The modelling of convective transport processes involving heat and mass transfer in an incompressible Newtonian fluid in cylindrical domains is a relevant research subject both for theoretical research and for industry. However, many of the available studies up to present are two-dimensional, and three-dimensional models using laterally heated cylindrical geometries are scarce. Although the two-dimensional approaches with lateral heating give some significant results, they cannot capture the fully three-dimensional nature of the velocity and temperature fields in three-dimensional geometries in bounded domains; besides, the wall effect in transport problems cannot be neglected. As an example, two-dimensional simulations predict solutions with multiple rolls for aspect ratio boxes greater than 2 that are not observed in three-dimensional studies, and fail to reproduce the nature of the first instability and the associated critical values. In this PhD thesis, we simulate numerically three problems in which the convective transport is produced either by temperature differences in the cylinder lids or by concentration differences within the fluid, as happens in the diffusion experiments in liquid metal mixtures or semiconductors. The system analyzed in the first two problems consists of a horizontal cylinder laterally heated; in the first case, the cylinder remains at rest, while in the second a rotation about its axis is included. Fluid behaviour under different heating intensities (Rayleigh number), materials (Prandtl number) and container size (shape parameter) is investigated. The effect of the rotation of the cylinder on the convective motion is discussed in detail. The values of the angular velocity have been kept low in order to analyze the transition from a fluid flow dominated by convection to a flow in which the fluid rotates as a solid-body with the walls. Much of the work is devoted to analyzing the basic solutions and their stability diagram, and to describing some of the secondary solutions. The aim of the third problem is to analyze the influence of convective pollution in the measurements of the diffusion coefficients when using the method of long capillary in low gravity. We will compare our numerical results with those of the experimental technique called shear cells implemented with a finite volume method and with the previously existing two-dimensional results. The influence on the diffusion coefficients measurements of other factors such as, the low gravity levels, the effects of the tilting and rotation of the capillary, the fluctuations of the gravitational field and the actual accelerometer signals g-jitter, will be also assessed. We numerically solve the Navier-Stokes equation in Boussinesq approximation for an incompressible viscous fluid, which is coupled to an equation for temperature or concentration in cylindrical coordinates. The equations are written in the laboratory reference frame, spatially discretized with a pseudospectral Chebyshev method for radial and axial dependence and with a Fourier-Galerkin method in the azimuthal direction and solved with a second order semi-implicit time splitting method. / La modelización de procesos de transporte convectivo, por transferencia de calor y masa, en un fluido newtoniano incompresible en dominios cilíndricos es un tema de investigación relevante para aplicaciones en la investigación teórica y en la industria. Sin embargo, los trabajos de investigación en modelos tridimensionales usando geometrías cilíndricas calentados lateralmente son más bien escasos. Aunque las aproximaciones bidimensionales del problema con calentamiento lateral dan resultados significativos, las geometrías tridimensionales en dominios acotados son más realistas porque los campos de velocidad y temperatura son totalmente tridimensionales y porque no se puede despreciar el efecto que tienen las paredes en este tipo de problemas de transporte. Por ejemplo en simulaciones en cajas bidimensionales se observa que pueden existir estados estacionarios con más de un rollo convectivo para valores del parámetro de forma mayores que 2 y, sin embargo, esto no se observa en los estudios en cajas rectangulares 3D o cilindros para iguales parámetros. También hay discrepancias en cuanto a la naturaleza de la inestabilidad primaria y a los valores críticos obtenidos para parámetros parecidos. En este trabajo de tesis simulamos tres problemas en los que el transporte convectivo se produce por diferencias de temperatura en las tapas del cilindro o por diferencias de concentración dentro del fluido, como ocurre en los experimentos de difusión en mezclas de metales líquidos o semiconductores. En los dos primeros problemas se simula un cilindro horizontal con una diferencia de temperatura entre sus tapas; en el segundo problema se incluye la rotación del cilindro alrededor de su eje. Se investiga el comportamiento del fluido en función de distintas intensidades en el calentamiento (número de Rayleigh), materiales (número de Prandtl) y tamaño del contenedor (parámetro de forma). Gran parte del trabajo estará dedicado a analizar las soluciones básicas y su estabilidad. En el segundo problema se analiza con detalle el efecto que tiene la rotación del cilindro sobre el movimiento convectivo en función de la velocidad angular, cuyos valores han sido mantenido bajos para poder observar la transición del tipo de flujo inicialmente dominado por la convección, al fluido rotando como un sólido rígido junto con la pared del cilindro. Para los dos problemas con calentamiento lateral caracterizamos las soluciones del estado básico y determinamos su diagrama de estabilidad. Describiremos algunas soluciones secundarias. El tercer problema estará centrado en analizar la influencia que tiene la contaminación convectiva en las medidas de los coeficientes de difusión con el método del ¿capilar largo¿ en baja gravedad. Se compararán estos resultados numéricos para el capilar largo con los resultados obtenidos con la técnica experimental shear cell simulada con el método de volúmenes finitos y con resultados 2D de la literatura. Se valorará la influencia de los bajos niveles de gravedad, así como el efecto de la inclinación y la rotación del capilar, las oscilaciones del campo gravitatorio y la influencia de señales acelerométricas reales conocidas como g-jitter en las medidas de los coeficientes de difusión de una mezcla. Empleamos las ecuaciones de Navier Stokes, en la aproximación de Boussinesq, para un fluido incompresible y viscoso acoplada a una ecuación para la temperatura o la concentración en coordenadas cilíndricas. Las ecuaciones se escribirán en el sistema de referencia de laboratorio. Estas ecuaciones serán discretizadas espacialmente mediante un método pseudoespectral de Chebyshev-colocación para la dependencia radial y axial y el método Galerkin-Fourier para la dependencia azimutal y resueltas con un algoritmo de segundo orden de paso de tiempo fraccionario semi-implícito.

L'objectiu d'aquesta tesi ha estat la caracterització de la resposta de les bandes en els números de manera d'alta. Tres experiments separats van ser executats per crear un conjunt de dades de resposta model per a matiners relació de massa realista baixes, i la determinació de les característiques deixant de bandes flexibles sotmesos a vibracions multimode. Es van utilitzar un conjunt de models verticals. Dues bandes llargues 3m van ser fabricats per a aquesta finalitat. Les bandes es classifiquen d'acord a la relació de massa, un model tenia una relació de massa de 2,7, i l'altre tenia relació de massa menor de 1,1. Els models van ser provats en un flux uniforme, amb una velocitat de fins a 2 m / s. Respostes tant en línia i de flux creuat es van mesurar utilitzant calibradors de tensió, i les dades es converteixen en desplaçaments. L'alta relació de pujada massiva indica oscil·lacions fins a quart manera. La resposta de baixa proporció de pujada massiva es va limitar a segon mode de flux creuat. Les contribucions modals es van determinar i es va observar la presència simultània de múltiples maneres en múltiples freqüències. Coeficients de resistència obtinguts van indicar similitud amb l'oscil·lació de flux transversal, amb valors d'arribar a 2,5 per al cilindre de relació de massa baixa. La resposta d'un tub vertical flexible en el deixant d'un cilindre rígid es va determinar utilitzant diferent distància de la cilindros. / El objetivo de esta tesis ha sido la caracterización de la respuesta de las bandas en los números de modo de alta. Tres experimentos separados fueron ejecutados para crear un conjunto de datos de respuesta modelo para madrugadores relación de masa realista bajas, y la determinación de las características estela de bandas flexibles sometidos a vibraciones multimodo. Se utilizaron un conjunto de modelos verticales. Dos bandas largas 3m fueron fabricados. Las bandas se clasifican de acuerdo a la relación de masa, un modelo tenía una relación de masa de 2,7, y el otro tenía relación de masa menor de 1,1. Los modelos fueron probados en un flujo uniforme, con una velocidad de hasta 2 m / s. Respuestas tanto en línea y de flujo cruzado se midieron usando calibradores de tensión, y los datos se convierten en desplazamientos. La alta relación de subida masiva indica oscilaciones hasta cuarto modo. La respuesta de baja proporción de subida masiva se limitó a segundo modo de flujo cruzado. Las contribuciones modales se determinaron y se observó la presencia simultánea de múltiples modos en múltiples frecuencias. Coeficientes de resistencia obtenidos indicaron similitud con la oscilación de flujo transversal, con valores de llegar a 2,5 para el cilindro de relación de masa baja. La respuesta de un tubo vertical flexible en la estela de un cilindro rígido se determinó usando diferente distancias. / The objective of this thesis was the characterization of the response of risers at high mode numbers. Three separate experiments were executed to create a set of model response data for realistically low mass ratio risers, and the determination of wake characteristics of flexible risers undergoing multi-mode vibrations. A set of riser models were used. Two 3m long risers were fabricated for this purpose. The risers were categorized according to the mass ratio, one model had a mass ratio of 2.7, and the other had lower mass ratio of 1.1. The models were tested in a uniform flow, with speeds up to 2m/s. Both in-line and cross-flow responses were measured using strain gages, and data was converted to displacements. The high mass ratio riser indicated oscillations up to 4th mode. The low mass ratio riser response was limited to 2nd mode in cross-flow. The modal contributions were determined and simultaneous presence of multiple modes at multiple frequencies were observed. Drag coefficients obtained indicated similarity with the cross-flow oscillation, with values reaching 2.5 for the low mass ratio cylinder. The response of a flexible riser in the wake of a rigid cylinder was determined using different separation distance from the leading cylinder. Significant similarities to those of an isolated flexible cylinder were observed, in form of response regimes at each structural mode of oscillation, with contribution from adjacent modes.

This thesis explores a very well understood area of physics: computational structural dynamics. The aim is to stretch its boundaries by merging it with another very well established discipline such as structural design and optimization. In the recent past both of them have made significant advances, often unaware one of each other for different reasons. It is the aim of this thesis to serve as a bridging tool between the realms of physics and engineering. The work in divided in three parts: variational mechanics, structural optimization and implementation. The initial part deals with deterministic variational mechanics. Two chapters are dedicated to probe the applicability of energy functionals in the structural analysis. First, by mapping the state of the art regarding the vast field of numerical methods for structural dynamics; second, by using those functionals as a tool to compare the methods. It is shown how, once the methods are grouped according to the kind of differential equations they integrate, it is easy to establish a framework for benchmarking. Moreover, if this comparison is made using balance of energy the only parameter needed to observe is a relatively easy to obtain scalar value. The second part, where structural optimization is treated, has also two chapters. In the first one the non-deterministic tools employed by structural designers are presented and examined. An important distinction between tools for optimization and tools for analysis is highlighted. In the following chapter, a framework for the objective characterization of structural systems is developed. This characterization is made on the basis of the thermodynamics and energetic characteristics of the system. Finally, it is successfully applied to drive a sample simulated annealing algorithm. In the third part the resulting code employed in the numerical experiments is shown and explained. This code was developed by means of a visual programming environment and allows for the fast implementation of programs within a consolidated CAD application. It was used to interconnect simultaneously with other applications to seamlessly share simulation data and process it. Those applications were, respectively, a spreadsheet and a general purpose finite element. / La presente tesis explora un area de la fisica ampliamente establecida: dinamica computacional de estructuras. El proposito es expandir los limites de la misma mediante la combinacion con otra disciplina como es el diseño y la optimizacion estructurales. Recientemente, ambas han experimentado avances significativos que, frecuentemente, han ocurrido de forma ajena una de la otra. Esta tesis busca servir de nexo entre el campo de la fisica y la ingenieria. El trabajo esta dividido en tres partes: mecanica variacional, optimizacion estructural e implementacion de una aplicacion de software para su uso en la practica real. La parte inicial trata la mecanica variacional desde el punto de vista determinista. Se dedican dos capitulos a demostrar la aplicabilidad de los funcionales energeticos en el analisis estructural. Primero, se hace un recorrido por el estado del arte de los metodos numericos para dinamica estructural; posteriormente, se emplean estos funcionales para comparar dichos metodos de forma objetiva y eficaz. Se demuestra como, una vez que los metodos han quedado agrupados de acuerdo al tipo de ecuaciones diferenciales que resuelven (ordinarias, parciales o algebraicas), es facil crear un marco de referencia para su evaluacion. Al hacerse la comparacion mediante equilibrio energetico el resultado es un valor escalar cuyo manejo es relativamente facil de interpretar. La segunda parte, donde se trata la optimizacion estructural, abarca tambien dos capitulos. En el primero se presentan y examinan las herramientas no deterministas utilizadas por los diseñadores estructurales y se pone de relevancia la importante distincion entre las herramientas de analisis y las de optimizacion. A continuacion, se desarrolla un marco para la caracterizacion objetiva de sistemas estructurales elaborado sobre la base de la mecanica estadistica y las caracteristicas energeticas de las estructuras. Finalmente, el marco se combina con un algoritmo de "Simulated Annealing" para la optimizacion de estructuras. En la tercera parte de la tesis el codigo resultante empleado en los experimentos numericos de los capitulos anteriores queda explicado. Este codigo, desarrollado mediante herramientas de programacion visual, permite la rapida implementacion de aplicaciones dentro de un entorno de CAD. para su posterior aplicacion a problemas reales.

La presente Tesis Doctoral consiste en el diseño de un sistema capaz de realizar tareas de verificación automática de locutores, para lo cual se basa en el modelado mediante los procedimientos DTW (Dynamic Time Warping) y MFCC (Mel-Frequency Cepstral Coefficients). Una vez diseñado éste, se ha evaluado el sistema de forma tanto a nivel de pruebas individuales, DTW y MFCC por separado, como múltiples, combinación de ambas en serie y en paralelo, para grabaciones obtenidas de la base de datos AHUMADA de la Guardia Civil. Todos los resultados han sido vistos teniendo en cuenta la significación estadística de los mismos, derivada de la realización de un determinado número finito de pruebas. Se han obtenido resultados estadísticos de dicho sistema para diferentes tamaños de las bases de datos utilizadas, lo que nos permite concluir la influencia de estos en el método. Como conclusión a los mismos, podemos identificar cuál es el mejor sistema, compuesto por el tipo de modelo y el tamaño de la muestra, que debemos utilizar en un estudio forense en función de la finalidad perseguida. / The present thesis is the design of a system capable of performing automatic speaker verification, for which is based on modeling using the DTW (Dynamic Time Warping) and procedures MFCC (Mel-Frequency Cepstral Coefficients). Once designed it, we have evaluated the system so both at individual events, DTW and MFCC separately as multiple, combining both in series and in parallel, to recordings obtained from the data base AHUMADA from the Guardia Civil. All results have been seen considering the statistical significance thereof, derived from performing a given finite number of tests. Statistical results have been obtained in such a system for different sizes of the databases used, allowing us to conclude the influence of these in the method in order to fix a priori the different variables of this, in order to make the best possible study. To the same conclusion, we can identify what is the best system, consisting of model type and sample size, we use a forensic study based on the intended purpose.

Nanotechnology was named one of the key enabling technologies by the European Commission and its tremendous impact was envisioned early by 20th century physicist R.Feynman in his now oft-quoted talk "Plenty of Room at the bottom". Nanotechnology and nanoscience deal with structures barely visible with an optical microscope, yet much bigger than simple molecules. Matter at this mesoscale is often awkward to explore as it contains too many atoms to be easily understood by straightforward application of quantum mechanics (although the fundamental laws still apply). Yet, these systems are not so large as to be completely free of quantum effects; thus, they do not simply obey the classical physics governing the macroworld. It is precisely in this intermediate regime, the mesoworld, that unforeseen properties of collective systems emerge. To fully exploit the potential of nanotechnology, a thorough understanding of these properties is paramount. The objective of the present thesis is to investigate and to control the dynamics of an optically levitated particle in high vacuum, a system which belongs to the broader class of nanomechanical oscillators. Nanomechanical oscillators exhibit high resonance frequencies, diminished active masses, low power consumption and high quality factors - significantly higher than those of electrical circuits. These attributes make them suitable for sensing, transduction and signal processing. Furthermore, nanomechanical systems are expected to open up investigations of the quantum behavior of mesoscopic systems. Testing the predictions of quantum theory on macroscopic scales is one of today's outstanding challenges of modern physics and addresses fundamental questions on our understanding of the world. The state-of-the-art in nanomechanics itself has exploded in recent years, driven by a combination of interesting new systems and vastly improved fabrication capabilities. Despite major break-throughs, including ground state cooling, observation of radiation pressure shot noise, squeezing and demonstrated ultra-high force and mass sensitivity, difficulties in reaching ultra-high mechanical quality (Q) factors still pose a major limitation for many of the envisioned applications and significant improvements in mechanical quality (Q) factors are generally needed to facilitate quantum coherent manipulation. This is difficult given that many mechanical systems are approaching fundamental limits of dissipation. To overcome the limitations set by dissipation, I developed an experiment to trap and cool nanoparticles in high vacuum. The combination of nanoparticles and vacuum trapping results in a very light and ultra-high-Q mechanical oscillator. In fact, the Q-factor achieved with this setup is the highest observed so far in any nano- or micromechanical system. The scope of the thesis ranges from a detailed description of the experimental apparatus and proof-of-principle experiments (parametric feedback cooling) to the first observation of phenomena owing to the unique parameters of this novel optomechanical system (thermal nonlinearities). Aside from optomechanics and optical trapping, the topics covered include the dynamics of complex (nonlinear) systems and the study of fluctuation theorems, the latter playing a pivotal role in statistical physics. Optically trapped nanoparticles are just beginning to emerge as a new class of optomechanical systems. Owing to their unique mechanical properties, there is clearly a vast and untapped potential for further research. Primary examples of how levitated particles in high vacuum can impact other fields and inspire new research avenues have been the first observation of thermal nonlinearities in a mechanical oscillator and the study of fluctuation relations with a high-Q nanomechanical resonator. Based on recent progress in the field, a plethora of fundamental research opportunities and novel applications are expected to emerge as this still young field matures.

This thesis explores the use of stabilized finite element formulations for the incompressible Navier-Stokes equations to simulate turbulent flow problems. Turbulence is a challenging problem due to its complex and dynamic nature and its simulation if further complicated by the fact that it involves fluid motions at vastly different length and time scales, requiring fine meshes and long simulation times. A solution to this issue is turbulence modeling, in which only the large scale part of the solution is retained and the effect of smaller turbulent motions is represented by a model, which is generally dissipative in nature. In the context of finite element simulations for fluids, a second problem is the apparition of numerical instabilities. These can be avoided by the use of stabilized formulations, in which the problem is modified to ensure that it has a stable solution. Since stabilization methods typically introduce numerical dissipation, the relation between numerical and physical dissipation plays a crucial role in the accuracy of turbulent flow simulations. We investigate this issue by studying the behavior of stabilized finite element formulations based on the Variational Multiscale framework and on Finite Calculus, analyzing the results they provide for well-known reference problems, with the final goal of obtaining a method that both ensures numerical stability and introduces physically correct turbulent dissipation. Given that, even with the use of turbulence models, turbulent flow problems require significant computational resources, we also focused on programming and implementation aspects of finite element codes, specially in ensuring that our solver can perform efficiently on distributed memory architectures and high-performance computing clusters. Finally, we have developed an adaptive mesh refinement technique to improve and optimize unstructured tetrahedral meshes, again with the goal of enabling the simulation of large turbulent flow problems. This technique combines an error estimator based on Variational Multiscale principles with a simple refinement procedure designed to work in a distributed memory context and we have applied it to the simulation of both turbulent and non-Newtonian flow problems. / Aquesta tesi estudia la possibilitat d'utilitzar formulacions estabilitzades d'elements finits de les equacions de Navier-Stokes incompressibles per a la simulació de problemes de flux turbulent. La descripció de la turbulència és un repte, ja que es tracta d'un problema altament dinàmic i complex i la seva simulació numèrica es veu complicada pel fet que hi intervenen moviments de masses fluides amb dimensions i temps característics molt diferents i per tant requereix malles de càlcul molt fines i temps de simulació llargs. Això s'ha provat de resoldre mitjançant l'ús de models de turbulència, mantenint únicament la part de la solució de més gran escala i introduint un model de l'efecte dels moviments de petita escala, que acostuma a tenir un efecte dissipatiu. En el context de la simulació de fluids amb elements finits es planteja un segon problema amb l'aparició d'inestabilitats numèriques. Aquestes es poden evitar amb l'ús de formulacions estabilitzades, en les quals el problema es modifica per assegurar que tingui una solució estable. Ja que els mètodes d'estabilització típicament introdueixen dissipació addicional, la relació entre la dissipació numèrica i la dissipació física té un paper fonamental en la qualitat de la solució. Per investigar aquest fenomen hem estudiat el comportament de diferents formulacions d'elements finits basades en mètodes variacionals de subescala (VMS) i en el càlcul finit (FIC) en termes del seu comportament en la simulació de problemes turbulents de referència, amb l'objectiu final de trobar un mètode que a la vegada garanteixi l'estabilitat de la solució i introdueixi la dissipació turbulenta físicament necessària. Tenint en compte que, fins i tot quan s'utilitzen models de turbulència, la simulació de problemes de flux turbulent requereix molts recursos de càlcul, també hem estudiat aspectes de la implementació paral·lela de programes d'elements finits per tal de garantir que el nostre codi pot treure partit d'arquitectures de memòria distribuïda i servidors de càlcul d'alt rendiment. Finalment, hem desenvolupat una tècnica de refinament adaptatiu de malla que permeti millorar la qualitat de malles de càlcul tetraèdriques, novament amb la intenció de facilitar la simulació de grans problemes de flux turbulent. Aquesta tècnica combina un estimador d'error basat en els principis de la formulació variacional de subescala amb un procediment de refinament dissenyat per funcionar fàcilment en un context de memòria distribuïda i s'ha utilitzat per simular problemes de flux turbulent i no-Newtonià.

This thesis is about the stabilization of the numerical solution of the Euler and Navier- Stokes equations of compressible flow. When simulating numerically the flow equations, if no stabilization is added, the solution presents non-physical (but numerical) oscillations. For this reason the stabilization of partial differential equations and of the fluid dynamics equations is of great importance. In the framework of the so-called variational multiscale stabilization, we present here a stabilization method for compressible flow. The method assessment is done first of all on a batch of academical examples for different Mach numbers, for viscous and inviscid, steady and transient flow. Afterwards the method is applied to atmospheric flow simulations. To this end we solve the Euler equations for dry and moist atmospheric flow. In the presence of moisture a set of transport equations for water species should be solved as well. This domain of application is a real challenge from the stabilization point of view because the correct amount of stabilization must be added in order to preserve the physical properties of the atmospheric flow. At this point, in order to even improve our method, we turn towards local preconditioning. Local preconditiong permits to reduce the stiffness problems that present the flow equations and cause a bad and slow convergence to the solution. With this purpose in mind we combine our stabilization method with local preconditioning and present a stabilization method for the preconditioned Navier-Stokes equations of compressible flow, that we call P-VMS. This method is tested over several examples at different Mach numbers and proves a significant improvement not only in the convergence to the solution but also in the accuracy and robustness of the method. Finally, the benefits of P-VMS are theoretically assessed using Fourier stability analysis. As a result of this analysis a modification on the computation of the time step is done even improving the convergence of the method. / Aquesta tesi tracta sobre l'estabilització de la solució numèrica de les equacions d'Euler i Navier-Stokes de flux compressible. Quan es simulen numèricament les equacions que governen els fluids, si no s'afegeix cap estabilització, la solució presenta oscil·lacions no físiques sinó numèriques. Per aquest motiu l'estabilització de les equacions en derivades parcials i de les equacions de la mecànica de fluids és de gran importància. Dins del marc de l'anomenada estabilització de multiescales variacionals, presentem aquí un mètode d'estabilització per flux compressible. L'evaluació del mètode es realitza primer en varis exemples acadèmics per diferents nombres de Mach, per flux viscós, inviscid, estacionari i transitori. Després el mètode s'aplica a simulacions de flux atmosfèric. Per això, resolem les equacions d'Euler per flux atmosfèric sec i humit. En presència d'humitat, també s'ha de resoldre un grup d'equacions de transport d'espècies d'aigua. Aquest domini d'aplicació representa un desafiament des del punt de vista de l'estabilització, donat que s'ha d'afegir la quantitat adequada d'estabilització per tal de preservar les propietats físiques del flux atmosfèric. Arribat aquest punt, per tal de millorar el nostre mètode, ens interessem pels precondicionadors locals. Els precondicionadors locals permeten reduir els problemes de rigidesa que presenten les equacions dels fluids i que són causa d'una pitjor i més lenta convergència cap a la solució. Amb aquest propòsit en ment, combinem el nostre mètode d'estabilització amb els precondicionadors locals i presentem un mètode d'estabilització per les equacions de Navier-Stokes de flux compressible, anomenem aquest màtode P-VMS. Aquest mètode es evaluat per mitjà de varis exemples per diferents nombres de Mach i demostra una millora sustancial no només pel que fa la convergència cap a la solució, sinó també en la precisió i robusteza del mètode. Finalment els beneficis del P-VMS es demostren teòricament a través de l'anàlisi d'estabilitat de Fourier. Com a resultat d'aquest anàlisi, sorgeix una modificació en el càlcul del pas de temps que millora un cop més la convergència del mètode

Modelling vibroacoustic problems in the field of building design is a challenging problem due to the large size of the domains and the wide frequency range required by regulations. Standard numerical techniques, for instance finite element methods (FEM), fail when trying to reach the highest frequencies. The required element size is too small compared to the problem dimensions and the computational cost becomes unaffordable for such an everyday calculation. Statistical energy analysis (SEA) is a framework of analysis for vibroacoustic problems, based on the wave behaviour at high frequencies. It works directly with averaged magnitudes, which is in fact what regulations require, and its computational cost is very low. However, this simplified approach presents several limitations when dealing with real-life structures. Experiments or other complementary data are often required to complete the definition of the SEA model. This thesis deals with the modelling of building acoustic problems with a reasonable computational cost. In this sense, two main research lines have been followed. In the first part of the thesis, the potential of numerical simulations for extending the SEA applicability is analysed. In particular, three main points are addressed: first, a systematic methodology for the estimation of coupling loss factors from numerical simulations is developed. These factors are estimated from small deterministic simulations, and then applied for solving larger problems with SEA. Then, an SEA-like model for non-conservative couplings is presented, and a strategy for obtaining conservative and non-conservative coupling loss factors from numerical simulations is developed. Finally, a methodology for identifying SEA subsystems with modal analysis is proposed. This technique consists in performing a cluster analysis based on the problem eigenmodes. It allows detecting optimal SEA subdivisions for complex domains, even when two subsystems coexist in the same region of the geometry. In the second part of the thesis, the sound transmission through double walls is analysed from different points of view, as a representative example of the complexities of vibroacoustic simulations. First, a compilation of classical approaches to this problem is presented. Then, the finite layer method is proposed as a new way of discretising the pressure field in the cavity inside double walls, especially when it is partially filled with an absorbing material. This method combines a FEM-like discretisation in the direction perpendicular to the wall with trigonometric functions in the two in-plane directions. This approach has less computational cost than FEM but allows the enforcement of continuity and equilibrium between fluid layers. It is compared with experimental data and also with other prediction models in order to check the influence of commonly assumed simplifications. Finally, a combination of deterministic and statistical methods is presented as a possible solution for dealing with vibroacoustic problems consisting of double walls and other elements. The global analysis is performed with SEA, and numerical simulations of small parts of the problem are used to obtain the required parameters. Combining these techniques, a realistic simulation of the vibroacoustic problem can be performed with a reasonable computational cost.

Nowadays there is great demand for realistic simulations in the computer graphics field. Physically-based animations are commonly used, and one of the more complex problems in this field is fluid simulation, more so if real-time applications are the goal. Videogames, in particular, resort to different techniques that, in order to represent fluids, just simulate the consequence and not the cause, using procedural or parametric methods and often discriminating the physical solution. This need motivates the present thesis, the interactive simulation of free-surface flows, usually liquids, which are the feature of interest in most common applications. Due to the complexity of fluid simulation, in order to achieve real-time framerates, we have resorted to use the high parallelism provided by actual consumer-level GPUs. The simulation algorithm, the Lattice Boltzmann Method, has been chosen accordingly due to its efficiency and the direct mapping to the hardware architecture because of its local operations. We have created two free-surface simulations in the GPU: one fully in 3D and another restricted only to the upper surface of a big bulk of fluid, limiting the simulation domain to 2D. We have extended the latter to track dry regions and is also coupled with obstacles in a geometry-independent fashion. As it is restricted to 2D, the simulation loses some features due to the impossibility of simulating vertical separation of the fluid. To account for this we have coupled the surface simulation to a generic particle system with breaking wave conditions; the simulations are totally independent and only the coupling binds the LBM with the chosen particle system. Furthermore, the visualization of both systems is also done in a realistic way within the interactive framerates; raycasting techniques are used to provide the expected light-related effects as refractions, reflections and caustics. Other techniques that improve the overall detail are also applied as low-level detail ripples and surface foam.

Se pretende analizar la posibilidad de utilizar un sistema ultrasónico como elemento sensor para el control inteligente del vehículo en tráfico urbano, es decir, a bajas velocidades y distancias cortas entre vehículos. Está comprobado que la mayoría de los accidentes de circulación tienen lugar en estas condiciones. Los sensores ultrasónicos requieren de una electrónica más sencilla y son más baratos que otros tipos como los basados en radar o láser. Para ello es necesario estudiar la influencia de los factores meteorológicos en la propagación de ultrasonidos en el aire. También se deben analizar diferentes técnicas que permitan mejorar el rendimiento de los sensores ultrasónicos conformando su diagrama de radiación, como la incorporación de bocinas. / We analyze the possibility of using an ultrasonic sensor for intelligent control of the vehicle in urban traffic, i.e., at low speeds and short distances. It is proven that most accidents occur in these conditions. Ultrasonic sensors require electronics that are simpler and cheaper than other types as those based on radar or laser. This requires studying the influence of meteorological conditions in the propagation of ultrasound in air. It also should discuss different techniques to improve the performance of ultrasonic sensors, as the inclusion of horns.