Automated wordlength optimization framework for multi-source statistical interval-based analysis of nonlinear systems with control-flow structures

El uso de aritmética de punto fijo es una opción de diseño muy extendida en sistemas con fuertes restricciones de área, consumo o rendimiento. Para producir implementaciones donde los costes se minimicen sin impactar negativamente en la precisión de los resultados debemos llevar a cabo una asignación cuidadosa de anchuras de palabra. Encontrar la combinación óptima de anchuras de palabra en coma fija para un sistema dado es un problema combinatorio NP-hard al que los diseñadores dedican entre el 25 y el 50 % del ciclo de diseño. Las plataformas hardware reconfigurables, como son las FPGAs, también se benefician de las ventajas que ofrece la aritmética de coma fija, ya que éstas compensan las frecuencias de reloj más bajas y el uso más ineficiente del hardware que hacen estas plataformas respecto a los ASICs. A medida que las FPGAs se popularizan para su uso en computación científica los diseños aumentan de tamaño y complejidad hasta llegar al punto en que no pueden ser manejados eficientemente por las técnicas actuales de modelado de señal y ruido de cuantificación y de optimización de anchura de palabra. En esta Tesis Doctoral exploramos distintos aspectos del problema de la cuantificación y presentamos nuevas metodologías para cada uno de ellos: Las técnicas basadas en extensiones de intervalos han permitido obtener modelos de propagación de señal y ruido de cuantificación muy precisos en sistemas con operaciones no lineales. Nosotros llevamos esta aproximación un paso más allá introduciendo elementos de Multi-Element Generalized Polynomial Chaos (ME-gPC) y combinándolos con una técnica moderna basada en Modified Affine Arithmetic (MAA) estadístico para así modelar sistemas que contienen estructuras de control de flujo. Nuestra metodología genera los distintos caminos de ejecución automáticamente, determina las regiones del dominio de entrada que ejercitarán cada uno de ellos y extrae los momentos estadísticos del sistema a partir de dichas soluciones parciales. Utilizamos esta técnica para estimar tanto el rango dinámico como el ruido de redondeo en sistemas con las ya mencionadas estructuras de control de flujo y mostramos la precisión de nuestra aproximación, que en determinados casos de uso con operadores no lineales llega a tener tan solo una desviación del 0.04% con respecto a los valores de referencia obtenidos mediante simulación. Un inconveniente conocido de las técnicas basadas en extensiones de intervalos es la explosión combinacional de términos a medida que el tamaño de los sistemas a estudiar crece, lo cual conlleva problemas de escalabilidad. Para afrontar este problema presen tamos una técnica de inyección de ruidos agrupados que hace grupos con las señales del sistema, introduce las fuentes de ruido para cada uno de los grupos por separado y finalmente combina los resultados de cada uno de ellos. De esta forma, el número de fuentes de ruido queda controlado en cada momento y, debido a ello, la explosión combinatoria se minimiza. También presentamos un algoritmo de particionado multi-vía destinado a minimizar la desviación de los resultados a causa de la pérdida de correlación entre términos de ruido con el objetivo de mantener los resultados tan precisos como sea posible. La presente Tesis Doctoral también aborda el desarrollo de metodologías de optimización de anchura de palabra basadas en simulaciones de Monte-Cario que se ejecuten en tiempos razonables. Para ello presentamos dos nuevas técnicas que exploran la reducción del tiempo de ejecución desde distintos ángulos: En primer lugar, el método interpolativo aplica un interpolador sencillo pero preciso para estimar la sensibilidad de cada señal, y que es usado después durante la etapa de optimización. En segundo lugar, el método incremental gira en torno al hecho de que, aunque es estrictamente necesario mantener un intervalo de confianza dado para los resultados finales de nuestra búsqueda, podemos emplear niveles de confianza más relajados, lo cual deriva en un menor número de pruebas por simulación, en las etapas iniciales de la búsqueda, cuando todavía estamos lejos de las soluciones optimizadas. Mediante estas dos aproximaciones demostramos que podemos acelerar el tiempo de ejecución de los algoritmos clásicos de búsqueda voraz en factores de hasta x240 para problemas de tamaño pequeño/mediano. Finalmente, este libro presenta HOPLITE, una infraestructura de cuantificación automatizada, flexible y modular que incluye la implementación de las técnicas anteriores y se proporciona de forma pública. Su objetivo es ofrecer a desabolladores e investigadores un entorno común para prototipar y verificar nuevas metodologías de cuantificación de forma sencilla. Describimos el flujo de trabajo, justificamos las decisiones de diseño tomadas, explicamos su API pública y hacemos una demostración paso a paso de su funcionamiento. Además mostramos, a través de un ejemplo sencillo, la forma en que conectar nuevas extensiones a la herramienta con las interfaces ya existentes para poder así expandir y mejorar las capacidades de HOPLITE. ABSTRACT Using fixed-point arithmetic is one of the most common design choices for systems where area, power or throughput are heavily constrained. In order to produce implementations where the cost is minimized without negatively impacting the accuracy of the results, a careful assignment of word-lengths is required. The problem of finding the optimal combination of fixed-point word-lengths for a given system is a combinatorial NP-hard problem to which developers devote between 25 and 50% of the design-cycle time. Reconfigurable hardware platforms such as FPGAs also benefit of the advantages of fixed-point arithmetic, as it compensates for the slower clock frequencies and less efficient area utilization of the hardware platform with respect to ASICs. As FPGAs become commonly used for scientific computation, designs constantly grow larger and more complex, up to the point where they cannot be handled efficiently by current signal and quantization noise modelling and word-length optimization methodologies. In this Ph.D. Thesis we explore different aspects of the quantization problem and we present new methodologies for each of them: The techniques based on extensions of intervals have allowed to obtain accurate models of the signal and quantization noise propagation in systems with non-linear operations. We take this approach a step further by introducing elements of MultiElement Generalized Polynomial Chaos (ME-gPC) and combining them with an stateof- the-art Statistical Modified Affine Arithmetic (MAA) based methodology in order to model systems that contain control-flow structures. Our methodology produces the different execution paths automatically, determines the regions of the input domain that will exercise them, and extracts the system statistical moments from the partial results. We use this technique to estimate both the dynamic range and the round-off noise in systems with the aforementioned control-flow structures. We show the good accuracy of our approach, which in some case studies with non-linear operators shows a 0.04 % deviation respect to the simulation-based reference values. A known drawback of the techniques based on extensions of intervals is the combinatorial explosion of terms as the size of the targeted systems grows, which leads to scalability problems. To address this issue we present a clustered noise injection technique that groups the signals in the system, introduces the noise terms in each group independently and then combines the results at the end. In this way, the number of noise sources in the system at a given time is controlled and, because of this, the combinato rial explosion is minimized. We also present a multi-way partitioning algorithm aimed at minimizing the deviation of the results due to the loss of correlation between noise terms, in order to keep the results as accurate as possible. This Ph.D. Thesis also covers the development of methodologies for word-length optimization based on Monte-Carlo simulations in reasonable times. We do so by presenting two novel techniques that explore the reduction of the execution times approaching the problem in two different ways: First, the interpolative method applies a simple but precise interpolator to estimate the sensitivity of each signal, which is later used to guide the optimization effort. Second, the incremental method revolves on the fact that, although we strictly need to guarantee a certain confidence level in the simulations for the final results of the optimization process, we can do it with more relaxed levels, which in turn implies using a considerably smaller amount of samples, in the initial stages of the process, when we are still far from the optimized solution. Through these two approaches we demonstrate that the execution time of classical greedy techniques can be accelerated by factors of up to ×240 for small/medium sized problems. Finally, this book introduces HOPLITE, an automated, flexible and modular framework for quantization that includes the implementation of the previous techniques and is provided for public access. The aim is to offer a common ground for developers and researches for prototyping and verifying new techniques for system modelling and word-length optimization easily. We describe its work flow, justifying the taken design decisions, explain its public API and we do a step-by-step demonstration of its execution. We also show, through an example, the way new extensions to the flow should be connected to the existing interfaces in order to expand and improve the capabilities of HOPLITE.

A generic persistence model for CLP systems (and two useful implementations)

This paper describes a model of persistence in (C)LP languages and two different and practically very useful ways to implement this model in current systems. The fundamental idea is that persistence is a characteristic of certain dynamic predicates (Le., those which encapsulate state). The main effect of declaring a predicate persistent is that the dynamic changes made to such predicates persist from one execution to the next one. After proposing a syntax for declaring persistent predicates, a simple, file-based implementation of the concept is presented and some examples shown. An additional implementation is presented which stores persistent predicates in an external datábase. The abstraction of the concept of persistence from its implementation allows developing applications which can store their persistent predicates alternatively in files or databases with only a few simple changes to a declaration stating the location and modality used for persistent storage. The paper presents the model, the implementation approach in both the cases of using files and relational databases, a number of optimizations of the process (using information obtained from static global analysis and goal clustering), and performance results from an implementation of these ideas.

Solving SAT in linear time with a neural-like membrane system

We present in this paper a neural-like membrane system solving the SAT problem in linear time. These neural Psystems are nets of cells working with multisets. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (?excitations?) to the neighboring cells. The maximal mode of rules application and the replicative mode of communication between cells are at the core of the eficiency of these systems.

Failure Detectors in Homonymous Distributed Systems (with an Application to Consensus).

This paper is on homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership (?homonymous? means that several processes may have the same identi?er). New classes of failure detectors suited to these systems are ?rst de?ned. Among them, the classes H? and H? are introduced that are the homonymous counterparts of the classes ? and ?, respectively. (Recall that the pair h?,?i de?nes the weakest failure detector to solve consensus.) Then, the paper shows how H? and H? can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge ofthe membership. One algorithm solves consensus with hH?, H?i, while the other uses only H?, but needs a majority of correct processes. Observe that the systems with unique identi?ers and anonymous systems are extreme cases of homonymous systems from which follows that all these results also apply to these systems. Interestingly, the new failure detector class H? can be implemented with partial synchrony, while the analogous class A? de?ned for anonymous systems can not be implemented (even in synchronous systems). Hence, the paper provides us with the ?rst proof showing that consensus can be solved in anonymous systems with only partial synchrony (and a majority of correct processes).

Morphological Functions to Quantify Three-Dimensional Tomograms of Macropore Structure in a Vineyard Soil with Two Different Management Regimes

Soil tomography and morphological functions built over Minkowski functionals were used to describe the impact on pore structure of two soil management practices in a Mediterranean vineyard. Soil structure controls important physical and biological processes in soil–plant–microbial systems. Those processes are dominated by the geometry of soil pore structure, and a correct model of this geometry is critical for understanding them. Soil tomography has been shown to provide rich three-dimensional digital information on soil pore geometry. Recently, mathematical morphological techniques have been proposed as powerful tools to analyze and quantify the geometrical features of porous media. Minkowski functionals and morphological functions built over Minkowski functionals provide computationally efficient means to measure four fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. We used the threshold and the dilation and erosion of three-dimensional images to generate morphological functions and explore the evolution of Minkowski functionals as the threshold and as the degree of dilation and erosion changes. We analyzed the three-dimensional geometry of soil pore space with X-ray computed tomography (CT) of intact soil columns from a Spanish Mediterranean vineyard by using two different management practices (conventional tillage versus permanent cover crop of resident vegetation). Our results suggested that morphological functions built over Minkowski functionals provide promising tools to characterize soil macropore structure and that the evolution of morphological features with dilation and erosion is more informative as an indicator of structure than moving threshold for both soil managements studied.

Generalized synchronization in relay systems with instantaneous coupling

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

Fault management techniques for systems with SRAM-based FPGAs

Las Field-Programmable Gate Arrays (FPGAs) SRAM se construyen sobre una memoria de configuración de tecnología RAM Estática (SRAM). Presentan múltiples características que las hacen muy interesantes para diseñar sistemas empotrados complejos. En primer lugar presentan un coste no-recurrente de ingeniería (NRE) bajo, ya que los elementos lógicos y de enrutado están pre-implementados (el diseño de usuario define su conexionado). También, a diferencia de otras tecnologías de FPGA, pueden ser reconfiguradas (incluso en campo) un número ilimitado de veces. Es más, las FPGAs SRAM de Xilinx soportan Reconfiguración Parcial Dinámica (DPR), la cual permite reconfigurar la FPGA sin interrumpir la aplicación. Finalmente, presentan una alta densidad de lógica, una alta capacidad de procesamiento y un rico juego de macro-bloques. Sin embargo, un inconveniente de esta tecnología es su susceptibilidad a la radiación ionizante, la cual aumenta con el grado de integración (geometrías más pequeñas, menores tensiones y mayores frecuencias). Esta es una precupación de primer nivel para aplicaciones en entornos altamente radiativos y con requisitos de alta confiabilidad. Este fenómeno conlleva una degradación a largo plazo y también puede inducir fallos instantáneos, los cuales pueden ser reversibles o producir daños irreversibles. En las FPGAs SRAM, los fallos inducidos por radiación pueden aparecer en en dos capas de arquitectura diferentes, que están físicamente superpuestas en el dado de silicio. La Capa de Aplicación (o A-Layer) contiene el hardware definido por el usuario, y la Capa de Configuración contiene la memoria de configuración y la circuitería de soporte. Los fallos en cualquiera de estas capas pueden hacer fracasar el sistema, lo cual puede ser ás o menos tolerable dependiendo de los requisitos de confiabilidad del sistema. En el caso general, estos fallos deben gestionados de alguna manera. Esta tesis trata sobre la gestión de fallos en FPGAs SRAM a nivel de sistema, en el contexto de sistemas empotrados autónomos y confiables operando en un entorno radiativo. La tesis se centra principalmente en aplicaciones espaciales, pero los mismos principios pueden aplicarse a aplicaciones terrenas. Las principales diferencias entre ambas son el nivel de radiación y la posibilidad de mantenimiento. Las diferentes técnicas para la gestión de fallos en A-Layer y C-Layer son clasificados, y sus implicaciones en la confiabilidad del sistema son analizados. Se proponen varias arquitecturas tanto para Gestores de Fallos de una capa como de doble-capa. Para estos últimos se propone una arquitectura novedosa, flexible y versátil. Gestiona las dos capas concurrentemente de manera coordinada, y permite equilibrar el nivel de redundancia y la confiabilidad. Con el objeto de validar técnicas de gestión de fallos dinámicas, se desarrollan dos diferentes soluciones. La primera es un entorno de simulación para Gestores de Fallos de C-Layer, basado en SystemC como lenguaje de modelado y como simulador basado en eventos. Este entorno y su metodología asociada permite explorar el espacio de diseño del Gestor de Fallos, desacoplando su diseño del desarrollo de la FPGA objetivo. El entorno incluye modelos tanto para la C-Layer de la FPGA como para el Gestor de Fallos, los cuales pueden interactuar a diferentes niveles de abstracción (a nivel de configuration frames y a nivel físico JTAG o SelectMAP). El entorno es configurable, escalable y versátil, e incluye capacidades de inyección de fallos. Los resultados de simulación para algunos escenarios son presentados y comentados. La segunda es una plataforma de validación para Gestores de Fallos de FPGAs Xilinx Virtex. La plataforma hardware aloja tres Módulos de FPGA Xilinx Virtex-4 FX12 y dos Módulos de Unidad de Microcontrolador (MCUs) de 32-bits de propósito general. Los Módulos MCU permiten prototipar Gestores de Fallos de C-Layer y A-Layer basados en software. Cada Módulo FPGA implementa un enlace de A-Layer Ethernet (a través de un switch Ethernet) con uno de los Módulos MCU, y un enlace de C-Layer JTAG con el otro. Además, ambos Módulos MCU intercambian comandos y datos a través de un enlace interno tipo UART. Al igual que para el entorno de simulación, se incluyen capacidades de inyección de fallos. Los resultados de pruebas para algunos escenarios son también presentados y comentados. En resumen, esta tesis cubre el proceso completo desde la descripción de los fallos FPGAs SRAM inducidos por radiación, pasando por la identificación y clasificación de técnicas de gestión de fallos, y por la propuesta de arquitecturas de Gestores de Fallos, para finalmente validarlas por simulación y pruebas. El trabajo futuro está relacionado sobre todo con la implementación de Gestores de Fallos de Sistema endurecidos para radiación. ABSTRACT SRAM-based Field-Programmable Gate Arrays (FPGAs) are built on Static RAM (SRAM) technology configuration memory. They present a number of features that make them very convenient for building complex embedded systems. First of all, they benefit from low Non-Recurrent Engineering (NRE) costs, as the logic and routing elements are pre-implemented (user design defines their connection). Also, as opposed to other FPGA technologies, they can be reconfigured (even in the field) an unlimited number of times. Moreover, Xilinx SRAM-based FPGAs feature Dynamic Partial Reconfiguration (DPR), which allows to partially reconfigure the FPGA without disrupting de application. Finally, they feature a high logic density, high processing capability and a rich set of hard macros. However, one limitation of this technology is its susceptibility to ionizing radiation, which increases with technology scaling (smaller geometries, lower voltages and higher frequencies). This is a first order concern for applications in harsh radiation environments and requiring high dependability. Ionizing radiation leads to long term degradation as well as instantaneous faults, which can in turn be reversible or produce irreversible damage. In SRAM-based FPGAs, radiation-induced faults can appear at two architectural layers, which are physically overlaid on the silicon die. The Application Layer (or A-Layer) contains the user-defined hardware, and the Configuration Layer (or C-Layer) contains the (volatile) configuration memory and its support circuitry. Faults at either layers can imply a system failure, which may be more ore less tolerated depending on the dependability requirements. In the general case, such faults must be managed in some way. This thesis is about managing SRAM-based FPGA faults at system level, in the context of autonomous and dependable embedded systems operating in a radiative environment. The focus is mainly on space applications, but the same principles can be applied to ground applications. The main differences between them are the radiation level and the possibility for maintenance. The different techniques for A-Layer and C-Layer fault management are classified and their implications in system dependability are assessed. Several architectures are proposed, both for single-layer and dual-layer Fault Managers. For the latter, a novel, flexible and versatile architecture is proposed. It manages both layers concurrently in a coordinated way, and allows balancing redundancy level and dependability. For the purpose of validating dynamic fault management techniques, two different solutions are developed. The first one is a simulation framework for C-Layer Fault Managers, based on SystemC as modeling language and event-driven simulator. This framework and its associated methodology allows exploring the Fault Manager design space, decoupling its design from the target FPGA development. The framework includes models for both the FPGA C-Layer and for the Fault Manager, which can interact at different abstraction levels (at configuration frame level and at JTAG or SelectMAP physical level). The framework is configurable, scalable and versatile, and includes fault injection capabilities. Simulation results for some scenarios are presented and discussed. The second one is a validation platform for Xilinx Virtex FPGA Fault Managers. The platform hosts three Xilinx Virtex-4 FX12 FPGA Modules and two general-purpose 32-bit Microcontroller Unit (MCU) Modules. The MCU Modules allow prototyping software-based CLayer and A-Layer Fault Managers. Each FPGA Module implements one A-Layer Ethernet link (through an Ethernet switch) with one of the MCU Modules, and one C-Layer JTAG link with the other. In addition, both MCU Modules exchange commands and data over an internal UART link. Similarly to the simulation framework, fault injection capabilities are implemented. Test results for some scenarios are also presented and discussed. In summary, this thesis covers the whole process from describing the problem of radiationinduced faults in SRAM-based FPGAs, then identifying and classifying fault management techniques, then proposing Fault Manager architectures and finally validating them by simulation and test. The proposed future work is mainly related to the implementation of radiation-hardened System Fault Managers.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Modulation-mode Assignment for SVD-assisted Multiuser MIMO Systems with Correlation.

Multiuser multiple-input multiple-output (MIMO) downlink (DL) transmission schemes experience both multiuser interference as well as inter-antenna interference. The singular value decomposition provides an appropriate mean to process channel information and allows us to take the individual user’s channel characteristics into account rather than treating all users channels jointly as in zero-forcing (ZF) multiuser transmission techniques. However, uncorrelated MIMO channels has attracted a lot of attention and reached a state of maturity. By contrast, the performance analysis in the presence of antenna fading correlation, which decreases the channel capacity, requires substantial further research. The joint optimization of the number of activated MIMO layers and the number of bits per symbol along with the appropriate allocation of the transmit power shows that not necessarily all user-specific MIMO layers has to be activated in order to minimize the overall BER under the constraint of a given fixed data throughput.

A visual object counter based on a multimodal data association for embedded systems with limited computational power

A low complex but highly-efficient object counter algorithm is presented that can be embedded in hardware with a low computational power. This is achieved by a novel soft-data association strategy that can handle multimodal distributions.

Accepting splicing systems with permitting and forbidding words

Abstract: In this paper we propose a generalization of the accepting splicingsystems introduced in Mitrana et al. (Theor Comput Sci 411:2414?2422,2010). More precisely, the input word is accepted as soon as a permittingword is obtained provided that no forbidding word has been obtained sofar, otherwise it is rejected. Note that in the new variant of acceptingsplicing system the input word is rejected if either no permitting word isever generated (like in Mitrana et al. in Theor Comput Sci 411:2414?2422,2010) or a forbidding word has been generated and no permitting wordhad been generated before. We investigate the computational power ofthe new variants of accepting splicing systems and the interrelationshipsamong them. We show that the new condition strictly increases thecomputational power of accepting splicing systems. Although there areregular languages that cannot be accepted by any of the splicing systemsconsidered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of(extended) finite splicing systems without additional restrictions. We alsoshow that the smallest class of languages out of the four classes definedby accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediatelyderived from the proof of this result.

solaR: Solar Radiation and Photovoltaic Systems with R

The solaR package allows for reproducible research both for photovoltaics (PV) systems performance and solar radiation. It includes a set of classes, methods and functions to calculate the sun geometry and the solar radiation incident on a photovoltaic generator and to simulate the performance of several applications of the photovoltaic energy. This package performs the whole calculation procedure from both daily and intradaily global horizontal irradiation to the final productivity of grid-connected PV systems and water pumping PV systems. It is designed using a set of S4 classes whose core is a group of slots with multivariate time series. The classes share a variety of methods to access the information and several visualization methods. In addition, the package provides a tool for the visual statistical analysis of the performance of a large PV plant composed of several systems. Although solaR is primarily designed for time series associated to a location defined by its latitude/longitude values and the temperature and irradiation conditions, it can be easily combined with spatial packages for space-time analysis.

Self-consistent resonance absorption with two layer profile steepening

Resonance absorption of p-polarized light, incident at angle 6 on a flowing, stratified plasma, is analyzed; profile steepening within (i) a layer around the turning point, and (ii) a thinner,embedded sublayer at the critical surface is taken into account self-consistently. The entire steepened region is taken as collisionless and isothermal. The structure of the main layer shows a variety of regimes, depending on how the flow crosses a sonic point. The structure of the sublayer is also determined; it is entirely subsonic (with no wave breaking) for a well-defined,broad parameter range. Density changes across both layer and sublayer, and fractional absorption, are given in terms of [(wavelength)2 Xintensity/temperature], and (temperature/mec2). The flow outside the double structure is also analyzed for particular conditions.

Optical Multistability and Oscillations in Hybrid Optical Bistable Systems with Short Delay Times

Optical instabilities in the output light from a bistable optical device (BOD) with a delayed feedback was predicted by Ikeda [1]. Gibbs et al. [2] gave the first experimental verification of this type of instabilities. From that time several groups have studied the instabilities of the BOD for different relations between the delay time tR and the time constant ح of the system. In a previous paper [3] an empirical and analytical study of instabilities in hybrid BOD was reported by us. The employed set up is shown in Fig. 1.

A general stability criterion for switched linear systems having stable and unstable subsystems

We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those having stable subsystems and mixtures of stable and unstable subsystems.