La motivation initiale de cette thèse est l'étude d'une discrétisation volumique de surface (Chapitre 2) naturellement liée à la structure de varifold. Le point clé est qu'il est possible de munir d'une structure de varifold la plupart des objets utilisés pour représenter ou discrétiser des surfaces c'est-à-dire aussi bien des objets tels que les sous variétés ou les ensembles rectifiables que des objets tels que des nuages de points ou encore la discrétisation volumique proposée, ce qui permet d'étudier dans un cadre unifié une surface et sa discrétisation. Une difficulté essentielle est que, généralement, ces structures discrètes ne sont pas rectifiables, ce qui soulève la question suivante : comment assurer qu'un varifold, obtenu comme limite de discrétisations volumiques, soit une surface, au moins en un sens faible ? De façon plus précise : quelles conditions sur une suite de varifolds quelconques assurent que le varifold limite est rectifiable (Chapitre 3) ou encore qu'il est à variation première bornée (Chapitre 5) ? On obtient des conditions quantitatives assurant la rectifiabilité grâce à des énergies liées aux nombres beta de Jones. On s'intéresse ensuite à la régularité du varifold limite en termes de courbure (variation première). On a essayé de contrôler la variation première en utilisant des techniques de construction de mesures de type packing (Chapitre 4), une forme régularisée de la variation première d'un varifold. Cette régularisation permet de définir des énergies de Willmore approchées qui Gamma convergent dans l'espace des varifolds vers l'énergie de Willmore ainsi qu'une approximation de la courbure qui est testée numériquement dans le Chapitre 6 / The starting point of this work is the study of a volumetric surface discretization model naturally connected to the varifolds structure introduced in Chapter 2. The point is that not only the discretization we propose can be endowed with a structure of varifold but also a great part of objects used for surface representation and discretization (triangulation, cloud points, level sets etc.) so that we can use varifolds tools to study in some unified setting different ways of discretizing surfaces. An important point to overcome is that these structures are generally not rectifiable so that we address the following question: how to ensure that the limit of a sequence of such discrete surfaces is regular? More precisely, what conditions on a sequence of varifolds (not necessarily rectifiable nor with bounded variation) ensure that the limit varifold is rectifiable (Chapter 3) or has bounded first variation (Chapter 5)? We obtain quantitative conditions of rectifiability for variflods considering energies linked to Jones' beta numbers. We then address the question in terms of first variation (generalized curvature) of a limit varifold. We first try a packing measure construction of the first variation of a varifold V (Chapter 4), then we define a regularized form of the classical first variation, allowing us to exhibit an energetic condition ensuring that a limit of a sequence of varifolds has bounded first variation. We use this regularized form to build an approximate Willmore energy Gamma-converging in the class of varifolds to the Willmore energy. In Chapter 6, we test numerically a notion of approximate curvature derived from the regularized first variation

Le séchage des matériaux cimentaires et le retrait induit ont des conséquences majeures sur le comportement structurel des dalles et chapes. Le retrait empêché est une des principales causes de la fissuration de ces ouvrages. En sus, si le séchage est unidirectionnel, le retrait différentiel favorise le tuilage qui traduit le soulèvement des coins et des bords des dalles minces. Afin de mieux cerner les phénomènes induits par les gradients d’humidité relative interne, des études expérimentales et numériques ont été menées conjointement, et de nouveaux dispositifs expérimentaux ont été développés. On montre que l’évolution du tuilage dépend principalement de la progression du front de séchage. L’influence prédominante du séchage impose donc de recourir à une cure adaptée. Grâce à sa forte capacité de rétention d’eau, une étude systématique a été conduite sur la chaux en vue d’étudier son potentiel effet de cure. La chaux hydraulique a permis, par son influence sur la microstructure et son effet de cure, de retarder et réduire le tuilage. Sur la base des résultats expérimentaux, deux approches différentes de modélisation du tuilage ont été développées : i/ un modèle analytique continu, et ii/ une modélisation par éléments discrets. Les calculs montrent que des retraits plus importants apparaissent en surface et entraînent une microfissuration qui permet de relaxer les contraintes internes. La chaux semble conduire à une profondeur d’endommagement plus importante, ce qui explique en partie son effet sur l’amplitude du tuilage. L’approche par éléments discrets est capable de reproduire l’évolution du tuilage aussi bien en cinétique qu’en amplitude à partir des seules mesures du retrait différentiel. La chaux s’est aussi révélée bénéfique quand elle est incorporée dans les bétons autoplaçants en agissant à la fois sur le retrait et sur les propriétés viscoélastiques. / Drying of cementitious materials and the induced shrinkage have major consequences on the structural behavior of slabs and screeds. The restrained shrinkage is one of the main causes of cracking. In addition, if the drying is unidirectional, the differential shrinkage leads to curling which is defined as the lifting of the corners and the edges of thin slabs.To understand the phenomena induced by internal relative humidity gradients, experimental and numerical studies have been jointly conducted, and new experimental devices have been developed. It is shown that the evolution of curling mainly depends on the progression of the drying front. The predominant influence of drying therefore requires the use of a suitable method for curing. Thanks to its high water retention capacity, a systematic study has been conducted on lime in order to study its potential curing effect. The hydraulic lime, through its influence on the microstructure and its curing effect, delayed and reduced curling. Based on the experimental results, two different approaches have been developed to model the curling of slabs: i / a continuous analytical model,and ii / a discrete element model. Calculations show that higher shrinkage appears on the surface and causes microcracking that may relax internal stresses. The lime seems to lead to a greater depth of damage, which partly explains its effect on the curling amplitude. The discrete element approach is able to reproduce the evolution of curling both in terms of kinetics and amplitude from the sole measurements of differential shrinkage. Lime is also shown to be beneficial when incorporated into self compacting concretes by acting on both shrinkage and viscoelastic properties.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaf 99. / by Michael Andrew Gennert. / M.S.

Thesis. 1976. Elec.E.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Microfiche copy available in Archives and Engineering. / Bibliography: leaves 138-140. / Elec.E.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Ph.D.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Bibliography: p.R1-R5. / by Joshua D. Borah. / M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / Microfiche copy available in Archives and Barker / Bibliography: leaves 108-109. / by William Neil McCasland. / M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Joseph A. Amram. / M.S.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 157-161. / by Gregory S. Lauer. / Ph.D.

Géons topológicos podem ser vistos como um tipo de excitação localizada na topologia espacial. Nesta dissertação, estudamos um modelo físico simples, dado por uma teoria de Yang-Mills-Higgs com simetria de gauge descrita por um grupo de Lie compacto G, e com quebra espontânea de simetria para um subgrupo finito H G. Esta teoria é definida em um espaço-tempo de (2 + 1)d com topologia da forma x IR, onde descreve o plano com um único géon. Estudamos mais especificamente o setor de baixas energias dessa teoria, deduzindo o espaço de configuração clássico e quantizando-o. A quantização é feita identificando certa álgebra que descreve matematicamente o sistema, analisando com detalhes sua estrutura e buscando suas representações irredutíveis. Cada representação é então interpretada como um determinado setor de um géon da teoria. Em outras palavras, cada uma destas representações irredutíveis descreve um tipo de géon diferente. Em seguida, mostramos como estender essa descrição para um número N qualquer de géons. A teoria aqui desenvolvida pode ser vista como um \"toy model\" para o estudo das consequências de se ter uma topologia espacial não-trivial, e em particular, o estudo das propriedades físicas de géons. / Topological geons can be viewed as a sort of localized excitations in spatial topology. In this dissertation, we study a simple physical model, given by a Yang-Mills-Higgs theory with a gauge symmetry described by a compact Lie group G, spontaneously broken down to a finite subgroup H C G. We shall consider this theory to be defined on a (2 + 1)d spacetime with topology of the form E x IR, where describes a plane with a single geon. More specifically, we investigate the low energy sector of this theory, obtain its classical configuration space and quantize it. Quantization is accomplished by identifying a certain algebra, which mathematically describes the system, analyzing its structure in detail and obtaining its irreducible representations. Each such representation is then interpreted as an specific geonic sector of the theory. In other words, each one of the irreducible representations describes a distinct geon type. Moreover, we show how the above description can be extended to any number N of geons. The theory developed here may be viewed as a toy model for studying the consequences of non-trivial spatial topology, and in particular the study of the physical properties of geons.