Comparison of existing formulae for estimating the overtopping rate in harbour breakwaters

The research that is summarized in this article, resultant of diverse studies realized in the CEDEX, has for object a comparative analysis of methods of overtopping rates developed by different authors. For that, the summary was realized first and the analysis of the existing formulations to estimate the rate of overtopping on rubble mound and vertical breakwaters. Later, there was carried out the contrast of the above mentioned formulations by the results obtained in a serie of hydraulic model tests of the Hydraulic Research Laboratory (the Center of Studies of Ports and Coasts of the CEDEX, Madrid, Spain).

Comparison of Existing Formulae for Estimating the Overtopping Rate in Harbour Breakwaters

The purpose of the research work resulting from various studies undertaken in the CEDEX, as summarized in this article, is to make a comparative analysis of methods for calculating overtopping rates developed by different authors. To this effect, in the first place, existing formulae for estimating the overtopping rate on rubble mound and vertical breakwaters were summarised and analysed. Later, the above mentioned formulae were compared using the results obtained in a series of hydraulic model tests at the CEDEX (the Center of Studies of Ports and Coasts of the CEDEX, Madrid, Spain). A calculation method based on the neural network theory, developed in the European CLASH Project, was applied to a series of sloping breakwater tests in order to complete this research. The results obtained in the Ferrol, Ciervana and Alicante breakwaters tests are presented here.

Mathematical model for manoeuvrability of a riverine support patrol vessel with a pump-jet propulsion system

A study on the manoeuvrability of a riverine support patrol vessel is made to derive a mathematical model and simulate maneuvers with this ship. The vessel is mainly characterized by both its wide-beam and the unconventional propulsion system, that is, a pump-jet type azimuthal propulsion. By processing experimental data and the ship characteristics with diverse formulae to find the proper hydrodynamic coefficients and propulsion forces, a system of three differential equations is completed and tuned to carry out simulations of the turning test. The simulation is able to accept variable speed, jet angle and water depth as input parameters and its output consists of time series of the state variables and a plot of the simulated path and heading of the ship during the maneuver. Thanks to the data of full-scale trials previously performed with the studied vessel, a process of validation was made, which shows a good fit between simulated and full-scale experimental results, especially on the turning diameter

Systematic Analysis of Direct-Drive Baseline Designs for Shock-Ignition with the Laser Megajoule

Direct-drive inertial confinement thermonuclear fusion consists in illuminating a shell of cryogenic Deuterium and Tritium (DT) mixture with many intense beams of laser light. Capsule is composed of DT gassurrounded by cryogenic DT as combustible fuel. Basic rules are used to define shell geometry from aspect ratio, fuel mass and layers densities. We define baseline designs using two aspect ratio (A=3 and A=5) who complete HiPER baseline design (A=7.7). Aspect ratio is defined as the ratio of ice DT shell inner radius over DT shell thickness. Low aspect ratio improves hydrodynamics stabilities of imploding shell. Laser impulsion shape and ablator thickness are initially defined by using Lindl (1995) pressure ablation and mass ablation formulae for direct-drive using CH layer as ablator. In flight adiabat parameter is close to one during implosion. Velocitie simplosions chosen are between 260 km/s and 365 km/s. More than thousand calculations are realized for each aspect ratio in order to optimize the laser pulse shape. Calculations are performed using the one-dimensional version of the Lagrangian radiation hydrodynamics FCI2. We choose implosion velocities for each initial aspect ratio, and we compute scaled-target family curves for each one to find self-ignition threshold. Then, we pick points on each curves that potentially product high thermonuclear gain and compute shock ignition in the context of Laser MegaJoule. This systematic analyze reveals many working points which complete previous studies ´allowing to highlight baseline designs, according to laser intensity and energy, combustible mass and initial aspect ratio to be relevant for Laser MegaJoule.

Novel application for exergy and thermoeconomic analysis of processes simulated with Aspen Plus

A visual basic application for Microsoft® Excel 2007 has been developed as a helpful tool to perform mass, energy, exergy and thermoeconomic (MHBT) calculations during the systematic analysis of energy processes simulated with Aspen Plus®. The application reads an Excel workbook containing three sheets with the matter, work and heat streams results of an Aspen Plus® simulation. The required information from the Aspen Plus® simulation and the algorithm/calculations of the application are described and applied to an Air Separation Unit (ASU). This application helps the designer when MHBT analyses are performed, as it increases the knowledge of the process simulated with Aspen Plus®. It’s a valuable tool not only because of the calculations performed, but also because it creates a new Excel workbook where the results and the formulae written on the cells are fully visible and editable. There is free access to the application and it has no protection allowing changes and improvements to be done.

La luz natural como generadora del espacio arquitectónico de la catedral gótica

La historia de la construcción de las catedrales góticas es la historia de la búsqueda de la luz. Esta afirmación casi metafísica, recoge una realidad asumida por todos los historiadores tanto de la arquitectura antigua como del resto de las artes. La luz en el gótico ha sido descrita bajo múltiples matices como son su carácter simbólico, cromático e incluso místico, sin embargo no existe, en el estudio del conocimiento de la luz gótica, ninguna referencia a la misma como realidad física cuantificable, cualificable y por tanto, clasificable. La presente tesis doctoral aborda el concepto de la iluminación gótica desde una perspectiva nueva. Demuestra, con un método analítico inédito, que la iluminación gótica es cuantificable y cualificable. Para ello analiza en profundidad la iluminación de una selección de 6 edificios muestra, las catedrales de Gerona, Toledo, Sevilla y León, la basílica de Santa María del Mar y la capilla de la Sainte Chapelle de París, mediante una toma de datos “in situ” de iluminación y su comparación con los datos lumínicos obtenidos por un programa de soleamiento de la simulación en tres dimensiones de los distintos proyectos originales góticos. El análisis exhaustivo de las muestras y su introducción en el método analítico descrito, permite determinar, en primer lugar, unas cualidades inéditas que identifican la luz de los espacios góticos según unos parámetros nuevos como son la intensidad, expresividad, recorrido, distorsión y color. También describe cuales son los factores determinantes, de nuevo inéditos, que modulan cada una de las cualidades y en que proporción lo hacen cada uno de ellos. Una vez establecidas las cualidades y los factores que las definen, la tesis doctoral establece los rangos en los que se mueven las distintas cualidades y que conformarán la definitiva clasificación según “tipos de cualidad lumínica”. Adicionalmente, la tesis propone un procedimiento abreviado de acercamiento a la realidad de la iluminación gótica a través de unas fórmulas matemáticas que relacionan los factores geométricos detectados y descritos en la tesis con el resultado luminoso del espacio en lo que concierne a las dos cualidades más importantes de las reflejadas, la intensidad y la expresividad. Gracias a este método y su procedimiento abreviado, la clasificación se hace extensible al resto de catedrales góticas del panorama español y europeo y abre el camino a nuevas clasificaciones de edificios históricos de distintas épocas, iniciando un apasionante camino por recorrer en la recuperación de “la luz original”. Esta clasificación y sus cualidades podrán a su vez, ser utilizadas como herramientas de conocimiento de un factor determinante a la hora de describir cualquier espacio gótico y su aportación pretende ser un nuevo condicionante a tener en cuenta en el futuro, ayudando a entender y respetar, en las posibles intervenciones a realizar sobre el patrimonio arquitectónico, aquello que fue en su inicio motor principal del proyecto arquitectónico y que hoy día no se valora suficientemente tan solo por falta de conocimiento: su luz. The history of the construction of the Gothic cathedrals is the history of the search for light. This almost etaphysical statement reflects a reality accepted by all historians both of ancient architecture and other arts. Light in the Gothic period has been described under multiple approaches such as its symbolic, chromatic and even mystical character. However, in the study of the Gothic light, no references exist to it as a physical quantifiable and qualifiable reality and therefore, classifiable. This dissertation deals with the concept of Gothic light from a new perspective. With a new analytical method, it shows that Gothic lighting is quantifiable and can be classified regarding quality. To this end, a selection of 6 buildings light samples are analyzed; the cathedrals of Gerona, Toledo, Seville and León, the basilica of Santa María of the Sea and the Sainte Chapelle in Paris. "In situ" lighting data is collected and it is compared with lighting data obtained by a program of sunlight of the 3D simulation of various Gothic original projects. The comprehensive analysis of the samples and the data introduced in the analytical method described, allows determining, first, important qualities that identify the light of Gothic spaces according to new parameters such as intensity, expressiveness, trajectory, distortion and color. It also describes the determinant factors, which modulate each of the qualities and in what proportion they do it. Once the qualities and factors that define them have been established, in this doctoral dissertation the ranges regarding different qualities are set, which will make up the final classification according to "types of light quality". In addition, this work proposes an abbreviated procedure approach to the reality of the Gothic lighting through some mathematical formulae, relating the geometric factors identified and described in the study with the bright result of space regarding the two most important qualities of the light,intensity and expressiveness. Thanks to this method and to the abbreviated procedure, the classification can be applied to other Spanish and European Gothic cathedrals and opens up the way to new classifications of historic buildings from different eras, starting an exciting road ahead in the recovery of the "original light". This classification and its qualities may in turn be used as tools to know a determinant factor when describing any Gothic space. Its contribution is intended to be a new conditioning factor to keep in mind in the future, helping to understand and respect, in possible interventions on the architectural heritage, what was the main engine to start the architectural project and which today is not valued enough due to the lack knowledge: the light.

Después de Einstein: una arquitectura para una teoría

En 1905, aparecen en la revista "Annalen der physik" tres artículos que revolucionarán las ciencias físicas y pondrán en jaque los asentados conceptos newtonianos de Espacio y Tiempo. La formulación de la Teoría de la Relatividad por Albert Einstein pone en crisis el valor absoluto de estos conceptos, y permite proponer nuevas reflexiones a propósito de su concepción dentro del campo de la física. Esta revolución ¿podría extrapolarse al campo de la arquitectura, donde Espacio y Tiempo tienen un papel protagonista? Hay que entender la complejidad del hecho arquitectónico y las innumerables variables que participan de su definición. Se estudia en esta Tesis Doctoral un aspecto muy concreto: cómo un paradigma (la Teoría de la Relatividad) puede intervenir y modificar, o no, la Arquitectura. Se plantea para ello ir al origen; desentrañar el momento de interacción entre la Teoría de la Relatividad y la Teoría de la Arquitectura, que permita determinar si aquella influyó sobre ésta en los escritos teóricos de las vanguardias aplicados a la Arquitectura. “Después de Einstein. Una arquitectura para una teoría” buscará los puntos de conexión de la Teoría de la Relatividad con la teoría arquitectónica de las vanguardias de principio del siglo XX, su influencia, la contaminación entre una y otra, con posibles resultados arquitectónicos a partir de esta interacción, capaz de definir nuevos argumentos formales para un nuevo lenguaje enArquitectura. Annalen der physik Después de Einstein. Una arquitectura para una teoría Para ello la Tesis se estructura en cuatro capítulos. El primero expone el ámbito geográfico y cronológico donde se desarrolla la Teoría de la Relatividad con la repercusión teórica que tiene para el arte, en función de una nueva definición de espacio vinculado al tiempo, como evento que se desarrolla en un ámbito cuatridimensional; la indeterminación de las medidas de espacio y de las medidas de tiempo, y la importancia de entender la materia como energía. El segundo capítulo estudia los movimientos de vanguardia coetáneos a la eclosión de la Relatividad, enmarcados en su ámbito geográfico más próximo. El cubismo se muestra como movimiento que participa ocasionalmente de las matemáticas y la geometría, bajo el influjo del científico Henri Poincaré y las geometrías no euclidianas. El futurismo indaga en los avances de la ciencia desde una cierta lejanía, cierta falta de rigor o profundidad científica para extraer las leyes de su nuevo idealismo plástico constructivo, definiendo e interpretando su Universo a partir de los avances de la ciencia, en respuesta a la crisis del espacio y del tiempo newtonianos. El lenguaje científico se encuentra presente en conceptos como "simultaneidad" (Boccioni), "expansión esférica de la luz en el espacio" (Severini y Carrá), "cuatridimensionalidad", "espacio-tiempo", "aire-luz-fuerza", "materia y energía" que paralelamente conforman el cuerpo operacional de la teoría de Einstein. Si bien no es posible atribuir a la Teoría de la Relatividad un papel protagonista como referente para el pensamiento artístico, en 1936, con la aparición del manifiesto Dimensionista, se atribuyen explícitamente a las teorías de Einstein las nuevas ideas de espacio-tiempo del espíritu europeo seguido por cubistas y futuristas. El tercer capítulo describe cómo la Teoría de la Relatividad llegó a ser fuente de inspiración para la Teoría de la Arquitectura. Estructurado en tres subcapítulos, se estudia el autor principal que aportó para la Arquitectura conceptos e ideas extrapoladas de la Teoría de la Relatividad después de su estudio e interpretación (Van Doesburg), dónde se produjeron las influencias y puntos de contacto (Lissitzky, Eggeling, Moholy-Nagy) y cómo fueron difundidas a través de la arquitectura (Einsteinturm de Mendelsohn) y de las revistas especializadas. El cuarto capítulo extrae las conclusiones del estudio realizado en esta Tesis, que bien pudiera resumir MoholyNagy en su texto "Vision inmotion" (1946) al comentar: "Ya que el "espacio-tiempo" puede ser un término engañoso, tiene que hacerse especialmente hincapié en que los problemas de espacio-tiempo en el arte no están necesariamente basados en la Teoría de la Relatividad de Einstein. Esto no tiene intención de descartar la relevancia de su teoría para las artes. Pero los artistas y los laicos rara vez tienen el conocimiento matemático para visualizar en fórmulas científicas las analogías con su propio trabajo. La terminología de Einstein del "espacio-tiempo" y la "relatividad" ha sido absorbida por nuestro lenguaje diario." ABSTRACT. "AFTER EINSTEIN:ANARCHITECTUREFORATHEORY." In 1905, three articles were published in the journal "Annalen der Physik ". They revolutionized physical sciences and threw into crisis the newtonian concepts of Space and Time. The formulation of the Theory of Relativity by Albert Einstein put a strain on the absolute value of these concepts, and proposed new reflections about them in the field of Physics. Could this revolution be extrapolated to the field of Architecture, where Space and Time have a main role? It is necessary to understand the complexity of architecture and the countless variables involved in its definition. For this reason, in this PhD. Thesis, we study a specific aspect: how a paradigm (Theory of Relativity) can intervene and modify -or not- Architecture. It is proposed to go back to the origin; to unravel the moment in which the interaction between the Theory of Relativity and the Theory of Architecture takes place, to determine whether the Theory of Relativity influenced on the theoretical avant-garde writings applied to Architecture. "After Einstein.An architecture for a theory " will search the connection points between the Theory of Relativity and architectural avant-garde theory of the early twentieth century, the influence and contamination between them, giving rise to new architectures that define new formal arguments for a new architectural language. Annalen der Physik This thesis is divided into four chapters. The first one describes the geographical and chronological scope in which the Theory of Relativity is developed showing its theoretical implications in the field of art, according to a new definition of Space linked to Time, as an event that takes place in a fourdimensional space; the indetermination of the measurement of space and time, and the importance of understanding "matter" as "energy". The second chapter examines the avant-garde movements contemporary to the theory of relativity. Cubism is shown as an artist movement that occasionally participates in mathematics and geometry, under the influence of Henri Poincaré and non-Euclidean geometries. Futurism explores the advances of science at a certain distance, with lack of scientific rigor to extract the laws of their new plastic constructive idealism. Scientific language is present in concepts like "simultaneity" (Boccioni), "expanding light in space" (Severini and Carra), "four-dimensional space", "space-time", "light-air-force," "matter and energy" similar to the operational concepts of Einstein´s theory. While it is not possible to attribute a leading role to the Theory of Relativity, as a benchmark for artistic laws, in 1936, with the publication of the Dimensionist manifest, the new ideas of space-time followed by cubist and futurist were attributed to the Einstein's theory. The third chapter describes how the Theory of Relativity became an inspiration for the architectural theory. Structured into three subsections, we study the main author who studied the theory of relativity and ,as a consequence, contributed with some concepts and ideas to the theory of architecture (Van Doesburg), where influences and contact points took place (Lissitzky, Eggeling, Moholy-Nagy) and how were disseminated throughArchitecture (Einsteinturm, by Mendelsohn) and journals. The fourth chapter draws the conclusions of this PhD. Thesis, which could be well summarized by Moholy Nagy in his text "Vision in Motion" (1946): vi Since "space-time" can be a misleading term, it especially has to be emphasized that the space-time problems in the arts are not necessarily based upon Einstein´s Theory of Relativity. This is not meant to discount the relevance of his theory to the arts. But artists and laymen seldom have the mathematical knowledge to visualize in scientific formulae the analogies to their own work. Einstein's terminology of "space-time" and "relativity" has been absorbed by our daily language.

Propagation mechanism modelling in the near region of circular tunnels

Artículo sobre comunicaciones ferroviarias. Abstract: Along with the increase in operating frequencies in advanced radio communication systems utilised inside tunnels, the location of the break point is further and further away from the transmitter. This means that the near region lengthens considerably and even occupies the whole propagation cell or the entire length of some short tunnels. To begin with, this study analyses the propagation loss resulting from the free-space mechanism and the multi-mode waveguide mechanism in the near region of circular tunnels, respectively. Then, by conjunctive employing the propagation theory and the three-dimensional solid geometry, a general analytical model of the dividing point between two propagation mechanisms is presented for the first time. Moreover, the model is validated by a wide range of measurement campaigns in different tunnels at different frequencies. Finally, discussions on the simplified formulae of the dividing point in some application situations are made. The results in this study can be helpful to grasp the essence of the propagation mechanism inside tunnels.

Contraste de las formulaciones existentes para la estimación de la tasa de rebase en diques de abrigo portuario

La investigación que se resume en este artículo, resultante de diversos trabajos realizados en el CEDEX [10, 12], tiene por objeto contrastar las formulaciones desarrolladas por diferentes autores en materia de rebases en distintas tipologías de diques de abrigo. Para ello, se realizó en primer lugar la recopilación y el análisis de las formulaciones existentes para estimar la tasa de rebase sobre diques en talud y verticales. Posteriormente, se llevó a cabo el contraste de dichas formulaciones con los resultados obtenidos en dos ensayos realizados en el Centro de Estudios de Puertos y Costas del CEDEX, en Cabo Prioriño, Ferrol y en la alineación tercera de Melilla. The research that is summarized in this article, resultant of several studies carried out in the CEDEX [10, 12], is focused in the existing methods to estimate overtopping rates developed by different authors. For that, the summary was carry out firstly we collected and analyzed the existing formulae, particularly for rubble mound and vertical breakwaters. These formulations was compared with the results obtained in two hydraulic model tests of the Hydraulic Research Laboratory (the Center of Studies of Ports and Coasts of the CEDEX, Madrid, Spain). Keywords: overtopping rates, rubble mound breakwater, vertical breakwater, crown wall, run-up.

Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation

It is well known that the evaluation of the influence matrices in the boundary-element method requires the computation of singular integrals. Quadrature formulae exist which are especially tailored to the specific nature of the singularity, i.e. log(*- x0)9 Ijx- JC0), etc. Clearly the nodes and weights of these formulae vary with the location Xo of the singular point. A drawback of this approach is that a given problem usually includes different types of singularities, and therefore a general-purpose code would have to include many alternative formulae to cater for all possible cases. Recently, several authors1"3 have suggested a type independent alternative technique based on the combination of standard Gaussian rules with non-linear co-ordinate transformations. The transformation approach is particularly appealing in connection with the p.adaptive version, where the location of the collocation points varies at each step of the refinement process. The purpose of this paper is to analyse the technique in eference 3. We show that this technique is asymptotically correct as the number of Gauss points increases. However, the method possesses a 'hidden' source of error that is analysed and can easily be removed.

A bi-cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods

The numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM). Thus, a new procedure, based upon a bi-cubic co-ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed. Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and-attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes. Some illustrative examples which assess the stability and accuracy of the new formulae are included.

Absorption coefficient for the intraband transitions in quantum dot materials

In this paper, we present calculations of the absorption coefficient for transitions between the bound states of quantum dots grown within a semiconductor and the extended states of the conduction band. For completeness, transitions among bound states are also presented. In the separation of variables, single band k·p model is used in which most elements may be expressed analytically. The analytical formulae are collected in the appendix of this paper. It is concluded that the transitions are strong enough to provide a quick path to the conduction band for electrons pumped from the valence to the intermediate band

Caracterización de los sistemas de protección basados en materiales naturales destinados al control de la socavación en obras marítimas presentes en instalaciones eólicas marinas

El fenómeno de la socavación puede poner en peligro la operatividad o la seguridad de estructuras offshore comprometiendo su estabilidad global. Hasta el momento, la gran mayoría de las investigaciones destinadas a estudiar el origen y el desarrollo de este fenómeno han estado centradas en entornos fluviales, bajo condiciones de corriente continua. En la última década, debido al crecimiento del mercado de la eólica marina, han surgido numerosos estudios para la caracterización de este fenómeno en el entorno marino, teniendo en cuenta que estas estructuras se encuentran sometidas de forma simultánea a los efectos de la corriente y el oleaje, y las corrientes provocadas por las mareas. Ante la observada carencia de criterios existentes para el diseño de protecciones frente a la socavación, la presente Tesis Doctoral surge con el objetivo principal de desarrollar una serie de recomendaciones que permitan mejorar y optimizar el diseño de estas estructuras, teniendo en cuenta no sólo los parámetros geométricos de las cimentaciones de los aerogeneradores, o la propia erosión, sino también, variables características del oleaje como la altura de ola, el periodo o la longitud de onda, así como la profundidad o la batimétrica de la cimentación. La caracterización de los sistemas de protección basados en materiales naturales destinados al control de la socavación en obras marítimas presentes en instalaciones eólicas marinas no es el único objetivo alcanzado en la presente Tesis Doctoral. A través de la calibración del parámetro de altura de ola adimensional (H0) en diferentes parques eólicos europeos, y de acuerdo al criterio propuesto por Van der Meer (1988), se propone la clasificación de este tipo de estructuras de protección, basadas en material granular o escollera. La información recopilada sobre la socavación registrada en numerosos parques eólicos con protección también ha permitido estudiar la funcionalidad de este tipo de protecciones instaladas hasta la fecha. Asímismo, gracias al conocimiento adquirido sobre el fenómeno de la socavación, se plantea una propuesta para la mejora de la caracterización de este fenómeno en ambiente marino basada en el estudio de la influencia del campo de aceleraciones. La presente Tesis Doctoral permite mejorar el diseño de las protecciones frente a la socavación que se utilizan en parques eólicos marinos teniendo en cuenta las acciones del clima marítimo, supliendo de este modo las carencias que hasta el momento presentan las formulaciones existentes, las cuales únicamente toman en consideración la geometría de las cimentaciones, el ángulo de rozamiento interno del terreno y la estimación de la máxima socavación que puede llegar a producirse. Scour phenomenon jeopardizes the stability and functionality of offshore structures compromising its overall stability. So far, most studies about the origin and the development of this phenomenon have been focused on river environments (under steady current conditions). In the last decade a lot of research projects about the characterization of this phenomenon have been carried out due to the growth of offshore wind industry. These projects take into account that these structures are subjected simultaneously to current, waves and tidal effects. This PhD Thesis arises due to the current lack of criteria for the design of scour protections. Its main objective is to develop some recommendations to improve and to optimize the design of scour protection structures. For that it is necessary to take into account not only the geometrical parameters of foundations or the erosion forecasted, but also wave variables such as wave height, wave period or wavelength. Characterization of protection systems based on natural materials for the control of the scour in offshore wind farms was not the only goal achieved in this PhD Thesis. Through the calibration of the dimensionless wave height parameter (H0) in different European offshore wind farms, and according to the criteria proposed by Van der Meer (1988), a classification of these protection structures based on natural elements (rocks or riprap) has been proposed. Scour data registered in numerous offshore wind farms with scour protection systems also allowed to study the functionality of this type of protection installed up to now. Thanks to the knowledge acquired about the scour development, a proposal for the improvement of the characterization of this phenomenon in marine environment is proposed. This has been based on the study of the influence of the acceleration parameters. This PhD Thesis improves the design of scour protections used in offshore wind facilities taking into account maritime climate actions. To solve the current formulae deficiencies only considering the foundation geometry, the internal friction angle of the seabed and the maximum scour depth forecasted.

Order 10 4 speedup in global linear instability analysis using matrix formation

A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.

Influence of the Second Flexural Mode on the Response of High-Speed Bridges

This paper deals with the assessment of the contribution of the second flexural mode to the dynamic behaviour of simply supported railway bridges. Alluding to the works of other authors, it is suggested in some references that the dynamic behaviour of simply supported bridges could be adequately represented taking into account only the contribution of the fundamental flexural mode. On the other hand, the European Rail Research Institute (ERRI) proposes that the second mode should also be included whenever the associated natural frequency is lower than 30 Hz]. This investigation endeavours to clarify the question as much as possible by establishing whether the maximum response of the bridge, in terms of displacements, accelerations and bending moments, can be computed accurately not taking account of the contribution of the second mode. To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed $ \alpha$=VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed high-speed bridges, a parametric analysis is conducted over realistic ranges of values of $ \alpha$ and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the so-called Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twenty-one different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode.