Some properties of finite-time stable stochastic nonlinear systems

In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Finite Element Analysis to Compare Complete Denture and Implant-Retained Overdentures With Different Attachment Systems

This finite element analysis compared stress distribution on complete dentures and implant-retained overdentures with different attachment systems. Four models of edentulous mandible were constructed: group A (control), complete denture; group B, overdenture retained by 2 splinted implants with bar-clip system; group C, overdenture retained by 2 unsplinted implants with o'ring system; and group D, overdenture retained by 2 splinted implants with bar-clip and 2 distally placed o'ring system. Evaluation was performed on Ansys software, with 100-N vertical load applied on central incisive teeth. The lowest maximum general stress value (in megapascal) was observed in group A (64.305) followed by groups C (119.006), D (258.650), and B (349.873). The same trend occurred it) supporting tissues with the highest stress value for cortical bone. Unsplinted implants associated with the o'ring attachment system showed the lowest maximum stress values among all overdenture groups. Furthermore, o'ring system also improved stress distribution when associated with bar-clip system.

QUASIDISTRIBUTIONS and COHERENT STATES FOR FINITE-DIMENSIONAL QUANTUM SYSTEMS

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber-Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.

Intersubband excitations at finite temperatures and their roles in different quasi-one-dimensional systems

We theoretically study many-body excitations in three different quasi-one-dimensional (Q1D) electron systems: (i) those formed on the surface of liquid Helium; (ii) in two coupled semiconductor quantum wires; and (iii) Q1D electrons embedded in polar semiconductor-based quantum wires. Our results show intersubband coupling between higher subbands and the two lowest subbands affecting even the lower energy intersubband plasmons on the liquid Helium surface. Concerning the second system, we show a pronounced extra peak appearing in the intersubband impurity spectral function for temperatures as high as 20 K. We finally show coupled intersubband plasmon-phonon modes surviving for temperatures up to 300 K.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, E3 (N+1) and E3 (N), can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r0/a (r0 is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited E3 (N+1) state disappears in the 2 + 1 threshold, is given by √E2/E3 (N) ≈ 0.38+0.12(r0/a). © 2012 Springer-Verlag.

Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

Dynamic analysis of road vehicle-bridge systems under turbulent wind by means of Finite Element Models

When an automobile passes over a bridge dynamic effects are produced in vehicle and structure. In addition, the bridge itself moves when exposed to the wind inducing dynamic effects on the vehicle that have to be considered. The main objective of this work is to understand the influence of the different parameters concerning the vehicle, the bridge, the road roughness or the wind in the comfort and safety of the vehicles when crossing bridges. Non linear finite element models are used for structures and multibody dynamic models are employed for vehicles. The interaction between the vehicle and the bridge is considered by contact methods. Road roughness is described by the power spectral density (PSD) proposed by the ISO 8608. To consider that the profiles under right and left wheels are different but not independent, the hypotheses of homogeneity and isotropy are assumed. To generate the wind velocity history along the road the Sandia method is employed. The global problem is solved by means of the finite element method. First the methodology for modelling the interaction is verified in a benchmark. Following, the case of a vehicle running along a rigid road and subjected to the action of the turbulent wind is analyzed and the road roughness is incorporated in a following step. Finally the flexibility of the bridge is added to the model by making the vehicle run over the structure. The application of this methodology will allow to understand the influence of the different parameters in the comfort and safety of road vehicles crossing wind exposed bridges. Those results will help to recommend measures to make the traffic over bridges more reliable without affecting the structural integrity of the viaduct

Energy-based Fair Queuing: Energy-centric Processor Scheduling Algorithm for Battery-limited Mobile Systems

Los dispositivos móviles modernos disponen cada vez de más funcionalidad debido al rápido avance de las tecnologías de las comunicaciones y computaciones móviles. Sin embargo, la capacidad de la batería no ha experimentado un aumento equivalente. Por ello, la experiencia de usuario en los sistemas móviles modernos se ve muy afectada por la vida de la batería, que es un factor inestable de difícil de control. Para abordar este problema, investigaciones anteriores han propuesto un esquema de gestion del consumo (PM) centrada en la energía y que proporciona una garantía sobre la vida operativa de la batería mediante la gestión de la energía como un recurso de primera clase en el sistema. Como el planificador juega un papel fundamental en la administración del consumo de energía y en la garantía del rendimiento de las aplicaciones, esta tesis explora la optimización de la experiencia de usuario para sistemas móviles con energía limitada desde la perspectiva de un planificador que tiene en cuenta el consumo de energía en un contexto en el que ésta es un recurso de primera clase. En esta tesis se analiza en primer lugar los factores que contribuyen de forma general a la experiencia de usuario en un sistema móvil. Después se determinan los requisitos esenciales que afectan a la experiencia de usuario en la planificación centrada en el consumo de energía, que son el reparto proporcional de la potencia, el cumplimiento de las restricciones temporales, y cuando sea necesario, el compromiso entre la cuota de potencia y las restricciones temporales. Para cumplir con los requisitos, el algoritmo clásico de fair queueing y su modelo de referencia se extienden desde los dominios de las comunicaciones y ancho de banda de CPU hacia el dominio de la energía, y en base a ésto, se propone el algoritmo energy-based fair queueing (EFQ) para proporcionar una planificación basada en la energía. El algoritmo EFQ está diseñado para compartir la potencia consumida entre las tareas mediante su planificación en función de la energía consumida y de la cuota reservada. La cuota de consumo de cada tarea con restricciones temporales está protegida frente a diversos cambios que puedan ocurrir en el sistema. Además, para dar mejor soporte a las tareas en tiempo real y multimedia, se propone un mecanismo para combinar con el algoritmo EFQ para dar preferencia en la planificación durante breves intervalos de tiempo a las tareas más urgentes con restricciones temporales.Las propiedades del algoritmo EFQ se evaluan a través del modelado de alto nivel y la simulación. Los resultados de las simulaciones indican que los requisitos esenciales de la planificación centrada en la energía pueden lograrse. El algoritmo EFQ se implementa más tarde en el kernel de Linux. Para evaluar las propiedades del planificador EFQ basado en Linux, se desarrolló un banco de pruebas experimental basado en una sitema empotrado, un programa de banco de pruebas multihilo, y un conjunto de pruebas de código abierto. A través de experimentos específicamente diseñados, esta tesis verifica primero las propiedades de EFQ en la gestión de la cuota de consumo de potencia y la planificación en tiempo real y, a continuación, explora los beneficios potenciales de emplear la planificación EFQ en la optimización de la experiencia de usuario para sistemas móviles con energía limitada. Los resultados experimentales sobre la gestión de la cuota de energía muestran que EFQ es más eficaz que el planificador de Linux-CFS en la gestión de energía, logrando un reparto proporcional de la energía del sistema independientemente de en qué dispositivo se consume la energía. Los resultados experimentales en la planificación en tiempo real demuestran que EFQ puede lograr de forma eficaz, flexible y robusta el cumplimiento de las restricciones temporales aunque se dé el caso de aumento del el número de tareas o del error en la estimación de energía. Por último, un análisis comparativo de los resultados experimentales sobre la optimización de la experiencia del usuario demuestra que, primero, EFQ es más eficaz y flexible que los algoritmos tradicionales de planificación del procesador, como el que se encuentra por defecto en el planificador de Linux y, segundo, que proporciona la posibilidad de optimizar y preservar la experiencia de usuario para los sistemas móviles con energía limitada. Abstract Modern mobiledevices have been becoming increasingly powerful in functionality and entertainment as the next-generation mobile computing and communication technologies are rapidly advanced. However, the battery capacity has not experienced anequivalent increase. The user experience of modern mobile systems is therefore greatly affected by the battery lifetime,which is an unstable factor that is hard to control. To address this problem, previous works proposed energy-centric power management (PM) schemes to provide strong guarantee on the battery lifetime by globally managing energy as the first-class resource in the system. As the processor scheduler plays a pivotal role in power management and application performance guarantee, this thesis explores the user experience optimization of energy-limited mobile systemsfrom the perspective of energy-centric processor scheduling in an energy-centric context. This thesis first analyzes the general contributing factors of the mobile system user experience.Then itdetermines the essential requirements on the energy-centric processor scheduling for user experience optimization, which are proportional power sharing, time-constraint compliance, and when necessary, a tradeoff between the power share and the time-constraint compliance. To meet the requirements, the classical fair queuing algorithm and its reference model are extended from the network and CPU bandwidth sharing domain to the energy sharing domain, and based on that, the energy-based fair queuing (EFQ) algorithm is proposed for performing energy-centric processor scheduling. The EFQ algorithm is designed to provide proportional power shares to tasks by scheduling the tasks based on their energy consumption and weights. The power share of each time-sensitive task is protected upon the change of the scheduling environment to guarantee a stable performance, and any instantaneous power share that is overly allocated to one time-sensitive task can be fairly re-allocated to the other tasks. In addition, to better support real-time and multimedia scheduling, certain real-time friendly mechanism is combined into the EFQ algorithm to give time-limited scheduling preference to the time-sensitive tasks. Through high-level modelling and simulation, the properties of the EFQ algorithm are evaluated. The simulation results indicate that the essential requirements of energy-centric processor scheduling can be achieved. The EFQ algorithm is later implemented in the Linux kernel. To assess the properties of the Linux-based EFQ scheduler, an experimental test-bench based on an embedded platform, a multithreading test-bench program, and an open-source benchmark suite is developed. Through specifically-designed experiments, this thesis first verifies the properties of EFQ in power share management and real-time scheduling, and then, explores the potential benefits of employing EFQ scheduling in the user experience optimization for energy-limited mobile systems. Experimental results on power share management show that EFQ is more effective than the Linux-CFS scheduler in managing power shares and it can achieve a proportional sharing of the system power regardless of on which device the energy is spent. Experimental results on real-time scheduling demonstrate that EFQ can achieve effective, flexible and robust time-constraint compliance upon the increase of energy estimation error and task number. Finally, a comparative analysis of the experimental results on user experience optimization demonstrates that EFQ is more effective and flexible than traditional processor scheduling algorithms, such as those of the default Linux scheduler, in optimizing and preserving the user experience of energy-limited mobile systems.

Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers the spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application show that the Finite Element Model constitutes a powerful tool to better understand the diffusion of an innovation as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.