts of the corporate world, companies are more routinely expected to perform to ever higher standards of behavior, going well beyond achieving the best rate of return for shareholders. They are also increasingly being asked to be more transparent and subject to third-party audit or review, especially in environmental aspects. In terms of environment, there are three inter-related areas where innovation and new business models can make the biggest difference: carbon, water and biodiversity. The focus in these three areas is for two reasons. First, the industrial and energetic minerals industry has significant footprints in each of these areas. Second, these three areas are where the potential environmental impacts go beyond local stakeholders and communities, and can even have global impacts, like in the case of carbon. So prioritizing efforts in these areas will ultimately be a strategic differentiator as the industry businesses continues to grow. Over the next forty years, world?s population is predicted to rise from 6.300 million to 9.500 million people. This will mean a huge demand of natural resources. Indeed, consumption rates are such that current demand for raw materials will probably soon exceed the planet?s capacity. As awareness of the actual situation grows, the public is demanding goods and services that are even more environmentally sustainable. This means that massive efforts are required to reduce the amount of materials we use, including freshwater, minerals and oil, biodiversity, and marine resources. It?s clear that business as usual is no longer possible. Today, companies face not only the economic fallout of the financial crisis; they face the substantial challenge of transitioning to a low-carbon economy that is constrained by dwindling natural resources easily accessible. Innovative business models offer pioneering companies an early start toward the future. They can signal to consumers how to make sustainable choices and provide reward for both the consumer and the shareholder. Climate change and carbon remain major risk discontinuities that we need to better understand and deal with. In the absence of a global carbon solution, the principal objective of any individual country should be to reduce its global carbon emissions by encouraging conservation. The mineral industry internal response is to continue to focus on reducing the energy intensity of our existing operations through energy efficiency and the progressive introduction of new technology. Planning of the new projects must ensure that their energy footprint is minimal from the start. These actions will increase the long term resilience of the business to uncertain energy and carbon markets. This focus, combined with a strong demand for skills in this strategic area for the future requires an appropriate change in initial and continuing training of engineers and technicians and their awareness of the issue of eco-design. It will also need the development of measurement tools for consistent comparisons between companies and the assessments integration of the carbon footprint of mining equipments and services in a comprehensive impact study on the sustainable development of the Economy.

Level II reliability methods for tunnels

In tunnel construction, as in every engineering work, it is usual the decision making, with incomplete data. Nevertheless, consciously or not, the builder weighs the risks (even if this is done subjectively) so that he can offer a cost. The objective of this paper is to recall the existence of a methodology to treat the uncertainties in the data so that it is possible to see their effect on the output of the computational model used and then to estimate the failure probability or the safety margin of a structure. In this scheme it is possible to include the subjective knowledge on the statistical properties of the random variables and, using a numerical model consistent with the degree of complexity appropiate to the problem at hand, to make rationally based decisions. As will be shown with the method it is possible to quantify the relative importance of the random variables and, in addition, it can be used, under certain conditions, to solve the inverse problem. It is then a method very well suited both to the project and to the control phases of tunnel construction.

Diseño del curso para operador "Coeficientes inherentes de reactividad" a plataforma e-Learning

Las centrales nucleares necesitan de personal altamente especializado y formado. Es por ello por lo que el sector de la formación especializada en centrales nucleares necesita incorporar los últimos avances en métodos formativos. Existe una gran cantidad de cursos de formación presenciales y es necesario transformar dichos cursos para utilizarlos con las nuevas tecnologías de la información. Para ello se necesitan equipos multidisciplinares, en los que se incluyen ingenieros, que deben identificar los objetivos formativos, competencias, contenidos y el control de calidad del propio curso. En este proyecto se utilizan técnicas de ingeniería del conocimiento como eje metodológico para transformar un curso de formación presencial en formación on-line a través de tecnologías de la información. En la actualidad, las nuevas tecnologías de la información y comunicación están en constante evolución. De esta forma se han sumergido en el mundo transformando la visión que teníamos de éste para dar lugar a nuevas oportunidades. Es por ello que este proyecto busca la unión entre el e-learning y el mundo empresarial. El objetivo es el diseño, en plataforma e-learning, de un curso técnico que instruya a operadores de sala de control de una central nuclear. El trabajo realizado en este proyecto ha sido, además de transformar un curso presencial en on-line, en obtener una metodología para que otros cursos se puedan transformar. Para conseguir este cometido, debemos preocuparnos tanto por el contenido de los cursos como por su gestión. Por este motivo, el proyecto comienza con definiciones básicas de terminología propia de e-learning. Continúa con la generación de una metodología que aplique la gestión de conocimiento para transformar cualquier curso presencial a esta plataforma. Definida la metodología, se aplicará para el diseño del curso específico de Coeficientes Inherentes de Reactividad. Finaliza con un estudio económico que dé viabilidad al proyecto y con la creación de un modelo económico que estime el precio para cualquier curso futuro. Abstract Nuclear power plants need highly specialized and trained personnel. Thus, nuclear power plant Specialized Training Sector requires the incorporation of the latest advances in training methods. A large array of face-to-face training courses exist and it has become necessary to transform said courses in order to apply them with the new information systems available. For this, multidisciplinary equipment is needed where the engineering workforce must identify educational objectives, competences and abilities, contents and quality control of the different courses. In this project, knowledge engineering techniques are employed as the methodological axis in order to transform a face-to-face training course into on-line training through the use of new information technologies. Nowadays, new information and communication technologies are in constant evolution. They have introduced themselves into our world, transforming our previous vision of them, leading to new opportunities. For this reason, the present Project seeks to unite the use of e-learning and the Business and Corporate world. The main objective is the design, in an e-learning platform, of a technical course that will train nuclear power plant control-room operators. The work carried out in this Project has been, in addition to the transformation of a face-to-face course into an online one, the obtainment of a methodology to employ in the future transformation of other courses. In order to achieve this mission, our interest must focus on the content as well as on the management of the various courses. Hence, the Project starts with basic definitions of e-learning terminology. Next, a methodology that applies knowledge management for the transformation of any face-to-face course into e-learning has been generated. Once this methodology is defined, it has been applied for the design process of the Inherent Coefficients of Reactivity course. Finally, an economic study has been developed in order to determine the viability of the Project and an economic model has been created to estimate the price of any given course

Atmospheric parameters, spectral indexes and their relation to CPV spectral performance

Air Mass and atmosphere components (basically aerosol (AOD) and precipitable water (PW)) define the absorption of the sunlight that arrive to Earth. Radiative models such as SMARTS or MODTRAN use these parameters to generate an equivalent spectrum. However, complex and expensive instruments (as AERONET network devices) are needed to obtain AOD and PW. On the other hand, the use of isotype cells is a convenient way to characterize spectrally a place for CPV considering that they provide the photocurrent of the different internal subcells individually. Crossing data from AERONET station and a Tri-band Spectroheliometer, a model that correlates Spectral Mismatch Ratios and atmospheric parameters is proposed. Considering the amount of stations of AERONET network, this model may be used to estimate the spectral influence on energy performance of CPV systems close to all the stations worldwide.

Comparative assessment of global irradiation from a satellite estimate model (CM SAF) and on-ground measurements (SIAR): a Spanish case study

An analysis and comparison of daily and yearly solar irradiation from the satellite CM SAF database and a set of 301 stations from the Spanish SIAR network is performed using data of 2010 and 2011. This analysis is completed with the comparison of the estimations of effective irradiation incident on three different tilted planes (fixed, two axis tracking, north-south hori- zontal axis) using irradiation from these two data sources. Finally, a new map of yearly values of irradiation both on the horizontal plane and on inclined planes is produced mixing both sources with geostatistical techniques (kriging with external drift, KED) The Mean Absolute Difference (MAD) between CM SAF and SIAR is approximately 4% for the irradiation on the horizontal plane and is comprised between 5% and 6% for the irradiation incident on the inclined planes. The MAD between KED and SIAR, and KED and CM SAF is approximately 3% for the irradiation on the horizontal plane and is comprised between 3% and 4% for the irradiation incident on the inclined planes. The methods have been implemented using free software, available as supplementary ma- terial, and the data sources are freely available without restrictions.

Comparative assessment of global irradiation from a satellite estimate model (CM SAF) and on-ground measurements (SIAR): a Spanish case study

An analysis and comparison of daily and yearly solar irradiation from the satellite CM SAF database and a set of 301 stations from the Spanish SIAR network is performed using data of 2010 and 2011. This analysis is completed with the comparison of the estimations of effective irradiation incident on three different tilted planes (fixed, two axis tracking, north-south hori- zontal axis) using irradiation from these two data sources. Finally, a new map of yearly values of irradiation both on the horizontal plane and on inclined planes is produced mixing both sources with geostatistical techniques (kriging with external drift, KED) The Mean Absolute Difference (MAD) between CM SAF and SIAR is approximately 4% for the irradiation on the horizontal plane and is comprised between 5% and 6% for the irradiation incident on the inclined planes. The MAD between KED and SIAR, and KED and CM SAF is approximately 3% for the irradiation on the horizontal plane and is comprised between 3% and 4% for the irradiation incident on the inclined planes. The methods have been implemented using free software, available as supplementary ma- terial, and the data sources are freely available without restrictions.

Estimate of the total ice volume of Svalbard glaciers and their potential contribution to sea-level rise = Estimación del volumen de hielo de Svalbard y su contribución potencial a la subida del nivel del mar

El objetivo final de las investigaciones recogidas en esta tesis doctoral es la estimación del volumen de hielo total de los ms de 1600 glaciares de Svalbard, en el Ártico, y, con ello, su contribución potencial a la subida del nivel medio del mar en un escenario de calentamiento global. Los cálculos más exactos del volumen de un glaciar se efectúan a partir de medidas del espesor de hielo obtenidas con georradar. Sin embargo, estas medidas no son viables para conjuntos grandes de glaciares, debido al coste, dificultades logísticas y tiempo requerido por ellas, especialmente en las regiones polares o de montaña. Frente a ello, la determinación de áreas de glaciares a partir de imágenes de satélite sí es viable a escalas global y regional, por lo que las relaciones de escala volumen-área constituyen el mecanismo más adecuado para las estimaciones de volúmenes globales y regionales, como las realizadas para Svalbard en esta tesis. Como parte del trabajo de tesis, hemos elaborado un inventario de los glaciares de Svalbard en los que se han efectuado radioecosondeos, y hemos realizado los cálculos del volumen de hielo de más de 80 cuencas glaciares de Svalbard a partir de datos de georradar. Estos volúmenes han sido utilizados para calibrar las relaciones volumen-área desarrolladas en la tesis. Los datos de georradar han sido obtenidos en diversas campañas llevadas a cabo por grupos de investigación internacionales, gran parte de ellas lideradas por el Grupo de Simulación Numérica en Ciencias e Ingeniería de la Universidad Politécnica de Madrid, del que forman parte la doctoranda y los directores de tesis. Además, se ha desarrollado una metodología para la estimación del error en el cálculo de volumen, que aporta una novedosa técnica de cálculo del error de interpolación para conjuntos de datos del tipo de los obtenidos con perfiles de georradar, que presentan distribuciones espaciales con unos patrones muy característicos pero con una densidad de datos muy irregular. Hemos obtenido en este trabajo de tesis relaciones de escala específicas para los glaciares de Svalbard, explorando la sensibilidad de los parámetros a diferentes morfologías glaciares, e incorporando nuevas variables. En particular, hemos efectuado experimentos orientados a verificar si las relaciones de escala obtenidas caracterizando los glaciares individuales por su tamaño, pendiente o forma implican diferencias significativas en el volumen total estimado para los glaciares de Svalbard, y si esta partición implica algún patrón significativo en los parámetros de las relaciones de escala. Nuestros resultados indican que, para un valor constante del factor multiplicativo de la relacin de escala, el exponente que afecta al área en la relación volumen-área decrece según aumentan la pendiente y el factor de forma, mientras que las clasificaciones basadas en tamaño no muestran un patrón significativo. Esto significa que los glaciares con mayores pendientes y de tipo circo son menos sensibles a los cambios de área. Además, los volúmenes de la población total de los glaciares de Svalbard calculados con fraccionamiento en grupos por tamaño y pendiente son un 1-4% menores que los obtenidas usando la totalidad de glaciares sin fraccionamiento en grupos, mientras que los volúmenes calculados fraccionando por forma son un 3-5% mayores. También realizamos experimentos multivariable para obtener estimaciones óptimas del volumen total mediante una combinación de distintos predictores. Nuestros resultados muestran que un modelo potencial simple volumen-área explica el 98.6% de la varianza. Sólo el predictor longitud del glaciar proporciona significación estadística cuando se usa además del área del glaciar, aunque el coeficiente de determinación disminuye en comparación con el modelo más simple V-A. El predictor intervalo de altitud no proporciona información adicional cuando se usa además del área del glaciar. Nuestras estimaciones del volumen de la totalidad de glaciares de Svalbard usando las diferentes relaciones de escala obtenidas en esta tesis oscilan entre 6890 y 8106 km3, con errores relativos del orden de 6.6-8.1%. El valor medio de nuestras estimaciones, que puede ser considerado como nuestra mejor estimación del volumen, es de 7.504 km3. En términos de equivalente en nivel del mar (SLE), nuestras estimaciones corresponden a una subida potencial del nivel del mar de 17-20 mm SLE, promediando 19_2 mm SLE, donde el error corresponde al error en volumen antes indicado. En comparación, las estimaciones usando las relaciones V-A de otros autores son de 13-26 mm SLE, promediando 20 _ 2 mm SLE, donde el error representa la desviación estándar de las distintas estimaciones. ABSTRACT The final aim of the research involved in this doctoral thesis is the estimation of the total ice volume of the more than 1600 glaciers of Svalbard, in the Arctic region, and thus their potential contribution to sea-level rise under a global warming scenario. The most accurate calculations of glacier volumes are those based on ice-thicknesses measured by groundpenetrating radar (GPR). However, such measurements are not viable for very large sets of glaciers, due to their cost, logistic difficulties and time requirements, especially in polar or mountain regions. On the contrary, the calculation of glacier areas from satellite images is perfectly viable at global and regional scales, so the volume-area scaling relationships are the most useful tool to determine glacier volumes at global and regional scales, as done for Svalbard in this PhD thesis. As part of the PhD work, we have compiled an inventory of the radio-echo sounded glaciers in Svalbard, and we have performed the volume calculations for more than 80 glacier basins in Svalbard from GPR data. These volumes have been used to calibrate the volume-area relationships derived in this dissertation. Such GPR data have been obtained during fieldwork campaigns carried out by international teams, often lead by the Group of Numerical Simulation in Science and Engineering of the Technical University of Madrid, to which the PhD candidate and her supervisors belong. Furthermore, we have developed a methodology to estimate the error in the volume calculation, which includes a novel technique to calculate the interpolation error for data sets of the type produced by GPR profiling, which show very characteristic data distribution patterns but with very irregular data density. We have derived in this dissertation scaling relationships specific for Svalbard glaciers, exploring the sensitivity of the scaling parameters to different glacier morphologies and adding new variables. In particular, we did experiments aimed to verify whether scaling relationships obtained through characterization of individual glacier shape, slope and size imply significant differences in the estimated volume of the total population of Svalbard glaciers, and whether this partitioning implies any noticeable pattern in the scaling relationship parameters. Our results indicate that, for a fixed value of the factor in the scaling relationship, the exponent of the area in the volume-area relationship decreases as slope and shape increase, whereas size-based classifications do not reveal any clear trend. This means that steep slopes and cirque-type glaciers are less sensitive to changes in glacier area. Moreover, the volumes of the total population of Svalbard glaciers calculated according to partitioning in subgroups by size and slope are smaller (by 1-4%) than that obtained considering all glaciers without partitioning into subgroups, whereas the volumes calculated according to partitioning in subgroups by shape are 3-5% larger. We also did multivariate experiments attempting to optimally predict the volume of Svalbard glaciers from a combination of different predictors. Our results show that a simple power-type V-A model explains 98.6% of the variance. Only the predictor glacier length provides statistical significance when used in addition to the predictor glacier area, though the coefficient of determination decreases as compared with the simpler V-A model. The predictor elevation range did not provide any additional information when used in addition to glacier area. Our estimates of the volume of the entire population of Svalbard glaciers using the different scaling relationships that we have derived along this thesis range within 6890-8106 km3, with estimated relative errors in total volume of the order of 6.6-8.1% The average value of all of our estimates, which could be used as a best estimate for the volume, is 7,504 km3. In terms of sea-level equivalent (SLE), our volume estimates correspond to a potential contribution to sea-level rise within 17-20 mm SLE, averaging 19 _ 2 mm SLE, where the quoted error corresponds to our estimated relative error in volume. For comparison, the estimates using the V-A scaling relations found in the literature range within 13-26 mm SLE, averaging 20 _ 2 mm SLE, where the quoted error represents the standard deviation of the different estimates.

Truncation error estimation in the Discontinuous Galerkin Spectral Element Method

En esta tesis, el método de estimación de error de truncación conocido como restimation ha sido extendido de esquemas de bajo orden a esquemas de alto orden. La mayoría de los trabajos en la bibliografía utilizan soluciones convergidas en mallas de distinto refinamiento para realizar la estimación. En este trabajo se utiliza una solución en una única malla con distintos órdenes polinómicos. Además, no se requiere que esta solución esté completamente convergida, resultando en el método conocido como quasi-a priori T-estimation. La aproximación quasi-a priori estima el error mientras el residuo del método iterativo no es despreciable. En este trabajo se demuestra que algunas de las hipótesis fundamentales sobre el comportamiento del error, establecidas para métodos de bajo orden, dejan de ser válidas en esquemas de alto orden, haciendo necesaria una revisión completa del comportamiento del error antes de redefinir el algoritmo. Para facilitar esta tarea, en una primera etapa se considera el método conocido como Chebyshev Collocation, limitando la aplicación a geometrías simples. La extensión al método Discontinuouos Galerkin Spectral Element Method presenta dificultades adicionales para la definición precisa y la estimación del error, debidos a la formulación débil, la discretización multidominio y la formulación discontinua. En primer lugar, el análisis se enfoca en leyes de conservación escalares para examinar la precisión de la estimación del error de truncación. Después, la validez del análisis se demuestra para las ecuaciones incompresibles y compresibles de Euler y Navier Stokes. El método de aproximación quasi-a priori r-estimation permite desacoplar las contribuciones superficiales y volumétricas del error de truncación, proveyendo información sobre la anisotropía de las soluciones así como su ratio de convergencia con el orden polinómico. Se demuestra que esta aproximación quasi-a priori produce estimaciones del error de truncación con precisión espectral. ABSTRACT In this thesis, the τ-estimation method to estimate the truncation error is extended from low order to spectral methods. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, only one grid with different polynomial orders is used in this work. Furthermore, a non timeconverged solution is used resulting in the quasi-a priori τ-estimation method. The quasi-a priori approach estimates the error when the residual of the time-iterative method is not negligible. It is shown in this work that some of the fundamental assumptions about error tendency, well established for low order methods, are no longer valid in high order schemes, making necessary a complete revision of the error behavior before redefining the algorithm. To facilitate this task, the Chebyshev Collocation Method is considered as a first step, limiting their application to simple geometries. The extension to the Discontinuous Galerkin Spectral Element Method introduces additional features to the accurate definition and estimation of the error due to the weak formulation, multidomain discretization and the discontinuous formulation. First, the analysis focuses on scalar conservation laws to examine the accuracy of the estimation of the truncation error. Then, the validity of the analysis is shown for the incompressible and compressible Euler and Navier Stokes equations. The developed quasi-a priori τ-estimation method permits one to decouple the interfacial and the interior contributions of the truncation error in the Discontinuous Galerkin Spectral Element Method, and provides information about the anisotropy of the solution, as well as its rate of convergence in polynomial order. It is demonstrated here that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

Design of a generalized tool for the performance assessment under sail based on analytical, numerical and empirical results : a global sailing yacht meta-model

La evaluación de las prestaciones de las embarcaciones a vela ha constituido un objetivo para ingenieros navales y marinos desde los principios de la historia de la navegación. El conocimiento acerca de estas prestaciones, ha crecido desde la identificación de los factores clave relacionados con ellas(eslora, estabilidad, desplazamiento y superficie vélica), a una comprensión más completa de las complejas fuerzas y acoplamientos involucrados en el equilibrio. Junto con este conocimiento, la aparición de los ordenadores ha hecho posible llevar a cabo estas tareas de una forma sistemática. Esto incluye el cálculo detallado de fuerzas, pero también, el uso de estas fuerzas junto con la descripción de una embarcación a vela para la predicción de su comportamiento y, finalmente, sus prestaciones. Esta investigación tiene como objetivo proporcionar una definición global y abierta de un conjunto de modelos y reglas para describir y analizar este comportamiento. Esto se lleva a cabo sin aplicar restricciones en cuanto al tipo de barco o cálculo, sino de una forma generalizada, de modo que sea posible resolver cualquier situación, tanto estacionaria como en el dominio del tiempo. Para ello se comienza con una definición básica de los factores que condicionan el comportamiento de una embarcación a vela. A continuación se proporciona una metodología para gestionar el uso de datos de diferentes orígenes para el cálculo de fuerzas, siempre con el la solución del problema como objetivo. Esta última parte se plasma en un programa de ordenador, PASim, cuyo propósito es evaluar las prestaciones de diferentes ti pos de embarcaciones a vela en un amplio rango de condiciones. Varios ejemplos presentan diferentes usos de PASim con el objetivo de ilustrar algunos de los aspectos discutidos a lo largo de la definición del problema y su solución . Finalmente, se presenta una estructura global de cara a proporcionar una representación virtual de la embarcación real, en la cual, no solo e l comportamiento sino también su manejo, son cercanos a la experiencia de los navegantes en el mundo real. Esta estructura global se propone como el núcleo (un motor de software) de un simulador físico para el que se proporciona una especificación básica. ABSTRACT The assessment of the performance of sailing yachts, and ships in general, has been an objective for naval architects and sailors since the beginning of the history of navigation. The knowledge has grown from identifying the key factors that influence performance(length, stability, displacement and sail area), to a much more complete understanding of the complex forces and couplings involved in the equilibrium. Along with this knowledge, the advent of computers has made it possible to perform the associated tasks in a systematic way. This includes the detailed calculation of forces, but also the use of those forces, along with the description of a sailing yacht, to predict its behavior, and ultimately, its performance. The aim of this investigation is to provide a global and open definition of a set of models and rules to describe and analyze the behavior of a sailing yacht. This is done without applying any restriction to the type of yacht or calculation, but rather in a generalized way, capable of solving any possible situation, whether it is in a steady state or in the time domain. First, the basic definition of the factors that condition the behavior of a sailing yacht is given. Then, a methodology is provided to assist with the use of data from different origins for the calculation of forces, always aiming towards the solution of the problem. This last part is implemented as a computational tool, PASim, intended to assess the performance of different types of sailing yachts in a wide range of conditions. Several examples then present different uses of PASim, as a way to illustrate some of the aspects discussed throughout the definition of the problem and its solution. Finally, a global structure is presented to provide a general virtual representation of the real yacht, in which not only the behavior, but also its handling is close to the experience of the sailors in the real world. This global structure is proposed as the core (a software engine) of a physical yacht simulator, for which a basic specification is provided.