Quel que soit le type d'onde étudié, on peut classer les systèmes ondulatoires complexes essentiellement en deux catégories, et ceci malgré la différence entre les équations d'ondes qui les régissent. On a d'une part ceux pour lesquels la géométrie des bords induit la complexité : on parle alors de chaos ondulatoire. On a d'autre part les systèmes rendus complexes du fait des hétérogénéités du milieu conduisant à un régime de diffusion multiple. L'utilisation des cavités micro-ondes bidimensionnelles (2D) comme système de base pour étudier ces deux régimes permet de réaliser des expériences modèles à l'échelle macroscopique. Dans le régime du chaos ondulatoire, nous étudions, pour la première fois dans une expérience, le cas d'une cavité rectangulaire perturbée par un défaut métallique quasi-ponctuel. En nous appuyant sur une approche semi-classique, basée sur la notion d'orbites périodiques, nous mettons en évidence, pour la première fois, les contributions des orbites diffractives dans les spectres de longueurs. L'utilisation de milieux désordonnés diélectriques fortement diffusifs ouverts, permet d'observer la localisation d'Anderson 2D par l'étude des modes localisés. Nous décrivons dans le détail le dispositif expérimental ainsi que le protocole suivi pour remonter à la représentation spatiale d'un mode localisé. Nous prouvons, pour la première fois expérimentalement, que les largeurs spectrales de ces modes localisés, liées aux fuites de l'énergie par les bords du système, décroissent exponentiellement avec la taille du système. Nous montrons, en outre, que cette décroissance exponentielle est contrôlée par les plus grandes longueurs de localisation.

This dissertation focuses on predictability problems regarding the behaviour of the professional librarians in public-, school- and research libraries in specific crucial situations. The material was obtained by observations/participations (over 10 years) in the daily work in Swedish libraries by non-structured interviews and “free” discussions with librarians and library visitors. Over 200 interviews with 87 librarians and over 300 discussions with 261 library visitors are the fundament of the empirical basis of my study. These findings build up a theoretical basis (a heuristic model) grounded in ideas of deterministic chaos and complexity theory. Deterministic means, that the current state is the consequence of its preceding states, in my terms, the corporate memory in organizations. Chaotic means the sensitivity of initial condition. Deterministic chaos describes behaviour which satisfies the conditions of determinism but even shows the characteristics of chaos. The study shows that differences between the behaviour of the librarians and the predictions of the behaviour in crucial situations from the political leadership are essentially grounded in ·The history of Swedish libraries (deterministic rationality and self-rationality). ·The asymmetric information between librarians and politicians. ·Self-organization of librarians in the daily work. ·The “free” will of librarians in crucial situations grounded in the philosophy of Kant. The behaviour I could observe was studied in the following situations: ·The demand of a law, which secures the existence of public- and school libraries. ·The selection, development and installation of appropriate computer based information systems in public- school- and research libraries. ·The GÖK- and KUR-projects, which was based on the assumption that new ways to work with the daily patterns in libraries should open the library for more visitors, book loaners and information seekers. The issues discussed in this dissertation gave the following results: ·That the long time, in many cases even short time, unpredictability of librarian behaviour in for the library crucial situations is not only understandable – but also necessary for the development of the library. ·That the deterministic chaotic behaviour of the librarians is generated by self-rationality, asymmetric information, and self-organization. ·That the library is not a chaotic organization but a deterministic chaotic organization. Further I could see tendencies for the same behaviour in other professional, knowledge based Non Profit Organizations like schools, universities and hospitals.

Conservation laws with uncertain initial and boundary conditions are approximated using a generalized polynomial chaos expansion approach where the solution is represented as a generalized Fourier series of stochastic basis functions, e.g. orthogonal polynomials or wavelets. The stochastic Galerkin method is used to project the governing partial differential equation onto the stochastic basis functions to obtain an extended deterministic system. The stochastic Galerkin and collocation methods are used to solve an advection-diffusion equation with uncertain viscosity. We investigate well-posedness, monotonicity and stability for the stochastic Galerkin system. High-order summation-by-parts operators and weak imposition of boundary conditions are used to prove stability. We investigate the impact of the total spatial operator on the convergence to steady-state.  Next we apply the stochastic Galerkin method to Burgers' equation with uncertain boundary conditions. An analysis of the truncated polynomial chaos system presents a qualitative description of the development of the solution over time. An analytical solution is derived and the true polynomial chaos coefficients are shown to be smooth, while the corresponding coefficients of the truncated stochastic Galerkin formulation are shown to be discontinuous. We discuss the problematic implications of the lack of known boundary data and possible ways of imposing stable and accurate boundary conditions. We present a new fully intrusive method for the Euler equations subject to uncertainty based on a Roe variable transformation. The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, it is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. A multiwavelet basis that can handle  discontinuities in a robust way is used. Finally, we investigate a two-phase flow problem. Based on regularity analysis of the generalized polynomial chaos coefficients, we present a hybrid method where solution regions of varying smoothness are coupled weakly through interfaces. In this way, we couple smooth solutions solved with high-order finite difference methods with non-smooth solutions solved for with shock-capturing methods.

Cette thèse s'intéresse aux interactions entre immunologie, épidémiologie et biologie évolutive. Nous utilisons une combinaison d'approches mathématiques et statistiques pour comprendre les processus gouvernant les dynamiques épidémiologiques et les phylogénies observées pour différents pathogènes de l'échelle individuelle aux populations. Nous prenons l'exemple de la grippe humaine. Trois hypothèses permettent de rendre compte de la phylodynamique particulière de la grippe: (i) il existe un mécanisme de densité-dépendance directe médié par une période temporaire d'immunité totale après infection ; (ii) le nombre de phénotypes possibles est limité, les virus les ré-explorant sans cesse ; (iii) l'évolution de l'antigène principal de la grippe est ponctuée, les échappements ponctuels à l'immunité induisant des balayages sélectifs. (iii) domine aujourd'hui et rend compte de la variabilité des épidémies de grippe, de larges échappements à l'immunité en induisant de plus grandes. Nous montrons que le formalisme ayant mené à (iii) induit de manière implicite un processus immunologique irréaliste pour la grippe. Nous révélons que les séries temporelles d'incidences grippales ne peuvent pas fournir une preuve du caractère ponctué de l'évolution antigénique, un modèle parcimonieux prenant en compte une évolution antigénique purement graduelle les reproduisant. La nature chaotique de ces dynamiques marque une limite fondamentale à la prédictibilité de la taille des épidémies de grippe et ce, indépendamment de la contingence évolutive. Nous développons un formalisme confrontable aux données pour tester les différentes hypothèses rendant compte de la phylodynamique de la grippe.

As part of the production of certain solid-dosage pharmaceuticals, granulated ingredients are dried in a batch fluidized bed dryer. Currently, the determination of the completion of the drying process is accomplished through measurements of product or outlet air temperatures. No quantitative measurement of hydrodynamic behaviour is employed. Changes in bed hydrodynamics caused by variations in fluidization velocity may lead to increased particle attrition. In addition, excessive desiccation of the granules caused by inaccurate determination of the drying endpoint may lead to an increase in the thermal and mechanical stresses within the granules. The activity of future high-potency or peptide based drug products may be influenced by these effects. Therefore, the quantification of hydrodynamic changes may be a key factor in the tighter control of both fluidization velocity and product moisture, which are critical for maintaining product quality. <p>High-frequency measurements of pressure fluctuations in a batch fluidized bed dryer containing pharmaceutical granulate have been used to provide a global, non-intrusive indication of the hydrodynamic changes occurring throughout the drying process. A chaotic attractor comparison statistical test known as the S-statistic, has been applied to quantify these changes in drying and a related unit operation, fluidized bed granulation. The S-statistic showed a sensitivity to moisture which is not seen with frequency and amplitude analysis. In addition, the S-statistic has been shown to be useful in identifying an undesirable bed state associated with the onset of entrainment in a bed instrumented for the collection of both pressure fluctuation and entrainment data. Thus, the use of the S-statistic analysis of pressure fluctuations may be utilized as a low-cost method for determining product moisture or changes hydrodynamic state during fluidized bed drying. <p>Electrical capacitance tomography (ECT) has also been applied in this study to image the flow structure within a batch fluidized bed used for the drying of pharmaceutical granulate. This represents the first time that ECT has been applied to a bed of wet granulate material. This was accomplished through the use of a novel dynamic correction technique which accounts for the significant reduction in electrical permittivity occurring as moisture is lost during the drying process. The correction has been independently verified using x-ray tomography. <p>Investigation of the ECT images taken in the drying bed indicates centralized bubbling behaviour for approximately the first 5 minutes of drying. This behaviour is a result of the high liquid loading of the particles at high moisture. Between moisture contents of 18-wt% and 10-wt%, the tomograms show an annular pattern of bubbling behaviour with a gradual decrease in the cross-sectional area involved in bubbling behaviour. The dynamic analysis of this voidage data with the S-statistic showed that a statistically significant change occurs during this period near the walls of the vessel, while the centre exhibits less variation in dynamic behaviour. The changes identified by the S-statistic analysis of voidage fluctuations near the wall were similar to those seen in the pressure fluctuation measurements. This indicates that the source of the changes identified by both these measurement techniques is a result of the reduction in the fraction of the bed cross-section involved in bubbling behaviour. At bed moisture contents below 5-wt%, rapid divergence was seen in the S-statistic applied to both ECT and pressure fluctuation measurements. This indicates that a rapid change in dynamics occurs near the end of the drying process. This is possibly caused by the entrainment of fines at this time, or the build-up of electrostatic charge. <p>The use of the complimentary pressure fluctuation and ECT measurement techniques have identified changes occurring as a result of the reduction of moisture during the drying process. Both the localized changes in the voidage fluctuations provided by the ECT imaging and the global changes shown by the pressure fluctuation measurements indicate significant changes in the dynamic behaviour caused by the reduction of moisture during the drying process. These measurement techniques could be utilized to provide an on-line indication of changes in hydrodynamic regime. This information may be invaluable for the future optimization of the batch drying process and accurate determination of the drying endpoint.

Le problème principalement étudié dans ce manuscrit est la stabilisation d'orbites périodiques de systèmes dynamiques non linéaires à l'aide d'une commande de rétroaction (feedback). Le but des méthodes de contrôle proposées ici est d'obtenir une oscillation périodique stable. Ces méthodes de contrôle sont appliquées à des systèmes présentant des orbites périodiques instables dans l'espace d'état, et ces dernières sont les orbites destinées à être stabilisées. Les méthodes proposées ici sont telles que l'oscillation stable qui en résulte est obtenue avec un effort de contrôle faible, et que la valeur de la commande tend vers zéro lorsque la trajectoire tend vers l'orbite stabilisée. La stabilité locale des orbites périodiques est analysée par l'étude de la stabilité des systèmes linéaires périodiques à l'aide de la théorie de Floquet. Ces systèmes linéaires sont obtenus par linéarisation des trajectoires au voisinage de l'orbite périodique. Les méthodes de contrôle utilisées ici pour la stabilisation des orbites périodiques sont une loi de commande proportionnelle, une loi de commande de rétroaction retardée et une loi de commande de rétroaction basée sur une prédiction. Ces méthodes sont appliquées aux systèmes en temps discret et aux systèmes en temps continu avec les modifications nécessaires. Les contributions principales de cette thèse sont associées à ces méthodes, proposant une méthode alternative de design de gain, une nouvelle loi de commande et des résultats associés.

Les modèles numériques, de plus en plus utilisés en tant que prototypes virtuels, requièrent la connaissance de paramètres d'entrée comme les dimensions géométriques, les caractéristiques physiques des matériaux et les sollicitations externes. Les modèles numériques disponibles actuellement sont très proches de la physique qu'il représente et les écarts que l'on constate avec la réalité peuvent maintenant incomber en partie à une méconnaissance des paramètres d'entrée. L'approche probabiliste qui consiste à modéliser les quantités incertaines par des variables ou champs aléatoires est la solution qui a été retenue dans cette thèse pour prendre en compte les incertitudes d'origine géométrique. Pour résoudre le problème, la méthode de transformation, permettant de ramener un problème aux incertitudes portées par la géométrie à un problème aux incertitudes portées par les lois de comportement, a été choisie. Comme il existe une infinité de transformations possibles, différentes méthodes de détermination de la transformation ont été mises en œuvre et comparées. En particulier, un estimateur d'erreur a-priori a été proposé de manière à dégager des critères de choix. Il a été aussi montré que la méthode de transformation peut prendre en compte naturellement des discontinuités au niveau stochastique des grandeurs locales. Enfin, la méthode étudiée a été employée pour étudier l'influence des incertitudes géométriques d'un stator sur les performances d'une machine électrique. Cette étude s'appuie sur un ensemble de mesures faites sur un lot de stators.

Nous calculons presque sûrement, simultanément, les dimensions de Hausdorff des ensembles de branches infinies de la frontière d'un arbre de Galton-Watson super-critique (muni d'une métrique aléatoire) le long desquelles les moyennes empiriques d'une marche aléatoire de branchement vectorielle admettent un ensemble donné de points limites. Cela va au-delà de l'analyse multifractale, question pour laquelle nous complétons les travaux antérieurs en considérant les ensembles associés à des niveaux situés dans la frontière du domaine d'étude. Nous utilisons une méthode originale dans ce contexte, consistant à construire des mesures de Mandelbrot inhomogènes appropriées. Cette méthode est inspirée de l'approche utilisée pour résoudre des questions similaires dans le contexte de la dynamique hyperboliques pour les moyennes de Birkhoff de potentiels continus. Elle exploite des idées provenant du chaos multiplicatif et de la théorie de la percolation pour estimer la dimension inférieure de Hausdorff des mesures de Mandelbrot inhomogènes. Cette méthode permet de renforcer l'analyse multifractale en raffinant les ensembles de niveaux de telle sorte qu'ils contiennent des branches infinies le long desquels on observe une version quantifiée de la loi des grands nombres d'Erdös Renyi ; de plus elle permet d'obtenir une loi de type $0-\infty$ pour les mesures de Hausdorff de ces ensembles. Nos résultats donnent naturellement des informations géométriques et de grandes déviations sur l'hétérogénéité du processus de naissance le long des différentes branches infinies de l'arbre de Galton-Watson.

As part of the production of certain solid-dosage pharmaceuticals, granulated ingredients are dried in a batch fluidized bed dryer. Currently, the determination of the completion of the drying process is accomplished through measurements of product or outlet air temperatures. No quantitative measurement of hydrodynamic behaviour is employed. Changes in bed hydrodynamics caused by variations in fluidization velocity may lead to increased particle attrition. In addition, excessive desiccation of the granules caused by inaccurate determination of the drying endpoint may lead to an increase in the thermal and mechanical stresses within the granules. The activity of future high-potency or peptide based drug products may be influenced by these effects. Therefore, the quantification of hydrodynamic changes may be a key factor in the tighter control of both fluidization velocity and product moisture, which are critical for maintaining product quality. <p>High-frequency measurements of pressure fluctuations in a batch fluidized bed dryer containing pharmaceutical granulate have been used to provide a global, non-intrusive indication of the hydrodynamic changes occurring throughout the drying process. A chaotic attractor comparison statistical test known as the S-statistic, has been applied to quantify these changes in drying and a related unit operation, fluidized bed granulation. The S-statistic showed a sensitivity to moisture which is not seen with frequency and amplitude analysis. In addition, the S-statistic has been shown to be useful in identifying an undesirable bed state associated with the onset of entrainment in a bed instrumented for the collection of both pressure fluctuation and entrainment data. Thus, the use of the S-statistic analysis of pressure fluctuations may be utilized as a low-cost method for determining product moisture or changes hydrodynamic state during fluidized bed drying. <p>Electrical capacitance tomography (ECT) has also been applied in this study to image the flow structure within a batch fluidized bed used for the drying of pharmaceutical granulate. This represents the first time that ECT has been applied to a bed of wet granulate material. This was accomplished through the use of a novel dynamic correction technique which accounts for the significant reduction in electrical permittivity occurring as moisture is lost during the drying process. The correction has been independently verified using x-ray tomography. <p>Investigation of the ECT images taken in the drying bed indicates centralized bubbling behaviour for approximately the first 5 minutes of drying. This behaviour is a result of the high liquid loading of the particles at high moisture. Between moisture contents of 18-wt% and 10-wt%, the tomograms show an annular pattern of bubbling behaviour with a gradual decrease in the cross-sectional area involved in bubbling behaviour. The dynamic analysis of this voidage data with the S-statistic showed that a statistically significant change occurs during this period near the walls of the vessel, while the centre exhibits less variation in dynamic behaviour. The changes identified by the S-statistic analysis of voidage fluctuations near the wall were similar to those seen in the pressure fluctuation measurements. This indicates that the source of the changes identified by both these measurement techniques is a result of the reduction in the fraction of the bed cross-section involved in bubbling behaviour. At bed moisture contents below 5-wt%, rapid divergence was seen in the S-statistic applied to both ECT and pressure fluctuation measurements. This indicates that a rapid change in dynamics occurs near the end of the drying process. This is possibly caused by the entrainment of fines at this time, or the build-up of electrostatic charge. <p>The use of the complimentary pressure fluctuation and ECT measurement techniques have identified changes occurring as a result of the reduction of moisture during the drying process. Both the localized changes in the voidage fluctuations provided by the ECT imaging and the global changes shown by the pressure fluctuation measurements indicate significant changes in the dynamic behaviour caused by the reduction of moisture during the drying process. These measurement techniques could be utilized to provide an on-line indication of changes in hydrodynamic regime. This information may be invaluable for the future optimization of the batch drying process and accurate determination of the drying endpoint.

In many systems, instabilities can lead to time-dependent behavior, and instabilities can act as mechanisms for sustained chaos; an understanding of the dynamical modes governing instability is thus essential for prediction and/or control in such systems. In this thesis work, we have developed an approach toward characterizing instabilities quantitatively, from experiments on the prototypical Rayleigh-Bénard convection system. We developed an experimental technique for preparing a given convection pattern using rapid optical actuation of pressurized SF6, a greenhouse gas. Real-time analysis of convection patterns was developed as part of the implementation of closed-loop control of straight roll patterns. Feedback control of the patterns via actuation was used to guide patterns to various system instabilities. Controlled, spatially localized perturbations were applied to the prepared states, which were observed to excite the dominant system modes. We extracted the spatial structure and growth rates of these modes from analysis of the pattern evolutions. The lifetimes of excitations were also measured, near a particular instability; a critical wavenumber was found from the observed dynamical slowing near the bifurcation. We will also describe preliminary results of using a state estimation algorithm (LETKF) on experimentally prepared non-periodic patterns in a cylindrical convection cell.