An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

Caracterización dinámica del glaciar Hurd combinando observaciones de campo y simulaciones numéricas

El objetivo fundamental de esta tesis es la caracterización de la morfología y del estado de deformaciones y tensiones del Glaciar Hurd (Isla Livingston, Archipiélago de las Shetland del Sur, Antártida), mediante una combinación de observaciones de campo, registros de georradar y simulaciones numéricas. La morfología y el estado de deformaciones y tensiones actuales son la expresión de la evolución dinámica del glaciar desde tiempos pretéritos hasta recientes, y su análisis nos dará las pautas con las cuales ser capaces de predecir, con el apoyo de las simulaciones numéricas, su evolución futura. El primer aspecto que se aborda es el estudio de las estructuras que pueden observarse en la superficie del glaciar. Describimos las distintas técnicas utilizadas (medidas de campo, fotointerpretación de ortofotografías, análisis geoquímico de cenizas volcánicas, etc.) y presentamos el análisis e interpretación de los resultados morfo-estructurales, así como la correlación, mediante análisis geoquímicos (fluorescencia de rayos X), entre las cenizas volcánicas que extruyen en la superficie del Glaciar Hurd y las del volcán Decepción, origen de las cenizas. Esto nos permite realizar una datación de las mismas como Tefra 1, correspondiente a la erupción de 1970, Tefra 2, correspondiente a las erupciones pre-1829, y el conjunto Tefra 3, asociado a las erupciones más antiguas. En segundo lugar nos ocupamos de las estructuras presentes en el interior del glaciar, cuya herramienta de detección fundamental es el georradar. Identificadas estas estructuras internas, las vinculamos con las observadas en la superficie del glaciar. También hemos estudiado la estructura hidrotérmica del glaciar, obteniendo una serie de evidencias adicionales de su carácter politérmico. Entre éstas se contaban, hasta ahora, las basadas en el valor del parámetro de rigidez de la relación constitutiva del hielo determinada por ajuste de modelos dinámicos y observaciones realizados por Otero (2008) y las basadas en las velocidades de las ondas de radar en el hielo determinadas con el método de punto medio común por Navarro y otros (2009). Las evidencias adicionales que aportamos en esta tesis son: 1) la presencia de estructuras típicas de régimen compresivo en la zona terminal del glaciar y de cizalla en los márgenes del mismo, y 2) la presencia de un estrato superficial de hielo frío (por encima de otro templado) en la zona de ablación de los tres lóbulos del Glaciar Hurd –Sally Rocks, Argentina y Las Palmas–, que alcanzan espesores de 70, 50 y 40 m, respectivamente. Este estrato de hielo frío está probablemente congelado al lecho subglaciar en la zona terminal (Molina y otros, 2007; esta tesis). Por último, nos ocupamos de la simulación numérica de la dinámica glaciar. Presentamos el modelo físico-matemático utilizado, discutimos sus condiciones de contorno y cómo éstas se miden en los trabajos de campo, y describimos el procedimiento de resolución numérica del sistema de ecuaciones parciales del modelo. Presentamos los resultados para los campos de velocidades, deformaciones y tensiones, comparando estos resultados con las estructuras observadas. También incluimos el análisis de las elipses de deformación acumulativa, que proporcionan información sobre las estructuras a las que puede dar lugar la evolución del estado de deformaciones y tensiones a las que se ve sometido el hielo según avanza, lentamente, desde la cabecera hasta la zona terminal del glaciar, con tiempos de tránsito de hasta 1.250 años, recogiendo así la historia de deformaciones en el glaciar. Concluyendo, ponemos de manifiesto en esta tesis que las medidas de campo de las estructuras y niveles de cenizas, las medidas de georradar y las simulaciones numéricas de la dinámica glaciar, realizadas de forma combinada, permiten caracterizar el régimen actual de velocidades, deformaciones y tensiones del glaciar, entender su evolución en el pasado y predecir su evolución futura. ABSTRACT The main objective of this thesis is to characterize the morphology and the state of strains and stresses of Hurd Glacier (Livingston Island, South Shetland Islands archipelago, Antarctica) through a combination of field observations, ground-penetrating radar measurements and numerical simulations. The morphology and the current state of strain and stresses are the expression of the dynamic evolution of the glacier from the past to recent times, and their analysis gives us the guidelines to be able to predict, with the support of numerical simulations, its future evolution. The first subject addressed is the study of structures that can be observed on the glacier surface. We describe the different techniques used (field measurements, photointerpretation of orthophotos, geochemical analysis of volcanic ashes, etc.) and we present the analysis and interpretation of the morpho-structural results, as well as the correlation with geochemical analysis (XRF) between the volcanic ashes extruded to the surface of Hurd Glacier and those of Deception Island volcano, from which the ashes originate. This allows us dating the ashes as Tephra 1, corresponding to the 1970 eruption, Tephra 2, corresponding to the pre-1829 eruptions, and the Tephra 3 group, associated with older eruptions. Secondly we focus on the study of the structures present within the glacier, which are detected with the help of ground-penetrating radar. Once identified, we link these internal structures with those observed on the glacier surface. We also study the hydrothermal structure of the glacier, getting a series of additional evidences of its polythermal structure. Among the evidences available so far, we can mention those based on the value of the stiffness parameter of the constitutive relation of ice, determined by fitting dynamic models to observations, as done by Otero (2008), and those based on the velocity of propagation of the radar waves through the glacier ice, measured using the common midpoint method, as done by Navarro et al. (2009). The additional evidences that we provide in this thesis are: 1) the presence of structures typical of compressive regime in the terminal zone of the glacier, together with shear at its margins, and 2) the presence of a surface layer of cold ice (overlying a layer of temperate ice) in the ablation zone of the three lobes of Hurd Glacier –Sally Rocks, Argentina and Las Palmas–, reaching thicknesses of 70, 50 and 40 m, respectively. This cold layer is probably frozen to the subglacial bed in the terminal zone (Molina and others 2007; this thesis). Finally, we deal with the numerical simulation of glacier dynamics. We present the physical-mathematical model, discuss its boundary conditions and how they are measured in the field work, and describe the method of numerical solution of the model’s partial differential equations. We present the results for the velocity, strain and stress fields, comparing these results with the observed structures. We also include an analysis of the ellipses of cumulative deformation, which provide information about the structures that can result from the evolution of the strain and stress regime of the glacier ice as it moves slowly from the head to the snout of the glacier, with transit times of up to 1,250 years, so picking the history of deformation of the glacier. Summarizing, we show in this thesis that field measurements of structures and ash layers, ground-penetrating radar measurements and numerical simulations of glacier dynamics, performed in combination, allow us to characterize the current regime of velocities, strains and stresses of the glacier, to understand its past evolution and to predict its future evolution.

Uncertainty in ellipse fitting using a flatbed scanner: development and experimental verification

In the field of dimensional metrology, the use of optical measuring machines requires the handling of a large number of measurement points, or scanning points, taken from the image of the measurand. The presence of correlation between these measurement points has a significant influence on the uncertainty of the result. The aim of this work is the development of an estimation procedure for the uncertainty of measurement in a geometrically elliptical shape, taking into account the correlation between the scanning points. These points are obtained from an image produced using a commercial flat bed scanner. The characteristic parameters of the ellipse (coordinates of the center, semi-axes and the angle of the semi-major axis with regard to the horizontal) are determined using a least squares fit and orthogonal distance regression. The uncertainty is estimated using the information from the auto-correlation function of the residuals and is propagated through the fitting algorithm according to the rules described in Evaluation of Measurement Data—Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’—Extension to any number of output quantities. By introducing the concept of cut-off length, it can be observed how it is possible to take into account the presence of the correlation in the estimation of uncertainty in a very simple way while avoiding underestimation.

Surface fitting in geomorphology - examples for regular-shaped volcanic landforms

In nature, several types of landforms have simple shapes: as they evolve they tend to take on an ideal, simple geometric form such as a cone, an ellipsoid or a paraboloid. Volcanic landforms are possibly the best examples of this ?ideal? geometry, since they develop as regular surface features due to the point-like (circular) or fissure-like (linear) manifestation of volcanic activity. In this paper, we present a geomorphometric method of fitting the ?ideal? surface onto the real surface of regular-shaped volcanoes through a number of case studies (Mt. Mayon, Mt. Somma, Mt. Semeru, and Mt. Cameroon). Volcanoes with circular, as well as elliptical, symmetry are addressed. For the best surface fit, we use the minimization library MINUIT which is made freely available by the CERN (European Organization for Nuclear Research). This library enables us to handle all the available surface data (every point of the digital elevation model) in a one-step, half-automated way regardless of the size of the dataset, and to consider simultaneously all the relevant parameters of the selected problem, such as the position of the center of the edifice, apex height, and cone slope, thanks to the highly performing adopted procedure. Fitting the geometric surface, along with calculating the related error, demonstrates the twofold advantage of the method. Firstly, we can determine quantitatively to what extent a given volcanic landform is regular, i.e. how much it follows an expected regular shape. Deviations from the ideal shape due to degradation (e.g. sector collapse and normal erosion) can be used in erosion rate calculations. Secondly, if we have a degraded volcanic landform, whose geometry is not clear, this method of surface fitting reconstructs the original shape with the maximum precision. Obviously, in addition to volcanic landforms, this method is also capable of constraining the shapes of other regular surface features such as aeolian, glacial or periglacial landforms.

Assessment of diastolic chamber properties of the right ventricle by global fitting of pressure-volume data and conformational analysis of 3D + T echocardiographic sequences

Assessment of diastolic chamber properties of the right ventricle by global fitting of pressure-volume data and conformational analysis of 3D + T echocardiographic sequences

Parameter-based mechanism for unifying user interaction, applications and communication protocols

In the smart building control industry, creating a platform to integrate different communication protocols and ease the interaction between users and devices is becoming increasingly important. BATMP is a platform designed to achieve this goal. In this paper, the authors describe a novel mechanism for information exchange, which introduces a new concept, Parameter, and uses it as the common object among all the BATMP components: Gateway Manager, Technology Manager, Application Manager, Model Manager and Data Warehouse. Parameter is an object which represents a physical magnitude and contains the information about its presentation, available actions, access type, etc. Each component of BATMP has a copy of the parameters. In the Technology Manager, three drivers for different communication protocols, KNX, CoAP and Modbus, are implemented to convert devices into parameters. In the Gateway Manager, users can control the parameters directly or by defining a scenario. In the Application Manager, the applications can subscribe to parameters and decide the values of parameters by negotiating. Finally, a Negotiator is implemented in the Model Manager to notify other components about the changes taking place in any component. By applying this mechanism, BATMP ensures the simultaneous and concurrent communication among users, applications and devices.

A methodology proposal to obtain operational parameter forecasts and operational risk assessment in container terminals

Las terminales de contenedores son sistemas complejos en los que un elevado número de actores económicos interactúan para ofrecer servicios de alta calidad bajo una estricta planificación y objetivos económicos. Las conocidas como "terminales de nueva generación" están diseñadas para prestar servicio a los mega-buques, que requieren tasas de productividad que alcanzan los 300 movimientos/ hora. Estas terminales han de satisfacer altos estándares dado que la competitividad entre terminales es elevada. Asegurar la fiabilidad de las planificaciones del atraque es clave para atraer clientes, así como reducir al mínimo el tiempo que el buque permanece en el puerto. La planificación de las operaciones es más compleja que antaño, y las tolerancias para posibles errores, menores. En este contexto, las interrupciones operativas deben reducirse al mínimo. Las principales causas de dichas perturbaciones operacionales, y por lo tanto de incertidumbre, se identifican y caracterizan en esta investigación. Existen una serie de factores que al interactuar con la infraestructura y/o las operaciones desencadenan modos de fallo o parada operativa. Los primeros pueden derivar no solo en retrasos en el servicio sino que además puede tener efectos colaterales sobre la reputación de la terminal, o incluso gasto de tiempo de gestión, todo lo cual supone un impacto para la terminal. En el futuro inmediato, la monitorización de las variables operativas presenta gran potencial de cara a mejorar cualitativamente la gestión de las operaciones y los modelos de planificación de las terminales, cuyo nivel de automatización va en aumento. La combinación del criterio experto con instrumentos que proporcionen datos a corto y largo plazo es fundamental para el desarrollo de herramientas que ayuden en la toma de decisiones, ya que de este modo estarán adaptadas a las auténticas condiciones climáticas y operativas que existen en cada emplazamiento. Para el corto plazo se propone una metodología con la que obtener predicciones de parámetros operativos en terminales de contenedores. Adicionalmente se ha desarrollado un caso de estudio en el que se aplica el modelo propuesto para obtener predicciones de la productividad del buque. Este trabajo se ha basado íntegramente en datos proporcionados por una terminal semi-automatizada española. Por otro lado, se analiza cómo gestionar, evaluar y mitigar el efecto de las interrupciones operativas a largo plazo a través de la evaluación del riesgo, una forma interesante de evaluar el effecto que eventos inciertos pero probables pueden generar sobre la productividad a largo plazo de la terminal. Además se propone una definición de riesgo operativo junto con una discusión de los términos que representan con mayor fidelidad la naturaleza de las actividades y finalmente, se proporcionan directrices para gestionar los resultados obtenidos. Container terminals are complex systems where a large number of factors and stakeholders interact to provide high-quality services under rigid planning schedules and economic objectives. The socalled next generation terminals are conceived to serve the new mega-vessels, which are demanding productivity rates up to 300 moves/hour. These terminals need to satisfy high standards because competition among terminals is fierce. Ensuring reliability in berth scheduling is key to attract clients, as well as to reduce at a minimum the time that vessels stay the port. Because of the aforementioned, operations planning is becoming more complex, and the tolerances for errors are smaller. In this context, operational disturbances must be reduced at a minimum. The main sources of operational disruptions and thus, of uncertainty, are identified and characterized in this study. External drivers interact with the infrastructure and/or the activities resulting in failure or stoppage modes. The later may derive not only in operational delays but in collateral and reputation damage or loss of time (especially management times), all what implies an impact for the terminal. In the near future, the monitoring of operational variables has great potential to make a qualitative improvement in the operations management and planning models of terminals that use increasing levels of automation. The combination of expert criteria with instruments that provide short- and long-run data is fundamental for the development of tools to guide decision-making, since they will be adapted to the real climatic and operational conditions that exist on site. For the short-term a method to obtain operational parameter forecasts in container terminals. To this end, a case study is presented, in which forecasts of vessel performance are obtained. This research has been entirely been based on data gathered from a semi-automated container terminal from Spain. In the other hand it is analyzed how to manage, evaluate and mitigate disruptions in the long-term by means of the risk assessment, an interesting approach to evaluate the effect of uncertain but likely events on the long-term throughput of the terminal. In addition, a definition for operational risk evaluation in port facilities is proposed along with a discussion of the terms that better represent the nature of the activities involved and finally, guidelines to manage the results obtained are provided.

El láser: una contundente arma de guerra o un afilado bisturí

José Antonio Martín Pereda, vicerrector de Investigación de la Universidad Politécnica de Madrid en 1983, nos cuenta cómo en 1957 el norteamericano Townes y los soviéticos Basov y Prokorov desarrollaron, al mismo tiempo, el primer máser, apareciendo posteriormente el citado láser de rubí, compuesto por dos espejos enfrentados y formando una cavidad óptica, en cuyo centro hay una varilla de rubí, que es irradiada muy intensamente por una radiación externa. El resultado es la obtención de un haz de luz de una única longitud de onda; esto es, monocolor, absolutamente direccional y paraleló, que puede propagarse indefinidamente si no hay un medio que lo absorba. Al láser de rubí siguió el de helio-neón. Desde el principio una de las más claras aplicaciones del rayo láser fueron las comunicaciones ópticas y, posteriormente, la medicina.

Design Parameter Analysis of Point Absorber WEC via an Evolutionary-Algorithm-Based Dimensioning Tool

Wave energy conversion has an essential difference from other renewable energies since the dependence between the devices design and the energy resource is stronger. Dimensioning is therefore considered a key stage when a design project of Wave Energy Converters (WEC) is undertaken. Location, WEC concept, Power Take-Off (PTO) type, control strategy and hydrodynamic resonance considerations are some of the critical aspects to take into account to achieve a good performance. The paper proposes an automatic dimensioning methodology to be accomplished at the initial design project stages and the following elements are described to carry out the study: an optimization design algorithm, its objective functions and restrictions, a PTO model, as well as a procedure to evaluate the WEC energy production. After that, a parametric analysis is included considering different combinations of the key parameters previously introduced. A variety of study cases are analysed from the point of view of energy production for different design-parameters and all of them are compared with a reference case. Finally, a discussion is presented based on the results obtained, and some recommendations to face the WEC design stage are given.