Ordering induced by chemical, thermal and mechanical constraints at solid interfaces

We know that classical thermodynamics even out of equilibrium always leads to stable situation which means degradation and consequently d sorder. Many experimental evidences in different fields show that gradation and order (symmetry breaking) during time and space evolution may appear when maintaining the system far from equilibrium. Order through fluctuations, stochastic processes which occur around critical points and dissipative structures are the fundamental background of the Prigogine-Glansdorff and Nicolis theory. The thermodynamics of macroscopic fluctuations to stochastic approach as well as the kinetic deterministic laws allow a better understanding of the peculiar fascinating behavior of organized matter. The reason for the occurence of this situation is directly related to intrinsic non linearities of the different mechanisms responsible for the evolution of the system. Moreover, when dealing with interfaces separating two immiscible phases (liquid - gas, liquid -liquid, liquid - solid, solid - solid), the situation is rather more complicated. Indeed coupling terms playing the major role in the conditions of instability arise from the peculiar singular static and dynamic properties of the surface and of its vicinity. In other words, the non linearities are not only intrinsic to classical steps involving feedbacks, but they may be imbedded with the non-autonomous character of the surface properties. In order to illustrate our goal we discuss three examples of ordering in far from equilibrium conditions: i) formation of chemical structures during the oxidation of metals and alloys; ii) formation of mechanical structures during the oxidation of metals iii) formation of patterns at a solid-liquid moving interface due to supercooling condition in a melt of alloy. © 1984, Walter de Gruyter. All rights reserved.

Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

Géodiversité sous-marine de Nouvelle-Calédonie. 1ère partie

The object of this article is to offer a synthesis of the knowledge clarifying the originality and the diversity of the submarine geological formations of the New Caledonian EEZ. A reminder is given onto the geologic history of the region, based upon the dislocation of the Gondwana Continent, the opening of the Tasman Sea, the presence of submarine volcanism, the setting up of heavy peridotitic rocks, the building up of the Fairway and Lord Howe Ridges and of sedimentary basins, the formation of volcanic domes and sea-mounts or guyots, the subduction along the Vanuatu Trench, the uplift of the Loyalty Islands, the development of carbonated ptatforms around the islands etc.... Of this complex history ensues an exceptional submarine geo-diversity. After this presentation the article clarifies the methods and the tools used in marine geosciences to map, explore, observe, analyze, sample, that they are embarked or are autonomous, teleoperated or inhabited systems. A chapter describes the programs which were set up since about forty years and the results obtained as well as the scientific teams concerned with. In conclusion, based on the unpublished character of this geo-diversity, the article introduces the second text to come in a next issue of theTai Kona magazine, text which will focus on the scientific, economic (mineral resources), environmental (deep biodiversity) and risks (seismicity) challenges that are worn by one of the most original submarine geologic context in the world.

Dissecting signaling pathways that control glia migration in the developing Drosophila retina

The function of a complex nervous system relies on an intricate interaction between neurons and glial cells. However, as glial cells are generally born distant from the place where they settle, molecular cues are important to direct their migration. Glial cell migration is important in both normal development and disease, thus current research in the laboratory has been focused on dissecting regulatory events underlying that crucial process. With this purpose, the Drosophila eye imaginal disc has been used as a model. In response to neuronal photoreceptor differentiation, glial cells migrate from the CNS into the eye disc where they act to correctly wrap axons. To ensure proper development, attractive and repulsive signals must coordinate glial cell migration. Importantly, one of these signals is Bnl, a Fibroblast Growth Factor (FGF) ligand expressed by retinal progenitor cells that was suggested to act as a non-autonomous negative regulator of excessive glial cell migration (overmigration) by binding and activating the Btl receptor expressed by glial cells. Through the experimental results described in chapter 3 we gained a detailed insight into the function of bnl in eye disc growth, photoreceptor development, and glia migration. Interestingly, we did not find a direct correlation between the defects on the ongoing photoreceptors and the glia overmigration phenotype; however, bnl knockdown caused apoptosis of eye progenitor cells what was strongly correlated with glia migration defects. Glia overmigration due to Bnl down-regulation in eye progenitor cells was rescued by inhibiting the pro-apoptotic genes or caspases activity, as well as, by depleting JNK or Dp53 function in retinal progenitor cells. Thus, we suggest a cross-talk between those developmental signals in the control of glia migration at a distance. Importantly, these results suggest that Bnl does not control glial migration in the eye disc exclusively through its ability to bind and activate its receptor Btl in glial cells. We also discuss possible biological roles for the glia overmigration in the bnl knockdown background. Previous results in the lab showed an interaction between dMyc, a master regulator of tissue growth, and Dpp, a Transforming Growth Factor-β important for retinal patterning and for accurate glia migration into the eye disc. Thus, we became interested in understanding putative relationships between Bnl and dMyc. In chapter 4, we show that they positively cooperate in order to ensure proper development of the eye disc. This work highlights the importance of the FGF signaling in eye disc development and reveals a signaling network where a range of extra- and intra-cellular signals cooperate to non-autonomously control glial cell migration. Therefore, such inter-relations could be important in other Drosophila cellular contexts, as well as in vertebrate tissue development.

A Collaborative IT Network for Three Adriatic Maritime Ports

Part 21: Mobility and Logistics

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

Power sharing and stability enhancement of an autonomous microgrid with inertial and non-inertial DGs with DSTATCOM

This paper proposes a method of enhancing system stability with a distribution static compensator (DSTATCOM) in an autonomous microgrid with multiple distributed generators (DG). It is assumed that there are both inertial and non-inertial DGs connected to the microgrid. The inertial DG can be a synchronous machine of smaller rating while inertia less DGs (solar) are assumed as DC sources. The inertia less DGs are connected through Voltage Source Converter (VSC) to the microgrid. The VSCs are controlled by either state feedback or current feedback mode to achieve desired voltage-current or power outputs respectively. The power sharing among the DGs is achieved by drooping voltage angle. Once the reference for the output voltage magnitude and angle is calculated from the droop, state feedback controllers are used to track the reference. The angle reference for the synchronous machine is compared with the output voltage angle of the machine and the error is fed to a PI controller. The controller output is used to set the power reference of the synchronous machine. The rate of change in the angle in a synchronous machine is restricted by the machine inertia and to mimic this nature, the rate of change in the VSCs angles are restricted by a derivative feedback in the droop control. The connected distribution static compensator (DSTATCOM) provides ride through capability during power imbalance in the microgrid, especially when the stored energy of the inertial DG is not sufficient to maintain stability. The inclusion of the DSATCOM in such cases ensures the system stability. The efficacies of the controllers are established through extensive simulation studies using PSCAD.

Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.

Cellular automata and non-static image processing for embodied robot systems on a massively parallel processor array

Huelse, M, Barr, D R W, Dudek, P: Cellular Automata and non-static image processing for embodied robot systems on a massively parallel processor array. In: Adamatzky, A et al. (eds) AUTOMATA 2008, Theory and Applications of Cellular Automata. Luniver Press, 2008, pp. 504-510. Sponsorship: EPSRC

Run-Time Dynamically-Adaptable FPGA-Based Architecture for High-Performance Autonomous Distributed Systems

Esta tesis doctoral se enmarca dentro del campo de los sistemas embebidos reconfigurables, redes de sensores inalámbricas para aplicaciones de altas prestaciones, y computación distribuida. El documento se centra en el estudio de alternativas de procesamiento para sistemas embebidos autónomos distribuidos de altas prestaciones (por sus siglas en inglés, High-Performance Autonomous Distributed Systems (HPADS)), así como su evolución hacia el procesamiento de alta resolución. El estudio se ha llevado a cabo tanto a nivel de plataforma como a nivel de las arquitecturas de procesamiento dentro de la plataforma con el objetivo de optimizar aspectos tan relevantes como la eficiencia energética, la capacidad de cómputo y la tolerancia a fallos del sistema. Los HPADS son sistemas realimentados, normalmente formados por elementos distribuidos conectados o no en red, con cierta capacidad de adaptación, y con inteligencia suficiente para llevar a cabo labores de prognosis y/o autoevaluación. Esta clase de sistemas suele formar parte de sistemas más complejos llamados sistemas ciber-físicos (por sus siglas en inglés, Cyber-Physical Systems (CPSs)). Los CPSs cubren un espectro enorme de aplicaciones, yendo desde aplicaciones médicas, fabricación, o aplicaciones aeroespaciales, entre otras muchas. Para el diseño de este tipo de sistemas, aspectos tales como la confiabilidad, la definición de modelos de computación, o el uso de metodologías y/o herramientas que faciliten el incremento de la escalabilidad y de la gestión de la complejidad, son fundamentales. La primera parte de esta tesis doctoral se centra en el estudio de aquellas plataformas existentes en el estado del arte que por sus características pueden ser aplicables en el campo de los CPSs, así como en la propuesta de un nuevo diseño de plataforma de altas prestaciones que se ajuste mejor a los nuevos y más exigentes requisitos de las nuevas aplicaciones. Esta primera parte incluye descripción, implementación y validación de la plataforma propuesta, así como conclusiones sobre su usabilidad y sus limitaciones. Los principales objetivos para el diseño de la plataforma propuesta se enumeran a continuación: • Estudiar la viabilidad del uso de una FPGA basada en RAM como principal procesador de la plataforma en cuanto a consumo energético y capacidad de cómputo. • Propuesta de técnicas de gestión del consumo de energía en cada etapa del perfil de trabajo de la plataforma. •Propuestas para la inclusión de reconfiguración dinámica y parcial de la FPGA (por sus siglas en inglés, Dynamic Partial Reconfiguration (DPR)) de forma que sea posible cambiar ciertas partes del sistema en tiempo de ejecución y sin necesidad de interrumpir al resto de las partes. Evaluar su aplicabilidad en el caso de HPADS. Las nuevas aplicaciones y nuevos escenarios a los que se enfrentan los CPSs, imponen nuevos requisitos en cuanto al ancho de banda necesario para el procesamiento de los datos, así como en la adquisición y comunicación de los mismos, además de un claro incremento en la complejidad de los algoritmos empleados. Para poder cumplir con estos nuevos requisitos, las plataformas están migrando desde sistemas tradicionales uni-procesador de 8 bits, a sistemas híbridos hardware-software que incluyen varios procesadores, o varios procesadores y lógica programable. Entre estas nuevas arquitecturas, las FPGAs y los sistemas en chip (por sus siglas en inglés, System on Chip (SoC)) que incluyen procesadores embebidos y lógica programable, proporcionan soluciones con muy buenos resultados en cuanto a consumo energético, precio, capacidad de cómputo y flexibilidad. Estos buenos resultados son aún mejores cuando las aplicaciones tienen altos requisitos de cómputo y cuando las condiciones de trabajo son muy susceptibles de cambiar en tiempo real. La plataforma propuesta en esta tesis doctoral se ha denominado HiReCookie. La arquitectura incluye una FPGA basada en RAM como único procesador, así como un diseño compatible con la plataforma para redes de sensores inalámbricas desarrollada en el Centro de Electrónica Industrial de la Universidad Politécnica de Madrid (CEI-UPM) conocida como Cookies. Esta FPGA, modelo Spartan-6 LX150, era, en el momento de inicio de este trabajo, la mejor opción en cuanto a consumo y cantidad de recursos integrados, cuando además, permite el uso de reconfiguración dinámica y parcial. Es importante resaltar que aunque los valores de consumo son los mínimos para esta familia de componentes, la potencia instantánea consumida sigue siendo muy alta para aquellos sistemas que han de trabajar distribuidos, de forma autónoma, y en la mayoría de los casos alimentados por baterías. Por esta razón, es necesario incluir en el diseño estrategias de ahorro energético para incrementar la usabilidad y el tiempo de vida de la plataforma. La primera estrategia implementada consiste en dividir la plataforma en distintas islas de alimentación de forma que sólo aquellos elementos que sean estrictamente necesarios permanecerán alimentados, cuando el resto puede estar completamente apagado. De esta forma es posible combinar distintos modos de operación y así optimizar enormemente el consumo de energía. El hecho de apagar la FPGA para ahora energía durante los periodos de inactividad, supone la pérdida de la configuración, puesto que la memoria de configuración es una memoria volátil. Para reducir el impacto en el consumo y en el tiempo que supone la reconfiguración total de la plataforma una vez encendida, en este trabajo, se incluye una técnica para la compresión del archivo de configuración de la FPGA, de forma que se consiga una reducción del tiempo de configuración y por ende de la energía consumida. Aunque varios de los requisitos de diseño pueden satisfacerse con el diseño de la plataforma HiReCookie, es necesario seguir optimizando diversos parámetros tales como el consumo energético, la tolerancia a fallos y la capacidad de procesamiento. Esto sólo es posible explotando todas las posibilidades ofrecidas por la arquitectura de procesamiento en la FPGA. Por lo tanto, la segunda parte de esta tesis doctoral está centrada en el diseño de una arquitectura reconfigurable denominada ARTICo3 (Arquitectura Reconfigurable para el Tratamiento Inteligente de Cómputo, Confiabilidad y Consumo de energía) para la mejora de estos parámetros por medio de un uso dinámico de recursos. ARTICo3 es una arquitectura de procesamiento para FPGAs basadas en RAM, con comunicación tipo bus, preparada para dar soporte para la gestión dinámica de los recursos internos de la FPGA en tiempo de ejecución gracias a la inclusión de reconfiguración dinámica y parcial. Gracias a esta capacidad de reconfiguración parcial, es posible adaptar los niveles de capacidad de procesamiento, energía consumida o tolerancia a fallos para responder a las demandas de la aplicación, entorno, o métricas internas del dispositivo mediante la adaptación del número de recursos asignados para cada tarea. Durante esta segunda parte de la tesis se detallan el diseño de la arquitectura, su implementación en la plataforma HiReCookie, así como en otra familia de FPGAs, y su validación por medio de diferentes pruebas y demostraciones. Los principales objetivos que se plantean la arquitectura son los siguientes: • Proponer una metodología basada en un enfoque multi-hilo, como las propuestas por CUDA (por sus siglas en inglés, Compute Unified Device Architecture) u Open CL, en la cual distintos kernels, o unidades de ejecución, se ejecuten en un numero variable de aceleradores hardware sin necesidad de cambios en el código de aplicación. • Proponer un diseño y proporcionar una arquitectura en la que las condiciones de trabajo cambien de forma dinámica dependiendo bien de parámetros externos o bien de parámetros que indiquen el estado de la plataforma. Estos cambios en el punto de trabajo de la arquitectura serán posibles gracias a la reconfiguración dinámica y parcial de aceleradores hardware en tiempo real. • Explotar las posibilidades de procesamiento concurrente, incluso en una arquitectura basada en bus, por medio de la optimización de las transacciones en ráfaga de datos hacia los aceleradores. •Aprovechar las ventajas ofrecidas por la aceleración lograda por módulos puramente hardware para conseguir una mejor eficiencia energética. • Ser capaces de cambiar los niveles de redundancia de hardware de forma dinámica según las necesidades del sistema en tiempo real y sin cambios para el código de aplicación. • Proponer una capa de abstracción entre el código de aplicación y el uso dinámico de los recursos de la FPGA. El diseño en FPGAs permite la utilización de módulos hardware específicamente creados para una aplicación concreta. De esta forma es posible obtener rendimientos mucho mayores que en el caso de las arquitecturas de propósito general. Además, algunas FPGAs permiten la reconfiguración dinámica y parcial de ciertas partes de su lógica en tiempo de ejecución, lo cual dota al diseño de una gran flexibilidad. Los fabricantes de FPGAs ofrecen arquitecturas predefinidas con la posibilidad de añadir bloques prediseñados y poder formar sistemas en chip de una forma más o menos directa. Sin embargo, la forma en la que estos módulos hardware están organizados dentro de la arquitectura interna ya sea estática o dinámicamente, o la forma en la que la información se intercambia entre ellos, influye enormemente en la capacidad de cómputo y eficiencia energética del sistema. De la misma forma, la capacidad de cargar módulos hardware bajo demanda, permite añadir bloques redundantes que permitan aumentar el nivel de tolerancia a fallos de los sistemas. Sin embargo, la complejidad ligada al diseño de bloques hardware dedicados no debe ser subestimada. Es necesario tener en cuenta que el diseño de un bloque hardware no es sólo su propio diseño, sino también el diseño de sus interfaces, y en algunos casos de los drivers software para su manejo. Además, al añadir más bloques, el espacio de diseño se hace más complejo, y su programación más difícil. Aunque la mayoría de los fabricantes ofrecen interfaces predefinidas, IPs (por sus siglas en inglés, Intelectual Property) comerciales y plantillas para ayudar al diseño de los sistemas, para ser capaces de explotar las posibilidades reales del sistema, es necesario construir arquitecturas sobre las ya establecidas para facilitar el uso del paralelismo, la redundancia, y proporcionar un entorno que soporte la gestión dinámica de los recursos. Para proporcionar este tipo de soporte, ARTICo3 trabaja con un espacio de soluciones formado por tres ejes fundamentales: computación, consumo energético y confiabilidad. De esta forma, cada punto de trabajo se obtiene como una solución de compromiso entre estos tres parámetros. Mediante el uso de la reconfiguración dinámica y parcial y una mejora en la transmisión de los datos entre la memoria principal y los aceleradores, es posible dedicar un número variable de recursos en el tiempo para cada tarea, lo que hace que los recursos internos de la FPGA sean virtualmente ilimitados. Este variación en el tiempo del número de recursos por tarea se puede usar bien para incrementar el nivel de paralelismo, y por ende de aceleración, o bien para aumentar la redundancia, y por lo tanto el nivel de tolerancia a fallos. Al mismo tiempo, usar un numero óptimo de recursos para una tarea mejora el consumo energético ya que bien es posible disminuir la potencia instantánea consumida, o bien el tiempo de procesamiento. Con el objetivo de mantener los niveles de complejidad dentro de unos límites lógicos, es importante que los cambios realizados en el hardware sean totalmente transparentes para el código de aplicación. A este respecto, se incluyen distintos niveles de transparencia: • Transparencia a la escalabilidad: los recursos usados por una misma tarea pueden ser modificados sin que el código de aplicación sufra ningún cambio. • Transparencia al rendimiento: el sistema aumentara su rendimiento cuando la carga de trabajo aumente, sin cambios en el código de aplicación. • Transparencia a la replicación: es posible usar múltiples instancias de un mismo módulo bien para añadir redundancia o bien para incrementar la capacidad de procesamiento. Todo ello sin que el código de aplicación cambie. • Transparencia a la posición: la posición física de los módulos hardware es arbitraria para su direccionamiento desde el código de aplicación. • Transparencia a los fallos: si existe un fallo en un módulo hardware, gracias a la redundancia, el código de aplicación tomará directamente el resultado correcto. • Transparencia a la concurrencia: el hecho de que una tarea sea realizada por más o menos bloques es transparente para el código que la invoca. Por lo tanto, esta tesis doctoral contribuye en dos líneas diferentes. En primer lugar, con el diseño de la plataforma HiReCookie y en segundo lugar con el diseño de la arquitectura ARTICo3. Las principales contribuciones de esta tesis se resumen a continuación. • Arquitectura de la HiReCookie incluyendo: o Compatibilidad con la plataforma Cookies para incrementar las capacidades de esta. o División de la arquitectura en distintas islas de alimentación. o Implementación de los diversos modos de bajo consumo y políticas de despertado del nodo. o Creación de un archivo de configuración de la FPGA comprimido para reducir el tiempo y el consumo de la configuración inicial. • Diseño de la arquitectura reconfigurable para FPGAs basadas en RAM ARTICo3: o Modelo de computación y modos de ejecución inspirados en el modelo de CUDA pero basados en hardware reconfigurable con un número variable de bloques de hilos por cada unidad de ejecución. o Estructura para optimizar las transacciones de datos en ráfaga proporcionando datos en cascada o en paralelo a los distinto módulos incluyendo un proceso de votado por mayoría y operaciones de reducción. o Capa de abstracción entre el procesador principal que incluye el código de aplicación y los recursos asignados para las diferentes tareas. o Arquitectura de los módulos hardware reconfigurables para mantener la escalabilidad añadiendo una la interfaz para las nuevas funcionalidades con un simple acceso a una memoria RAM interna. o Caracterización online de las tareas para proporcionar información a un módulo de gestión de recursos para mejorar la operación en términos de energía y procesamiento cuando además se opera entre distintos nieles de tolerancia a fallos. El documento está dividido en dos partes principales formando un total de cinco capítulos. En primer lugar, después de motivar la necesidad de nuevas plataformas para cubrir las nuevas aplicaciones, se detalla el diseño de la plataforma HiReCookie, sus partes, las posibilidades para bajar el consumo energético y se muestran casos de uso de la plataforma así como pruebas de validación del diseño. La segunda parte del documento describe la arquitectura reconfigurable, su implementación en varias FPGAs, y pruebas de validación en términos de capacidad de procesamiento y consumo energético, incluyendo cómo estos aspectos se ven afectados por el nivel de tolerancia a fallos elegido. Los capítulos a lo largo del documento son los siguientes: El capítulo 1 analiza los principales objetivos, motivación y aspectos teóricos necesarios para seguir el resto del documento. El capítulo 2 está centrado en el diseño de la plataforma HiReCookie y sus posibilidades para disminuir el consumo de energía. El capítulo 3 describe la arquitectura reconfigurable ARTICo3. El capítulo 4 se centra en las pruebas de validación de la arquitectura usando la plataforma HiReCookie para la mayoría de los tests. Un ejemplo de aplicación es mostrado para analizar el funcionamiento de la arquitectura. El capítulo 5 concluye esta tesis doctoral comentando las conclusiones obtenidas, las contribuciones originales del trabajo y resultados y líneas futuras. ABSTRACT This PhD Thesis is framed within the field of dynamically reconfigurable embedded systems, advanced sensor networks and distributed computing. The document is centred on the study of processing solutions for high-performance autonomous distributed systems (HPADS) as well as their evolution towards High performance Computing (HPC) systems. The approach of the study is focused on both platform and processor levels to optimise critical aspects such as computing performance, energy efficiency and fault tolerance. HPADS are considered feedback systems, normally networked and/or distributed, with real-time adaptive and predictive functionality. These systems, as part of more complex systems known as Cyber-Physical Systems (CPSs), can be applied in a wide range of fields such as military, health care, manufacturing, aerospace, etc. For the design of HPADS, high levels of dependability, the definition of suitable models of computation, and the use of methodologies and tools to support scalability and complexity management, are required. The first part of the document studies the different possibilities at platform design level in the state of the art, together with description, development and validation tests of the platform proposed in this work to cope with the previously mentioned requirements. The main objectives targeted by this platform design are the following: • Study the feasibility of using SRAM-based FPGAs as the main processor of the platform in terms of energy consumption and performance for high demanding applications. • Analyse and propose energy management techniques to reduce energy consumption in every stage of the working profile of the platform. • Provide a solution with dynamic partial and wireless remote HW reconfiguration (DPR) to be able to change certain parts of the FPGA design at run time and on demand without interrupting the rest of the system. • Demonstrate the applicability of the platform in different test-bench applications. In order to select the best approach for the platform design in terms of processing alternatives, a study of the evolution of the state-of-the-art platforms is required to analyse how different architectures cope with new more demanding applications and scenarios: security, mixed-critical systems for aerospace, multimedia applications, or military environments, among others. In all these scenarios, important changes in the required processing bandwidth or the complexity of the algorithms used are provoking the migration of the platforms from single microprocessor architectures to multiprocessing and heterogeneous solutions with more instant power consumption but higher energy efficiency. Within these solutions, FPGAs and Systems on Chip including FPGA fabric and dedicated hard processors, offer a good trade of among flexibility, processing performance, energy consumption and price, when they are used in demanding applications where working conditions are very likely to vary over time and high complex algorithms are required. The platform architecture proposed in this PhD Thesis is called HiReCookie. It includes an SRAM-based FPGA as the main and only processing unit. The FPGA selected, the Xilinx Spartan-6 LX150, was at the beginning of this work the best choice in terms of amount of resources and power. Although, the power levels are the lowest of these kind of devices, they can be still very high for distributed systems that normally work powered by batteries. For that reason, it is necessary to include different energy saving possibilities to increase the usability of the platform. In order to reduce energy consumption, the platform architecture is divided into different power islands so that only those parts of the systems that are strictly needed are powered on, while the rest of the islands can be completely switched off. This allows a combination of different low power modes to decrease energy. In addition, one of the most important handicaps of SRAM-based FPGAs is that they are not alive at power up. Therefore, recovering the system from a switch-off state requires to reload the FPGA configuration from a non-volatile memory device. For that reason, this PhD Thesis also proposes a methodology to compress the FPGA configuration file in order to reduce time and energy during the initial configuration process. Although some of the requirements for the design of HPADS are already covered by the design of the HiReCookie platform, it is necessary to continue improving energy efficiency, computing performance and fault tolerance. This is only possible by exploiting all the opportunities provided by the processing architectures configured inside the FPGA. Therefore, the second part of the thesis details the design of the so called ARTICo3 FPGA architecture to enhance the already intrinsic capabilities of the FPGA. ARTICo3 is a DPR-capable bus-based virtual architecture for multiple HW acceleration in SRAM-based FPGAs. The architecture provides support for dynamic resource management in real time. In this way, by using DPR, it will be possible to change the levels of computing performance, energy consumption and fault tolerance on demand by increasing or decreasing the amount of resources used by the different tasks. Apart from the detailed design of the architecture and its implementation in different FPGA devices, different validation tests and comparisons are also shown. The main objectives targeted by this FPGA architecture are listed as follows: • Provide a method based on a multithread approach such as those offered by CUDA (Compute Unified Device Architecture) or OpenCL kernel executions, where kernels are executed in a variable number of HW accelerators without requiring application code changes. • Provide an architecture to dynamically adapt working points according to either self-measured or external parameters in terms of energy consumption, fault tolerance and computing performance. Taking advantage of DPR capabilities, the architecture must provide support for a dynamic use of resources in real time. • Exploit concurrent processing capabilities in a standard bus-based system by optimizing data transactions to and from HW accelerators. • Measure the advantage of HW acceleration as a technique to boost performance to improve processing times and save energy by reducing active times for distributed embedded systems. • Dynamically change the levels of HW redundancy to adapt fault tolerance in real time. • Provide HW abstraction from SW application design. FPGAs give the possibility of designing specific HW blocks for every required task to optimise performance while some of them include the possibility of including DPR. Apart from the possibilities provided by manufacturers, the way these HW modules are organised, addressed and multiplexed in area and time can improve computing performance and energy consumption. At the same time, fault tolerance and security techniques can also be dynamically included using DPR. However, the inherent complexity of designing new HW modules for every application is not negligible. It does not only consist of the HW description, but also the design of drivers and interfaces with the rest of the system, while the design space is widened and more complex to define and program. Even though the tools provided by the majority of manufacturers already include predefined bus interfaces, commercial IPs, and templates to ease application prototyping, it is necessary to improve these capabilities. By adding new architectures on top of them, it is possible to take advantage of parallelization and HW redundancy while providing a framework to ease the use of dynamic resource management. ARTICo3 works within a solution space where working points change at run time in a 3D space defined by three different axes: Computation, Consumption, and Fault Tolerance. Therefore, every working point is found as a trade-off solution among these three axes. By means of DPR, different accelerators can be multiplexed so that the amount of available resources for any application is virtually unlimited. Taking advantage of DPR capabilities and a novel way of transmitting data to the reconfigurable HW accelerators, it is possible to dedicate a dynamically-changing number of resources for a given task in order to either boost computing speed or adding HW redundancy and a voting process to increase fault-tolerance levels. At the same time, using an optimised amount of resources for a given task reduces energy consumption by reducing instant power or computing time. In order to keep level complexity under certain limits, it is important that HW changes are transparent for the application code. Therefore, different levels of transparency are targeted by the system: • Scalability transparency: a task must be able to expand its resources without changing the system structure or application algorithms. • Performance transparency: the system must reconfigure itself as load changes. • Replication transparency: multiple instances of the same task are loaded to increase reliability and performance. • Location transparency: resources are accessed with no knowledge of their location by the application code. • Failure transparency: task must be completed despite a failure in some components. • Concurrency transparency: different tasks will work in a concurrent way transparent to the application code. Therefore, as it can be seen, the Thesis is contributing in two different ways. First with the design of the HiReCookie platform and, second with the design of the ARTICo3 architecture. The main contributions of this PhD Thesis are then listed below: • Architecture of the HiReCookie platform including: o Compatibility of the processing layer for high performance applications with the Cookies Wireless Sensor Network platform for fast prototyping and implementation. o A division of the architecture in power islands. o All the different low-power modes. o The creation of the partial-initial bitstream together with the wake-up policies of the node. • The design of the reconfigurable architecture for SRAM FPGAs: ARTICo3: o A model of computation and execution modes inspired in CUDA but based on reconfigurable HW with a dynamic number of thread blocks per kernel. o A structure to optimise burst data transactions providing coalesced or parallel data to HW accelerators, parallel voting process and reduction operation. o The abstraction provided to the host processor with respect to the operation of the kernels in terms of the number of replicas, modes of operation, location in the reconfigurable area and addressing. o The architecture of the modules representing the thread blocks to make the system scalable by adding functional units only adding an access to a BRAM port. o The online characterization of the kernels to provide information to a scheduler or resource manager in terms of energy consumption and processing time when changing among different fault-tolerance levels, as well as if a kernel is expected to work in the memory-bounded or computing-bounded areas. The document of the Thesis is divided into two main parts with a total of five chapters. First, after motivating the need for new platforms to cover new more demanding applications, the design of the HiReCookie platform, its parts and several partial tests are detailed. The design of the platform alone does not cover all the needs of these applications. Therefore, the second part describes the architecture inside the FPGA, called ARTICo3, proposed in this PhD Thesis. The architecture and its implementation are tested in terms of energy consumption and computing performance showing different possibilities to improve fault tolerance and how this impact in energy and time of processing. Chapter 1 shows the main goals of this PhD Thesis and the technology background required to follow the rest of the document. Chapter 2 shows all the details about the design of the FPGA-based platform HiReCookie. Chapter 3 describes the ARTICo3 architecture. Chapter 4 is focused on the validation tests of the ARTICo3 architecture. An application for proof of concept is explained where typical kernels related to image processing and encryption algorithms are used. Further experimental analyses are performed using these kernels. Chapter 5 concludes the document analysing conclusions, comments about the contributions of the work, and some possible future lines for the work.

Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

MSC 2010: 26A33, 34D05, 37C25

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.