Extracting non-strict independent and-parallelism using sharing and freeness information

Logic programming systems which exploit and-parallelism among non-deterministic goals rely on notions of independence among those goals in order to ensure certain efficiency properties. "Non-strict" independence (NSI) is a more relaxed notion than the traditional notion of "strict" independence (SI) which still ensures the relevant efficiency properties and can allow considerable more parallelism than SI. However, all compilation technology developed to date has been based on SI, because of the intrinsic complexity of exploiting NSI. This is related to the fact that NSI cannot be determined "a priori" as SI. This paper filis this gap by developing a technique for compile-time detection and annotation of NSI. It also proposes algorithms for combined compiletime/ run-time detection, presenting novel run-time checks for this type of parallelism. Also, a transformation procedure to eliminate shared variables among parallel goals is presented, aimed at performing as much work as possible at compile-time. The approach is based on the knowledge of certain properties regarding the run-time instantiations of program variables —sharing and freeness— for which compile-time technology is available, with new approaches being currently proposed. Thus, the paper does not deal with the analysis itself, but rather with how the analysis results can be used to parallelize programs.

Program development using abstract interpretation (and the ciao system preprocessor)

The technique of Abstract Interpretation has allowed the development of very sophisticated global program analyses which are at the same time provably correct and practical. We present in a tutorial fashion a novel program development framework which uses abstract interpretation as a fundamental tool. The framework uses modular, incremental abstract interpretation to obtain information about the program. This information is used to validate programs, to detect bugs with respect to partial specifications written using assertions (in the program itself and/or in system librarles), to genérate and simplify run-time tests, and to perform high-level program transformations such as múltiple abstract specialization, parallelization, and resource usage control, all in a provably correct way. In the case of validation and debugging, the assertions can refer to a variety of program points such as procedure entry, procedure exit, points within procedures, or global computations. The system can reason with much richer information than, for example, traditional types. This includes data structure shape (including pointer sharing), bounds on data structure sizes, and other operational variable instantiation properties, as well as procedure-level properties such as determinacy, termination, non-failure, and bounds on resource consumption (time or space cost). CiaoPP, the preprocessor of the Ciao multi-paradigm programming system, which implements the described functionality, will be used to illustrate the fundamental ideas.

Estimating the computational cost of logic programs

Information about the computational cost of programs is potentially useful for a variety of purposes, including selecting among different algorithms, guiding program transformations, in granularity control and mapping decisions in parallelizing compilers, and query optimization in deductive databases. Cost analysis of logic programs is complicated by nondeterminism: on the one hand, procedures can return múltiple Solutions, making it necessary to estímate the number of solutions in order to give nontrivial upper bound cost estimates; on the other hand, the possibility of failure has to be taken into account while estimating lower bounds. Here we discuss techniques to address these problems to some extent.

A practical application of sharing and freeness inference

Abstract is not available.

A generic preprocessor for program validation and debugging

We present a generic preprocessor for combined static/dynamic validation and debugging of constraint logic programs. Passing programs through the preprocessor prior to execution allows detecting many bugs automatically. This is achieved by performing a repertoire of tests which range from simple syntactic checks to much more advanced checks based on static analysis of the program. Together with the program, the user may provide a series of assertions which trigger further automatic checking of the program. Such assertions are written using the assertion language presented in Chapter 2, which allows expressing a wide variety of properties. These properties extend beyond the predefined set which may be understandable by the available static analyzers and include properties defined by means of user programs. In addition to user-provided assertions, in each particular CLP system assertions may be available for predefined system predicates. Checking of both user-provided assertions and assertions for system predicates is attempted first at compile-time by comparing them with the results of static analysis. This may allow statically proving that the assertions hold (Le., they are validated) or that they are violated (and thus bugs detected). User-provided assertions (or parts of assertions) which cannot be statically proved ñor disproved are optionally translated into run-time tests. The implementation of the preprocessor is generic in that it can be easily customized to different CLP systems and dialects and in that it is designed to allow the integration of additional analyses in a simple way. We also report on two tools which are instances of the generic preprocessor: CiaoPP (for the Ciao Prolog system) and CHIPRE (for the CHIP CLP(FL>) system). The currently existing analyses include types, modes, non-failure, determinacy, and computational cost, and can treat modules separately, performing incremental analysis.

An abstract interpretation-based approach to mobile code safety

Recent approaches to mobile code safety, like proof- arrying code, involve associating safety information to programs. The code supplier provides a program and also includes with it a certifícate (or proof) whose validity entails compliance with a predefined safety policy. The intended benefit is that the program consumer can locally validate the certifícate w.r.t. the "untrusted" program by means of a certifícate checker—a process which should be much simpler, eflicient, and automatic than generating the original proof. We herein introduce a novel approach to mobile code safety which follows a similar scheme, but which is based throughout on the use of abstract interpretation techniques. In our framework the safety policy is specified by using an expressive assertion language defined over abstract domains. We identify a particular slice of the abstract interpretation-based static analysis results which is especially useful as a certifícate. We propose an algorithm for checking the validity of the certifícate on the consumer side which is itself in fact a very simplified and eflicient specialized abstract-interpreter. Our ideas are illustrated through an example implemented in the CiaoPP system. Though further experimentation is still required, we believe the proposed approach is of interest for bringing the automation and expressiveness which is inherent in the abstract interpretation techniques to the área of mobile code safety.

Análisis estático de sistemas de membranas para la determinación de reglas activas

Esta tesis doctoral se enmarca dentro de la computación con membranas. Se trata de un tipo de computación bio-inspirado, concretamente basado en las células de los organismos vivos, en las que se producen múltiples reacciones de forma simultánea. A partir de la estructura y funcionamiento de las células se han definido diferentes modelos formales, denominados P sistemas. Estos modelos no tratan de modelar el comportamiento biológico de una célula, sino que abstraen sus principios básicos con objeto de encontrar nuevos paradigmas computacionales. Los P sistemas son modelos de computación no deterministas y masivamente paralelos. De ahí el interés que en los últimos años estos modelos han suscitado para la resolución de problemas complejos. En muchos casos, consiguen resolver de forma teórica problemas NP-completos en tiempo polinómico o lineal. Por otra parte, cabe destacar también la aplicación que la computación con membranas ha tenido en la investigación de otros muchos campos, sobre todo relacionados con la biología. Actualmente, una gran cantidad de estos modelos de computación han sido estudiados desde el punto de vista teórico. Sin embargo, el modo en que pueden ser implementados es un reto de investigación todavía abierto. Existen varias líneas en este sentido, basadas en arquitecturas distribuidas o en hardware dedicado, que pretenden acercarse en lo posible a su carácter no determinista y masivamente paralelo, dentro de un contexto de viabilidad y eficiencia. En esta tesis doctoral se propone la realización de un análisis estático del P sistema, como vía para optimizar la ejecución del mismo en estas plataformas. Se pretende que la información recogida en tiempo de análisis sirva para configurar adecuadamente la plataforma donde se vaya a ejecutar posteriormente el P sistema, obteniendo como consecuencia una mejora en el rendimiento. Concretamente, en esta tesis se han tomado como referencia los P sistemas de transiciones para llevar a cabo el estudio de dicho análisis estático. De manera un poco más específica, el análisis estático propuesto en esta tesis persigue que cada membrana sea capaz de determinar sus reglas activas de forma eficiente en cada paso de evolución, es decir, aquellas reglas que reúnen las condiciones adecuadas para poder ser aplicadas. En esta línea, se afronta el problema de los estados de utilidad de una membrana dada, que en tiempo de ejecución permitirán a la misma conocer en todo momento las membranas con las que puede comunicarse, cuestión que determina las reglas que pueden aplicarse en cada momento. Además, el análisis estático propuesto en esta tesis se basa en otra serie de características del P sistema como la estructura de membranas, antecedentes de las reglas, consecuentes de las reglas o prioridades. Una vez obtenida toda esta información en tiempo de análisis, se estructura en forma de árbol de decisión, con objeto de que en tiempo de ejecución la membrana obtenga las reglas activas de la forma más eficiente posible. Por otra parte, en esta tesis se lleva a cabo un recorrido por un número importante de arquitecturas hardware y software que diferentes autores han propuesto para implementar P sistemas. Fundamentalmente, arquitecturas distribuidas, hardware dedicado basado en tarjetas FPGA y plataformas basadas en microcontroladores PIC. El objetivo es proponer soluciones que permitan implantar en dichas arquitecturas los resultados obtenidos del análisis estático (estados de utilidad y árboles de decisión para reglas activas). En líneas generales, se obtienen conclusiones positivas, en el sentido de que dichas optimizaciones se integran adecuadamente en las arquitecturas sin penalizaciones significativas. Summary Membrane computing is the focus of this doctoral thesis. It can be considered a bio-inspired computing type. Specifically, it is based on living cells, in which many reactions take place simultaneously. From cell structure and operation, many different formal models have been defined, named P systems. These models do not try to model the biological behavior of the cell, but they abstract the basic principles of the cell in order to find out new computational paradigms. P systems are non-deterministic and massively parallel computational models. This is why, they have aroused interest when dealing with complex problems nowadays. In many cases, they manage to solve in theory NP problems in polynomial or lineal time. On the other hand, it is important to note that membrane computing has been successfully applied in many researching areas, specially related to biology. Nowadays, lots of these computing models have been sufficiently characterized from a theoretical point of view. However, the way in which they can be implemented is a research challenge, that it is still open nowadays. There are some lines in this way, based on distributed architectures or dedicated hardware. All of them are trying to approach to its non-deterministic and parallel character as much as possible, taking into account viability and efficiency. In this doctoral thesis it is proposed carrying out a static analysis of the P system in order to optimize its performance in a computing platform. The general idea is that after data are collected in analysis time, they are used for getting a suitable configuration of the computing platform in which P system is going to be performed. As a consequence, the system throughput will improve. Specifically, this thesis has made use of Transition P systems for carrying out the study in static analysis. In particular, the static analysis proposed in this doctoral thesis tries to achieve that every membrane can efficiently determine its active rules in every evolution step. These rules are the ones that can be applied depending on the system configuration at each computational step. In this line, we are going to tackle the problem of the usefulness states for a membrane. This state will allow this membrane to know the set of membranes with which communication is possible at any time. This is a very important issue in determining the set of rules that can be applied. Moreover, static analysis in this thesis is carried out taking into account other properties such as membrane structure, rule antecedents, rule consequents and priorities among rules. After collecting all data in analysis time, they are arranged in a decision tree structure, enabling membranes to obtain the set of active rules as efficiently as possible in run-time system. On the other hand, in this doctoral thesis is going to carry out an overview of hardware and software architectures, proposed by different authors in order to implement P systems, such as distributed architectures, dedicated hardware based on PFGA, and computing platforms based on PIC microcontrollers. The aim of this overview is to propose solutions for implementing the results of the static analysis, that is, usefulness states and decision trees for active rules. In general, conclusions are satisfactory, because these optimizations can be properly integrated in most of the architectures without significant penalties.

Conceptual framework for the design, implementation and validation of psychomotor skills’ assessment systems in minimally invasive surgery

Las técnicas de cirugía de mínima invasión (CMI) se están consolidando hoy en día como alternativa a la cirugía tradicional, debido a sus numerosos beneficios para los pacientes. Este cambio de paradigma implica que los cirujanos deben aprender una serie de habilidades distintas de aquellas requeridas en cirugía abierta. El entrenamiento y evaluación de estas habilidades se ha convertido en una de las mayores preocupaciones en los programas de formación de cirujanos, debido en gran parte a la presión de una sociedad que exige cirujanos bien preparados y una reducción en el número de errores médicos. Por tanto, se está prestando especial atención a la definición de nuevos programas que permitan el entrenamiento y la evaluación de las habilidades psicomotoras en entornos seguros antes de que los nuevos cirujanos puedan operar sobre pacientes reales. Para tal fin, hospitales y centros de formación están gradualmente incorporando instalaciones de entrenamiento donde los residentes puedan practicar y aprender sin riesgos. Es cada vez más común que estos laboratorios dispongan de simuladores virtuales o simuladores físicos capaces de registrar los movimientos del instrumental de cada residente. Estos simuladores ofrecen una gran variedad de tareas de entrenamiento y evaluación, así como la posibilidad de obtener información objetiva de los ejercicios. Los diferentes estudios de validación llevados a cabo dan muestra de su utilidad; pese a todo, los niveles de evidencia presentados son en muchas ocasiones insuficientes. Lo que es más importante, no existe un consenso claro a la hora de definir qué métricas son más útiles para caracterizar la pericia quirúrgica. El objetivo de esta tesis doctoral es diseñar y validar un marco de trabajo conceptual para la definición y validación de entornos para la evaluación de habilidades en CMI, en base a un modelo en tres fases: pedagógica (tareas y métricas a emplear), tecnológica (tecnologías de adquisición de métricas) y analítica (interpretación de la competencia en base a las métricas). Para tal fin, se describe la implementación práctica de un entorno basado en (1) un sistema de seguimiento de instrumental fundamentado en el análisis del vídeo laparoscópico; y (2) la determinación de la pericia en base a métricas de movimiento del instrumental. Para la fase pedagógica se diseñó e implementó un conjunto de tareas para la evaluación de habilidades psicomotoras básicas, así como una serie de métricas de movimiento. La validación de construcción llevada a cabo sobre ellas mostró buenos resultados para tiempo, camino recorrido, profundidad, velocidad media, aceleración media, economía de área y economía de volumen. Adicionalmente, los resultados obtenidos en la validación de apariencia fueron en general positivos en todos los grupos considerados (noveles, residentes, expertos). Para la fase tecnológica, se introdujo el EVA Tracking System, una solución para el seguimiento del instrumental quirúrgico basado en el análisis del vídeo endoscópico. La precisión del sistema se evaluó a 16,33ppRMS para el seguimiento 2D de la herramienta en la imagen; y a 13mmRMS para el seguimiento espacial de la misma. La validación de construcción con una de las tareas de evaluación mostró buenos resultados para tiempo, camino recorrido, profundidad, velocidad media, aceleración media, economía de área y economía de volumen. La validación concurrente con el TrEndo® Tracking System por su parte presentó valores altos de correlación para 8 de las 9 métricas analizadas. Finalmente, para la fase analítica se comparó el comportamiento de tres clasificadores supervisados a la hora de determinar automáticamente la pericia quirúrgica en base a la información de movimiento del instrumental, basados en aproximaciones lineales (análisis lineal discriminante, LDA), no lineales (máquinas de soporte vectorial, SVM) y difusas (sistemas adaptativos de inferencia neurodifusa, ANFIS). Los resultados muestran que en media SVM presenta un comportamiento ligeramente superior: 78,2% frente a los 71% y 71,7% obtenidos por ANFIS y LDA respectivamente. Sin embargo las diferencias estadísticas medidas entre los tres no fueron demostradas significativas. En general, esta tesis doctoral corrobora las hipótesis de investigación postuladas relativas a la definición de sistemas de evaluación de habilidades para cirugía de mínima invasión, a la utilidad del análisis de vídeo como fuente de información y a la importancia de la información de movimiento de instrumental a la hora de caracterizar la pericia quirúrgica. Basándose en estos cimientos, se han de abrir nuevos campos de investigación que contribuyan a la definición de programas de formación estructurados y objetivos, que puedan garantizar la acreditación de cirujanos sobradamente preparados y promocionen la seguridad del paciente en el quirófano. Abstract Minimally invasive surgery (MIS) techniques have become a standard in many surgical sub-specialties, due to their many benefits for patients. However, this shift in paradigm implies that surgeons must acquire a complete different set of skills than those normally attributed to open surgery. Training and assessment of these skills has become a major concern in surgical learning programmes, especially considering the social demand for better-prepared professionals and for the decrease of medical errors. Therefore, much effort is being put in the definition of structured MIS learning programmes, where practice with real patients in the operating room (OR) can be delayed until the resident can attest for a minimum level of psychomotor competence. To this end, skills’ laboratory settings are being introduced in hospitals and training centres where residents may practice and be assessed on their psychomotor skills. Technological advances in the field of tracking technologies and virtual reality (VR) have enabled the creation of new learning systems such as VR simulators or enhanced box trainers. These systems offer a wide range of tasks, as well as the capability of registering objective data on the trainees’ performance. Validation studies give proof of their usefulness; however, levels of evidence reported are in many cases low. More importantly, there is still no clear consensus on topics such as the optimal metrics that must be used to assess competence, the validity of VR simulation, the portability of tracking technologies into real surgeries (for advanced assessment) or the degree to which the skills measured and obtained in laboratory environments transfer to the OR. The purpose of this PhD is to design and validate a conceptual framework for the definition and validation of MIS assessment environments based on a three-pillared model defining three main stages: pedagogical (tasks and metrics to employ), technological (metric acquisition technologies) and analytical (interpretation of competence based on metrics). To this end, a practical implementation of the framework is presented, focused on (1) a video-based tracking system and (2) the determination of surgical competence based on the laparoscopic instruments’ motionrelated data. The pedagogical stage’s results led to the design and implementation of a set of basic tasks for MIS psychomotor skills’ assessment, as well as the definition of motion analysis parameters (MAPs) to measure performance on said tasks. Validation yielded good construct results for parameters such as time, path length, depth, average speed, average acceleration, economy of area and economy of volume. Additionally, face validation results showed positive acceptance on behalf of the experts, residents and novices. For the technological stage the EVA Tracking System is introduced. EVA provides a solution for tracking laparoscopic instruments from the analysis of the monoscopic video image. Accuracy tests for the system are presented, which yielded an average RMSE of 16.33pp for 2D tracking of the instrument on the image and of 13mm for 3D spatial tracking. A validation experiment was conducted using one of the tasks and the most relevant MAPs. Construct validation showed significant differences for time, path length, depth, average speed, average acceleration, economy of area and economy of volume; especially between novices and residents/experts. More importantly, concurrent validation with the TrEndo® Tracking System presented high correlation values (>0.7) for 8 of the 9 MAPs proposed. Finally, the analytical stage allowed comparing the performance of three different supervised classification strategies in the determination of surgical competence based on motion-related information. The three classifiers were based on linear (linear discriminant analysis, LDA), non-linear (support vector machines, SVM) and fuzzy (adaptive neuro fuzzy inference systems, ANFIS) approaches. Results for SVM show slightly better performance than the other two classifiers: on average, accuracy for LDA, SVM and ANFIS was of 71.7%, 78.2% and 71% respectively. However, when confronted, no statistical significance was found between any of the three. Overall, this PhD corroborates the investigated research hypotheses regarding the definition of MIS assessment systems, the use of endoscopic video analysis as the main source of information and the relevance of motion analysis in the determination of surgical competence. New research fields in the training and assessment of MIS surgeons can be proposed based on these foundations, in order to contribute to the definition of structured and objective learning programmes that guarantee the accreditation of well-prepared professionals and the promotion of patient safety in the OR.

Desarrollo de un sistema de optimización económica para instalaciones de régimen especial

. Este proyecto tiene por objeto el desarrollo y la implantación de un sistema de optimización económica de instalaciones de producción de Régimen Especial, en una compañía eléctrica que representa a este tipo de instalaciones para su participación en los distintos mercados de electricidad. Inicialmente, se analizarán las opciones de participación en los distintos mercados de cada tecnología, en función de la legislación a la que pudieran estar acogidas las instalaciones del Régimen Especial; según tamaño y tipología de instalaciones, características o combustibles utilizados. En segundo lugar, se estudiará la relación entre dichas instalaciones y los distintos organismos reguladores del mercado; la Comisión Nacional de la Energía, el Ministerio de Industria y Turismo, Red Eléctrica de España y el Operador del mercado eléctrico. Posteriormente, se realizará un modelo de análisis estático de la situación actual de los mercados eléctricos, su estructura y funcionamiento, obteniendo para cada tipo de instalación el escenario de optimización de base, a partir del cual se podrá desarrollar el modelo dinámico que permitirá conocer en cualquier momento cuál será la mejor opción técnico-económica para cada tipo de instalación, optimizando así el presupuesto de las instalaciones objeto del estudio. Finalmente, este modelo se implementará en los sistemas de la compañía eléctrica, como una herramienta que permitirá asegurar la optimización en tiempo real a las instalaciones a las que representa en el mercado, optimizando sus propios costes a través de la implementación de este sistema automático y logrando así maximizar los ingresos de la compañía eléctrica. ABSTRACT DEVELOPMENT OF A SYSTEM OF ECONOMIC OPTIMIZATION FOR PLANTS OF SPECIAL REGIME. This project takes as an object the development and the implantation of a system of economic optimization of facilities of production of Special Regime, in an electrical company that it represents to this type of facilities for his participation in the different markets of electricity. Initially, there will be analyzed the options of participation in the different markets of every technology, depending on the legislation to which there could be received the facilities of the Special Regime; according to size and typology of facilities, characteristics or used fuels. Secondly, the relation will be studied between the above mentioned facilities and the different regulatory organisms of the market; the National Commission of the Energy, the Department of Industry and Tourism, Electrical Network of Spain and the Operator of the electrical market. Later, there will carry out a model of static analysis of the current situation of the electrical markets, his structure and functioning, obtaining for every type of installation the scene of base optimization, from which there will be able to develop the dynamic model who will allow to know at any time which will be the best technical - economic option for every type of installation, optimizing this way the budget of the facilities I object of the study. Finally, this model will be implemented in the systems of the electrical company, as a tool that will allow to assure the real time optimization to the facilities to which it represents on the market, optimizing his own costs across the implementation of this automatic system and managing this way to maximize the income of the electrical company.

Self-consistent numerical dispersion relation of the ablative Rayleigh-Taylor instability of double ablation fronts in inertial confinement fusion

The linear stability analysis of accelerated double ablation fronts is carried out numerically with a self-consistent approach. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using 1D simulation results. Numerical dispersión relation is compared to an analytical sharp boundary model [Yan˜ez et al., Phys. Plasmas 18, 052701 (2011)] showing an excellent agreement for the radiation dominated regime of very steep ablation fronts, and the stabilization due to smooth profiles. 2D simulations are presented to validate the numerical self-consistent theory.

Compression of matter by hypersphsericla shock waves

A novel compression scheme is proposed, in which hollow targets with specifically curved structures initially filled with uniform matter, are driven by converging shock waves. The self-similar dynamics is analyzed for converging and diverging shock waves. The shock-compressed densities and pressures are much higher than those achieved using spherical shocks due to the geometric accumulation. Dynamic behavior is demonstrated using two-dimensional hydrodynamic simulations. The linear stability analysis for the spherical geometry reveals a new dispersion relation with cut-off mode numbers as a function of the specific heat ratio, above which eigenmode perturbations are smeared out in the converging phase.

Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability

An earlier analysis of the Hall-magnetohydrodynamics (MHD) tearing instability [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)] is extended to cover the regime where the growth rate becomes comparable or exceeds the sound frequency. Like in the previous subsonic work, a resistive, two-fluid Hall-MHD model with massless electrons and zero-Larmor-radius ions is adopted and a linear stability analysis about a force-free equilibrium in slab geometry is carried out. A salient feature of this supersonic regime is that the mode eigenfunctions become intrinsically complex, but the growth rate remains purely real. Even more interestingly, the dispersion relation remains of the same form as in the subsonic regime for any value of the instability Mach number, provided only that the ion skin depth is sufficiently small for the mode ion inertial layer width to be smaller than the macroscopic lengths, a generous bound that scales like a positive power of the Lundquist number

Instabilities in two-liquid layers subject to a horizontal temperature gradient

We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B2 O3 , a configuration of considerable technological importance. Four dif- ferent flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscilla- tory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques.

Convective instabilities in two superposed horizontal liquid layers heated laterally.

This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a nondeformable interface. The forces acting on the system are buoyancy and interfacial tension. Four different flow patterns and temperature profiles are found for the basic state. A linear perturbative analysis with respect to two- and three-dimensional perturbations reveals the existence of three kinds of patterns. Depending on the relative height of both liquids several situations are predicted: either wave propa- gation from cold to the hot regions, or waves propagating in the opposite direction or still stationary longitu- dinal rolls. The behavior of three different pairs of liquids which have been used in experiments on bilayers under vertical gradient by other authors have been examined. The instability mechanisms are discussed and a qualitative interpretation of the different behaviors exhibited by the system is provided. In some configurations it is possible to find a codimension-two point created by the interaction of two Hopf modes with different frequencies and wave numbers. These results suggest to consider two liquid layers as an interesting prototype ? nard-Marangoni problem.

Matrix-free time-stepping methods for the solution of TriGlobal instability problems

La inmensa mayoría de los flujos de relevancia ingenieril permanecen sin estudiar en el marco de la teoría de estabilidad global. Esto es debido a dos razones fundamentalmente, las dificultades asociadas con el análisis de los flujos turbulentos y los inmensos recursos computacionales requeridos para obtener la solución del problema de autovalores asociado al análisis de inestabilidad de flujos tridimensionales, también conocido como problema TriGlobal. En esta tesis se aborda el problema asociado con la tridimensionalidad. Se ha desarrollado una metodología general para obtener soluciones de problemas de análisis modal de las inestabilidades lineales globales mediante el acoplamiento de métodos de evolución temporal, desarrollados en este trabajo, con códigos de mecánica de fluidos computacional de segundo orden, utilizados de forma general en la industria. Esta metodología consiste en la resolución del problema de autovalores asociado al análisis de inestabilidad mediante métodos de proyección en subespacios de Krylov, con la particularidad de que dichos subespacios son generados por medio de la integración temporal de un vector inicial usando cualquier código de mecánica de fluidos computacional. Se han elegido tres problemas desafiantes en función de la exigencia de recursos computacionales necesarios y de la complejidad física para la demostración de la presente metodología: (i) el flujo en el interior de una cavidad tridimensional impulsada por una de sus tapas, (ii) el flujo alrededor de un cilindro equipado con aletas helicoidales a lo largo su envergadura y (iii) el flujo a través de una cavidad abierta tridimensinal en ausencia de homogeneidades espaciales. Para la validación de la tecnología se ha obtenido la solución del problema TriGlobal asociado al flujo en la cavidad tridimensional, utilizando el método de evolución temporal desarrollado acoplado con los operadores numéricos de flujo incompresible del código CFD OpenFOAM (código libre). Los resultados obtenidos coinciden plentamente con la literatura. La aplicación de esta metodología al estudio de inestabilidades globales de flujos abiertos tridimensionales ha proporcionado por primera vez, información sobre la transición tridimensional de estos flujos. Además, la metodología ha sido adaptada para resolver problemas adjuntos TriGlobales, permitiendo el control de flujo basado en modificaciones de las inestabilidades globales. Finalmente, se ha demostrado que la cantidad moderada de los recursos computacionales requeridos para la solución del problema de valor propio TriGlobal usando este método numérico, junto a su versatilidad al poder acoplarse a cualquier código aerodinámico, permite la realización de análisis de inestabilidad global y control de flujos complejos de relevancia industrial. Abstract Most flows of engineering relevance still remain unexplored in a global instability theory context for two reasons. First, because of the difficulties associated with the analysis of turbulent flows and, second, for the formidable computational resources required for the solution of the eigenvalue problem associated with the instability analysis of three-dimensional base flows, also known as TriGlobal problem. In this thesis, the problem associated with the three-dimensionality is addressed by means of the development of a general approach to the solution of large-scale global linear instability analysis by coupling a time-stepping approach with second order aerodynamic codes employed in industry. Three challenging flows in the terms of required computational resources and physical complexity have been chosen for demonstration of the present methodology; (i) the flow inside a wall-bounded three-dimensional lid-driven cavity, (ii) the flow past a cylinder fitted with helical strakes and (iii) the flow over a inhomogeneous three-dimensional open cavity. Results in excellent agreement with the literature have been obtained for the three-dimensional lid-driven cavity by using this methodology coupled with the incompressible solver of the open-source toolbox OpenFOAM®, which has served as validation. Moreover, significant physical insight of the instability of three-dimensional open flows has been gained through the application of the present time-stepping methodology to the other two cases. In addition, modifications to the present approach have been proposed in order to perform adjoint instability analysis of three-dimensional base flows and flow control; validation and TriGlobal examples are presented. Finally, it has been demonstrated that the moderate amount of computational resources required for the solution of the TriGlobal eigenvalue problem using this method enables the performance of instability analysis and control of flows of industrial relevance.