Dans cette thèse, nous étudions la robustesse dans le contexte de la modélisation de systèmes complexes par les automates cellulaires. En effet, si l'on cherche à reproduire un comportement émergent à partir d'un modèle d'automate cellulaire, il nous semble nécessaire de se demander si les comportements observés sont bien le résultat d'interactions entre entités constituantes, ou bien s'ils dépendent d'une définition particulière du modèle. Nous allons ainsi être amenés à considérer la robustesse du modèle, à savoir la résistance de son comportement à de petites variations sur les attributs de sa définition. Dans un premier temps, nous montrons la pertinence de cette approche en considérant plusieurs définitions possibles d'une perturbation de la mise à jour globale et en les appliquant à une classe simple et représentative de modèles d'automates cellulaires, les Automates Cellulaires Elémentaires. Nous observons que, malgré le fait que nos perturbations soient proches et qu'une majorité des modèles considérés ne change pas de comportement, quelques cas particuliers montrent des changements qualitatifs du comportement que nous étudions plus en détail. Dans un second temps, nous appliquons cette approche en nous penchant sur un modèle particulier d'automate cellulaire, qui simule le phénomène de formation d'essaim à partir d'un modèle évolué d'automate cellulaire, le gaz sur réseau. Nous explorons la robustesse du comportement du modèle en considérant la perturbation de deux attributs du modèle, la forme de la grille cellulaire et la mise à jour globale, et en tirons les conclusions sur la relation entre l'observation du comportement et la définition précise du modèle / In this thesis, we study the role of robustness in the context of the modelling of complex systems by cellular automata. Indeed, if we consider a cellular automaton which aims at reproducing an emergent behaviour from a similar structure, we want to determine whether its observed dynamics are the result of the interaction of entities, or whether it depends a precise definition of the model. We thus consider the model's robustness, that is, the resistance of the behaviour to small perturbations on the model features. First, we show the relevance of this approach by considering several definitions of a perturbation of the global updating and by applying them to a simple and representative class of cellular automata, the Elementary Cellular Automata. We observe that, despite the fact that most models show little or no change between the different perturbations, some particular cases show qualitative changes that we study in detail. Second, we apply this approach to a particular model of cellular automata, which simulates a swarming behaviour based on a lattice-gas model. We then explore the model robustness by considering the pertubations of two of the model's attributes, the lattice shape and the global updating, and discuss the relationship between the observation of the behaviour and the precise definitions of the model

Ce travail a été développé dans le cadre du projet européen FACETS-ITN, dans le domaine des Neurosciences Computationnelles. Son but est d’améliorer la compréhension des réseaux de neurones stochastiques de taille finie, pour des sources corrélées à caractère aléatoire et pour des matrices de connectivité biologiquement réalistes. Ce résultat est obtenu par l’analyse de la matrice de corrélation du réseau et la quantification de la capacité de codage du système en termes de son information de Fisher. Les méthodes comprennent diverses techniques mathématiques, statistiques et numériques, dont certaines ont été importés d’autres domaines scientifiques, comme la physique et la théorie de l’estimation. Ce travail étend de précédents résultats fondées sur des hypothèses simplifiées qui ne sont pas réaliste d’un point de vue biologique et qui peuvent être pertinents pour la compréhension des principes de travail liés cerveau. De plus, ce travail fournit les outils nécessaires à une analyse complète de la capacité de traitement de l’information des réseaux de neurones, qui sont toujours manquante dans la communauté scientifique. / The brain is the most complex system in the known universe. Its nested structure with small-world properties determines its function and behavior. The analysis of its structure requires sophisticated mathematical and statistical techniques. In this thesis we shed new light on neural networks, attacking the problem from different points of view, in the spirit of the Theory of Complexity and in terms of their information processing capabilities. In particular, we quantify the Fisher information of the system, which is a measure of its encoding capability. The first technique developed in this work is the mean-field theory of rate and FitzHugh-Nagumo networks without correlations in the thermodynamic limit, through both mathematical and numerical analysis. The second technique, the Mayer’s cluster expansion, is taken from the physics of plasma, and allows us to determine numerically the finite size effects of rate neurons, as well as the relationship of the Fisher information to the size of the network for independent Brownian motions. The third technique is a perturbative expansion, which allows us to determine the correlation structure of the rate network for a variety of different types of connectivity matrices and for different values of the correlation between the sources of randomness in the system. With this method we can also quantify numerically the Fisher information not only as a function of the network size, but also for different correlation structures of the system. The fourth technique is a slightly different type of perturbative expansion, with which we can study the behavior of completely generic connectivity matrices with random topologies. Moreover this method provides an analytic formula for the Fisher information, which is in qualitative agreement with the other results in this thesis. Finally, the fifth technique is purely numerical, and uses an Expectation-Maximization algorithm and Monte Carlo integration in order to evaluate the Fisher information of the FitzHugh-Nagumo network. In summary, this thesis provides an analysis of the dynamics and the correlation structure of the neural networks, confirms this through numerical simulation and makes two key counterintuitive predictions. The first is the formation of a perfect correlation between the neurons for particular values of the parameters of the system, a phenomenon that we term stochastic synchronization. The second, which is somewhat contrary to received opinion, is the explosion of the Fisher information and therefore of the encoding capability of the network for highly correlated neurons. The techniques developed in this thesis can be used also for a complete quantification of the information processing capabilities of the network in terms of information storage, transmission and modification, but this would need to be performed in the future.

Contrary to elastic deformation, plastic deformation of crystalline materials, such as metals, is size-dependent. Most commonly, this phenomenon is present but unnoticed, such as the effect of microstructural length scales. The grain size in metallic materials is a length scale that affects material parameters such as yield stress and hardening moduli. In addition, several experiments performed in recent years on specimens with geometrical dimensions on the micron scale have shown that these dimensions also influence the mechanical behaviour. The work presented in this thesis involves continuum modelling and simulation of size-dependent plastic deformation, with emphasis on thin films and the formulation of interface conditions. A recently published strain gradient plasticity framework for isotropic materials [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379-1406] is used as a basis for the work. The theory is higher-order in the sense that additional boundary conditions are required and, as a consequence, higher-order stresses appear in the theory. For dimensional consistency, length scale parameters enter the theory, which is not the case for conventional plasticity theory. In Paper A and B, interface conditions are formulated in terms of a surface energy. The surface energy is assumed to depend on the plastic strain state at the interface and different functional forms are investigated. Numerical results are generated with the finite element method and it is found that this type of interface condition can capture the boundary layers that develop at the substrate interface in thin films. Size-effects are captured in the hardening behaviour as well as the yield strength. In addition, it is shown that there is an equivalence between a surface energy varying linearly in plastic strain and a viscoplastic interface law for monotonous loading. In paper C, a framework of finite element equations is formulated, of which a plane strain version is implemented in a commercial finite element program. Results are presented for an idealized problem of a metal matrix composite and several element types are examined numerically. In paper D, the implementation is used in a numerical study of wedge indentation of a thin film on an elastic substrate. Several trends that have been observed experimentally are captured in the theoretical predictions. Increased hardness at shallow depths due to gradient effects as well as increased hardness at more significant depths due to the presence of the substrate are found. It is shown that the hardening behaviour of the film has a large impact on the substrate effect and that either pile-up or sink-in deformation modes may be obtained depending on the material length scale parameter. Finally, it is qualitatively demonstrated that the substrate compliance has a significant effect on the calculated hardness of the film. / QC 20100723

Nanostructured materials are the next generation of high-performance materials, harnessing the novel properties of their nanosized constituents. The controlled assembly of nanosized particles and the design of the optimal nanostructure require a detailed understanding of particle interactions and robust methods to tune them. This thesis describes innovative approaches to these challenges, relating to the determination of Hamaker constants for iron oxide nanoparticles, the packaging of nanopowders into redispersible granules, the tuning of the wetting behavior of nanocrystals and the simulation of collective magnetic properties in arrays of superparamagnetic nanoparticles. The non-retarded Hamaker constants for iron oxides have been calculated from their optical properties based on Lifshitz theory. The results show that the magnitude of vdW interactions in non-polar solvents has previously been overestimated up to 10 times. Our calculations support the experimental observations that oleate-capped nanoparticles smaller than 15 nm in diameter can indeed form colloidally-stable dispersions in hydrocarbons. In addition, a simple procedure has been devised to remove the oleate-capping on the iron oxide nanoparticles, enabling their use in fluorometric assays for water remediation, with a sensitivity more than 100 times below the critical micelle concentration for non-ionic surfactants. Nanosized particles are inherently more difficult to handle in the dry state than larger micron-sized powders, e.g. because of poor flowability, agglomeration and potential toxicity. The rheology of concentrated slurries of TiO2 powder was optimized by the addition of sodium polyacrylate, and spray-dried into fully redispersible micron-sized granules. The polymer was embedded into the granules, where it could serve as a re-dispersing aid. Monte Carlo (MC) simulations have been applied to the collective magnetic behavior of nanoparticle arrays of various thicknesses. The decrease in magnetic susceptibility with the thickness observed experimentally was reproduced by the simulations. Ferromagnetic couplings in the arrays are enhanced by the finite thickness, and decrease in strength with increasing thickness. The simulations indicate the formation of vortex states with increasing thickness, along with a change in their orientation, which becomes more and more isotropic as the thickness increases. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 2: Manuscript.</p>

Silizide spielen ein wesentliche Rolle in den technologisch fortschrittlichsten CMOS Bauteilen. Sie finden Verwendung als Kontaktmaterial auf den Aktivgebieten und dem Silizium Gatter von Transistoren. Diese Arbeit beschäftigt sich mit den Systemen: Co-Si, Co-Ni-Si und Ni-Si. Sowohl in situ Hochtemperatur-SR-XRD Experimente als auch CBED wurden zur Phasenidentifikation herangezogen. AES erlaubte es, Elementverteilungen in Schichtstapeln zu bestimmen. Für Studien über Agglomerationserscheinungen wurde REM eingesetzt. TEM und analytisches TEM trugen nicht nur zu Einblicken in Schichtstrukturen und Kornformen bei, sondern lieferten auch Daten zu Elementverteilungen in Silizidschichten. Diese Dissertation gliedert sich in zwei Hauptteile. Der erste Teil beschäftigt sich mit den Phasenbildungsabfolgen und den Phasenbildungs- und Umwandlungstemperaturen in nanoskaligen dünnen Schichten. Als Trägermaterial wurden einkristalline und polykristalline Siliziumsubstrate verwendet. Der Einfluß verschiedener Dotierungen im Vergleich zu undotierten Substraten sowie die Beeinflussung der Silizidierung durch eine Deckschicht wurden untersucht. Im zweiten Teil waren Größeneffekte verschiedener Schichtdicken und Agglomerationserscheinungen Gegenstand von Untersuchungen. Unterschiede bei der Silizidierung in Zusammenhang mit unterschiedlichen Schichtdicken wurden bestimmt. Darüberhinaus wurde eine ternäre CoTiSi Phase gefunden und identifiziert. Außerdem konnte die stark eingeschränkte Mischbarkeit der Monosilizide CoSi und NiSi gezeigt werden. Der thermische Ausdehnungskoeffizient von NiSi im Temperaturbereich 400?700°C und sein nicht-lineares Verhalten wurden bestimmt. / Silicides are an essential part of state-of-the-art CMOS devices. They are used as contact material on the active regions as well as on the Si gate of a transistor. In this work, investigations were performed in the systems Co-Si, Co-Ni-Si, and Ni-Si. In situ high temperature SR-XRD and CBED techniques were used for phase identification. AES enabled the determination of elemental concentrations in layer stacks. SEM was applied to agglomeration studies. TEM imaging and analytical TEM provided insights into layer structures, grain morphology as well as information about the distribution of chemical elements within silicide layers. This thesis is divided into two main parts. The first part deals with the phase formation sequences and the phase formation and conversion temperatures in nanoscale thin films on either single crystal or polycrystalline Si substrates. The effect of different types of dopants vs. no doping and the impact of a capping layer on the phase formation and conversion temperatures were studied. In the second part, size effects and agglomeration of thin silicide films were investigated. The effect of different layer thicknesses on the silicidation process was studied. Additionally, the degree of agglomeration of silicide films was calculated. Furthermore, the ternary CoTiSi phase was found and identified as well as the severely limited miscibility of the monosilicides CoSi and NiSi could be shown. The CTE of NiSi between 400?700 ±C and its non-linear behavior was determined.

The 2006 International Technology Roadmap for Semiconductors projects that for 2020, interconnects will be as narrow as 14 nm and will operate at frequencies as high as 50GHz. For a wire that operates at ultra-high frequencies, such that skin depth and the mean free path of the electrons are in the same order, skin effect and surface scattering should be considered simultaneously. This is known as the anomalous skin effect (ASE). The objective of this work is to identify the challenges and opportunities for using GSI interconnects in the nanometer and GHz regime. The increase in the resistivity of a thin wire caused by the ASE is studied. The delay of a digital transmission line resulting from this effect is modeled. Compact models are presented for the bit-rate limit of transmission lines using a general form of resistance that for the first time simultaneously considers dc resistance, skin effect, and surface scattering. A conventional low-loss approximation that is only valid for fast rising signals is also relaxed. The impact of size effects on the design of multi-level interconnect networks is studied. For high-performance chips at the 18 nm technology node, it is shown that despite a more than four times increase in the resistivity of copper for minimum-size interconnects, the increase in the number of metal levels is negligible (less than 7%), and interconnects that will be affected most are so short that their impact on chip performance is inconsequential. It is shown that for low-cost applications where very few wiring pitches are normally used, the number of metal levels needed to compensate for the impact of size effects on the average rc delay of a copper interconnect is drastically high. An optimization methodology has been presented for power distribution interconnects at the local level. For a given IR drop budget, compact models are presented for the optimal widths of power and ground lines in the first two metal levels for which the total metal area used for power distribution is minimized.

Ce mémoire présente des travaux de thèse consacrés à la caractérisation et la modélisation des hétérogénéités spatio-temporelles dans les écoulements granulaires cisaillés entre deux parois rigides. De nombreuses simulations ont permis de révéler le rôle crucial des dimensions de l’écoulement et l’influence des interactions des grains avec les parois (avec leur rugosité) sur le comportement global. Pour des systèmes allant jusqu'à une épaisseur de cent diamètres, des profils de vitesse non homogènes ont été mis en évidence, alors que la contrainte cisaillante est constante dans le volume, mettant en défaut le modèle viscoplastique au sein de l’écoulement. Pour réconcilier ces deux observations, nous avons enrichi le modèle viscoplastique en reliant la viscosité à une variable interne qui porte la perturbation due à la présence des parois. Cette nouvelle formulation de la viscosité permet de rétablir la validité d'une loi de comportement locale prenant en compte simultanément l’épaisseur de l’écoulement, la rugosité des parois et le nombre inertiel.Cette dépendance de la viscosité à une variable interne liée à la connectivité des grains ou à leur agitation à compacité fixée, suggère que, d’une manière générale,les écoulements granulaires doivent être décrits en termes d’au moins trois paramètres en fonction du nombre inertiel : le coefficient de frottement, la compacité et la connectivité. / This PhD work is devoted to the description and modeling of spatiotemporal inhomogeneities in granular flows sheared between two rigid walls. Our extensive simulations reveal the crucial role played by flow dimensions and the interactions of the grains with the walls and their roughness. For granular systems with increasingly larger thickness, non uniform strain profiles are evidenced while the shear stress remains uniform. This observation contradicts the common viscoelastic approach based on inertial number in the bulk of the flow. In order to reconcile these observations, we propose a viscoplastic model by a introducing an internal variable carrying the wall-induced perturbations of the flow. This re-formulation of granular viscosity reaffirms the local rheology by accounting for flow thickness, wall routines and inertialeffects. The well-defined dependence of the viscosity on an internal variable pertaining to grain connectivity or kinematic randomness at constant packing fraction, suggests that granular flows should be described by at least three parameters as a function of the inertial number:friction coefficient, packing fraction and connectivity.

The growth of atomically flat silver films on Si(111) usually requires a two-step growth, including deposition at low temperature (≈100 K) followed by slowly annealing to room temperature. In addition, flat silver films are usually only obtained on Si(111) for film thicknesses larger than the critical thickness of 6 monolayer. In this work, Ag thin film formation at ambient temperature on Sn/Si(111)-√3×√3 has been investigated experimentally using a combination of scanning tunneling microscopy, scanning tunneling spectroscopy and low-energy electron diffraction. The first buffer layer, probably consisting of both Ag and Sn, formed a partially ordered structure consisting of atomic rows which mainly followed the high-symmetry directions of the underlying Si(111) lattice. From 3 ML coverage, an atomically flat Ag film was formed. Low-energy electron diffraction confirmed that the films grew in the [111]-direction. This shows that atomically flat Ag films as thin as 3 ML can be grown on Sn/Si(111)-√3×√3 by conventional deposition at room temperature. The electronic structures of the films were studied for a range of different coverages by scanning tunneling spectroscopy. The normalized tunneling conductance showed quantum well states in the occupied electronic states, which moved towards the Fermi energy with increasing film thicknesses.

Les électrodes transparentes (ET) sont présentes dans de nombreux dispositifs optoélectroniques. Par exemple, on peut les trouver au sein de cellules solaires, d'écrans tactiles, d'OLEDs ou encore de films chauffants transparents. Les propriétés physiques de ces électrodes influencent l'efficacité de ces dispositifs. Les ET sont fabriquées à partir de matériaux transparents conducteurs (TCM) dont le développement a débuté dans les années 1950 notamment avec les oxydes métalliques. Parmi ces oxydes transparents conducteurs (TCO), l'oxyde d'étain-indium (ITO) est celui le plus communément utilisé dans les cellules solaires et les écrans de télévision ou de smartphones. Cependant, de nouvelles exigences telles qu'une réduction des coûts, la flexibilité et la fabrication à faible température et/ou faible coût, ont orienté les recherches vers de nouveaux TCM, notamment à base de nanostructures. Parmi ces matériaux émergents, les réseaux de nanofils métalliques, en particulier de nanofils d'argent, présentent déjà des propriétés optiques et électriques approchant celles de l'ITO, c'est-à-dire une conductivité électrique et une transparence élevées. Ces deux propriétés sont cependant intrinsèquement liées à la densité de nanofils constituant le réseau, et lorsque la conductivité augmente, la transparence diminue. Des traitements post-dépôt existent et permettent d'augmenter la conductivité électrique des ET sans changer la densité du réseau. Plusieurs de ces méthodes d'optimisation ont été étudiées pendant ce travail de thèse, en particulier le recuit thermique, analysé minutieusement afin de comprendre les différents mécanismes de réduction de la conductivité électrique induits par la température. L'examen des effets thermiques a soulevé la question de l'instabilité des nanofils en température, qui est aussi abordée et discutée dans ce document. Le paramètre clé de la densité de nanofils optimale menant au meilleur compromis entre transparence et conductivité a été recherché pour des nanofils de différentes dimensions. La taille des nanofils a en effet un fort impact sur les propriétés du réseau. Ainsi, les propriétés électriques, dans le cadre de la théorie de la percolation, les propriétés optiques comme la transmittance et le facteur de haze, et même l'instabilité thermique ont été reliées aux dimensions des nanofils ainsi qu'à la densité du réseau en utilisant des modèles physiques simples. En ce qui concerne les applications de ces ET émergentes, des études ont été menées sur l'application des réseaux de nanofils d'argent comme film chauffant transparent, et les résultats sont rapportés à la fin de ce document. Les limitations soulevées par cette application, comme les limites de stabilités électrique et thermique ont aussi été abordées. Pour finir, des études préliminaires menées sur de nouvelles applications comme des antennes transparentes ou le blindage électromagnétique transparent utilisant les nanofils d'argent sont présentées. / Transparent electrodes (TE) are used in a variety of optoelectrical devices. Among them, solar cells, flat panel displays, touch screens, OLEDs and transparent heaters can be cited. The physical properties of the TE influence the efficiency of the device as a whole. Such electrodes are fabricated from transparent conducting materials (TCM) that have been undergoing development since the 1950s, initially from metallic oxides. Among these transparent conducting oxides (TCO), indium tin oxide (ITO) is the most commonly used in solar cells, and television or smartphone screens. However requirements such as cost reduction, flexibility and low cost/temperature fabrication techniques have oriented the researches toward emerging TCM, mostly using nanostructures. Among them, metallic nanowire networks, and in particular silver nanowires (AgNW), already present optical and electrical properties approaching those of ITO, i.e. a high electrical conductivity and a high transparency. These two properties are intrinsically linked to the network density, therefore a tradeoff has to be considered knowing that when conductivity increases, transparency decreases. Some post-deposition treatments do exist, allowing an increase of the TE electrical conductivity without changing the network density. Several of these optimization methods have been thoroughly studied during this thesis work, especially thermal annealing. This method have been investigated in details to understand the different thermally-induced mechanisms of conductivity improvement. In addition, the investigation of thermal effects raised the question of thermal instability of the nanowires, which is also addressed and discussed in this document. The key issue of density optimization, allowing the best tradeoff between transparency and conductivity, has been investigated for nanowires with different dimensions. Nanowire size has a strong impact on the network properties. Thus, electrical properties, within the framework of percolation theory, optical properties such as transmittance or haziness, and even thermal instability have been linked to the nanowires' dimensions and the network density by using simple physical models. Regarding the application of these emerging TE, studies were conducted on the application of AgNWs as transparent heaters, and the results are reported at the end of the document. Limitations arising from this application, like thermal and electrical stabilities, have also been addressed. To finish, preliminary studies conducted on new applications such as transparent antennas and transparent electromagnetic shielding using AgNW are presented.

Le but de ce travail de thèse est l’étude de la dynamique de sphères de grande taille dans un écoulement fortement turbulent. Pour ce faire, nous avons développé une nouvelle technique optique permettant de suivre la dynamique à 6 dimensions – position et orientation absolues – de plusieurs particules dans un écoulement complexe. Bien que la taille des particules soit comparable à l’échelle intégrale de l’écoulement, nous trouvons que sa dynamique de rotation et de translation est intermittente. De plus, nous observons que la translation et la rotation sont reliées par la force de Magnus. La répartition statistique de l’accélération n’est pas gaussienne et l’échange d’énergie avec le fluide est gouverné par la théorie mathématique des grandes déviations. Nous trouvons que le diamètre influence fortement la manière dont la particule explore l’écoulement. Nous avons ensuite appliqué le suivi de position et d’orientation à une particule instrumentée. Ce système mesure en permanence l’accélération lagrangienne qu’il subit via un accéléromètre embarqué et émet l’information à travers une électronique radio fréquence. L’orientation absolue est nécessaire pour exprimer les signaux de l’accéléromètre et ceux du suivi optique dans un repère commun; cela nous permet de comparer rigoureusement les mesures issues de ces deux techniques indépendantes. À partir de ces résultats nous avons développé des méthodes pour inférer des propriétés de l’écoulement à partir des signaux d’accélération de la particule instrumentée. / The aim of this dissertation is to gain a better understanding of the Lagrangian dynamics of solid large spheres in a complex turbulent environment. Therefore, a novel measurement technique to optically track the 6–dimensional dynamics – position and absolute orientation – of large spheres advected by a complex flow is developed. Although the sphere’s diameter is comparable to the integral length of the underlying flow, we find intermittency for both the translation and the rotation. Moreover, rotation and translation couple in agreement with a lift force. Apart from the fact that the acceleration statistics are not gaussian, and the exchange of energy between the particle and the carrier flow falls into the mathematical theory of large deviations. Additionally, we find that the particle diameter has a surprisingly strong influence on how a particle samples the flow. The 6D–tracking technique is then applied to an instrumented particle, which embarks a 3D–accelerometer and a radio-transmission system to constantly emit the felt Lagrangian acceleration as it is advected in the flow. Measuring the particle’s absolute orientation is a crucial step here to project the acceleration measured by the particle into the laboratory reference frame and enables us to compare the forces obtained by the two independent measurements. Based thereon methods for interpreting the acceleration signals of the instrumented particle are developed and tested.