This work deals with the study of the drying-mediated assembly of colloidal gold nanoparticles (Au NPs) in mesoscale aggregation patterns and their manipulation by atomic force microscopy (AFM) on model surfaces. The assembly of NPs in mesoscale and complex aggregation patterns assisted by the wetting and the drying of complex fluids (suspensions of NPs, NPs/biopolymers mixed solutions) on homogeneous and heterogeneous molecular surfaces was studied. This issue is important, both for understanding fundamental processes of self-organization, and for generating new functional mesostructures. The drying of complex fluids often leads to the emergence of highly complex aggregation structures as shown and discussed in this work. The richness and the aesthetics of these complex structures generated by these interfacial phenomena reflect not only the bulk properties of fluids (different sizes and lengths- scales, kinetic changes in state), but more importantly, the coupling between the fluid properties and those of the substrate surface (wetting interactions, confinement, hydrodynamics). In the case of two important heterogeneous fluids which are Au NPs and polysaccharide solutions, these drying-mediated structure formation lead to the genesis of unusually large and highly ramified dendrites aggregation patterns. The growth mechanism and the critical parameters that control the morphogenesis of these complexes structures are addressed in this work. In addition, the aging mechanisms and kinetics of these structures that are metastable and evolve either through direct dislocation via clusters NPs mobility on the surface, or through undulation-induced roughning of the dendrite branches. To better understanding this NPs mobility and thus the dislocation mechanism of the aging, a detailed study based on the manipulation of NPs by atomic force microscopy in tapping mode (AFM) was developed. The threshold dissipated energy to manipulate (move) the NPs can be quantified according to the intrinsic parameters of the particle (size, shape, and chemical nature), the chemical nature and topography of the substrate, and finally the operating and environment conditions. This work enabled us to understand the mechanisms and characterize the critical parameters that may intervene in the dislocation (aging) of NPs-based functional structures, depending on the nature of the environment liquid and the substrate. Finally, this work proposes an approch of evaluation and of monitoring the stability and the aging of these aggregation structures, in particular, those formed from the drying of films and drops of nano-particles solutions (metal nanoparticles, blood: proteins, viruses ...).

Dans cette recherche, on construit un modèle simplifié en basses et moyennes fréquences de complexes insonorisants (habillages) de l’industrie automobile à partir d'un élément élastoacoustique stochastique. Le modèle simplifié moyen est issu d'une extension de la théorie des structures floues et dépend de trois paramètres physiques : densité modale, amortissement et masse participante. Le modèle simplifié stochastique qui prend en compte les incertitudes de modèle et de données est construit en utilisant une approche probabiliste non paramétrique et dépend de trois paramètres de dispersion. Le modèle simplifié de l'habillage est implémenté dans un modèle vibroacoustique stochastique industriel d’automobile. Deux problèmes inverses sont résolus à l’aide d'une base de données expérimentales sur véhicules construite en parallèle et permettent d’identifier les paramètres du modèle complet. L'analyse des résultats permet de valider les développements théoriques et la méthodologie proposée / This research aims at developing a simplified low- and medium-frequency model for automotive sound-insulation layers based on a stochastic elastoacoustic element. The mean simplified model comes from an extension of the fuzzy structures theory and depends on three physical parameters : modal density, damping and participating mass. A nonparametric probabilistic approach is used to build the uncertainty-accounting stochastic simplified model. This model takes into account the modeling and system parameters uncertainties and depends on three dispersion parameters. The insulation simplified model is then implemented in an industrial stochastic vibroacoustic model of a car. An experimental database of tests on vehicles has been concomitantly carried out and has led to inverse problems allowing the identification of the simplified model parameters to be performed. The analysis of these results shows the validation of the theory and the relevance of the proposed methodology

No presente trabalho, estudamos alguns aspectos da teoria de estruturas complexas em espaços de Banach. Demonstramos que se um espaço de Banach real $X$ tem a propriedade $P$, então todas as estruturas complexas em $X$ também satisfazem $P$, quando $P$ é qualquer uma das seguintes propriedades: propriedade de aproximação limitada, \\emph{G.L-l.u.st}, ser injetivo e ser complementado num espaço dual. Abordamos o problema da unicidade de estruturas complexas em espaços de Banach com base subsimétrica, provando que um espaço de Banach real $E$ com base subsimétrica e isomorfo ao espaço de sequências $E[E]$ admite estrutura complexa única. Por outro lado, apresentamos um exemplo de espaço de Banach com exatamente $\\omega$ estruturas complexas distintas. Também usamos a teoria de estruturas complexas para estudar o clássico problema dos hiperplanos no espaço $Z_2$ de Kalton-Peck. Com o propósito de distinguir $Z_2$ de seus hiperplanos nos perguntamos se os hiperplanos admitem estrutura complexa. Nesse sentido, provamos que os hiperplanos de $Z_2$ contendo a cópia canônica de $\\ell_2$ não admitem estruturas complexas que sejam extensões de estruturas complexas em $\\ell_2$. Também construímos uma estrutura complexa em $\\ell_2$ que não pode-se estender a nenhum operador em $Z_2$. / In this work, we study some aspects of the theory of complex structures in Banach spaces. We show that if a real Banach space $X$ has the property $P$, then all its complex structures also satisfy $P$, where $P$ is any of the following properties: bounded approximation property, \\emph{G.L-l.u.st}, being injective and being complemented in a dual space. We address the problem of uniqueness of complex structures in Banach spaces with subsymmetric basis by proving that a real Banach space $E$ with subsymmetric basis and isomorphic to the space of sequences $E [E]$ admits a unique complex structure. On the other hand, we show an example of Banach space with exactly $\\omega$ different complex structures. We also use the theory of complex structures to study the classical problem of hyperplanes in the Kalton-Peck space $Z_2$. In order to distinguish between $Z_2$ and its hyperplanes we wonder whether the hyperplanes admit complex structures. In this sense we prove that no complex structure on $\\ell_2$ can be extended to a complex structure on the hyperplanes of $Z_2$ containing the canonical copy $l_2$. We also constructed a complex structure on $l_2$ that can not be extended to any operator in $Z_2$.

No presente trabalho, estudamos alguns aspectos da teoria de estruturas complexas em espaços de Banach. Demonstramos que se um espaço de Banach real $X$ tem a propriedade $P$, então todas as estruturas complexas em $X$ também satisfazem $P$, quando $P$ é qualquer uma das seguintes propriedades: propriedade de aproximação limitada, \\emph{G.L-l.u.st}, ser injetivo e ser complementado num espaço dual. Abordamos o problema da unicidade de estruturas complexas em espaços de Banach com base subsimétrica, provando que um espaço de Banach real $E$ com base subsimétrica e isomorfo ao espaço de sequências $E[E]$ admite estrutura complexa única. Por outro lado, apresentamos um exemplo de espaço de Banach com exatamente $\\omega$ estruturas complexas distintas. Também usamos a teoria de estruturas complexas para estudar o clássico problema dos hiperplanos no espaço $Z_2$ de Kalton-Peck. Com o propósito de distinguir $Z_2$ de seus hiperplanos nos perguntamos se os hiperplanos admitem estrutura complexa. Nesse sentido, provamos que os hiperplanos de $Z_2$ contendo a cópia canônica de $\\ell_2$ não admitem estruturas complexas que sejam extensões de estruturas complexas em $\\ell_2$. Também construímos uma estrutura complexa em $\\ell_2$ que não pode-se estender a nenhum operador em $Z_2$. / In this work, we study some aspects of the theory of complex structures in Banach spaces. We show that if a real Banach space $X$ has the property $P$, then all its complex structures also satisfy $P$, where $P$ is any of the following properties: bounded approximation property, \\emph{G.L-l.u.st}, being injective and being complemented in a dual space. We address the problem of uniqueness of complex structures in Banach spaces with subsymmetric basis by proving that a real Banach space $E$ with subsymmetric basis and isomorphic to the space of sequences $E [E]$ admits a unique complex structure. On the other hand, we show an example of Banach space with exactly $\\omega$ different complex structures. We also use the theory of complex structures to study the classical problem of hyperplanes in the Kalton-Peck space $Z_2$. In order to distinguish between $Z_2$ and its hyperplanes we wonder whether the hyperplanes admit complex structures. In this sense we prove that no complex structure on $\\ell_2$ can be extended to a complex structure on the hyperplanes of $Z_2$ containing the canonical copy $l_2$. We also constructed a complex structure on $l_2$ that can not be extended to any operator in $Z_2$.

Le premier problème qui se pose naturellement lors de l'étude des algèbres de Lie nilpotentes est la classification de celles-ci en petite dimension. La classification des algèbres de Lie nilpotentes complexes a été complétée jusqu'en dimension 7. Pour les dimensions inférieures ou égales à 6, il n'existe, sauf isomorphismes, qu'un nombre fini d'algèbres de Lie nilpotentes complexes. Ancochea a classé les algèbres de Lie nilpotentes complexes en dimension 7 selon leur suite caractéristique. On obtient ainsi, une liste plus étendue qui contient des familles d'algèbres de Lie non isomorphes entre elles.On envisage alors d'étudier les algèbres de Lie nilpotentes selon leur nilindice, en commençant par celles qui ont un nilindice maximal, c'est-à-dire , les algèbres de Lie filiformes. Dès 1970. Vergne a initié l'étude des algèbres de Lie filiformes. Elle a montré que sur un corps ayant une infinité d'éléments, il n'existe, sauf isomorphismes, que deux algèbres de Lie filiformes naturellement graduées de dimension paire 2n, nommées L2n et Q2n, et une seule en dimension impaire 2n + 1, appelée L2n+ avec n E N.Plus récemment, Snobl et Winternitz ont déterminé les algèbres de Lie ayant comme nilradical l'algèbre Ln, sur le corps des complexes et des réels. Afin de compléter cette classification à toutes les algèbres de Lie filiformes naturellement graduées, nous avons procéder de même avec les algèbres Q2n,. Nous démontrons ensuite que si une algèbre de Lie indécomposable de dimension finie possède un nilradical filiforme alors elle est forcément résoluble. Les algèbres de Lie filiformes ne présentent donc aucun intérêt dans l'étude des algèbres de Lie non résolubles.Ce résultat n'est plus vrai pour les algèbres de Lie quasi-filiformes dont leur nilradical est abaissé d'une unité par rapport aux filiformes. En effet, en cherchant toutes les algèbres de Lie dont le nilradical est quasi-filiforme naturellement gradué, on a trouvé des algèbres de Lie non résolubles ayant un nilradical quasi-filiforme.Ce même contre-exemple, révèle aussi des différences entre la notion de rigidité dans R et dans C. La classification des algèbres de Lie rigides complexes ayant été déjà faite jusqu'à dimension 8, on est alors amené à trouver cette classification dans le cas réel.Par ailleurs, on a déterminé les algèbres de Lie quasi-filiformes ayant un tore non nul, on obtient une liste beaucoup plus riche que pour le cas filiforme. Cette liste nous permet de prouver la complétude des algèbres de Lie quasi-filiformes. Rappelons que toutes les algèbres de Lie filiformes sont aussi complètes.Finalement, on s'intéresse à l'existence de structures complexes associées aux algèbres de Lie filiformes et quasi-filiformes. Goze et Remm ont démontré que les algèbres filiformes n'admettaient pas ce type de structure. Depuis une approche différente, nous allons redémontrer ce résultat et nous allons voir qu'il existe par contre des algèbres de Lie quasi-filiformes munies d'une structure complexe, mais seulement en dimension 4 et 6. / The first problem which arises naturally in the study of the nilpotenttie algebras is their classification in small dimension. The classification of nilpotent complex Lie algebras was completed until dimension 7. For dimensions lower or equal to 6, there is, except isomotphisms, a finite number of nilpotent complex Lie algebras. In dimension 7, Ancochea classified the nilpotent complex Lie algebras according to their characteristic sequence and he obtains a more extensive list which contains families of non isomorphic Lie algebras.We intend then to study the nilpotent Lie algebras according to their nilindex by beginning with those which have a maximal nilindex. also called filiform Lie algebras. From 1970. Vergne started the study of the filiform Lie algebras. She showed that on a field having an infinity of elements. there are, except isomorphisme, only two naturally graded Lie algebras of even dimension 2n, named L2n, and Q2n,. and there is only one in odd dimension 2n+1, called L2n+1.More recently, Snobl and Winternitz determined the complex and real Lie algebras having the algebra L„ as nilradieal. To generalize this classification to all filiform naturally graded Lie algebra_ we have proceed in a similar wav with the algebra Q2n,. Moreover, we prove that indecomposable Lie algebras with filiform nilradieal are necessarily solvable. Thus, the filiform Lie algebra are irrelevant in the study of the non solvable Lie algebras.This result is not truc for the quasi-filiform Lie algebras. Let us recall that the nilindex of quasi-filiform Lie algebras is, by definition, lowered by a unit with regard to the filiform. Indeed, by looking for all the Lie algebras having a quasifiliform naturally graded nilradieal, we found non solvable Lie algebras having a quasi-filiform nilradical.The same counterexample also reveals differences between the notion of rigidity in R and in C. The classification of complex rigid Lie algebras having been already made until dimension 8, we are then brought to find this classification in the real case.Besides, we determined the quasi-filiform Lie algebras admitting a tonus of derivations, we obtain a list much richer than for the filiform case. This list allows us to prove that all quasi-fi liform Lie algebras are complete. Let us remind that all the filiform Lie algebras are also complete.Finally, we are interested in the existence of complex structures associated to the filiform and quasi-filiform Lie algebras Goze and Remm proved that the filiform algebras did not admit this type of structure. Since a different approach, we are going to re-demonstrate this result and we see that there are, on the other hand, quasi-filiform Lie algebras provided with a complex structure, but only in dimension 4 and 6.

The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic properties of a complex structure. The helicopter structure is normally designed to avoid resonance at the main rotor rotational frequency. However, very often military helicopters have to be modified (such as to carry a different weapon system or an additional fuel tank) to fulfill operational requirements. Any modification to a helicopter structure has the potential of changing its resonance frequencies and mode shapes. The dynamic properties of the modified structure can be determined by experimental testing or numerical simulation, both of which are complex, expensive and time-consuming. Assuming that the original dynamic characteristics are already established and that the modification is a relatively simple attachment such as beam or plate modification, the modified dynamic properties may be determined numerically without solving the equations of motion of the full-modified structure. The frequency response functions (FRFs) of the modified structure can be computed by coupling the original FRFs and a delta dynamic stiffness matrix for the modification introduced. The validity of this approach is investigated by applying it to several cases, 1) 1D structure with structural modification but no change in the number of degree of freedom (DOFs). A simply supported beam with double thickness in the middle section is treated as an example for this case; 2) 1D structure with additional DOFs. A cantilever beam to which a smaller beam is attached is treated as an example for this case, 3) 2D structure with a reduction in DOFs. A four-edge-clamped plate with a cut-out in the centre is treated as an example for this case; and 4) 3D structure with additional DOFs. A box frame with a plate attached to it as structural modification with additional DOFs and combination of different structures. The original FRFs were obtained numerically and experimentally except for the first case. The delta dynamic stiffness matrix was determined numerically by modelling the part of the modified structure including the modifying structure and part of the original structure at the same location. The FRFs of the modified structure were then computed. Good agreement is obtained by comparing the results to the FRFs of the modified structure determined experimentally as well as by numerical modelling of the complete modified structure.

Élaborer ou structurer des matériaux à l’échelle nanométrique permet d’aborder une physique nouvelle mais également de réaliser des dispositifs fonctionnant sur des principes originaux utilisées dans divers domaines (médecine, énergie, électronique, optique, catalyse..). Ce travail porte sur l’étude de l’assemblage des nanoparticules d’or colloïdales (NPs) en structures d’agrégation mésoscopiques, assisté par le séchage des fluides complexes et de leur manipulation par Microscope à Force Atomique (AFM) sur des surfaces modèles. Une première partie présente la synthèse des NPs d’or et des surfaces moléculaires auto-assemblées sur des substrats rigides. Ensuite, l’étude de la formation des structures d’agrégation assistée par le mouillage et le séchage des fluides complexes ( NPs et polysaccharide) sur des surfaces moléculaires a permis de mettre en évidence le rôle crucial du couplage entre les propriétés de volume singulières de ces fluides, et celles de surface du substrat dans la formation de structures d’agrégation complexes (fractales, et dendrites en particulier). Dans un troisième temps, les travaux abordent à l’étude et la compréhension du vieillissement (dégénérescence et reconstruction) des structures mésoscopiques élaborées. Entre autres résultats, ces travaux ont mis en évidence la nature ‘diffusionnelle’ de la dislocation des structures, laquelle se traduit par la mobilité d’agrégats nanoparticulaires en surface. Afin de mieux appréhender cette problématique de mobilité individuelle et/ou collective (cluster) des NPs, une étude détaillée basée sur la manipulation des NPs par AFM en mode Tapping a été réalisée. L’ensemble des résultats obtenus au cours de ce travail de thèse a permis d’une part, i) de proposer de nouvelles approches d’assemblage de macromolécules et de particules, assisté par les phénomènes de mouillage, ii) de comprendre les mécanismes à l’origine de la formation de ces structures d’agrégation complexes (fractales compactes et fibrillaires) sur des substrats homogènes et hétérogènes, et d’autre part, iii) de contrôler la stabilité et le vieillissement de ces structures d’agrégation complexes en vue d’une validation de la fiabilité éventuelle de nanomatériaux issus d’assemblages à base de NPs. / This work deals with the study of the drying-mediated assembly of colloidal gold nanoparticles (Au NPs) in mesoscale aggregation patterns and their manipulation by atomic force microscopy (AFM) on model surfaces. The assembly of NPs in mesoscale and complex aggregation patterns assisted by the wetting and the drying of complex fluids (suspensions of NPs, NPs/biopolymers mixed solutions) on homogeneous and heterogeneous molecular surfaces was studied. This issue is important, both for understanding fundamental processes of self-organization, and for generating new functional mesostructures. The drying of complex fluids often leads to the emergence of highly complex aggregation structures as shown and discussed in this work. The richness and the aesthetics of these complex structures generated by these interfacial phenomena reflect not only the bulk properties of fluids (different sizes and lengths- scales, kinetic changes in state), but more importantly, the coupling between the fluid properties and those of the substrate surface (wetting interactions, confinement, hydrodynamics). In the case of two important heterogeneous fluids which are Au NPs and polysaccharide solutions, these drying-mediated structure formation lead to the genesis of unusually large and highly ramified dendrites aggregation patterns. The growth mechanism and the critical parameters that control the morphogenesis of these complexes structures are addressed in this work. In addition, the aging mechanisms and kinetics of these structures that are metastable and evolve either through direct dislocation via clusters NPs mobility on the surface, or through undulation-induced roughning of the dendrite branches. To better understanding this NPs mobility and thus the dislocation mechanism of the aging, a detailed study based on the manipulation of NPs by atomic force microscopy in tapping mode (AFM) was developed. The threshold dissipated energy to manipulate (move) the NPs can be quantified according to the intrinsic parameters of the particle (size, shape, and chemical nature), the chemical nature and topography of the substrate, and finally the operating and environment conditions. This work enabled us to understand the mechanisms and characterize the critical parameters that may intervene in the dislocation (aging) of NPs-based functional structures, depending on the nature of the environment liquid and the substrate. Finally, this work proposes an approch of evaluation and of monitoring the stability and the aging of these aggregation structures, in particular, those formed from the drying of films and drops of nano-particles solutions (metal nanoparticles, blood: proteins, viruses ...).