京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18783号 / 理博第4041号 / 新制||理||1582(附属図書館) / 31734 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 准教授 篠本 滋, 准教授 武末 真二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Le but de cette étude expérimentale est de caractériser la dynamique de particules solides, à flottabilité nulle, incluse dans un écoulement turbulent isotrope en décroissance libre. Les particules utilisées sont de forme sphérique et ont un diamètre de 4 à 5 fois plus grand que l'échelle spatial de Kolmogorov de l'écoulement. De part leur taille, les particules ont également un nombre de Stokes proche de l'unité. On s'attend alors à ce que ces particules aient une dynamique différente de celle du fluide environnant. Dans cette étude, ont se propose de quantifier les différences de vitesses entre les deux phases à l'aide d'une technique de vélocimétrie simultanée / In this experimental study, the focus is made on the characterization of the dynamics of solid neutrally buoyant particles embedded in a freely decaying, nearly isotropic turbulence, with a weak mean flow. The particles are spherical with diameters several times larger than the Kolmogorov scale. The study of this flow configuration is still challenging both theoretically and numerically. Due to large particle sizes, the local flow around particles can not be considered as uniform and due to fluid-particle density ratio of around unity, the history and Basset forces cannot be neglected in comparison with the viscous drag force. Particle equation of motion is then fully non-linear, in contrast to the equation for heavy particles with diameters smaller then the Kolmogorov scale, for which only the Stokes drag is considered. In several experimental and numerical studies, the effect of particle size on velocity and acceleration statistics has been investigated (Homann and Bec 2010 ; Qureshi et al. 2008 ; Ouellette et al. 2008 ; Xu and Bodenschatz 2008). In the case of isotropic turbulence, Homann and Bec (2010) show that while the PDF of the particle velocity normalized by the square root of its variance does not vary with particle size, the variance itself is size dependent. A scaling relation for particle velocity variance has been proposed by using the Faxen correction (Gatignol 1983) which takes into account the non uniformity of the fluid flow at the scale of the particle. The aim of our research is to further study the dependence of particle dynamics on particle size. To that purpose, a turbulence generator has been set-up and the resulting turbulence is characterized. Then the flow was seeded with millimeter sized, neutrally-buoyant particles and the velocity of the two phases have been measured simultaneously. Simultaneous measurements of particle and surrounding fluid velocities show that although the global velocity statistics of the two phases have comparable values, the particles may have different local velocity from the velocity of the neighboring fluid

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

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-07-04T18:39:14Z No. of bitstreams: 1 Dissertaçao_PierreSoares (1).pdf: 729793 bytes, checksum: 12e5898e33b9602f7b327e003b58716b (MD5) / Made available in DSpace on 2017-07-04T18:39:14Z (GMT). No. of bitstreams: 1 Dissertaçao_PierreSoares (1).pdf: 729793 bytes, checksum: 12e5898e33b9602f7b327e003b58716b (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / O uso de redes neurais na solução de problemas é bastante atrativa pois suas características possibilitam desempenho superior ao de métodos convencionais [1]. Dentre os diferentes modelos de redes neurais, o modelo de Hopfield apresenta uma grande importância histórica nesse campo. Neste trabalho estudaremos o problema da capacidade de reconhecimento em uma rede de Hopfield utilizando técnicas de análise de tamanho finito. Vamos comparar os resultados obtidos por diferentes métodos com o intuito de obter o valor de [alfa c], o ponto onde a rede passa por uma transição de fase. Para isso utilizaremos simulações computacionais de redes de Hopfield. / The use of neural networks in problem solution is quite attractive because its characteristics enable superior performance than the conventional methods [1]. Among the different models of neural networks, the Hopfield model has a great historic importance in this field. In this work we will study the capacity problem of a Hopfield network by using finite-size analysis. We will compare the results obtained by different methods to find the value of [alpha c], the point where the network undergoes a phase transition. For this we will use computational simulations of Hopfield networks.

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-07-14T18:59:48Z No. of bitstreams: 1 Dissertaçao_PierreSoares (1).pdf: 729793 bytes, checksum: 12e5898e33b9602f7b327e003b58716b (MD5) / Made available in DSpace on 2017-07-14T18:59:48Z (GMT). No. of bitstreams: 1 Dissertaçao_PierreSoares (1).pdf: 729793 bytes, checksum: 12e5898e33b9602f7b327e003b58716b (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / O uso de redes neurais na solução de problemas é bastante atrativa pois suas características possibilitam desempenho superior ao de métodos convencionais [1]. Dentre os diferentes modelos de redes neurais, o modelo de Hopfield apresenta uma grande importância histórica nesse campo. Neste trabalho estudaremos o problema da capacidade de reconhecimento em uma rede de Hopfield utilizando técnicas de análise de tamanho finito. Vamos comparar os resultados obtidos por diferentes métodos com o intuito de obter o valor de , o ponto onde a rede passa por uma transição de fase. Para isso utilizaremos simulações computacionais de redes de Hopfield. / The use of neural networks in problem solution is quite attractive because its characteristics enable superior performance than the conventional methods [1]. Among the different models of neural networks, the Hopfield model has a great historic importance in this field. In this work we will study the capacity problem of a Hopfield network by using finite-size analysis. We will compare the results obtained by different methods to find the value of , the point where the network undergoes a phase transition. For this we will use computational simulations of Hopfield networks.

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.

<p>We have studied the critical properties of three-dimensional U(1)-symmetric lattice gauge theories. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. This thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication.</p><p>Paper I: Critical properties of the 2+1-dimensional compact abelian Higgs model with gauge charge q=2 are studied. We introduce a novel method of computing the third moment M₃ of the action which allows us to extract correlation length and specific heat critical exponents ν and α without invoking hyperscaling. Finite-size scaling analysis of M₃ yields the ratio (1+α)/ν and 1/ν separately. We find that α and ν vary along the critical line of the theory, which however exhibits a remarkable resilience of Z₂ criticality. We conclude that the model is a fixed-line theory, which we propose to characterize the zero temperature quantum phase transition from a Mott-Hubbard insulator to a charge fractionalized insulator in two spatial dimensions.</p><p>Paper II: Large scale Monte Carlo simulations are employed to study phase transitions in the three-dimensional compact abelian Higgs model in adjoint representations of the matter field, labeled by an integer q, for q=2,3,4,5. We also study various limiting cases of the model, such as the Z_q lattice gauge theory, dual to the 3DZ_q spin model, and the 3D xy spin model which is dual to the Z_q lattice gauge theory in the limit q → ∞. In addition, for benchmark purposes, we study the 2D square lattice 8-vertex model, which is exactly solvable and features non-universal critical exponents. The critical exponents α and ν are calculated from finite size scaling of the third moment of the action, and the method is tested thoroughly on models with known values for these exponents. We have found that for q=3, the three-dimensional compact abelian Higgs model exhibits a second order phase transition line which joins a first order phase transition line at a tricritical point. The results for q=2 in Paper I are reported with a higher lever of detail.</p><p>Paper III: This paper is based on a talk by F. S. Nogueira in the Aachen HEP 2003 conference where a review of the results for the compact abelian Higgs model from Paper I and Paper II was presented, as well as the results for the q=1 case studied by F. S. Nogueira, H. Kleinert and A. Sudbø.</p><p>Paper IV: We study the effects of a Chern-Simons (CS) term in the phase structure of two different abelian gauge theories in three dimensions. By duality transformations we show how the compact U(1) gauge theory with a CS term for certain values of the CS coupling can be written as a gas of vortex loops interacting through steric repulsion. This theory is known to exhibit a phase transition governed by proliferation of vortex loops. We also employ Monte Carlo simulations to study the non-compact U(1) abelian Higgs model with a CS term. Finite size scaling of the third moment of the action yields critical exponents α and ν that vary continuously with the strength of the CS term, and a comparison with available analytical results is made.</p><p>Paper V: The critical properties of N-component Ginzburg-Landau theory are studied in d=2+1 dimensions. The model is dualized to a theory of N vortex fields interacting through a Coulomb and a screened potential. The model with N=2 shows two anomalies in the specific heat. From Monte Carlo simulations we calculate the critical exponents α and ν and the mass of the gauge field. We conclude that one anomaly corresponds to an inverted 3D xy fixed point, while the other corresponds to a 3D xy fixed point. There are N fixed points, namely one corresponding to an inverted 3D xy fixed point, and N-1corresponding to neutral 3D xy fixed points. Applications are briefly discussed.</p><p>Paper VI: The phase diagram and critical properties of the N-component London superconductor are studied both analytically and through large-scale Monte-Carlo simulations in d=2+1 dimensions. The model with different bare phase stiffnesses for each flavor is a model of superconductivity which should arise out of metallic phases of light atoms under extreme pressure. A projected mixture of electronic and protonic condensates in liquid metallic hydrogen under extreme pressure is the simplest example, corresponding to N=2 with individually conserved matter fields. We compute critical exponents α and ν for N=2 and N=3. The results from Paper V are presented at a higher level of detail. For the arbitrary N case, there are N fixed points,namely one charged inverted 3D xy fixed point, and N-1 neutral 3D xy fixed points. We explicitly identify one charged vortex mode and N-1 neutral vortex modes. The model for N=2 and equal bare phase stiffnesses corresponds to a field theoretical description of an easy-plane quantum antiferromagnet. In this case, the critical exponents are computed and found to be non 3D xy values. Furthermore, we study the model in an external magnetic field, and find a novel feature, namely N-1 superfluid phases arising out of N charged condensates. In particular, for N=2 we point out the possibility of two novel types of field-induced phase transitions in ordered quantum fluids: i) A phase transition from a superconductor to a superfluid or vice versa, driven by tuning an external magnetic field. This identifies the superconducting phase of liquid metallic hydrogen as a novel quantum fluid. ii) A phase transition corresponding to a quantum fluid analogue of sublattice melting, where a composite field-induced Abrikosov vortex lattice is decomposed and disorders the phases of the constituent condensate with lowest bare phase stiffness. Both transitions belong to the 3D xy universality class.</p><p>Paper VII: We consider the vortex superconductor with two individually conserved condensates in a finite magnetic field. The ground state is a lattice of cocentered vortices in both order parameters. We find two novel phase transitions when temperature is increased at fixed magnetic field. i) A "vortex sublattice melting" transition where vortices in the field with lowest phase stiffness ("light vortices") loose cocentricity with the vortices with large phase stiffness ("heavy vortices"), entering a liquid state (the structure factor of the light vortex sublattice vanishes continuously.) This transition is in the 3D xy universality class. ii) A first order melting transition of the lattice of heavy vortices in a liquid of light vortices.</p><p>Paper VIII: We report on large-scale Monte Carlo simulations of a novel type of a vortex matter phase transition which should take place in a three dimensional two-component superconductor. We identify the regime where first, at a certain temperature a field-induced lattice of co-centered vortices of both order parameters melts, causing the system to loose superconductivity. In this state the two-gap system retains a broken composite symmetry and we observe that at a higher temperature it undergoes an extra phase transition where the disordered composite one-flux-quantum vortex lines are "ionized" into a "plasma" of constituent fractional flux vortex lines in individual order parameters. This is the hallmark of the superconductor-to-superfluid-to-normal fluid phase transitions projected to occur in e.g. liquid metallic hydrogen.</p>

We have studied the critical properties of three-dimensional U(1)-symmetric lattice gauge theories. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. This thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. Paper I: Critical properties of the 2+1-dimensional compact abelian Higgs model with gauge charge q=2 are studied. We introduce a novel method of computing the third moment M3 of the action which allows us to extract correlation length and specific heat critical exponents ν and α without invoking hyperscaling. Finite-size scaling analysis of M3 yields the ratio (1+α)/ν and 1/ν separately. We find that α and ν vary along the critical line of the theory, which however exhibits a remarkable resilience of Z2 criticality. We conclude that the model is a fixed-line theory, which we propose to characterize the zero temperature quantum phase transition from a Mott-Hubbard insulator to a charge fractionalized insulator in two spatial dimensions. Paper II: Large scale Monte Carlo simulations are employed to study phase transitions in the three-dimensional compact abelian Higgs model in adjoint representations of the matter field, labeled by an integer q, for q=2,3,4,5. We also study various limiting cases of the model, such as the Zq lattice gauge theory, dual to the 3DZq spin model, and the 3D xy spin model which is dual to the Zq lattice gauge theory in the limit q → ∞. In addition, for benchmark purposes, we study the 2D square lattice 8-vertex model, which is exactly solvable and features non-universal critical exponents. The critical exponents α and ν are calculated from finite size scaling of the third moment of the action, and the method is tested thoroughly on models with known values for these exponents. We have found that for q=3, the three-dimensional compact abelian Higgs model exhibits a second order phase transition line which joins a first order phase transition line at a tricritical point. The results for q=2 in Paper I are reported with a higher lever of detail. Paper III: This paper is based on a talk by F. S. Nogueira in the Aachen HEP 2003 conference where a review of the results for the compact abelian Higgs model from Paper I and Paper II was presented, as well as the results for the q=1 case studied by F. S. Nogueira, H. Kleinert and A. Sudbø. Paper IV: We study the effects of a Chern-Simons (CS) term in the phase structure of two different abelian gauge theories in three dimensions. By duality transformations we show how the compact U(1) gauge theory with a CS term for certain values of the CS coupling can be written as a gas of vortex loops interacting through steric repulsion. This theory is known to exhibit a phase transition governed by proliferation of vortex loops. We also employ Monte Carlo simulations to study the non-compact U(1) abelian Higgs model with a CS term. Finite size scaling of the third moment of the action yields critical exponents α and ν that vary continuously with the strength of the CS term, and a comparison with available analytical results is made. Paper V: The critical properties of N-component Ginzburg-Landau theory are studied in d=2+1 dimensions. The model is dualized to a theory of N vortex fields interacting through a Coulomb and a screened potential. The model with N=2 shows two anomalies in the specific heat. From Monte Carlo simulations we calculate the critical exponents α and ν and the mass of the gauge field. We conclude that one anomaly corresponds to an inverted 3D xy fixed point, while the other corresponds to a 3D xy fixed point. There are N fixed points, namely one corresponding to an inverted 3D xy fixed point, and N-1corresponding to neutral 3D xy fixed points. Applications are briefly discussed. Paper VI: The phase diagram and critical properties of the N-component London superconductor are studied both analytically and through large-scale Monte-Carlo simulations in d=2+1 dimensions. The model with different bare phase stiffnesses for each flavor is a model of superconductivity which should arise out of metallic phases of light atoms under extreme pressure. A projected mixture of electronic and protonic condensates in liquid metallic hydrogen under extreme pressure is the simplest example, corresponding to N=2 with individually conserved matter fields. We compute critical exponents α and ν for N=2 and N=3. The results from Paper V are presented at a higher level of detail. For the arbitrary N case, there are N fixed points,namely one charged inverted 3D xy fixed point, and N-1 neutral 3D xy fixed points. We explicitly identify one charged vortex mode and N-1 neutral vortex modes. The model for N=2 and equal bare phase stiffnesses corresponds to a field theoretical description of an easy-plane quantum antiferromagnet. In this case, the critical exponents are computed and found to be non 3D xy values. Furthermore, we study the model in an external magnetic field, and find a novel feature, namely N-1 superfluid phases arising out of N charged condensates. In particular, for N=2 we point out the possibility of two novel types of field-induced phase transitions in ordered quantum fluids: i) A phase transition from a superconductor to a superfluid or vice versa, driven by tuning an external magnetic field. This identifies the superconducting phase of liquid metallic hydrogen as a novel quantum fluid. ii) A phase transition corresponding to a quantum fluid analogue of sublattice melting, where a composite field-induced Abrikosov vortex lattice is decomposed and disorders the phases of the constituent condensate with lowest bare phase stiffness. Both transitions belong to the 3D xy universality class. Paper VII: We consider the vortex superconductor with two individually conserved condensates in a finite magnetic field. The ground state is a lattice of cocentered vortices in both order parameters. We find two novel phase transitions when temperature is increased at fixed magnetic field. i) A "vortex sublattice melting" transition where vortices in the field with lowest phase stiffness ("light vortices") loose cocentricity with the vortices with large phase stiffness ("heavy vortices"), entering a liquid state (the structure factor of the light vortex sublattice vanishes continuously.) This transition is in the 3D xy universality class. ii) A first order melting transition of the lattice of heavy vortices in a liquid of light vortices. Paper VIII: We report on large-scale Monte Carlo simulations of a novel type of a vortex matter phase transition which should take place in a three dimensional two-component superconductor. We identify the regime where first, at a certain temperature a field-induced lattice of co-centered vortices of both order parameters melts, causing the system to loose superconductivity. In this state the two-gap system retains a broken composite symmetry and we observe that at a higher temperature it undergoes an extra phase transition where the disordered composite one-flux-quantum vortex lines are "ionized" into a "plasma" of constituent fractional flux vortex lines in individual order parameters. This is the hallmark of the superconductor-to-superfluid-to-normal fluid phase transitions projected to occur in e.g. liquid metallic hydrogen.

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>

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.