Dissertations / Theses on the topic 'Long-Time stability'

Thesis (Ph. D.) -- University of Maryland, College Park, 2007.
Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Este trabalho analisa o fenômeno da estabilidade de tensão no domínio do tempo incluindo fenômenos rápidos (transitórios) e lentos (longo-termo). As diferentes formas de estabilidade existentes nos sistemas elétricos de potência são definidas e classificadas de acordo com a variável de interesse e com a amplitude do distúrbio. Utilizando-se um simples sistema elétrico de potência, verifica-se através de formulações dinâmicas fatores relevantes ao fenômeno da estabilidade de tensão. Investiga-se a influência de cargas do tipo potência constante e impedância constante sobre a estabilidade de tensão. Compensadores estáticos são incluídos nas análises e verifica-se a existência de regiões de operação onde as ações de controle não apresentam o efeito esperado. Investiga-se através de cenários o efeito adverso de dispositivos de controle com o limitador de sobre- excitação e o transformador de tape variável sobre a estabilidade de tensão. A partir de uma versão do programa de estabilidade transitória TRANSTAB, foram desenvolvidas duas versões do programa computacional VOLTDYN para simular no domínio do tempo o fenômeno da estabilidade de tensão. A primeira versão do programa Utiliza um algoritmo de integração de passo variável usando o método trapezoidal implícito enquanto que a segunda versão utiliza o método de Adams-Bashforth- Moulton. Diversos testes computacionais com as duas versões são realizados comprovando-se a importância desta forma de análise.
This work is concerned with voltage stability analysis in time domain including transient and long-term time frames. Different power system stability forms are defined and classified according to the variable of interest and with the disturbance magnitude. Using a simple power system model, it is shown through dynamics formulations important aspects of the voltage stability phenomenon. Important aspects of load characteristics of constant power type and mixed (constant power/constant impedance) type on voltage stability are investigated. A static compensator model is included in the analysis and it is verified that under specific operation conditions the control actions are not efficient. Scenarios show the adverse effects of long-term control devices such as overexcitation limiters and under load tap changers on voltage stability. One version of the transient stability program TRANSTAB is modified in order to simulate transient and long-term voltage phenomena. The resulting modified computer program is called VOLTDYN. Two versions of the VOLTDYN progran are available. The first version uses a variable step-size algorithm based on the trapezoidal method. The other includes a variable step-size algorithm based on the Adams- Bashforth-Moulton method.

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2008.
Title from electronic title page (viewed Jun. 26, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Statistics and Operations Research Statistics." Discipline: Statistics and Operations Research; Department/School: Statistics and Operations Research.

Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2006.
"Title from dissertation home page (viewed June 28, 2007)." Source: Dissertation Abstracts International, Volume: 67-06, Section: B, page: 3172. Adviser: Roger Temam.

In order to optimize limited infrastructure, many power systems are frequently operated close to critical, or bifurcation, points. While operating close to such critical points can be economically advantageous, doing so increases the probability of a blackout. With the continued deployment of Phasor Measurement Units (PMUs), high sample rate data are dramatically increasing the real time observability of the power grids. Prior research has shown that the statistics of these data can provide useful information regarding network stability and associated bifurcation proximity. Currently, it is not common practice for transmission and distribution control centers to leverage the higher order statistical properties of PMU data. If grid operators have the tools to determine when these statistics warrant control action, though, then the otherwise unused statistical data present in PMU streams can be transformed into actionable information. In order to address this problem, we present two methods that aim to gauge and improve system stability using the statistics of PMU data. The first method shows how sensitivity factors associated with the spectral analysis of the reduced power flow Jacobian can be used to weight and filter incoming PMU data. We do so by demonstrating how the derived participation factors directly predict the relative strength of bus voltage variances throughout a system. The second method leverages an analytical solver to determine a range of "critical" bus voltage variances. The monitoring and testing of raw statistical data in a highly observable load pocket of a large system are then used to reveal when control actions are needed to mitigate the risk of voltage collapse. A simple reactive power controller is then implemented that pushes the stability of the system back to a stable operating paradigm. Full order dynamic time domain simulations are used in order to test this method on both the IEEE 39 bus system and the 2383 bus Polish system. We also compare this method to two other, more conventional, controllers. The first relies on voltage magnitude signals, and the second depends only on local control of a reactive power resource. This comparison illustrates how the use of statistical information from PMU measurements can substantially improve the performance of voltage collapse mitigation methods.

Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2008.
Title from PDF t.p. (viewed on Jul 28, 2009). Source: Dissertation Abstracts International, Volume: 69-12, Section: B, page: 7553. Adviser: Kevin Zumbrun.

Cette thèse traite de deux problèmes indépendants liés aux phénomènes de propagation des ondes dans les milieux dispersifs. Dans la première partie, nous étudions le comportement en temps long des solutions des équations de Maxwell dans des milieux dissipatifs généralisés de Drude-Lorentz. Plus précisément, nous souhaitons quantifier les pertes dans de tels milieux à l'aide du taux de décroissance de l'énergie électromagnétique pour le problème de Cauchy correspondant. Cette première partie est elle-même composée de deux approches. La première, l'approche par fonctions de Lyapunov en fréquence, consiste à obtenir une inégalité différentielle (en temps) pour certaines fonctionnelles de la solution, les fonctions de Lyapunov L(k) où k désigne la fréquence spatiale. Les estimations de stabilité sont ensuite obtenues par l'intégration en temps de l'inégalité différentielle. En développant cette méthode, nous obtenons un résultat de stabilité polynomiale sous des hypothèses de dissipation fortes. La deuxième approche, l'approche modale, exploite les propriétés spectrales de l'opérateur hamiltonien apparaissant dans le problème de Cauchy. Cette dernière approche améliore la première en autorisant des hypothèses de dissipation faibles. Dans la deuxième partie du travail, nous nous intéressons au problème de transmission d'une couche de métamatériau de Drude non dissipatif dans un milieu diélectrique. Dans ce contexte, nous considérons les équations de Maxwell temporelles bidimensionnel en polarisation TM et nous les reformulons en une équation de Schrödinger dont le Hamiltonien, A, est un opérateur autoadjoint non borné. La transformation de Fourier nous permet de travailler avec des Hamiltoniens réduits A(k), k ∈ R. Enfin, nous nous intéressons au spectre ponctuel du Hamiltonien réduit qui est lié aux modes guidés du problème original. Cette étude débouche sur une relation de dispersion dont la difficulté réside dans son caractère hautement non linéaire par rapport au paramètre spectral. Nous prouvons l'existence d'une infinité dénombrable de branches de solutions pour la relation de dispersion : les courbes de dispersion. Nous donnons une analyse précise de ces courbes et mettons en lumière, notamment, l'existence d'ondes guidées correspondant à des palsmons surface
This PhD thesis addresses two independent problems related to wave propagation phenomena in dispersive media. In the first part, we investigate the long-time behavior of solutions of Maxwell’s equations in dissipative generalized Drude-Lorentz media. More precisely, we wish to quantify the loss in such media in terms of the decay rate of the electromagnetic energy for the corresponding Cauchy problem. This first part is in turn composed by two approaches. The first one, namely, the frequency dependent Lyapunov approach, consists in deriving a differential inequality (in time) for certain functionals of the solution, the Lyapunov functions L(k), where k is the spatial frequency. The stability estimates are then obtained from the time integration of the differential inequality. By developing this method, we obtain a polynomial stability result under strong dissipative assumptions. The second approach, the modal approach, exploits the spectral properties of the Hamiltonian operator appearing in the Cauchy problem. This last approach ameliorates the first one by considering weak dissipation assumptions. In the second part of the work, we are interested in the transmission problem of a slab of non-dissipative Drude metamaterial within a dielectric. In this context, we consider the TM two dimensional time-dependent Maxwell’s equations and we reformulate it into a Schrödinger equation whose Hamiltonian, A, is a unbounded self-adjoint operator. Fourier transform allow us to work with the reduced Hamiltonians A(k), k ∈ R. Finally, we are interested in the point spectrum of the reduced Hamiltonian which is related to the guided modes of the original problem. This study leads to a diseprsion relation whose difficulty lies in its highly non-linear character with respect to the spectral parameter. We prove the existence of a countable infinity of solution branches for the dispersion relation: the so-called dispersion curves. We give a precise analysis of these curves and enlighten the existence of guided waves which correspond to surface plasmons

Cette thèse porte sur l’étude des propriétés qualitatives des solutions des équations des ondes et de la chaleur semi-linéaires. Les résultats qui y sont décrits sont les suivants. Les deux premiers concernent l’existence et la description de dynamiques explosives de concentration en temps fini de l’état stationnaire à symétrie radiale dans le régime dit énergie surcritique ; en outre, pour l’équation des ondes la stabilité de ces phénomènes est étudiée dans le cas radial, et pour l’équation de la chaleur le cas plus général d’un domaine borné avec conditions de Dirichlet au bord est considéré. Le troisième porte sur la classification des dynamiques possibles près de l’état stationnaire radial pour l’équation de la chaleur dans le régime dit énergie critique, trois scénarios ayant lieu : la stabilisation, l’instabilité par explosion auto-similaire à profil explosif constant en espace, et l’instabilité par dissipation vers la solution nulle. Enfin, le quatrième a pour objet l’existence et la stabilité de profils explosifs auto-similaires non constants en espace pour l’équation de la chaleur dans le cas énergie surcritique
This thesis is devoted to the study of qualitative properties for solutions to the semilinear heat and wave equations. The results that are described are the following. The first two concern the existence and description of blow-up dynamics in which the radially symmetric stationary state is concentrated in finite time in the so-called energy supercritical regime; in addition, for the wave equation the stability of these phenomena is studied in the radial case, and for the heat equation the more general case of a bounded domain with Dirichlet condition at the boundary is considered. The third one deals with the classification of the possible dynamics near the radial stationary state for the heat equation in the so-called energy critical regime, where three scenarii occur: stabilization, instability by blow-up with the constant in space blow-up profile, and instability by dissipation to the null solution. Eventually, in the forth result we investigate the existence and the stability of self-similar blow-up profiles that are not constant in space, for the heat equation in the energy supercritical case

Policies at assisted living facilities should be designed to develop high quality social relationships among older persons that could increase the contentment of the residents. Despite the broad consensus on this mission, the role of social support in the perceived contentment of assisted living facility residents has not been adequately explored. Using social network theory as the framework for this study, the purpose of this quantitative study was to determine whether (a) perceived level of social support was related to perceived level of contentment with life among assisted living facility residents, (b) the length of time spent in the facility was related to perceived levels of contentment, and (c) perceived social support moderated the relationship between the length of time in the facility and perceived levels of contentment with life. The sample included 100 residents from 2 assisted living facilities in North Carolina. The Multidimensional Scale of Perceived Social Support and the Generalized Contentment Scale were used in this study. Linear regression analyses were employed to answer the research questions. Participants with higher levels of perceived social support tended to have higher levels of perceived contentment with life, and the length of time residents had spent in the facility was not related to their perceived contentment with life. In addition, levels of social support did not moderate the relationship between the length of time respondents had been in the facility and contentment; age, gender, ethnicity, and marital status were not related to perceived contentment with life. This study leads to positive social change by providing long-term care providers with information on social support systems and how staff can create conditions for them to enjoy better social relationships and experience greater support, thereby facilitating their contentment with life.

This thesis deal with design of multi-quadrant power supply in linear and switching mode. In the case of the switching mode energy recuparation is also considered as well as optimalization of change of load response over time. Power supplies are designed as general purpose laboratory and process power supplies. Power supplies are designed so that they can be connected via galvanic insulated USB interface with a PC

Cette thèse est essentiellement composée de deux parties traitant des problèmes de Cauchy ou des problèmes périodiques. Dans la première partie, on étudie la stabilité de solutions régulières au voisinage d'états d'équilibre non constants pour un système d'Euler-Maxwell isentropique compressible bipolaire. Par des estimations d'énergie classiques et un argument de récurrence sur l'ordre des dérivées des solutions, on montre l'existence globale et l'unicité des solutions régulières du système lorsque les données initiales sont proches des états d'équilibre. On obtient aussi le comportement asymptotique des solutions quand le temps tend vers l'infini. Dans la deuxième partie, on considère la stabilité en temps long des solutions régulières de systèmes d'Euler-Maxwell et de Navier-Stokes-Maxwell compressibles dans le cas non isentropique lorsque les états d'équilibre sont constants. Grâce à des choix convenables de symétriseurs des systèmes et à des estimations d'énergie, on montre l'existence globale et l'unicité des solutions régulières des systèmes avec données initiales petites. De plus, par le principe de Duhamel et l'outil d'analyse de Fourier, on obtient des taux de décroissance des solutions quand le temps tend vers l'infini
This thesis is essentially composed of two parts dealing with Cauchy problems and periodic problems. In the first part, we study the stability of smooth solutions near non constant equilibrium states for a two-fluid isentropic compressible Euler-Maxwell system.By classical energy estimates together with an induction argument on the order of the derivatives of solutions, we prove the existence and uniqueness of global solutions to the system when the given initial data are near the equilibrium states. We also obtain the asymptotic behavior of solutions when the time goes to infinity. In the second part, we consider the long time stability of the global smooth solutions for compressible Euler-Maxwell and Navier-Stokes-Maxwell systems in non isentropic case when the equilibrium solutions are constants. With the help of suitable choices of symmetrizers and energy estimates, we prove the existence and uniqueness of global solutions to the systems with given small initial data. Furthermore, using the Duhamel principle and the Fourier analysis tool, we obtain the decay rates of smooth solutions as the time goes to infinity

The current intellectual climate regarding economics seems to be at an agreement regarding the theory of uncovered interest parity and its unreliability within real life application. The purpose of this thesis is to test how the theory holds over periods with varying economic stability, both using a short- and long-horizon test in order to establish the usefulness of uncovered interest parity as a predictor for exchange rate movements. The short-horizon test will utilize the interbank offering rate, and the long-horizon test the yield to maturity of government 10-year benchmark bonds as the interest rate. The sample period is 2000 to 2018, covering the financial crisis of 2007. We will focus on three different time periods: pre-crisis, crisis and post-crisis. We will use ordinary least squares (OLS) regression and an extreme sampling. From the regressions we conclude that most of the time periods move against the uncovered interest parity, where only the crisis period is in line with the theory. The extreme sampling supports this result, as larger interest differentials provide the rational expectations with more predictive power of the future spot exchange rate.

Je décris le comportement en temps long de plusieurs processus qui illustrent les mécanismes de sélection naturelle. Il arrive que ces effets de sélection s’interprètent comme un conditionnement qui biaise la dynamique d’un processus aléatoire "neutre". Ce processus évolue sur un espace potentiellement très général, notamment continu et non borné. On peut ainsi caractériser aussi bien la dynamique du profil complet de la population que celle du profil d’un individu choisi uniformément dans la population. On voit naturellement apparaître dans ces modèles des transitions brutales de ces lois qui rendent l’analyse plus délicate que pour les modèles sans conditionnement. La première partie de ce travail consiste à mettre en place des conditions permettant d’obtenir des résultats analogues à la stationnarité lorsqu’on prend en compte un tel conditionnement. La seconde porte sur l’application de ces critères à différents modèles de population sous sélection et sur leur interprétation. Les exemples d'applications concernent le modèle de l'optimum mobile pour l'adaptation à un changement environnemental, un modèle de sélection de groupes et celui du cliquet de Müller sur le maintien d'une sous-population préservée des mutations délétères
I describe the long term behavior of several processes that model the mechanisms of natural selection. In the cases under consideration, one can interpret those selective effects as a conditioning which introduces a bias on the dynamics of some « neutral » stochastic process. This process evolves in a potentially very general space, notably continuous and unbounded. By these means, one can characterize the dynamics of the whole profile of individuals in the population of study as well as the profile of an individual uniformly chosen in the population. One can naturally see in these descriptions some brutal transitions of the distribution laws as time evolves, which makes the analysis much trickier than for the models without conditioning. The first part of this thesis consists in setting the conditions under which one can prove results analogous to the notion of stationarity while taking the conditioning into account. The second part is dedicated to the application of these criteria for a diversity of models of populations under selection and their interpretation. Examples of application include the mobile optimum model for adaptation to environmental change, a group selection model and Müller's ratchet model that describes how the sub-population unaffected by deleterious mutations can maintain itself

L’étude des variations temporelles de gravité ont une longue tradition en Europe Centrale. Dans la station, J9, située à Strasbourg depuis les années 1970, les trois principaux types de gravimètre (ressort, supraconducteur (SG), absolu) ont été utilisés. Ces séries permettent l’examen des améliorations instrumentales à partir de la stabilité à long terme et de la dérive instrumentale. Nous montrons que le SG est l’instrument le plus performant pour l’étude des marées de longues périodes et de faibles amplitudes. Nous montrons les résultats obtenus par analyse de marée de ces petites ondes. Nous estimons la période de la Free Core Nutation et nous recherchons celle de la Free Inner Core Nutation (FICN), qui n'a pas encore été observée. Pour cela nous faisons une étude précise, afin de séparer les ondes de faible amplitude, au voisinage de périodes possibles de la FICN
The study of temporal variations of gravity has a long tradition in Central Europe. Since the 1970s three main gravimeter types (spring, superconducting (SG) and absolute) have been set up at the J9 gravity station located in Strasbourg. These series allow us to review the instrumental improvements from the analyses of long term stability and instrumental drift. We show that the SG is the most powerful tool for thestudy of the low frequency and small amplitudes tides. We show the tidal analysis results for these tidal waves. We estimate the period of the Free Core Nutation and we seek the one of the Free Inner Core Nutation (FICN), which has not yet been observed. For this we make a careful study, in order to separate the low-amplitude waves in the vicinity of possible periods of FICN
La deformación elasto-gravitacional de la Tierra y las correspondientes variaciones temporales de la gravedad asociadas, registradas en la superficie terrestre mediante los gravímetros, son debidas a distintos fenómenos geofísicos con diferentes períodos y amplitudes, incluyendo entre otros a las denominadas mareas terrestres, que son el fenómeno que genera los efectos más fuertes (dichas mareas terrestres son los movimientos inducidos en la Tierra sólida y los cambios en su potencial gravitatorio derivados de las fuerzas de marea generadas por los cuerpos celestes).El objetivo principal de este trabajo consiste en mostrar la importancia tanto de la longitud de las series de datos de gravedad, como de la calidad de dichas series para mejorar nuestro conocimiento sobre la dinámica de la Tierra a través de los análisis de las mareas terrestres. [...]

Since the past decade, use of electro-osmotic flow (EOF) as an alternative flow mechanism in microdevices is becoming more popular due to its less bulky and low maintenance system design. However, one of the biggest shortcomings for its usage in mainstream applications is that it requires the concerned liquid to be electrically conductive. One idea can be to use the flow of conductive fluids to transport non-conductive liquids passively via interfacial shear transfer. Such an idea can has numerous applications in a wide range of fields like bio-chemical processing (e.g. lab-on-a-chip reactors, mixers, etc.), to oil extraction from porous rock formations. One of the significant characteristics of micro-scale flows is high surface to volume ratio, which significantly highlights the role of multi-phase interfaces in such dynamics. The presence of a fluid-fluid interface in an EOF necessitates the characterization of the parameters responsible for hydrodynamic instability of such systems. The present work focuses on the role of steady and time-dependent electric stress (Maxwell stress), capillary force and disjoining pressure on fluid-fluid interfacial instability. A linear stability analysis of interfacial perturbation was performed for a thin film of electrolyte under DC and AC electric fields. Through long wave asymptotic analysis of the Orr-Sommerfeld equations, parametric stability thresholds of a thin aqueous film explored. Further, a set of experiments were performed in order to characterize the EOF in a rectangular microchannel. With the help of a Particle Tracking Velocimetry analysis, velocity distributions were obtained which agreed well to the theoretical values. This was further used to estimate PDMS zeta potential, which was found to be within the reported values in the existing literature. Liquid-liquid interfacial deformation was also explored under a time-periodic EOF and a wide range of the magnitudes of capillary force, and diffusive and convective transport.