Simulación numérica de un problema de contaminación atmosférica

La ecuación en derivadas parciales de advección difusión con reacción química es la base de los modelos de dispersión de contaminantes en la atmósfera, y los diferentes métodos numéricos empleados para su resolución han sido objeto de amplios estudios a lo largo de su desarrollo. En esta Tesis se presenta la implementación de un nuevo método conservativo para la resolución de la parte advectiva de la ecuación en derivadas parciales que modela la dispersión de contaminantes dentro del modelo mesoescalar de transporte químico CHIMERE. Este método está basado en una técnica de volúmenes finitos junto con una interpolación racional. La ventaja de este método es la conservación exacta de la masa transportada debido al empleo de la ley de conservación de masas. Para ello emplea una formulación de flujo basado en el cálculo de la integral ponderada dentro de cada celda definida para la discretización del espacio en el método de volúmenes finitos. Los resultados numéricos obtenidos en las simulaciones realizadas (implementando el modelo conservativo para la advección en el modelo CHIMERE) se han comparado con los datos observados de concentración de contaminantes registrados en la red de estaciones de seguimiento y medición distribuidas por la Península Ibérica. Los datos estadísticos de medición del error, la media normalizada y la media absoluta normalizada del error, presentan valores que están dentro de los rangos propuestos por la EPA para considerar el modelo preciso. Además, se introduce un nuevo método para resolver la parte advectivadifusiva de la ecuación en derivadas parciales que modeliza la dispersión de contaminantes en la atmósfera. Se ha empleado un método de diferencias finitas de alto orden para resolver la parte difusiva de la ecuación de transporte de contaminantes junto con el método racional conservativo para la parte advectiva en una y dos dimensiones. Los resultados obtenidos de la aplicación del método a diferentes situaciones incluyendo casos académicos y reales han sido comparados con la solución analítica de la ecuación de advección-difusión, demostrando que el nuevo método proporciona un resultado preciso para aproximar la solución. Por último, se ha desarrollado un modelo completo que contempla los fenómenos advectivo y difusivo con reacción química, usando los métodos anteriores junto con una técnica de diferenciación regresiva (BDF2). Esta técnica consiste en un método implícito multipaso de diferenciación regresiva de segundo orden, que nos permite resolver los problemas rígidos típicos de la química atmosférica, modelizados a través de sistemas de ecuaciones diferenciales ordinarias. Este método hace uso de la técnica iterativa Gauss- Seidel para obtener la solución de la parte implícita de la fórmula BDF2. El empleo de la técnica de Gauss-Seidel en lugar de otras técnicas comúnmente empleadas, como la iteración por el método de Newton, nos proporciona rapidez de cálculo y bajo consumo de memoria, ideal para obtener modelos operativos para la resolución de la cinética química atmosférica. ABSTRACT Extensive research has been performed to solve the atmospheric chemicaladvection- diffusion equation and different numerical methods have been proposed. This Thesis presents the implementation of an exactly conservative method for the advection equation in the European scale Eulerian chemistry transport model CHIMERE based on a rational interpolation and a finite volume algorithm. The advantage of the method is that the cell-integrated average is predicted via a flux formulation, thus the mass is exactly conserved. Numerical results are compared with a set of observation registered at some monitoring sites in Spain. The mean normalized bias and the mean normalized absolute error present values that are inside the range to consider an accurate model performance. In addition, it has been introduced a new method to solve the advectiondiffusion equation. It is based on a high-order accurate finite difference method to solve de diffusion equation together with a rational interpolation and a finite volume to solve the advection equation in one dimension and two dimensions. Numerical results obtained from solving several problems include academic and real atmospheric problems have been compared with the analytical solution of the advection-diffusion equation, showing that the new method give an efficient algorithm for solving such problems. Finally, a complete model has been developed to solve the atmospheric chemical-advection-diffusion equation, adding the conservative method for the advection equation, the high-order finite difference method for the diffusion equation and a second-order backward differentiation formula (BDF2) to solve the atmospheric chemical kinetics. The BDF2 is an implicit, second order multistep backward differentiation formula used to solve the stiff systems of ordinary differential equations (ODEs) from atmospheric chemistry. The Gauss-Seidel iteration is used for approximately solving the implicitly defined BDF solution, giving a faster tool than the more commonly used iterative modified Newton technique. This method implies low start-up costs and a low memory demand due to the use of Gauss-Seidel iteration.

Contributions to trajectory prediction theory and its application to arrival management for air traffic control

La gestión del tráfico aéreo (Air Traffic Management, ATM) está experimentando un cambio de paradigma hacia las denominadas operaciones basadas trayectoria. Bajo dicho paradigma se modifica el papel de los controladores de tráfico aéreo desde una operativa basada su intervención táctica continuada hacia una labor de supervisión a más largo plazo. Esto se apoya en la creciente confianza en las soluciones aportadas por las herramientas automatizadas de soporte a la decisión más modernas. Para dar soporte a este concepto, se precisa una importante inversión para el desarrollo, junto con la adquisición de nuevos equipos en tierra y embarcados, que permitan la sincronización precisa de la visión de la trayectoria, basada en el intercambio de información entre ambos actores. Durante los últimos 30 a 40 años las aerolíneas han generado uno de los menores retornos de la inversión de entre todas las industrias. Sin beneficios tangibles, la industria aérea tiene dificultades para atraer el capital requerido para su modernización, lo que retrasa la implantación de dichas mejoras. Esta tesis tiene como objetivo responder a la pregunta de si las capacidades actualmente instaladas en las aeronaves comerciales se pueden aplicar para lograr la sincronización de la trayectoria con el nivel de calidad requerido. Además, se analiza en ella si, conjuntamente con mejoras en las herramientas de predicción trayectorias instaladas en tierra en para facilitar la gestión de las arribadas, dichas capacidades permiten obtener los beneficios esperados en el marco de las operaciones basadas en trayectoria. Esto podría proporcionar un incentivo para futuras actualizaciones de la aviónica que podrían llevar a mejoras adicionales. El concepto operacional propuesto en esta tesis tiene como objetivo permitir que los aviones sean pilotados de una manera consistente con las técnicas actuales de vuelo optimizado. Se permite a las aeronaves que desciendan en el denominado “modo de ángulo de descenso gestionado” (path-managed mode), que es el preferido por la mayoría de las compañías aéreas, debido a que conlleva un reducido consumo de combustible. El problema de este modo es que en él no se controla de forma activa el tiempo de llegada al punto de interés. En nuestro concepto operacional, la incertidumbre temporal se gestiona en mediante de la medición del tiempo en puntos estratégicamente escogidos a lo largo de la trayectoria de la aeronave, y permitiendo la modificación por el control de tierra de la velocidad de la aeronave. Aunque la base del concepto es la gestión de las ordenes de velocidad que se proporcionan al piloto, para ser capaces de operar con los niveles de equipamiento típicos actualmente, dicho concepto también constituye un marco en el que la aviónica más avanzada (por ejemplo, que permita el control por el FMS del tiempo de llegada) puede integrarse de forma natural, una vez que esta tecnología este instalada. Además de gestionar la incertidumbre temporal a través de la medición en múltiples puntos, se intenta reducir dicha incertidumbre al mínimo mediante la mejora de las herramienta de predicción de la trayectoria en tierra. En esta tesis se presenta una novedosa descomposición del proceso de predicción de trayectorias en dos etapas. Dicha descomposición permite integrar adecuadamente los datos de la trayectoria de referencia calculada por el Flight Management System (FMS), disponibles usando Futuro Sistema de Navegación Aérea (FANS), en el sistema de predicción de trayectorias en tierra. FANS es un equipo presente en los aviones comerciales de fuselaje ancho actualmente en la producción, e incluso algunos aviones de fuselaje estrecho pueden tener instalada avionica FANS. Además de informar automáticamente de la posición de la aeronave, FANS permite proporcionar (parte de) la trayectoria de referencia en poder de los FMS, pero la explotación de esta capacidad para la mejora de la predicción de trayectorias no se ha estudiado en profundidad en el pasado. La predicción en dos etapas proporciona una solución adecuada al problema de sincronización de trayectorias aire-tierra dado que permite la sincronización de las dimensiones controladas por el sistema de guiado utilizando la información de la trayectoria de referencia proporcionada mediante FANS, y también facilita la mejora en la predicción de las dimensiones abiertas restantes usado un modelo del guiado que explota los modelos meteorológicos mejorados disponibles en tierra. Este proceso de predicción de la trayectoria de dos etapas se aplicó a una muestra de 438 vuelos reales que realizaron un descenso continuo (sin intervención del controlador) con destino Melbourne. Dichos vuelos son de aeronaves del modelo Boeing 737-800, si bien la metodología descrita es extrapolable a otros tipos de aeronave. El método propuesto de predicción de trayectorias permite una mejora en la desviación estándar del error de la estimación del tiempo de llegada al punto de interés, que es un 30% menor que la que obtiene el FMS. Dicha trayectoria prevista mejorada se puede utilizar para establecer la secuencia de arribadas y para la asignación de las franjas horarias para cada aterrizaje (slots). Sobre la base del slot asignado, se determina un perfil de velocidades que permita cumplir con dicho slot con un impacto mínimo en la eficiencia del vuelo. En la tesis se propone un nuevo algoritmo que determina las velocidades requeridas sin necesidad de un proceso iterativo de búsqueda sobre el sistema de predicción de trayectorias. El algoritmo se basa en una parametrización inteligente del proceso de predicción de la trayectoria, que permite relacionar el tiempo estimado de llegada con una función polinómica. Resolviendo dicho polinomio para el tiempo de llegada deseado, se obtiene de forma natural el perfil de velocidades optimo para cumplir con dicho tiempo de llegada sin comprometer la eficiencia. El diseño de los sistemas de gestión de arribadas propuesto en esta tesis aprovecha la aviónica y los sistemas de comunicación instalados de un modo mucho más eficiente, proporcionando valor añadido para la industria. Por tanto, la solución es compatible con la transición hacia los sistemas de aviónica avanzados que están desarrollándose actualmente. Los beneficios que se obtengan a lo largo de dicha transición son un incentivo para inversiones subsiguientes en la aviónica y en los sistemas de control de tráfico en tierra. ABSTRACT Air traffic management (ATM) is undergoing a paradigm shift towards trajectory based operations where the role of an air traffic controller evolves from that of continuous intervention towards supervision, as decision making is improved based on increased confidence in the solutions provided by advanced automation. To support this concept, significant investment for the development and acquisition of new equipment is required on the ground as well as in the air, to facilitate the high degree of trajectory synchronisation and information exchange required. Over the past 30-40 years the airline industry has generated one of the lowest returns on invested capital among all industries. Without tangible benefits realised, the airline industry may find it difficult to attract the required investment capital and delay acquiring equipment needed to realise the concept of trajectory based operations. In response to these challenges facing the modernisation of ATM, this thesis aims to answer the question whether existing aircraft capabilities can be applied to achieve sufficient trajectory synchronisation and improvements to ground-based trajectory prediction in support of the arrival management process, to realise some of the benefits envisioned under trajectory based operations, and to provide an incentive for further avionics upgrades. The proposed operational concept aims to permit aircraft to operate in a manner consistent with current optimal aircraft operating techniques. It allows aircraft to descend in the fuel efficient path managed mode as preferred by a majority of airlines, with arrival time not actively controlled by the airborne automation. The temporal uncertainty is managed through metering at strategically chosen points along the aircraft’s trajectory with primary use of speed advisories. While the focus is on speed advisories to support all aircraft and different levels of equipage, the concept also constitutes a framework in which advanced avionics as airborne time-of-arrival control can be integrated once this technology is widely available. In addition to managing temporal uncertainty through metering at multiple points, this temporal uncertainty is minimised by improving the supporting trajectory prediction capability. A novel two-stage trajectory prediction process is presented to adequately integrate aircraft trajectory data available through Future Air Navigation Systems (FANS) into the ground-based trajectory predictor. FANS is standard equipment on any wide-body aircraft in production today, and some single-aisle aircraft are easily capable of being fitted with FANS. In addition to automatic position reporting, FANS provides the ability to provide (part of) the reference trajectory held by the aircraft’s Flight Management System (FMS), but this capability has yet been widely overlooked. The two-stage process provides a ‘best of both world’s’ solution to the air-ground synchronisation problem by synchronising with the FMS reference trajectory those dimensions controlled by the guidance mode, and improving on the prediction of the remaining open dimensions by exploiting the high resolution meteorological forecast available to a ground-based system. The two-stage trajectory prediction process was applied to a sample of 438 FANS-equipped Boeing 737-800 flights into Melbourne conducting a continuous descent free from ATC intervention, and can be extrapolated to other types of aircraft. Trajectories predicted through the two-stage approach provided estimated time of arrivals with a 30% reduction in standard deviation of the error compared to estimated time of arrival calculated by the FMS. This improved predicted trajectory can subsequently be used to set the sequence and allocate landing slots. Based on the allocated landing slot, the proposed system calculates a speed schedule for the aircraft to meet this landing slot at minimal flight efficiency impact. A novel algorithm is presented that determines this speed schedule without requiring an iterative process in which multiple calls to a trajectory predictor need to be made. The algorithm is based on parameterisation of the trajectory prediction process, allowing the estimate time of arrival to be represented by a polynomial function of the speed schedule, providing an analytical solution to the speed schedule required to meet a set arrival time. The arrival management solution proposed in this thesis leverages the use of existing avionics and communications systems resulting in new value for industry for current investment. The solution therefore supports a transition concept from mixed equipage towards advanced avionics currently under development. Benefits realised under this transition may provide an incentive for ongoing investment in avionics.

Inverse kinematics of a humanoid robot with non-spherical hip: a hybrid algorithm approach

This paper describes an approach to solve the inverse kinematics problem of humanoid robots whose construction shows a small but non negligible offset at the hip which prevents any purely analytical solution to be developed. Knowing that a purely numerical solution is not feasible due to variable efficiency problems, the proposed one first neglects the offset presence in order to obtain an approximate “solution” by means of an analytical algorithm based on screw theory, and then uses it as the initial condition of a numerical refining procedure based on the Levenberg‐Marquardt algorithm. In this way, few iterations are needed for any specified attitude, making it possible to implement the algorithm for real‐time applications. As a way to show the algorithm’s implementation, one case of study is considered throughout the paper, represented by the SILO2 humanoid robot.

Simulación numérica computacional de fenómenos dinámicos

En este proyecto se trata la simulación numérica de un fenómeno dinámico, basado en el comportamiento de una onda transmitida a lo largo de una cuerda elástica de un instrumento musical, cuyos extremos se encuentran anclados. El fenómeno físico, se desarrolla utilizando una ecuación en derivadas parciales hiperbólicas con variables espacial y temporal, acompañada por unas condiciones de contorno tipo Dirichlet en los extremos y por más condiciones iniciales que dan comienzo al proceso. Posteriormente se han generado algoritmos para el método numérico empleado (Diferencias finitas centrales y progresivas) y la programación del problema aproximado con su consistencia, estabilidad y convergencia, obteniéndose unos resultados acordes con la solución analítica del problema matemático. La programación y salida de resultados se ha realizado con Visual Studio 8.0. y la programación de objetos con Visual Basic .Net In this project the topic is the numerical simulation of a dynamic phenomenon, based on the behavior of a transmitted wave along an elastic string of a musical instrument, whose ends are anchored. The physical phenomenon is developed using a hyperbolic partial differential equation with spatial and temporal variables, accompanied by a Dirichlet boundary conditions at the ends and more initial conditions that start the process. Subsequently generated algorithms for the numerical method used (central and forward finite differences) and the programming of the approximate problem with consistency, stability and convergence, yielding results in line with the analytical solution of the mathematical problem. Programming and output results has been made with Visual Studio 8.0. and object programming with Visual Basic. Net

La estabilidad del frente de excavación de un túnel en terrenos heterogéneos o con un criterio de rotura no-lineal

El frente de un túnel puede colapsar si la presión aplicada sobre el es inferior a un valor limite denominado presión “critica” o “de colapso”. En este trabajo se desarrolla y presenta un mecanismo de rotura rotacional generado punto a punto para el cálculo de la presión de colapso del frente de túneles excavados en terrenos estratificados o en materiales que siguen un criterio de rotura nolineal. La solución propuesta es una solución de contorno superior en el marco del Análisis Límite y supone una generalización del mecanismo de rotura mas reciente existente en la bibliografía. La presencia de un terreno estratificado o con un criterio de rotura no-lineal implica una variabilidad espacial de las propiedades resistentes. Debido a esto, se generaliza el mecanismo desarrollado por Mollon et al. (2011b) para suelos, de tal forma que se puedan considerar valores locales del ángulo de rozamiento y de la cohesión. Además, la estratificación del terreno permite una rotura parcial del frente, por lo que se implementa esta posibilidad en el mecanismo, siendo la primera solución que emplea un mecanismo de rotura que se ajusta a la estratigrafía del terreno. Por otro lado, la presencia de un material con un criterio de rotura no-lineal exige introducir en el modelo, como variable de estudio, el estado tensional en el frente, el cual se somete al mismo proceso de optimización que las variables geométricas del mecanismo. Se emplea un modelo numérico 3D para validar las predicciones del mecanismo de Análisis Limite, demostrando que proporciona, con un esfuerzo computacional significativamente reducido, buenas predicciones de la presión critica, del tipo de rotura (global o parcial) en terrenos estratificados y de la geometría de fallo. El mecanismo validado se utiliza para realizar diferentes estudios paramétricos sobre la influencia de la estratigrafía en la presión de colapso. Igualmente, se emplea para elaborar cuadros de diseño de la presión de colapso para túneles ejecutados con tuneladora en macizos rocosos de mala calidad y para analizar la influencia en la estabilidad del frente del método constructivo. Asimismo, se lleva a cabo un estudio de fiabilidad de la estabilidad del frente de un túnel excavado en un macizo rocoso altamente fracturado. A partir de el se analiza como afectan las diferentes hipótesis acerca de los tipos de distribución y de las estructuras de correlación a los resultados de fiabilidad. Se investiga también la sensibilidad de los índices de fiabilidad a los cambios en las variables aleatorias, identificando las mas relevantes para el diseño. Por ultimo, se lleva a cabo un estudio experimental mediante un modelo de laboratorio a escala reducida. El modelo representa medio túnel, lo cual permite registrar el movimiento del material mediante una técnica de correlación de imágenes fotográficas. El ensayo se realiza con una arena seca y se controla por deformaciones mediante un pistón que simula el frente. Los resultados obtenidos se comparan con las estimaciones de la solución de Análisis Límite, obteniéndose un ajuste razonable, de acuerdo a la literatura, tanto en la geometría de rotura como en la presión de colapso. A tunnel face may collapse if the applied support pressure is lower than a limit value called the ‘critical’ or ‘collapse’ pressure. In this work, an advanced rotational failure mechanism generated ‘‘point-by-point” is developed to compute the collapse pressure for tunnel faces in layered (or stratified) grounds or in materials that follow a non-linear failure criterion. The proposed solution is an upper bound solution in the framework of limit analysis which extends the most advanced face failure mechanism in the literature. The excavation of the tunnel in a layered ground or in materials with a non-linear failure criterion may lead to a spatial variability of the strength properties. Because of this, the rotational mechanism recently proposed by Mollon et al. (2011b) for Mohr-Coulomb soils is generalized so that it can consider local values of the friction angle and of the cohesion. For layered soils, the mechanism needs to be extended to consider the possibility for partial collapse. The proposed methodology is the first solution with a partial collapse mechanism that can fit to the stratification. Similarly, the use of a nonlinear failure criterion introduces the need to introduce new parameters in the optimization problem to consider the distribution of normal stresses along the failure surface. A 3D numerical model is employed to validate the predictions of the limit analysis mechanism, demonstrating that it provides, with a significantly reduced computational effort, good predictions of critical pressure, of the type of collapse (global or partial) in layered soils, and of its geometry. The mechanism is then employed to conduct parametric studies of the influence of several geometrical and mechanical parameters on face stability of tunnels in layered soils. Similarly, the methodology has been further employed to develop simple design charts that provide the face collapse pressure of tunnels driven by TBM in low quality rock masses and to study the influence of the construction method. Finally, a reliability analysis of the stability of a tunnel face driven in a highly fractured rock mass is performed. The objective is to analyze how different assumptions about distributions types and correlation structures affect the reliability results. In addition, the sensitivity of the reliability index to changes in the random variables is studied, identifying the most relevant variables for engineering design. Finally, an experimental study is carried out using a small-scale laboratory model. The problem is modeled in half, cutting through the tunnel axis vertically, so that displacements of soil particles can be recorded by a digital image correlation technique. The tests were performed with dry sand and displacements are controlled by a piston that supports the soil. The results of the model are compared with the predictions of the Limit Analysis mechanism. A reasonable agreement, according to literature, is obtained between the shapes of the failure surfaces and between the collapse pressures observed in the model tests and computed with the analytical solution.

Comparison of the seismic behaviour between three building tests, all based on a two storey model house

Integral Masonry System consisting of intersecting steel trusses alo ng each of the three dimensional directions of space on walls and slabs using any masonry material, had yet been backed up by the previous adobe test for seismic areas. This paper presents the comparison this last test and the adaptation of the IMS using h ollow brick. A prototype based on a two storey model house (6mx6mx6m) has being also built in two different scales in order to maximize the load and size of the shake table: the first one half size the whole building (3mx3mx3m) and the second, a quarter of the real size (3mx3mx6m). Both tests have suffered some mild to moderate damages while supporting the higher seismic action subjected by the shake table, without even fissuring the first test and with very few damages the second one. The thickness of the hollow brick wall and the diameter of the tree - dimensional truss reinforcement were scaled to the real size test in order to ascertain its great structural behaviour in relation to the previous structural model calculations. The aim of this study is to sum marize the results of the research collaboration between the ETSAM - UPM and the PUCP in whose laboratory these tests were carried out.

Limit load instabilities in structural elements

Este trabajo analiza distintas inestabilidades en estructuras formadas por distintos materiales. En particular, se capturan y se modelan las inestabilidades usando el método de Riks. Inicialmente, se analiza la bifurcación en depósitos cilíndricos formados por material anisótropo sometidos a carga axial y presión interna. El análisis de bifurcación y post-bifurcación asociados con cilindros de pared gruesa se formula para un material incompresible reforzado con dos fibras que son mecánicamente equivalentes y están dispuestas simétricamente. Consideramos dos casos en la naturaleza de la anisotropía: (i) Fibras refuerzo que tienen una influencia particular sobre la respuesta a cortante del material y (ii) Fibras refuerzo que influyen sólo si la fibra cambia de longitud con la deformación. Se analiza la propagación de las inestabilidades. En concreto, se diferencia en el abultamiento (bulging) entre la propagación axial y la propagación radial de la inestabilidad. Distintos modelos sufren una u otra propagación. Por último, distintas inestabilidades asociadas al mecanismo de ablandamiento del material (material softening) en contraposición al de endurecimiento (hardening) en una estructura (viga) de a: hormigón y b: hormigón reforzado son modeladas utilizando una metodología paralela a la desarrollada en el análisis de inestabilidades en tubos sometidos a presión interna. This present work deals with the instability of structures made of various materials. It captures and models different types of instabilities using numerical analysis. Firstly, we consider bifurcation for anisotropic cylindrical shells subject to axial loading and internal pressure. Analysis of bifurcation and post bifurcation of inflated hyperelastic thick-walled cylinder is formulated using a numerical procedure based on the modified Riks method for an incompressible material with two preferred directions which are mechanically equivalent and are symmetrically disposed. Secondly, bulging/necking motion in doubly fiber-reinforced incompressible nonlinearly elastic cylindrical shells is captured and we consider two cases for the nature of the anisotropy: (i) reinforcing models that have a particular influence on the shear response of the material and (ii) reinforcing models that depend only on the stretch in the fiber direction. The different instability motions are considered. Axial propagation of the bulging instability mode in thin-walled cylinders under inflation is analyzed. We present the analytical solution for this particular motion as well as for radial expansion during bulging evolution. For illustration, cylinders that are made of either isotropic incompressible non-linearly elastic materials or doubly fiber reinforced incompressible non-linearly elastic materials are considered. Finally, strain-softening constitutive models are considered to analyze two concrete structures: a reinforced concrete beam and an unreinforced notch beam. The bifurcation point is captured using the Riks method used previously to analyze bifurcation of a pressurized cylinder.

Stability of liquid bridges between an elliptical and a circular supporting disk

A numerical method has been developed to determine the stability limits for liquid bridges held between noncircular supporting disks and the application to a configuration with a circular and an elliptical disk subjected to axial acceleration has been made. The numerical method led to results very different from the available analytical solution which has been revisited and a better approximation has been obtained. It has been found that just retaining one more term in the asymptotic analysis the solution reproduces the real behavior of the configuration and the numerical results.

Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects

This paper presents an overview of depth averaged modelling of fast catastrophic landslides where coupling of solid skeleton and pore fluid (air and water) is important. The first goal is to show how Biot-Zienkiewicz models can be applied to develop depth integrated, coupled models. The second objective of the paper is to consider a link which can be established between rheological and constitutive models. Perzyna´s viscoplasticity can be considered a general framework within which rheological models such as Bingham and cohesive frictional fluids can be derived. Among the several alternative numerical models, we will focus here on SPH which has not been widely applied by engineers to model landslide propagation. We propose an improvement, based on combining Finite Difference meshes associated to SPH nodes to describe pore pressure evolution inside the landslide mass. We devote a Section to analyze the performance of the models, considering three sets of tests and examples which allows to assess the model performance and limitations: (i) Problems having an analytical solution, (ii) Small scale laboratory tests, and (iii) Real cases for which we have had access to reliable information

Uma formulação por média-variância multi-período para o erro de rastreamento em carteiras de investimento.

Neste trabalho, deriva-se uma política de escolha ótima baseada na análise de média-variância para o Erro de Rastreamento no cenário Multi-período - ERM -. Referindo-se ao ERM como a diferença entre o capital acumulado pela carteira escolhida e o acumulado pela carteira de um benchmark. Assim, foi aplicada a metodologia abordada por Li-Ng em [24] para a solução analítica, obtendo-se dessa maneira uma generalização do caso uniperíodo introduzido por Roll em [38]. Em seguida, selecionou-se um portfólio do mercado de ações brasileiro baseado no fator de orrelação, e adotou-se como benchmark o índice da bolsa de valores do estado de São Paulo IBOVESPA, além da taxa básica de juros SELIC como ativo de renda fixa. Dois casos foram abordados: carteira composta somente de ativos de risco, caso I, e carteira com um ativo sem risco indexado à SELIC - e ativos do caso I (caso II).

Estudo da remediação de um aquífero contaminado com sulfato e metais através de barreira reativa permeável orgânica.

Este trabalho teve como objetivo geral estudar a viabilidade técnica de utilizar bagaço de cana como meio reativo de barreiras reativas permeáveis (BRP) para remoção de sulfato e metais de águas subterrâneas contaminadas. O estudo baseou-se em investigação experimental, por meio de ensaios laboratoriais de coluna, e em modelagem matemática, para a qual utilizaram-se também alguns dados obtidos em um estudo de caso de uma unidade industrial contaminada com sulfato e metais. Neste local contaminado, as características hidrogeológicas e topográficas propiciam a utilização de uma barreira reativa permeável como técnica de remediação. Barreiras reativas permeáveis são uma alternativa para remediação de águas subterrâneas que vem progredindo rapidamente na última década, a partir de ensaios de bancada e coluna em laboratório para implementação em escala real em campo. Três colunas bióticas foram montadas utilizando bagaço de cana como meio reativo e um material de base poroso constituído de areia e cascalho para fornecer adequada condutividade hidráulica, com a proporção de 1:28 em massa seca. Também foi adicionado ao meio reativo um inóculo bacteriano composto por esterco bovino dissolvido. Uma quarta coluna, sem inóculo e contendo um agente biocida, compôs o experimento branco (abiótico). Uma solução sintética foi introduzida nas colunas simulando condições da água subterrânea do estudo de caso, com velocidade de Darcy em torno de 2,0x10-7 m/s composta por sulfato e metais (zinco e níquel) com concentrações de 6.000 mg/L e 15 mg/L, respectivamente. Os resultados das análises da fase líquida das colunas bióticas apresentaram: (i) média da taxa de remoção de sulfato durante todo o tempo do experimento de 49 mg/L/dia; (ii) as concentrações de Zn e Ni diminuíram de 15 mg/L para valores não detectáveis pela técnica analítica utilizada (< 0,01 mg/L); (iii) aumento do pH de 5.5-5.8 para valores entre 6,8-8,0; (iv) redução do valor do potencial de óxido redução (Eh) para valores de até -200mV. Não foram observadas reduções das concentrações de metais e sulfato na fase líquida da coluna abiótica e os valores de pH e Eh permaneceram dentro das faixas iniciais. Análises nas fases sólidas das colunas bióticas por MEV e EDS após o término do experimento identificaram a presença de Ni, Zn, S e Mn, indicando a precipitação desses metais em forma de sulfetos. Estes elementos não foram detectados na fase sólida da coluna abiótica. Assim, pôde-se inferir que toda a remoção de sulfato verificada nas colunas bióticas pode ser atribuída a redução bacteriana de sulfato. A partir das condições experimentais dos ensaios, foi realizada a modelagem e o dimensionamento da BRP. Para a estimativa da cinética de redução de sulfato, aplicou-se a solução analítica de Van Genuchten para transporte de contaminantes com degradação, obtendo-se uma taxa de decaimento de primeira ordem de 0,01 dia-1. A determinação da espessura e tempo de residência da barreira foi realizada considerando que a concentração de sulfato na saída da barreira fosse menor ou igual a 250 mg/L. O resultado do dimensionamento de uma BRP preenchida com bagaço de cana e areia nas proporções de 1:28 em massa seca resultaria em uma BRP de 7,1 m de espessura, com tempo de residência de 950 dias, no local de estudo de caso. Caso fosse utilizado o dobro da proporção de bagaço de cana e areia em massa seca (1:14), a implantação da BRP apresentar-se-ia viável, com espessura aproximada de 4 m. Através destes resultados, pôde ser comprovada a hipótese de que bagaço de cana como substrato e esterco bovino como inóculo compõem um meio reativo viável para a redução de sulfato e precipitação de metais em uma BRP.

Parameters of the Earths orbit for the last 5 Million years in 1 kyr resolution

New values for the astronomical parameters of the Earth's orbit and rotation (eccentricity, obliquity and precession) are proposed for paleoclimatic research related to the Late Miocene, the Pliocene and the Quaternary. They have been obtained from a numerical solution of the Lagrangian system of the planetary point masses and from an analytical solution of the Poisson equations of the Earth-Moon system. The analytical expansion developed in this paper allows the direct determination of the main frequencies with their phase and amplitude. Numerical and analytical comparisons with the former astronomical solution BER78 are performed so that the accuracy and the interval of time over which the new solution is valid can be estimated. The corresponding insolation values have also been computed and compared to the former ones. This analysis leads to the conclusion that the new values are expected to be reliable over the last 5 Ma in the time domain and at least over the last 10 Ma in the frequency domain.

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model. (C) 2004 Elsevier Inc. All rights reserved.

Response of coastal groundwater table to offshore storms

Large groundwater table fluctuations were observed in a coastal aquifer during an offshore storm. The storm induced significant changes of the mean shoreline elevation, characterized by a pulse-like oscillation. This pulse propagated in the aquifer, resulting in the water table fluctuations. A general analytical solution is derived to quantify this new mechanism of water table fluctuation. The solution is applied to field observations and is found to be able to predict reasonably well the observed storm-induced water table fluctuations. Based on the analytical solution, the damping characteristics and phase shift of the oscillation as it propagates inland are examined.

Swash overtopping and sediment overwash on a truncated beach

New experimental laboratory data are presented on swash overtopping and sediment overwash on a truncated beach, approximating the conditions at the crest of a beach berm or inter-tidal ridge-runnel. The experiments provide a measure of the uprush sediment transport rate in the swash zone that is unaffected by the difficulties inherent in deploying instrumentation or sediment trapping techniques at laboratory scale. Overtopping flow volumes are compared with an analytical solution for swash flows as well as a simple numerical model, both of which are restricted to individual swash events. The analytical solution underestimates the overtopping volume by an order of magnitude while the model provides good overall agreement with the data and the reason for this difference is discussed. Modelled flow velocities are input to simple sediment transport formulae appropriate to the swash zone in order to predict the overwash sediment transport rates. Calculations performed with traditional expressions for the wave friction factor tend to underestimate the measured transport. Additional sediment transport calculations using standard total load equations are used to derive an optimum constant wave friction factor of f(w)=0.024. This is in good agreement with a broad range of published field and laboratory data. However, the influence of long waves and irregular wave run-up on the overtopping and overwash remains to be assessed. The good agreement between modelled and measured sediment transport rates suggests that the model provides accurate predictions of the uprush sediment transport rates in the swash zone, which has application in predicting the growth and height of beach berms. (c) 2005 Elsevier B.V. All rights reserved.