La thèse est consacrée à l'étude des membranes sous contrainte en mettant l'accent sur les structures biologiques telles que les tissus en croissance et la membrane cellulaire. Elle combine des approches analytiques et numériques pour étudier le lien entre la géométrie et la mécanique. Elle contient également quelques résultats expérimentaux mais ce ne sont que peu nombreux et à petite échelle. Après un chapitre d'introduction, nous explorons trois modèles physiques abordés dans trois chapitres différents. Dans le premier modèle, les déformations des tissus mous lors de la croissance sont traitées comme des singularités ponctuelles gaussiennes dans les surfaces bidimensionnelles. Les formes d'équilibre sont calculées pour deux défauts qui forment un dipôle. Les prédictions du modèle sont par ailleurs comparées aux résultats des expériences. Le chapitre suivant étudie les invaginations des membranes fluides auto-évitantes dans des espaces confinés. À cette fin, nous avons développé un code basé sur la méthode des éléments finis et effectué des simulations afin de construire un diagramme de phase (volume/surface) pour des membranes piégées à l'intérieur d'une sphère. Nous analysons également les effets de la courbure spontanée de la membrane et les déformations de la paroi extérieure sur la forme de l'invagination. Enfin, dans le quatrième chapitre de la thèse, en vue de modéliser des tiges biologiques, nous construisons une membrane tubulaire à partir d'éléments caractérisés par deux états géométriques. Cette approche nous a permis d'examiner, par le biais des simulations du type dynamique brownienne, comment la forme globale émerge des interactions locales / The present thesis is devoted to the study of constrained membranes with a focus on biological structures such as growing tissues and the cell membrane. It combines analytical and numerical approaches to investigate the interplay of geometry and mechanics. It also includes some experimental results albeit they are few in number and modest in size. After an introductory chapter, we explore three physical models addressed in three distinct chapters. In the first model, the deformations of growing soft tissues are treated as Gaussian point singularities in two dimensional surfaces. The equilibrium shapes are evaluated for two such defects forming a dipole. The predictions of the theory are also compared to tabletop experiments. The next chapter studies the invaginations of self-avoiding fluid membranes in constrained spaces. To this end, we developed a Finite Element code and performed extensive simulations to construct a geometric phase diagram for a fluid membrane vesicle in a spherical confinement. We also investigate the effects of the membrane's spontaneous curvature and the deformations of the container on the geometry of the invagination. In the fourth chapter of the manuscript, a tubular membrane composed of switchable components is proposed as a model to study conformations of intrinsically curved biological rods. We translated this system to a computational framework based on the Brownian Dynamics method and inquired how global shape emerges from local interactions

archives@tulane.edu / There is a deep analogy between the theory of covering spaces and the theory offield extensions. Indeed, for many theorems about the Galois groups of field extensionsthere are analogous statements for the fundamental groups of covering spaces. Thepurpose of this thesis is to present an expository account of the connections betweenthese two useful concepts of algebra and geometry. / 1 / Dejun Zhang

The possibility of increasing the amount of readily accessible surface area by enlarging the 5 A pore was examined via pretreating the PSOC-371 coal with gases such as nitrogen, nitrogen-oxygen, and ozone-oxygen and hydrogen peroxide solutions. Surface areas were obtained from nitrogen adsorption at 77 K and carbon dioxide adsorption at either 298 or 195 K for each sample before and after treatment.

Accurate terrain models provide the chassis designer with a powerful tool to make informed design decisions early in the design process. During this stage, engineers are challenged with predicting vehicle loads through modeling and simulation. The accuracy of these simulation results depends not only on the fidelity of the model, but also on the excitation to the model. It is clear that the terrain is the main excitation to the vehicle [1]. The inputs to these models are often based directly on physical measurements (terrain profiles); therefore, the terrain measurements must be as accurate as possible. A collection of novel methods can be developed to aid in the study and application of 3D terrain measurements, which are dense and non-uniform, including efficient gridding, stochastic modeling, and compact characterization. Terrain measurements are not collected with uniform spacing, which is necessary for efficient data storage and simulation. Many techniques are developed to help effectively grid dense terrain point clouds in a curved regular grid (CRG) format, including center and random vehicle paths, sorted gridding methods, and software implementation. In addition, it is beneficial to characterize the terrain as a realization of an underlying stochastic process and to develop a mathematical model of that process. A method is developed to represent a continuous-state Markov chain as a collection of univariate distributions, to be applied to terrain road profiles. The resulting form is extremely customizable and significantly more compact than a discrete-state Markov chain, yet it still provides a viable alternative for stochastically modeling terrain. Many new simulation techniques take advantage of 3D gridded roads along with traditional 2D terrain profiles. A technique is developed to model and synthesize 3D terrain surfaces by applying a variety of 2D stochastic models to the topological components of terrain, which are also decomposed into frequency bandwidths and down-sampled. The quality of the synthetic surface is determined using many statistical tests, and the entire work is implemented into a powerful software suite. Engineers from many disciplines who work with terrain surfaces need to describe the overall physical characteristics compactly and consistently. A method is developed to characterize terrain surfaces with a few coefficients by performing a principal component analysis, via singular value decomposition (SVD), to the parameter sets that define a collection of surface models. / Master of Science

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / The present investigation focuses on the mathematical concept of convexity, as the main tool for the graphic construction of bounded surfaces explicitly and implicitly described, as well as the construction of unconventional solids using GeoGebra. Two cases are presented in which the importance of the concept of convexity is highlighted, in the first situation the convexity is used in the argument of the surface command together with the curves that delimit it to graph a bounded surface, while in the second situation the convexity is evidenced by expressing the coordinates of the surface in parametric form. On the other hand, the 3D graphic view combined with the GeoGebra AR tool allows one to visualize, manipulate, understand and improve the abstraction of mathematical objects that are built in three-dimensional space in a dynamic and friendly environment. These constructions in three-dimensional space that are complex when sketching them with pencil and paper are easier when linking the mathematical definitions with free software such as GeoGebra. / Revisón por pares

An aircraft may experience inlight ice accretion and corresponding reductions in performance and control when the vehicle encounters clouds of super-cooled water droplets. The EADS-IW Surface Engineering Group is investigating passive anti-icing possibilities, such as functional and ice phobic coatings. Ice-resistant coatings require investigating droplet impact on dry surfaces and wet films, including microscopic effects such as droplet splashing. To investigate droplet impacts, a volume of fluid (VOF) flow solver was used for droplets impacting dry and wetted hydrophobic and superhydrophobic surfaces, focusing on meso-scale simulations. The effects of structured, micro-scale surface roughness and the effects of a thin wet film on the surface, corresponding to a saturated surface under high humidity conditions, were investigated. Axisymmetric domains produced acceptable results for smooth, dry surfaces. It was determined that in order to properly predict behavior of droplets impacting surfaces with structured micro-scale roughness, three-dimensional simulations are recommended.

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