This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared.

This research project was carried out at the von Karman Institute for Fluid Dynamics (VKI), in Belgium, in collaboration and with the funding of Centre Technique des Industries Mécaniques (CETIM) in France.<p>The flow of a mixture of two fluids in pipes can be frequently encountered in nuclear, chemical or mechanical engineering, where gas-liquid eactors, boilers, condensers, evaporators and combustion systems can be used. The presence of section changes or more generally geometrical singularities in pipes may affect significantly the behavior of twophase flow and subsequently the resulting pressure drop and mass flow rate. Therefore, it is an important subject of investigation in particular when the application concerns industrial safety valves.<p>This thesis is intended to provide a thorough research on two-phase (air-water) flow phenomena under various circumstances. The project is split in the following steps. At first, experiments are carried out in simple geometries such as smooth and sudden divergence and convergence singularities. Two experimental facilities are built; one in smaller scale in von Karman Institute and one in larger scale in CETIM. During the first part of the study, relatively simple geometrical discontinuities are investigated. The characterization and modeling of contraction and expansion nozzles (sudden and smooth change of section) is carried out. The pressure evolution is measured and pressure drop correlations are deduced. Flow visualization is also performed with a high-speed camera; the different flow patterns are identified and flow regime maps are established for a specific configuration.<p>A dual optical probe is used to determine the void fraction, bubble size and velocity upstream and downstream the singularities.<p>In the second part of the project, a more complex device, i.e. a Safety Relief Valve (SRV), mainly used in nuclear and chemistry industry, is thoroughly studied. A transparent model of a specific type of safety valve (1 1/2" G 3") is built and investigated in terms of pressure evolution. Additionally, flow rate measurements for several volumetric qualities and valve openings are carried out for air, water and two-phase mixtures. Full optical access allowed identification of the structure of the flow. The results are compared with measurements performed at the original industrial valve. Flowforce analysis is performed revealing that compressible and incompressible flowforces in SRV are inversed above a certain value of valve lift. This value varies with critical pressure ratio, therefore is directly linked to the position at which chocked flow occurs during air valve operation. In two-phase flow, for volumetric quality of air=20%, pure compressible flow behavior, in terms of flowforce, is remarked at full lift. Numerical simulations with commercial CFD code are carried out for air and water in axisymmetric 2D model of the valve in order to verify experimental findings.<p>The subject of modeling the discharge through a throttling device in two-phase flow is an important industrial problem. The proper design and sizing of this apparatus is a crucial issue which would prevent its wrong function or accidental operation failure that could cause a hazardous situation. So far reliability of existing models predicting the pressure drop and flow discharge in two-phase flow through the valve for various flow conditions is questionable. Nowadays, a common practice is widely adopted (standard ISO 4126-10 (2010), API RP 520 (2000)); the Homogeneous Equilibrium Method with the so-called !-method, although it still needs further validation. Additionally, based on !-methodology, Homogeneous Non-Equilibrium model has been proposed by Diener and Schmidt (2004) (HNE-DS), introducing a boiling delay coefficient. The accuracy of the aforementioned models is checked against experimental data both for transparent model and industrial SRV. The HNE-DS methodology is proved to be the most precise among the others. Finally, after application of HNE-DS method for air-water flow with cavitation, it is concluded that the behavior of flashing liquid is simulated in such case. Hence, for the specific tested conditions, this type of flow can be modeled with modified method of Diener and Schmidt (CF-HNE-DS) although further validation of this observation is required. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Dans cette thèse, nous nous intéressons à des singularités particulières dans les variétés de caractères. Dans le premier chapitre, on justifie que les caractères de représentations irréductibles d'un groupe fuchsien vers un groupe de Lie complexe semi-simple forment une orbifolde. Le lieu orbifold (i.e. l'ensemble des points dont l'isotropie n'est pas triviale) est constitué des caractères de représentations exceptionnelles. Dans le second chapitre, nous décrivons précisément le lieu orbifold quand le groupe de Lie est le groupe projectif linéaire sur un espace vectoriel complexe dont la dimension est un nombre premier. Dans le troisième et le quatrième chapitre nous cherchons à classifier les groupes d'isotropies possibles à conjugaison près apparaissant quand le groupe de Lie est respectivement un quotient du groupe spécial linéaire pour un espace vectoriel complexe de dimension finie quelconque dans le troisième chapitre et un quotient du groupe de spin complexe dans le quatrième chapitre. / Ln this thesis, we want to understand some singularities in the character variety. ln a first chapter, we justify that the characters of irreducible representations from a Fuchsian group to a complex semi-simple Lie group is an orbifold. The orbifold locus is, then, the characters of bad representations. ln the second chapter, we focus on the case where the Lie group is the projectif linear group over a complex vector space whose dimension is a prime number. ln particular we give an explicit description of this locus. ln the third and fourth chapter, we describe the isotropy groups (i.e. the centralizers of bad subgroups) arising in the cases when the Lie group is a quotient of the special linear group of a complex vector space of finite dimension (third chapter) and when the Lie group is a quotient of a complex spin group in the fourth chapter.

This thesis is concerned with the analysis of the finite element method and the discontinuous Galerkin method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity, if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained with numerical integration. The theoretical results are verified by numerical experiments. 1

No description available.

A toute variété algébrique on peut associer différents objets algébrico-géométriques qui rendent compte en particulier des singularités de la variété. Cette thèse traite de l'interaction entre l'étude des singularités, le schéma des arcs et le module des dérivations dans le cadre des courbes algébriques affines planes. Elle démontre que les d-tissus quasi-homogènes incomplets sont linéarisables pour d > 3 en utilisant un théorème d'Alain Hénaut. Enfin, dans un dernier chapitre, cette thèse introduit le formalisme des fonctions zêta motiviques associées à une 1-forme locale. / To any algebraic variety one can associate several algebraic-geometric objets which in particular provide information on the singularities of the variety. This thesis deals with the interaction between the study of singularities, arc spaces and derivations module in the context of affine algebraic plane curves. Using a theorem of Alain Hénaut, we show that quasi-homogeneous incomplete d-webs are linearizable for d > 3. Finally, in the last chapter, this thesis intoduces the formalism of motivic zêta function of a local 1-form.

Orientador: Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T09:33:59Z (GMT). No. of bitstreams: 1 Souza_WenderJosede_D.pdf: 1230622 bytes, checksum: 578f86e5fe4ff35247fcfb0fb04975b8 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho consideramos alguns aspectos da teoria qualitativa de sistemas dinâmicos suaves por partes. Nosso principal objetivo é estudar uma classe de tais sistemas, onde o conjunto de descontinuidade é dado por uma hipersuperfície ? e além disso, assumimos que em cada região determinada por ? o campo de vetores definido é um sistema Hamiltoniano. Apresentamos estudos relacionados à regularização de campos de vetores suaves por partes em Rn que preservam volume nas componentes suaves. Abordamos também singularidades de funções suaves por partes, onde formas normais e seus desdobramentos são apresentados. Por fim estudamos bifurcações de campos de vetores Hamiltonianos refrativos / Abstract: In this work, we consider some aspects of the qualitative theory of non smooth dynamical systems in Rn. Our main goal is to study a class of such systems where the discontinuity set is concentrated in a hypersurface ? and moreover, we assume that in each region determined by ? the vector field is a Hamiltonian system. We present studies related to the regularization of piecewise vector fields in Rn that are volume preserving on each smooth components. We also analyze singularities of piecewise smooth functions where normal forms and their unfolding are presented. Finally, we study bifurcations of refractive Hamiltonian vector fields / Doutorado / Matematica / Doutor em Matemática

In the field of singularly perturbed reaction- or convection-diffusion boundary value problems the research area of a priori error analysis for the finite element method, has already been thoroughly investigated. In particular, for mesh adapted methods and/or various stabilization techniques, works have been done that prove optimal rates of convergence or supercloseness uniformly in the perturbation parameter epsilon. Commonly, however, it is assumed that the exact solution behaves nicely in that it obeys certain regularity assumptions although in general, e.g. due to corner singularities, these regularity requirements are not satisfied. So far, insufficient regularity has been met by assuming compatibility conditions on the data. The present thesis originated from the question: What can be shown if these rather unrealistic additional assumptions are dropped? We are interested in epsilon-uniform a priori estimates for convergence and superconvergence that include some regularity parameter that is adjustable to the smoothness of the exact solution. A major difficulty that occurs when seeking the numerical error decay is that the exact solution is not known. Since we strive for reliable rates of convergence we want to avoid the standard approach of the "double-mesh principle". Our choice is to use reference solutions as a substitute for the exact solution. Numerical experiments are intended to confirm the theoretical results and to bring further insights into the interplay between layers and singularities. To computationally realize the thereby arising demanding practical aspects of the finite element method, a new software is developed that turns out to be particularly suited for the needs of the numerical analyst. Its design, features and implementation is described in detail in the second part of the thesis.

The aim of this thesis is to construct exact, axially symmetric solutions of Einstein- Maxwell(-dilaton) equations, which possess a discrete translational symmetry along an axis. We present two possible approaches to their construction. The first one is to solve Einstein-Maxwell equations, the second one relies on a dimensional reduction from a higher dimension. We examine the geometry of the solutions, their horizons and singu- larities, motions of charged test particles and compare them. 1

In this work we investigate the Weyl anomaly from a new perspective. Our goal is to identify a set-up for which the classical Weyl symmetry is not broken, at the quantum level by the usual arguments related to the Euler invariants, but rather by the impact of other geometrical obstructions. Therefore, we work, mostly, in three spatiotemporal dimensions, where general arguments guarantee the absence of trace anomalies. In par- ticular, our interest here is on whether various types of singularities, emerging in the description of the differential geometry of surfaces, could induce some form of quantum inequivalence, even though the classical symmetry is at work. To this end, we work with a very special three-dimensional metric, whose nontriviality is fully in its spatial two-dimensional part. The last ingredient we use, to clean-up the way from other com- plications, is to work with physical systems where no Weyl gauge field is necessary, to have the classical invariance. The system we focus on is then the massless Dirac field the- ory (that, as well known, enjoys local Weyl symmetry) in three-dimensional conformally flat spacetimes. With these premises, the research programme consists of three steps. The first step is to find the coordinate transformations that link the conformal factor identifying the...