[pt] Este trabalho trata do escoamento na escala das gotas e da Reologia de emulsões diluídas. Técnicas analíticas e numéricas são empregadas na solução do problema. Nas vizinhan»cas das gotas o escoamento pode ser considerado livre de efeitos de inércia e conseqüentemente as equações governantes são as equações de Stokes. Esse limite é conhecido na literatura como Microhidrodinâmica. O campo de velocidade e de tensão sobre a superfície das gotas é calculado. Um processo de média espacial é realizado em um volume representativo da suspensão tal que a mesma possa ser estudada como um ruido contínuo equivalente. Métodos assintóticos baseados em aproximações de pequenas deformações das gotas são empregados para produzir teorias de primeira e segunda ordens da razão de viscosidade. Uma extensão da teoria para emulsões diluídas polidispersas é desenvolvida. Uma teoria viscoelástica quasi-linear é construída para emulsões diluídas de alta razão de viscosidade em cisalhamento oscilatório. Em regimes de grandes deformações utiliza-se o Método Integral de Contorno para determinar-se a forma da gota e o campos de velocidade sobre a mesma. O método é descrito em detalhes, tanto do ponto de vista teórico como de sua implementação numérica. A validação da metodologia numérica é feita utilizando resultados teóricos e experimentais, disponíveis na literatura. A reologia da emulsão é estudada em escoamentos de cisalhamento simples, oscilatório, pura extensão e cisalhamento quadrático (escoamento de Poiseuille). Os resultados numéricos para cisalhamento simples são utilizados para determinar constantes materiais da teoria assintótica de segunda ordem para a tensão. Limites não-lineares de escoamento em regimes de razões de viscosidade moderadas para os cisalhamentos simples, oscilatório e quadrático são estudados / [en] This work deals with the flow in the scale of the drops and the Rheology of diluted emulsions. Analytic and numerical techniques are employed in order to solve the problem. In the drop neighborhoods the flow may be considered as free of inertia effects and consequently governed by Stokes equations. In the literature this limit is known as Microhydrodynamics. The flow field and the stress tensor on the drop surface are calculated. A spatial mean process was taken, in a representative suspension volume, in order to study the emulsion as an homogeneous and continuous fluid. Asymptotic methods based in small drop deformation approximation are used to produce first and second orders theories which the parameter is the viscosity ratio. An extension of these theories for polydisperse diluted emulsion is developed. A quasi-linear viscoelasticity theory is constructed for diluted emulsion of high viscosity ratios in oscillatory shear flows. In the regimes of large deformations, the velocity and the stress on the particles are evaluated by a numerical procedure based on the Boundary Integral Method for deformable drops. The theoretical and numerical aspects of the Boundary Integral Method are described in details. The code is validated by comparison the numerical results with the experimental data presented in the literature, and also by comparison with the theoretical results of small deformation. The emulsion rheology is studied in simple shear, oscillatory shear, extensional and also in pressure driven flows. The numerical results are used to determine material constants of the stress theory of the second order. Non linear flow regimes of moderate viscosity ratios in simple shear, oscillatory shear and pressure driven flows are also studied.

Le rôle crucial des interfaces solides dans les problèmes de structures dans de nombreux domaines de l'Ingénierie est désormais bien connue et c'est certainement un sujet de grand intérêt scientifique. Aujourd'hui, la modélisation analytique et numérique des interfaces structurelles représentent un défi du fait desphénomènes physiques très complexes qu'il faut prendre en compte (tels que adhésion, contact non-conforme,microfissuration, frottement, contact unilatéral) autant que le besoin d'avoir des méthodes numériques qui soient capables de traiter à la fois la faible épaisseur des zones d'interface et les sauts dans les champs physiques concernés. Cette thèse vise à développer un outil analytique cohérent et général qui soit capable de dépasser les limitations des stratégies existantes et concernant la modélisation des interfaces emph{soft} et emph{hard} caractérisées par une microfissuration évolutive. Une nouvelle approche, appelée emph{Imperfect Interface Approach} (IIA), est proposée. Elle couple de manière cohérente arguments de théorie asymptotique et techniques d'homogénéisation pour les milieux microfissurés dans le cadre de la emph{Non-Interacting Approximation} (NIA). Dans le cadre de l'élasticité linéaire, l'IIA est employée avec succès pour obtenir un ensemble de modèles d'interfaces imparfaites.En généralisant la méthode de développement asymptotique à la théorie élastique des déformations finies, un modèle d'interface soft non-linéaire a été dérivé. Comme une nouvelle application, l'IIA est appliquée afin de formuler un modèle de contact non-conforme à raideurs equivalents. Simulations numériques appliquées à la maçonnerie ont été effectuées. / The crucial role of solid interfaces in structural problems in several engineering fields is well-established and they represent certainly a scientific topic of great interest. Nowadays, analytical and numerical modeling of structural interfaces are challenging tasks, due to the complex physical phenomena to take into account (such as adhesion, non-conforming contact, microcracking, friction, unilateral contact), as well as to the need of numerical methods suitable for treating small thickness of the interface zones and jumps in the physically relevant fields.Present PhD thesis aims to develop a consistent and general analytical tool able to overcome some modeling shortcomings of available modeling strategies accounting for soft and hard interfaces, and characterized by evolving microcracking. A novel approach, referred to as emph{Imperfect Interface Approach} (IIA), is proposed. It consistently couples asymptotic arguments and homogenization techniques for microcracked media in the framework of the Non-Interacting Approximation (NIA). In the context of linear elasticity, the IIA is successfully employed to derive a set of imperfect interface. By generalizing the matched asymptotic expansion method to finite strains, a nonlinear soft interface model has been derived. As a new general application, the IIA is applied to formulate a spring-type model for non-conforming contact. Finally, numerical simulations applying the soft interface models obtained in both linear and nonlinear cases to masonry structures, are carried out, showing effectiveness and soundness of the proposed formulation.

L'objectif de ce travail fut le développement de nouvelles méthodes pour aborder certainsproblèmes inverses en élasticité, en tirant parti de la présence d'un petit paramètre dans ces problèmespour construire des approximation asymptotiques d'ordre élevé.La première partie est consacrée à l'identification de la taille et la position d'une inhomogénéité$BTrue$ enfouie dans un domaine élastique tridimensionnel. Nous nous concentrons sur l'étude defonctions-co^uts $Jbb(Br)$ quantifiant l'écart entre $BTrue$ et une hétérogénéité ``test'' $Br$. Unetelle fonction-co^ut peut en effet être minimisée par rapport à tout ou partie des caractéristiques del'inclusion ``test'' $Br$ (position, taille, propriétés mécaniques ...) pour établir la meilleurecorrespondance possible entre $Br$ et $BTrue$. A cet effet, nous produisons un développement asymptotique de $Jbb$en la taille $incsize$ de $Br$, qui en constitue une approximation polynomiale plus aisée à minimiser. Cedéveloppement, établi jusqu'à l'ordre $O(incsize^6)$, est justifié par une estimation du résidu. Uneméthode d'identification adaptée est ensuite présentée et illustrée par des exemples numériques portant surdes obstacles de formes simples dans l'espace libre $Rbb^3$.L'objet de la seconde partie est de caractériser une inclusion microstructurée de longueur $ltot$, modéliséeen une dimension, composée de couches de deux matériaux alternés périodiquement, en supposant que les plusbasses de ses fréquences propres de transmission (TEs) sont connues. Ces fréquences sont les valeurs propres d'unproblème dit de transmission intérieur (ITP). Afin de disposer d'un modèle propiceà l'inversion, tout en prenant en compte les effets de la microstructure, nous nous reposons sur des approximationsde l'ITP exact obtenues par homogénéisation. A partir du modèle homogénéisé d'ordre 0, nous établissonstout d'abord une méthode simple pour déterminer les paramètres macroscopiques ($ltot$ et contrastes matériaux)d'une telle inclusion. Pour avoir accès à la période de la microstructure, nous nous intéressons ensuite àdes modèles homogénéisés d'ordre élevé, pour lesquels nous soulignons le besoin de conditions aux limitesadaptées. / The purpose of this work was to develop new methods to address inverse problems in elasticity,taking advantage of the presence of a small parameter in the considered problems by means of higher-order asymptoticexpansions.The first part is dedicated to the localization and size identification of a buried inhomogeneity $BTrue$ in a 3Delastic domain. In this goal, we focused on the study of functionals $Jbb(Br)$ quantifying the misfit between $BTrue$and a trial homogeneity $Br$. Such functionals are to be minimized w.r.t. some or all the characteristics of the trialinclusion $Br$ (location, size, mechanical properties ...) to find the best agreement with $BTrue$. To this end, weproduced an expansion of $Jbb$ with respect to the size $incsize$ of $Br$, providing a polynomial approximationeasier to minimize. This expansion, established up to $O(incsize^6)$ in a volume integral equations framework, isjustified by an estimate of the residual. A suited identification procedure is then given and supported by numericalillustrations for simple obstacles in full-space $Rbb^3$.The main purpose of this second part is to characterize a microstructured two-phases layered1D inclusion of length $ltot$, supposing we already know its low-frequency transmission eigenvalues (TEs). Thoseare computed as the eigenvalues of the so-called interior transmission problem (ITP). To provide a convenient invertiblemodel, while accounting for the microstructure effects, we then relied on homogenized approximations of the exact ITPfor the periodic inclusion. Focusing on the leading-order homogenized ITP, we first provide a straightforward method torecover the macroscopic parameters ($ltot$ and material contrast) of such inclusion. To access to the period of themicrostructure, higher-order homogenization is finally addressed, with emphasis on the need for suitable boundaryconditions.

No description available.

<div>The Subword Complexity of a character string refers to the number of distinct substrings of any length that occur as contiguous patterns in the string. The kth Subword Complexity in particular, refers to the number of distinct substrings of length k in a string of length n. In this work, we evaluate the expected value and the second factorial moment of the kth Subword Complexity for the binary strings over memory-less sources. We first take a combinatorial approach to derive a probability generating function for the number of occurrences of patterns in strings of finite length. This enables us to have an exact expression for the two moments in terms of patterns' auto-correlation and correlation polynomials. We then investigate the asymptotic behavior for values of k=a log n. In the proof, we compare the distribution of the kth Subword Complexity of binary strings to the distribution of distinct prefixes of independent strings stored in a trie. </div><div>The methodology that we use involves complex analysis, analytical poissonization and depoissonization, the Mellin transform, and saddle point analysis.</div>

Microorganisms and drops are ubiquitous in nature: while drops can be found in sneezes, ink-jet printers, oceans etc, microorganisms are present in our stomach, intestine, soil, oceans etc. In most situations they are present in complex conditions: drop spreading on a rigid or soft substrate, drop covered with impurities that act as surfactants, marine microbe approaching a surfactant laden drop in density stratified oceanic waters in the event of an oil spill etc. In this thesis, we extract the physics underlying the influence of two such complicated effects (surfactant redistribution and density-stratification) on the motion of drops and swimming microorganisms when they are in isolation or in the vicinity of each other. This thesis is relevant in understanding the bioremediation of oil spill by marine microbes.<div><br></div><div>We divide this thesis into two themes. In the first theme, we analyze the motion of motile microorganisms near a surfactant-laden interface in homogeneous fluids. We begin by calculating the translational and angular velocities of a swimming microorganism outside a surfactant-laden drop by assuming the surfactant is insoluble, incompressible, and non-diffusing, as such system is relevant in the context of bioremediation of oil spill. We then study the motion of swimming microorganism lying inside a surfactant-laden drop by assuming the surfactant is insoluble, compressible, and has large surface diffusivity. This system is ideal for exploring the nonlinearities associated with the surfactant transport phenomena and is relevant in the context of targeted drug delivery systems wherein one uses synthetic swimmers to transport the drops containing drug. We then analyze the motion of a swimming organism in a liquid film covered with surfactant without making any assumptions about the surfactant and this system is relevant in the case of free-standing films containing swimming organisms as well as in the initial stages of the biofilm formation. In the second theme, we consider a density-stratified background fluid without any surfactants. In this theme, we examine separately a towed drop and a swimming microorganism, and find the drag acting on the drop, drop deformation, and the drift volume induced by the drop as well as the motility of the swimming microorganism.</div>

<div><div>In this work we use and develop Riemann-Hilbert techniques to study the asymptotic behavior of structured determinants. In chapter one we will review the main underlying</div><div>definitions and ideas which will be extensively used throughout the thesis. Chapter two is devoted to the asymptotic analysis of Hankel determinants with Laguerre-type and Jacobi-type potentials with Fisher-Hartwig singularities. In chapter three we will propose a Riemann-Hilbert problem for Toeplitz+Hankel determinants. We will then analyze this Riemann-Hilbert problem for a certain family of Toeplitz and Hankel symbols. In Chapter four we will study the asymptotics of a certain bordered-Toeplitz determinant which is related to the next-to-diagonal correlations of the anisotropic Ising model. The analysis is based upon relating the bordered-Toeplitz determinant to the solution of the Riemann-Hilbert problem associated to pure Toeplitz determinants. Finally in chapter ve we will study the emptiness formation probability in the XXZ-spin 1/2 Heisenberg chain, or equivalently, the asymptotic analysis of the associated Fredholm determinant.</div></div>

<p dir="ltr">We present first order asymptotic estimates for the divisor function problem, the set of lists (restricted number of divisors) problem, and a generalization of the overpartition problem. In particular, we prove Kotesovec's conjecture for A294363 from the OEIS and also extend his conjecture to a full asymptotic treatment by providing an estimate in terms of elementary functions for the EGF coefficients directly rather than the log of the coefficients. We also provide asymptotic estimates for generalizations of the set of lists and overpartition problem, while making comparisons to any existing Kotesovec conjectures. We perform the asymptotic analysis via Mellin transforms, residue analysis, and the saddle point method. These families of generating functions have potential application to families of randomly generated partitions in which ordered subsets of a partition that exceed a certain fixed size may be one of two different objects and to overpartitions with potential heading labels.</p>

Le but de cette thèse pluridisciplinaire est d’étudier le problème de l’interaction fluide-structure à partir du point de vue mathématique et physique. Des problèmes d’interaction d’un fluide visqueux avec une structure élastique décrivent, par exemple, des interactions entre le manteau terrestre et de la croûte terrestre, le sang et la paroi vasculaire dans un vaisseau sanguin, etc. En génie l’interaction fluide visqueux-structure apparaît lors de la formation de solution colloïdale quand un laser passe à travers le fluide influençant le substrat (ablation laser dans un liquide). Fusion sélective au laser (FSL) est utilisée pour étudier le comportement des contraintes résiduelles en dépendance des propriétés thermoélastiques et mécaniques du matériau et des formes variées des cordons rechargés. A partir du point de vue mathématique le système couplé “flux fluide visqueux – plaque mince élastique” en 3D lorsque l’épaisseur de la plaque, E, tend vers zéro, tandis que la densité et le module de Young du matériau élastique sont d’ordre 1 et E-3, respectivement, est considéré. Le solide est couché par le fluide qui occupe un domaine épais. La modélisation multi-échelle est effectuée pour la partie élastique. Le développement asymptotique complet est construit lorsque E tend vers zéro. L’existence, la régularité et l’unicité de la solution pour le problème initial sont étudiées au moyen de techniques variationnelles. La méthode de décomposition asymptotique partielle du domaine est appliquée pour le système couplé. L’erreur de la méthode est évaluée / The goal of this multi-disciplinary thesis is to study the fluid-structure interaction problem from mathematical and physical viewpoints. Viscous fluid-structure interaction problems describe, for example, interactions between the Earth mantle and the Earth crust, the blood and the vascular wall in a blood vessels, etc. In engineering viscous fluid-structure interaction appears during colloidal solution formation when a laser pierce through the fluid influencing the substrate (laser ablation in a liquid). Selective laser melting (SLM) is used to study the behavior of residual stresses depending on the thermoelastic and mechanical properties of the material and on various forms of reloaded beads. From mathematical point of view the coupled system “viscous fluid flow-thin elastic plate” in 3D when the thickness of the plate, E, tends to zero, while the density and the Young’s modulus of the plate material are of order 1 and E-3, respectively, is considered. The plate lies on the fluid which occupies a thick domain. The multi-scale modeling is performed for the elastic part. The complete asymptotic expansion is constructed when E tends to zero. The existence, the regularity and the uniqueness of the solution for the original problem are studied by means of variational techniques. The method of asymptotic partial domain decomposition is applied for the coupled system. The error of the method is evaluated

Le travail réalisé dans cette thèse s'intègre globalement dans le cadre de I'observation et la surveillance maritime.Afin d'améliorer la reconnaissance et I'identification automatique de cibles noyées dans un environnement perturbé, nous avons opté à la fusion de différentes connaissances et informations concernant une scène observée à distance par des capteurs micro-ondes. En effet, plusieurs phénomènes physiques co-existent et perturbent la propagation des ondes électromagnétiques au-dessus d'une surface et notamment au-dessus d'une surface maritime hétérogène (la réfraction due aux gradients d'indice, la rugosité de la surface de mer, les effets hydrodynamiques non linéaires du type vagues déferlantes, la présence d'objets, les polluants, sillage de navires, zones côtières, ...). Dans ce contexte, le travail présenté dans cette thèse porte sur l'étude de la signature électromagnétique (coefficients de diffusion) d'une surface maritime hétérogène avec la prise en compte des phénomènes hydrodynamiques (linéaires : vagues de capillarité et de gravité, non linéaires : vagues déferlantes). Cette estimation de la signature électromagnétique est effectuée en configuration bistatique (monostatique et propagation avant) et en bande X. L'étude complète de cette problématique est difficile. En effet, le déferlement est un processus dissipatif de l'énergie qui correspond à la dernière étape de la vie d'une vague et qui a donc le plus souvent lieu à I'approche du rivage. Ce phénomène non linéaire produit un pic de mer qui est une augmentation rapide des coefficients de diffusion et qui peut dépasser 10 dB dans une période de 100 ms. Ce pic peut conduire à des échos parasites, qui peuvent être identifiés comme des cibles virtuelles, et par la suite elles peuvent perturber le système de détection radar (fausses alarmes). Par conséquent, pour améliorer le processus de détection et pour réduire le taux de fausses alarmes, il est important de distinguer entre les cibles et les pics de mer générés par des vagues déferlantes. Ceci constitue I’une des motivations et aussi I'intérêt d'étudier la signature électromagnétique des vagues déferlantes dans différentes configurations d'observation de sorte que nous puissions facilement indiquer la présence voir I'identification des pics de mer. Pour contribuer à cette problématique, nous avons proposé une méthodologie basée sur un modèle électromagnétique hybride basé sur une combinaison d'une part de méthodes asymptotiques(SPMI utilisée dans le cadre de ce travail) pour simuler la réponse radar des vagues linéaire (vagues de capillarité et de gravité décrites via le spectre de mer d'Elfouhaily), et d'autre part de méthodes exactes (MoM, FB < Forward-Backward ) retenue dans le travail présenté dans ce manuscrit) pour calculer la réponse électromagnétique des vagues non-linéaires (profils considérés sont issus des résultats du code LONGTANK). Afìn de compléter l'étude théorique et les simulations réalisées, nous avons effectué une phase d'évaluation et de validation par des mesures de signature radar réalisées dans la chambre anéchoïque de I'Ensta Bretagne. / The work done in this thesis fits generally under the observation and maritime surveillance. To improve the detection and automatic identification of targets embedded in a noisy environment targets, we opted for the fusion of different knowledge and information regarding a remotely observed scene by microwave sensors. Indeed, several physical phenomena co-exist and interfere with the propagation of electromagnetic waves over a heterogeneous sea surface (the refraction due to the index gradients, the roughness of the sea surface, nonlinear hydrodynamic effects like waves breaking, the presence of objects, pollutants, ship wake, coastal areas,..). In this context, the work presented in this thesis focuses on the study of electromagnetic signature (diffusion coefficients) of a heterogeneous sea surface with consideration of hydrodynamic phenomena (linear: capillary and gravity waves, nonlinear: breaking waves). The electromagnetic signature is performed in bistatic configuration (monostatic and forward propagating) and in X-band. The complete study of this problem is difficult.Indeed, the breaking wave is a dissipative process of energy that corresponds to the last stage of the life of a wave and therefore has most often held in the shore. This nonlinear phenomenon produces a sea peak which is a rapid increase of the diffusion coefficients and can exceed l0 dB in a 100 ms period. This peak can lead to clutter, which can be identified as virtual targets, and then they can disrupt the detection radar system (false alarms). Therefore, to improve the detection process and reduce the false alarm rate, it is important to distinguish between targets and sea peaks generated by breaking waves. This represents one of the motivations and also the interest to study the electromagnetic signature of breaking waves in different observation configurations so that we can easily detect and identify the sea peaks. To solve this problem, we proposed a methodology based on a hybrid electromagnetic model which is on a combination of asymptotic methods (SPMI used in this work) to simulate the radar response of linear waves (capillary and gravity waves described via the Elfouhaily sea spectrum) and an exact methods, the method of moment (the FB "Forward-Backward" method is used in this work), to calculate the electromagnetic response of nonlinear waves (profiles are produced by the LONGTANK code). To complement the theoretical study and simulations, we carried out an evaluation and validation phase by measuring the radar signature of breaking wave profiles in the ENSTA Bretagne anechoic chamber.