De nombreuses applications industrielles mettent en jeu des écoulements gaz-particules, comme les turbines aéronautiques et les réacteurs à lit fluidifié de l'industrie chimique. La prédiction des propriétés de la phase dispersée, est essentielle à l'amélioration et la conception des dispositifs conformément aux nouvelles normes européennes des émissions polluantes. L'objectif de cette thèse est de développer le formalisme Euler-Lagrange dans un solveur parallèle et non-structure pour la simulation aux grandes échelles pour ce type d'écoulements. Ce travail est motivé par l'augmentation rapide de la puissance de calcul des machines massivement parallèles qui ouvre une nouvelle voie pour des simulations qui étaient prohibitives il y a une décennie. Une attention particulière a été portée aux structures de données afin de conserver une certaine simplicité et la portabilité du code sur des différentes architectures. Les développements sont valides pour deux configurations : un cas académique de turbulence homogène isotrope décroissante et un calcul polydisperse d'un jet recirculant charge en particules. L'équilibrage de charges de particules est mis en évidence comme une solution prometteuse pour les simulations diphasiques Lagrangiennes afin d'améliorer les performances des calculs lorsque le deséquilibrage est trop important.

Dans cette thèse, nous nous sommes intéressés au problème de la stabilité aéroélastique d'une structure au sein d'un écoulement fluide incompressible. La motivation de ce travail est le dimensionnement au vent des ouvrages d'art du génie civil, par l'analyse et la simulation numérique de l'interaction vent-structure. Notre approche consiste à chercher la vitesse de vent minimale permettant, soit de maximiser les effets du vent sur la structure, soit de contraindre la structure à suivre une évolution instable donnée. Après une analyse générale de ces concepts, nous montrons, numériquement, qu'il est possible de contrôler, par une donnée frontière, les trajectoires de l'écoulement d'un fluide incompressible autour d'un profil fixe. Dans une deuxième partie, nous obtenons les systèmes linéarisé et adjoint lorsque le contrôle s'exerce à travers le mouvement du domaine fluide, grâce à de nouveaux outils de dérivation de forme. Finalement dans une troisième partie, nous obtenons le système adjoint associé au problème de suivi d'instabilités pour une structure rigide élastiquement supportée au sein d'un écoulement fluide incompressible, en utilisant une formulation Min-Max. Dans le cas plus complexe d'une structure élastique en grands déplacements, nous obtenons la structure du problème linéarisé, par l'utilisation de la dérivation intrinsèque liée aux perturbations de l'identité.

Les méthodes barrières proposent de résoudre le problème non linéaire en résolvant une suite de problèmes pénalisés. Le lien entre la suite, dite externe, des solutions des fonctions pénalisées et la solution du problème initial a été établie dans les années soixante.<br /><br /> Dans cette thèse, nous avons utilisé une fonction barrière logarithmique. A chaque itération externe, la technique SQP se charge de produire une série de sous-problèmes quadratiques dont les solutions forment une suite, dite interne, de directions de descente pour résoudre le problème non linéaire pénalisé.<br /><br /> Nous avons introduit un changement de variable sur le pas de déplacement ce qui a permis d'obtenir des conditions d'optimalité plus stable numériquement.<br /><br /> Nous avons réalisé des simulations numériques pour comparer les performances de la méthode des gradients conjugués à celle de la méthode D.C., appliquées pour résoudre des problèmes quadratiques de région de confiance.<br /><br /> Nous avons adapté la méthode D.C. pour résoudre les sous-problèmes verticaux, ce qui nous a permis de ramener leurs dimensions de $n+m$ à $m+p$ ($ p < n $).<br /><br /> L'évolution de l'algorithme est contrôlée par la fonction de mérite. Des tests numériques permettent de comparer les avantages de différentes formes de la fonction de mérite. Nous avons introduit de nouvelles règles pour améliorer cette évolution.<br /><br /> Les expériences numériques montrent un gain concernant le nombre de problèmes résolus. L'étude de la convergence de notre méthode SDC, clôt ce travail.

This dissertation consists of 3 essays In the first essay, A Simple Variable Selection Technique for Nonlinear Models, written in cooperation with Timo Teräsvirta and Rolf Tschernig, I propose a variable selection method based on a polynomial expansion of the unknown regression function and an appropriate model selection criterion. The hypothesis of linearity is tested by a Lagrange multiplier test based on this polynomial expansion. If rejected, a kth order general polynomial is used as a base for estimating all submodels by ordinary least squares. The combination of regressors leading to the lowest value of the model selection criterion is selected.  The second essay, Modelling and Forecasting Economic Time Series with Single Hidden-layer Feedforward Autoregressive Artificial Neural Networks, proposes an unified framework for artificial neural network modelling. Linearity is tested and the selection of regressors performed by the methodology developed in essay I. The number of hidden units is detected by a procedure based on a sequence of Lagrange multiplier (LM) tests. Serial correlation of errors and parameter constancy are checked by LM tests as well. A Monte-Carlo study, the two classical series of the lynx and the sunspots, and an application on the monthly S&amp;P 500 index return series are used to demonstrate the performance of the overall procedure. In the third essay, Forecasting with Artificial Neural Network Models (in cooperation with Marcelo Medeiros), the methodology developed in essay II, the most popular methods for artificial neural network estimation, and the linear autoregressive model are compared by forecasting performance on 30 time series from different subject areas. Early stopping, pruning, information criterion pruning, cross-validation pruning, weight decay, and Bayesian regularization are considered. The findings are that 1) the linear models very often outperform the neural network ones and 2) the modelling approach to neural networks developed in this thesis stands up well with in comparison when compared to the other neural network modelling methods considered here. / <p>Diss. Stockholm : Handelshögskolan, 2002. Spikblad saknas</p>

In this work, flow through synthetic arrangements of contacting spheres is studied as a model problem for porous media and packed bed type flows. Direct numerical simulations are performed for moderate pore Reynolds numbers in the range, 10 ≤ Re ≤ 600, where non-linear porescale flow features are known to contribute significantly to macroscale properties of engineering interest. To first choose and validate appropriate computational models for this problem, the relative performance of two numerical approaches involving body conforming and non-conforming grids for simulating porescale flows is examined. In the first approach, an unstructured solver is used with tetrahedral meshes, which conform to the boundaries of the porespace. In the second approach, a fictitious domain formulation (Apte et al., 2009. J Comput. Phys. 228 (8), 2712-2738) is used, which employs non-body conforming Cartesian grids and enforces the no-slip conditions on the pore boundaries implicitly through a rigidity constraint force. Detailed grid convergence studies of both steady and unsteady flow through prototypical arrangements of spheres indicate that for a fixed level of uncertainty, significantly lower grid densities may be used with the fictitious domain approach, which also does not require complex grid generation techniques. Next, flows through both random and structured arrangements of spheres are simulated at pore Reynolds numbers in the steady inertial ( 10 ≲ Re ≲ 200) and unsteady inertial (Re ≈ 600) regimes, and used to analyze the characteristics of porescale vortical structures. Even at similar Reynolds numbers, the vortical structures observed in structured and random packings are remarkably different. The interior of the structured packings are dominated by multi-lobed vortex rings structures that align with the principal axes of the packing, but perpendicular to the mean flow. The random packing is dominated by helical vortices, elongated parallel to the mean flow direction. The unsteady dynamics observed in random and structured arrangements are also distinct, and are linked to the behavior of the porescale vortices. Finally, to investigate the existence and behavior of transport barriers in packed beds, a numerical tool is developed to compute high resolution finite-time Lyapunov exponent (FTLE) fields on-the-fly during DNS of unsteady flows. Ridges in this field are known to correspond to Lagrangian Coherent Structures (LCS), which are invariant barriers to transport and form the skeleton of time dependent Lagrangian fluid motion. The algorithm and its implementation into a parallel DNS solver are described in detail and used to explore several flows, including unsteady inertial flow in a random sphere packing. The resulting FTLE fields unambiguously define the boundaries of dynamically distinct porescale features such as counter rotating helical vortices and jets, and capture time dependent phenomena including vortex shedding at the pore level. / Graduation date: 2013

The aim of this study is to obtain optimal position and orientation of a trajectory frame with respect to the fixed frame of the manipulator. The work path which is given in the trajectory frame is also constrained in the workspace of the 3 &ndash / PRS parallel kinematic machine. In the analysis, forward and inverse kinematics solutions are derived as well as the inverse dynamics model using Lagrange&rsquo / s Method. Several algorithms governing the motion of the manipulator are developed. Moreover, optimization goals are defined and evaluated with the genetic algorithm.

Lagrangian relaxation is a successful solution approach for many combinatorial optimisation problems, one of them being the train timetabling problem (TTP). We model this problem using time expanded networks for the single train schedules and coupling constraints to enforce restrictions like station capacities and headway times. Lagrangian relaxation of these coupling constraints leads to shortest path subproblems in the time expanded networks and is solved using a proximal bundle method. However, large instances of our practical partner Deutsche Bahn lead to computationally intractable models. In this thesis we develop two new algorithmic techniques to improve the solution process for this kind of optimisation problems. The first new technique, Dynamic Graph Generation (DGG), aims at improving the computation of the shortest path subproblems in large time expanded networks. Without sacrificing any accuracy, DGG allows to store only small parts of the networks and to dynamically extend them whenever the stored part proves to be too small. This is possible by exploiting the properties of the objective function in many scheduling applications to prefer early paths or due times, respectively. We prove that DGG can be implemented very efficiently and its running time and the size of nodes that have to be stored additionally does not depend on the size of the time expanded network but only on the length of the train routes. The second technique is an asynchronous and parallel bundle method (APBM). Traditional bundle methods require one solution of each subproblem in each iteration. However, many practical applications, e.g. the TTP, consist of rather loosely coupled subproblems. The APBM chooses only small subspaces corresponding to the Lagrange multipliers of strongly violated coupling constraints and optimises only these variables while keeping all other variables fixed. Several subspaces of disjoint variables may be chosen simultaneously and are optimised in parallel. The solutions of the subspace problem are incorporated into the global data as soon as it is available without any synchronisation mechanism. However, in order to guarantee convergence, the algorithm detects automatically dependencies between different subspaces and respects these dependencies in future subspace selections. We prove the convergence of the APBM under reasonable assumptions for both, the dual and associated primal aggregate data. The APBM is then further extended to problems with unknown dependencies between subproblems and constraints in the Lagrangian relaxation problem. The algorithm automatically detects these dependencies and respects them in future iterations. Again we prove the convergence of this algorithm under reasonable assumptions. Finally we test our solution approach for the TTP on some real world instances of Deutsche Bahn. Using an iterative rounding heuristic based on the approximate fractional solutions obtained by the Lagrangian relaxation we are able to compute feasible schedules for all trains in a subnetwork of about 10% of the whole German network in about 12 hours. In these timetables 99% of all passenger trains could be scheduled with no significant delay and the travel time of the freight trains could be reduced by about one hour on average.

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area.

When a mechanical system is subject to constraints its motion is in some way restricted. In accordance with Newton's second law, motion is a direct result of forces acting on a system; hence, constraint is inextricably linked to force. The presence of a constraint implies the application of particular forces needed to compel motion in accordance with the constraint; absence of a constraint implies the absence of such forces. The objective of this thesis is to formulate a comprehensive, consistent, and concise method for identifying a set of forces needed to constrain the behavior of a mechanical system modeled as a set of particles and rigid bodies. The goal is accomplished in large part by expressing constraint equations in vector form rather than entirely in terms of scalars. The method developed here can be applied whenever constraints can be described at the acceleration level by a set of independent equations that are linear in acceleration. Hence, the range of applicability extends to servo-constraints or program constraints described at the velocity level with relationships that are nonlinear in velocity. All configuration constraints, and an important class of classical motion constraints, can be expressed at the velocity level by using equations that are linear in velocity; therefore, the associated constraint equations are linear in acceleration when written at the acceleration level. Two new approaches are presented for deriving equations governing motion of a system subject to constraints expressed at the velocity level with equations that are nonlinear in velocity. By using partial accelerations instead of the partial velocities normally employed with Kane's method, it is possible to form dynamical equations that either do or do not contain evidence of the constraint forces, depending on the analyst's interests.

Dans ce travail, nous étudions le raffinement de maillage pour des méthodes d'éléments finis mixtes duales pour deux types de problèmes : le premier concerne le problème de l'élasticité linéaire et le second problème celui de l'élastodynamique.<br /> <br /> Pour ces deux types de problèmes et dans des domaines non réguliers, les méthodes d'éléments finis mixtes analysées jusqu'à présent, sont celles qui concernent des méthodes mixtes "classiques". Ici, nous analysons la formulation mixte duale pour les deux problèmes de l'élasticité linéaire et de l'élastodynamique. <br /> Pour le problème d'élasticité, nous sommes concernés premièrement par une analyse a priori d'erreur en utilisant l'approximation par l'élément fini $BDM_1$ stabilisé. Afin de dériver une estimation a priori optimales d'erreur, nous établissons des règles de raffinement de maillage. <br /> Ensuite, nous faisons une analyse d'erreur à posteriori sur un domaine simplement ou multiplement connexe. En fait nous établissons un estimateur résiduel fiable et efficace. Cet estimateur est alors utilisé dans un algorithme adaptatif pour le raffinement automatique de maillage. Pour le problème de l'élastodynamique, nous faisons une analyse a priori d'erreur en utilisant le même élément fini que pour le problème d'élasticité, en utilisant une formulation mixte duale pour la discrétisation des variables spatiales. <br /> Pour la discrétisation en temps nous étudions les deux schémas de Newmark explicite et implicite. Par des règles de raffinement de maillage appropriées, nous dérivons des estimées d'erreur optimales pour les deux schémas numérique.