Orientador: Pedro Ganzeli / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-27T07:24:59Z (GMT). No. of bitstreams: 1 Evangelista_SergioRicardo_M.pdf: 2296917 bytes, checksum: 86c8717964ee17d10deb5fbfbe8679e8 (MD5) Previous issue date: 2015 / Resumo: Esta pesquisa teve por objetivo analisar a influência do Plano de Desenvolvimento da Escola (PDE-Escola) no processo de democratização da escola pública. Preocupou-se em compreender se esse modelo de planejamento favoreceu ou não a participação nos processos de organização da unidade escolar. Adotamos como metodologia de pesquisa a abordagem qualitativa, utilizando como procedimentos metodológicos o levantamento bibliográfico referente ao PDE-Escola e à gestão democrática da escola pública no banco de dados de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), bem como nos artigos científicos publicados no Scientific Electronic Library Online (SciELO). Outro procedimento metodológico utilizado foi a análise documental de fontes primárias (Legislação, Planos de Ação do PDE-Escola e de Relatórios do PDE-Escola), acessados pela plataforma online Sistema Integrado de Monitoramento, Execução e Controle do Ministério da Educação (SIMEC). Verificamos que o modelo gerencial que informa o PDE-Escola, ao utilizar instrumentos de responsabilização e controle sobre o processo de gestão, ressignificou os conceitos de participação e autonomia no contexto da administração pública, não contribuindo com a ampliação da democratização da gestão escolar / Abstract: This research had as main goal to analyze the influence of the School Development Plan (PDE-School) in the public school democratization. It concerned in understanding whether this planning model favored or not the participation in the organization processes of school unit. We have adopted as a research methodology the qualitative approach, using as procedures the literature regarding to the PDE-School and democratic management of public schools in the database of Theses and Dissertations of Higher Education Personnel Training Coordination (CAPES) and as in scientific articles published in the Scientific Electronic Library Online (SCIELO). Another approach used was the documentary analysis of primary sources (legislation, PDE-School Action Plans and PDE-School Reports), accessed by the online platform Integrated Monitoring System, Implementation and Control of the Ministry of Education (SIMEC). We found that the management model that informs the PDE-School, using tools of accountability and control over the management process, meant the concepts of participation and autonomy in the context of public administration, not contributing to the expansion of democratization of school management / Mestrado / Politicas, Administração e Sistemas Educacionais / Mestre em Educação

Cette thèse a pour objet l’étude des solutions à l’équation des vagues en régime dit toit rigide lorsque l’amplitude des vagues tend vers zéro. Plus précisément, l’équation des vagues modélise le mouvement d’un fluide à surface libre borné en dessous par un fond fixe. Les équations dépendent de plusieurs paramètres physiques, notamment du rapport epsilon entre l’amplitude des vagues et la profondeur. Le modèle asymptotique toit rigide consiste à changer l’échelle de temps d’un rapport epsilon, puis de faire tendre ce paramètre, et donc l’amplitude des vagues, vers zéro. L’étude mathématique de cette limite correspond à un problème de perturbation singulière d’une équation dispersive. Dans cette thèse, on commence par utiliser des outils de résolution d’équations aux dérivées partielles de type hyperbolique pour démontrer un résultat d’existence locale pour l’équation des vagues en temps long. Ceci est suivi par un résultat de dispersion sur l’équation des vagues, utilisant des techniques de type phase stationnaire et décomposition de Paley-Littlewood pour l’étude des intégrales oscillantes. Enfin, la dernière partie de la thèse utilise les résultats obtenus ci-dessus pour étudier un défaut de compacité dans la convergence faible (mais non forte) des solutions de l’équation des vagues lorsque l’amplitude tend vers 0. / In this thesis, we study the behavior of the solutions of the Water-Waves equations in the rigid lid regime as the amplitude of the waves goes to zero. More precisely, the Water-Waves equations investigate the dynamic of a free surface fluid, bounded from below by a fixed bottom. The equations depends on many physical parameters, as the ratio epsilon between the wave amplitude and the deepness of the water. The rigid lid model consists in scaling the time by an epsilon factor and taking the limit epsilon goes to zero, simulating a situation where the amplitude of the waves goes to zero. The mathematical study of this limit correspond to a singular perturbation problem of a dispersive equation. In this thesis, we first use classical tools of hyperbolics equations to prove a long time existence result for the Water-Waves equations. We then prove a dispersion result for these equations, using stationary phase methods and Paley-Littlewood decomposition. We then combine these results to highlight the lack of compactness in the weak (but non strong) convergence of the solutions of the Water-Waves equations as the amplitude goes to zero.

Probability theory is the study of random phenomena. Many dynamical systems with random influence, in nature or artificial complex systems, are better modeled by equations incorporating the intrinsic stochasticity involved. In probability theory, stochastic partial differential equations (SPDEs) generalize partial differential equations through random force terms and coefficients, while stochastic differential equations (SDEs) generalize ordinary differential equations. They are both abound in models involving Brownian motion throughout science, engineering and economics. However, Brownian motion is just one example of a random noisy input. The goal of this thesis is to make contributions in the study and applications of stochastic dynamical systems involving a wider variety of stochastic processes and noises. This is achieved by considering different models arising out of applications in thermal engineering, population dynamics and mathematical finance.<br><div><br></div><div>1. Power-type non-linearities in SDEs with rough noise: We consider a noisy differential equation driven by a rough noise that could be a fractional Brownian motion, a generalization of Brownian motion, while the equation's coefficient behaves like a power function. These coefficients are interesting because of their relation to classical population dynamics models, while their analysis is particularly challenging because of the intrinsic singularities. Two different methods are used to construct solutions: (i) In the one-dimensional case, a well-known transformation is used; (ii) For multidimensional situations, we find and quantify an improved regularity structure of the solution as it approaches the origin. Our research is the first successful analysis of the system described under a truly rough noise context. We find that the system is well-defined and yields non-unique solutions. In addition, the solutions possess the same roughness as that of the noise.<br></div><div><br></div><div>2. Parabolic Anderson model in rough environment: The parabolic Anderson model is one of the most interesting and challenging SPDEs used to model varied physical phenomena. Its original motivation involved bound states for electrons in crystals with impurities. It also provides a model for the growth of magnetic field in young stars and has an interpretation as a population growth model. The model can be expressed as a stochastic heat equation with additional multiplicative noise. This noise is traditionally a generalized derivative of Brownian motion. Here we consider a one dimensional parabolic Anderson model which is continuous in space and includes a more general rough noise. We first show that the equation admits a solution and that it is unique under some regularity assumptions on the initial condition. In addition, we show that it can be represented using the Feynman-Kac formula, thus providing a connection with the SPDE and a stochastic process, in this case a Brownian motion. The bulk of our study is devoted to explore the large time behavior of the solution, and we provide an explicit formula for the asymptotic behavior of the logarithm of the solution.<br></div><div><br></div><div>3. Heat conduction in semiconductors: Standard heat flow, at a macroscopic level, is modeled by the random erratic movements of Brownian motions starting at the source of heat. However, this diffusive nature of heat flow predicted by Brownian motion is not observed in certain materials (semiconductors, dielectric solids) over short length and time scales. The thermal transport in these materials is more akin to a super-diffusive heat flow, and necessitates the need for processes beyond Brownian motion to capture this heavy tailed behavior. In this context, we propose the use of a well-defined Lévy process, the so-called relativistic stable process to better model the observed phenomenon. This process captures the observed heat dynamics at short length-time scales and is also closely related to the relativistic Schrödinger operator. In addition, it serves as a good candidate for explaining the usual diffusive nature of heat flow under large length-time regimes. The goal is to verify our model against experimental data, retrieve the best parameters of the process and discuss their connections to material thermal properties.<br></div><div><br></div><div>4. Bond-pricing under partial information: We study an information asymmetry problem in a bond market. Especially we derive bond price dynamics of traders with different levels of information. We allow all information processes as well as the short rate to have jumps in their sample paths, thus representing more dramatic movements. In addition we allow the short rate to be modulated by all information processes in addition to having instantaneous feedbacks from the current levels of itself. A fully informed trader observes all information which affects the bond price while a partially informed trader observes only a part of it. We first obtain the bond price dynamic under the full information, and also derive the bond price of the partially informed trader using Bayesian filtering method. The key step is to perform a change of measure so that the dynamic under the new measure becomes computationally efficient.</div>

The subsurface flow is usually subject to uncertain porous media structures. However, in most cases we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters as random fields, then the expectation of Quantity of Interest(QoI) can be evaluated by the Monte Carlo method. In this study, we develop a full multigrid-multilevel Monte Carlo (FMG-MLMC) method to speed up the evaluation of random parameters effects on single-phase porous flows. In general, MLMC method applies a series of discretization with increasing resolution and computes the QoI on each of them, the success of which lies in the effective variance reduction. We exploit the similar hierarchies of MLMC and multigrid methods, and obtain the solution on coarse mesh Qcl as a byproduct of the multigrid solution on fine mesh Qfl on each level l. In the cases considered in this thesis, the computational saving is 20% theoretically. In addition, a comparison of Monte Carlo and Quasi-Monte Carlo (QMC) methods reveals a smaller estimator variance and faster convergence rate of the latter method in this study.

Moment methods derived from the kinetic theory of gases can be used for the prediction of continuum and non-equilibrium flows and offer numerical advantages over other methods, such as the Navier-Stokes model. Models developed in this fashion are described by first-order hyperbolic partial differential equations (PDEs) with stiff local relaxation source terms. The application of discontinuous-Galerkin (DG) methods for the solution of such models has many benefits. Of particular interest is the third-order accurate, coupled space-time discontinuous-Galerkin Hancock (DGH) method. This scheme is accurate, as well as highly efficient on large-scale distributed-memory computers. The current study outlines a general implementation of the DGH method used for the parallel solution of moment methods in one, two, and three dimensions on modern distributed clusters. An algorithm for adaptive mesh refinement (AMR) was developed alongside the implementation of the scheme, and is used to achieve even higher accuracy and efficiency. Many different first-order hyperbolic and hyperbolic-relaxation PDEs are solved to demonstrate the robustness of the scheme. First, a linear convection-relaxation equation is solved to verify the order of accuracy of the scheme in three dimensions. Next, some classical compressible Euler problems are solved in one, two, and three dimensions to demonstrate the scheme's ability to capture discontinuities and strong shocks, as well as the efficacy of the implemented AMR. A special case, Ringleb's flow, is also solved in two-dimensions to verify the order of accuracy of the scheme for non-linear PDEs on curved meshes. Following this, the shallow water equations are solved in two dimensions. Afterwards, the ten-moment (Gaussian) closure is applied to two-dimensional Stokes flow past a cylinder, showing the abilities of both the closure and scheme to accurately compute classical viscous solutions. Finally, the one-dimensional fourteen-moment closure is solved.

This project concerns the computational solution of inverse problems formulated as partial differential equation (PDE)-constrained optimization problems with interior data. The areas addressed are twofold. First, we present a novel software architecture designed to solve inverse problems constrained by an elliptic system of PDEs. These generally require the solution of forward and adjoint problems, evaluation of the objective function, and computation of its gradient, all of which are approximated numerically using finite elements. The creation of specialized "layered"' elements to perform these tasks leads to a modular software structure that improves code maintainability and promotes functional interoperability between different software components. Second, we address issues related to forward model definition in the presence of boundary condition (BC) uncertainty. We propose two variational formulations to accommodate that uncertainty: (a) a Bayesian formulation that assumes Gaussian measurement noise and a minimum strain energy prior, and (b) a Lagrangian formulation that is completely free of displacement and traction BCs. This work is motivated by applications in the field of biomechanical imaging, where the mechanical properties within soft tissues are inferred from observations of tissue motion. In this context, the constraint PDE is well accepted, but considerable uncertainty exists in the BCs. The approaches developed here are demonstrated on a variety of applications, including simulated and experimental data. We present modulus reconstructions of individual cells, tissue-mimicking phantoms, and breast tumors.

We study a free boundary problem with initial data given on three-dimensional cones. In particular, we study when the free boundary is allowed to pass through the vertex of the cone, which depends on the cone’s slope, determined by a parameter c. With a mix of analytical and computational methods, we show that the free boundary may pass through the vertex of the cone when c ≤ 0.43.

PDE models are a major tool used in quantitative modeling of biological and scientific phenomena. Their major shortcoming is the high computational complexity of solving each model. When scaling up to millions of simulations needed to find their optimal parameters we frequently have to wait days or weeks for results to come back. To cope with that we propose a neural network approach that can produce comparable results to a PDE model while being about 1000x faster. We quantitatively and qualitatively show the neural network metamodels are accurate and demonstrate their potential for multi-objective optimization in biology. We hope this approach can speed up scientific research and discovery in biology and beyond.<br>

Cette thèse porte sur l’étude de nouveaux modèles de jeux à champ moyen. On étudie dans un premier temps des modèles d’arrêt optimal et de contrôle impulsionnel en l’absence de bruit commun. On construit pour ces modèles une notion de solution adaptée pour laquelle on prouve des résultats d’existence et d’unicité sous des hypothèses naturelles. Ensuite, on s’intéresse à plusieurs propriétés des jeux à champ moyen. On étudie la limite de ces modèles vers des modèles d’évolution pures lorsque l’anticipation des joueurs tend vers 0. On montre l’unicité des équilibres pour des systèmes fortement couples (couples par les stratégies) sous certaines hypothèses. On prouve ensuite certains résultats de régularités sur une ”master equation” qui modélise un jeu à champ moyen avec bruit commun dans un espace d’états discret. Par la suite on présente une généralisation de l’algorithme standard d’Uzawa et on l’applique à la résolution numérique de certains modèles de jeux à champ moyen, notamment d’arrêt optimal ou de contrôle impulsionnel. Enfin on présente un cas concret de jeu à champ moyen qui provient de problèmes faisant intervenir un grand nombre d’appareils connectés dans les télécommunications. / This thesis is concerned with new models of mean field games. First, we study models of optimal stopping and impulse control in the case when there is no common noise. We build an appropriate notion of solutions for those models. We prove the existence and the uniqueness of such solutions under natural assumptions. Then, we are interested with several properties of mean field games. We study the limit of such models when the anticipation of the players vanishes. We show that uniqueness holds for strongly coupled mean field games (coupled via strategies) under certain assumptions. We then prove some regularity results for the master equation in a discrete state space case with common noise. We continue by giving a generalization of Uzawa’s algorithm and we apply it to solve numerically some mean field games, especially optimal stopping and impulse control problems. The last chapter presents an application of mean field games. This application originates from problems in telecommunications which involve a huge number of connected devices.

L'analyse du comportement d'un solide ou de plusieurs solides à l'intérieur d'un fluide est un problème de longue date, que l'on peut voir décrit dans de nombreux manuels classiques d'hydrodynamique. Son étude d'un point de vue mathématique a suscité une attention croissante, en particulier au cours des 15 dernières années. Ce projet de recherche vise à mettre l'accent sur plusieurs aspects de cette analyse mathématique, en particulier sur le contrôle et les problèmes asymptotiques. Un modèle simple d'évolution fluide-solide est celui d'un seul corps rigide entouré d'un fluide incompressible parfait. Le fluide est modelé par les équations d'Euler, tandis que le solide évolue selon la loi de Newton et est influencé par la pression du fluide sur la limite. L'objectif de cette thèse de doctorat consisterait en diverses études dans cette branche et, en particulier, étudierait les questions de contrôlabilité de ce système, ainsi que des modèles de limite pour les solides minces qui convergent vers une courbe. Nous souhaitons également étudier le système de contrôle Navier-Stokes / solid d'une manière similaire au problème de contrôlabilité du système Euler / solid. Une autre direction pour ce projet de doctorat est d'obtenir une limite lorsque le solide se concentre dans une courbe. Est-il possible d'obtenir un modèle simplifié d'un objet mince évoluant dans un fluide parfait, de la même manière que des modèles simplifiés ont été obtenus pour des objets qui sont petits dans toutes les directions? Cela pourrait ouvrir la voie à des recherches futures sur la dérivation des flux de cristaux liquides comme limite du système décrivant l'interaction entre le fluide et un filet de tubes solides lorsque le diamètre des tubes converge à zéro. / The analysis of the behavior of a solid or several solids inside a fluid is a long-standing problem, that one can see described in many classical textbooks of hydrodynamics. Its study from a mathematical viewpoint has attracted a growing attention, in particular in the last 15 years. This research project aims at focusing on several aspect of this mathematical analysis, in particular on control and asymptotic issues. A simple model of fluid-solid evolution is that of a single rigid body surrounded by a perfect incompressible fluid. The fluid is modeled by the Euler equations, while the solid evolves according to Newton’s law, and is influenced by the fluid’s pressure on the boundary. The goal of this PhD thesis would consist in various studies in this branch, and in particular would investigate questions of controllability of this system, as well as limit models for thin solids converging to a curve. We would also like to study the Navier-Stokes/solid control system in a similar manner to the previously discussed controllability problem for the Euler/solid system. Another direction for this PhD project is to obtain a limit when the solid concentrates into a curve. Is it possible to obtain a simplified model of a thin object evolving in a perfect fluid, in the same way as simplified models were obtained for objects that are small in all directions? This could open the way to future investigations on derivation of liquid crystal flows as the limit of the system describing the interaction between the fluid and a net of solid tubes when the diameter of the tubes is converging to zero.