We investigate how the formation of heterogeneity and structures in flows through explicit porous microstructures depends upon the geometric and topological observables of the porous medium. Using direct numerical simulations of single-phase, isothermal, laminar fluid flow through realistic three-dimensional stochastically generated pore structures, hereafter referred to as pore spaces, the characteristics of the resulting steady state velocity fields are related to physical characteristics of the pore spaces. The results suggest that the spatially variable resistance offered by the geometry and topology of the pore space induces a highly heterogeneous fluid velocity field therein. Focus is placed on three different length scales: macroscopic (cm), mesoscopic (mm), and microscopic (microns). At the macroscopic length scale, volume averaging is used to relate porosity, mean hydraulic radius, and their product to the permeability of the pore space. At the mesoscopic scale, the effect of a medium's porosity on fluid particle trajectory attributes, such as passage time and tortuosity, is studied. At the final length scale, that of the microscopic in-pore fluid dynamics, finite time Lyapunov exponents are used to determine expanding, contracting, and hyperbolic regions in the flow field, which are then related to the local structure of the pore space. The results have implications to contaminant transport, mixing, and how chemical reactions are induced at the pore-scale. A description of the adopted numerical methods to simulate flow and generate the pore space are provided as well.

Neste trabalho, estudamos a teoria quântica de correção de erros, um dos principais métodos de prevenção de perda de informação num computador quântico. Este método, porém, normalmente é estudado considerando-se condições ideais em que a atuação das portas lógicas que constituem o algoritmo quântico não interfere com o tipo de erro que o sistema sofre. Além disso, as medidas de síndrome empregadas no método tradicional são consideradas instantâneas. Nossos objetivos neste trabalho serão avaliar como a alteração dessas duas suposições modificaria o processo de correção de erros. Com relação ao primeiro objetivo, verificamos que, para erros causados por ambientes externos, a atuação de uma porta lógica simultânea ao ruído pode gerar erros que, a princípio, podem não ser corrigíveis pelo código empregado. Propomos em seguida um método de correção a pequenos passos que pode ser usado para tornar desprezíveis os erros incorrigíveis, além de poder ser usado para reduzir a probabilidade de erros corrigíveis. Para o segundo objetivo, estudamos primeiro como medidas de tempo finito afetam a descoerência de apenas um qubit, concluindo que esse tipo de medida pode na verdade proteger o estado que está sendo medido. Motivados por isso, mostramos que, em certos casos, medidas de síndrome finitas realizadas conjuntamente ao ruído são capazes de proteger o estado dos qubits contra os erros mais eficientemente do que se as medidas fossem realizadas instantaneamente ao fim do processo. / In this work, we study the theory of quantum error correction, one of the main methods of preventing loss of information in a quantum computer. This method, however, is normally studied under ideal conditions in which the operation of the quantum gates that constitute the quantum algorithm do not interefere with the kind of error the system undergoes. Moreover, the syndrome measurements employed in the traditional method are considered instantaneous. Our aims with this work are to evaluate how altering these two suppositions would modify the quantum error correction process. In respect with the first objective, we verify that, for errors caused by external environments, the action of a logical gate simultaneously to the noise can provoke errors that, in principle, may not be correctable by the code employed. We subsequently propose a short-step correction method that can be used to render negligible the uncorrectable errors, besides being capable of reducing the probability of occurrence of correctable errors. For the second objective, we first study how finite-time measurements affect the decoherence of a single qubit, concluding that this kind of measurement can actually protect the state under scrutiny. Motivated by that, we demonstrate, that, in certain cases, finite syndrome measurements performed concurrently with the noise are capable of protecting more efficiently the state of the qubits against errors than if the measurements had been performed instantaneously at the the end of the process.

L'objet de ce travail est l’étude des propriétés de stabilité et de robustesse des systèmes non-linéaires via des méthodes basées sur l'homogénéité. Dans un premier temps, nous rappelons le contexte usuel des systèmes homogènes ainsi que leurs caractéristiques principales. La suite du travail porte sur l'extension de l'homogénéisation des systèmes non-linéaires, déjà proposée dans le cadre de l'homogénéité à poids, au cadre plus général de l'homogénéité géométrique. Les principaux résultats d'approximation sont étendus. Nous développons ensuite un cadre théorique pour définir l'homogénéité de systèmes discontinus et/ou donnés par des inclusions différentielles. Nous montrons que les propriétés bien connues des systèmes homogènes restent vérifiées dans ce contexte. Ce travail se poursuit par l'étude de la robustesse des systèmes homogènes ou homogénéisables. Nous montrons que sous des hypothèses peu restrictives, ces systèmes sont input-to-state stable. Enfin, la dernière partie de ce travail consiste en l'étude du cas particulier du double intégrateur. Nous développons pour ce système un retour de sortie qui le stabilise en temps fini, et pour lequel nous prouvons des propriétés de robustesse par rapport à des perturbations ou à la discrétisation en exploitant les résultats développés précédemment. Des simulations viennent compléter l'étude théorique de ce système et illustrer son comportement / The purpose of this work is the study of stability and robustness properties of nonlinear systems using homogeneity-based methods. Firstly, we recall the usual context of homogeneous systems as well as their main features. The sequel of this work extends the homogenization of nonlinear systems, which was already defined in the framework of weighted homogeneity, to the more general setting of the geometric homogeneity. The main approximation results are extended. Then we develop a theoretical framework for defining homogeneity of discontinuous systems and/or systems given by a differential inclusion. We show that the well-known properties of homogeneous systems persist in this context. This work is continued by a study of the robustness properties of homogeneous or homogenizable systems. We show that under mild assumptions, these systems are input-to-state stable. Finally, the last part of this work consists in the study of the example of the double integrator system. We synthesize a finite-time stabilizing output feedback, which is shown to be robust with respect to perturbations or discretization by using techniques developed before. Simulations conclude the theoretical study of this system and illustrate its behavior

No description available.

Precise navigation of autonomous underwater vehicles (AUV) is one of the most important challenges in the realization of distributed and cooperative algorithms for marine applications. We investigate an underwater navigation technology that enables an AUV to compute its trajectory in the presence of unknown currents in real time and simultaneously estimate the currents, using range or distance measurements from a single known location. This approach is potentially useful for small AUVs which have severe volume and power constraints. The main contribution of this work is observability analysis of the proposed navigation system using novel approaches towards uniform observability of linear time-varying (LTV) systems. We utilize the notion of limiting systems in order to address uniform observability of LTV systems. Uniform observability of an LTV system can be studied by assessing finite time observability of its limiting systems. A new definition of uniform observability over a finite interval is introduced in order to address existence of an observer whose estimation error is bounded by an exponentially decaying function on the finite interval. We also show that for a class of LTV systems, uniform observability of a lower dimensional subsystem derived from an LTV system is sufficient for uniform observability of the LTV system. / Ph. D.

Identifying a globally optimal solution for an intractable discrete optimization problem is often cost prohibitive. Therefore, solutions that are within a predetermined threshold are often acceptable in practice. This dissertation introduces the concept of B-acceptable solutions where B is a predetermined threshold for the objective function value. It is difficult to assess a priori the effectiveness of local search algorithms, which makes the process of choosing parameters to improve their performance difficult. This dissertation introduces the B-acceptable solution probability in terms of B-acceptable solutions as a finite-time performance measure for local search algorithms. The B-acceptable solution probability reflects how effectively an algorithm has performed to date and how effectively an algorithm can be expected to perform in the future. The B-acceptable solution probability is also used to obtain necessary asymptotic convergence (with probability one) conditions. Upper and lower bounds for the B-acceptable solution probability are presented. These expressions assume particularly simple forms when applied to specific local search strategies such as Monte Carlo search and threshold accepting. Moreover, these expressions provide guidelines on how to manage the execution of local search algorithm runs. Computational experiments are reported to estimate the probability of reaching a B-acceptable solution for a fixed number of iterations. Logistic regression is applied as a tool to estimate the probability of reaching a B-acceptable solution for values of B close to the objective function value of a globally optimal solution as well as to estimate this objective function value. Computational experiments are reported with logistic regression for pure local search, simulated annealing and threshold accepting applied to instances of the TSP with known optimal solutions. / Ph. D.

Time varying flow structures are involved in a large percentage of fluid flows although there is still much unknown regarding their behavior. With the development of high spatiotemporal resolution measurement systems it is becoming more feasible to measure these complex flow structures, which in turn will lead to a better understanding of their impact. One method that has been developed for studying these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly impact a wide range of applications, from aircraft design and performance, to an improved understanding of mixing and transport in the human body. This work provides the development of new methodologies for measuring and studying three-dimensional time varying structures. Provided herein is a method to improve replacement of erroneous measurements in particle image velocimetry data, which leads to increased accuracy in the data. Also, a method for directly measuring the finite time Lyapunov exponents from particle images is developed, as well as an experimental demonstration in a three-dimensional flow field. This method takes advantage of the information inherently contained in these images to improve accuracy and reduce computational requirements. Lastly, this work provides an in depth look at the flow field for developing wall jets across a wide range of Reynolds numbers investigating the mechanisms that contribute to their development. / Ph. D.

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.

Le consensus des systèmes multi-agents a eu une attention considérable au cours de la dernière décennie. Le consensus est un processus coopératif dans lequel les agents interagissent afin de parvenir à un accord. La plupart des études se sont engagés à l'analyse de l'état d'équilibre du comportement de ce processus. Toutefois, au cours de la transitoire de ce processus une énorme quantité de données est produite. Dans cette thèse, notre objectif est d'exploiter les données produites au cours de la transitoire d'algorithmes de consensus moyenne asymptotique afin de concevoir des protocoles de consensus moyenne en temps fini, évaluer la robustesse du graphique, et éventuellement récupérer la topologie du graphe de manière distribuée. Le consensus de moyenne en temps fini garantit un temps d'exécution minimal qui peut assurer l'efficacité et la précision des algorithmes distribués complexes dans lesquels il est impliqué. Nous nous concentrons d'abord sur l'étape de configuration consacrée à la conception de protocoles de consensus qui garantissent la convergence de la moyenne exacte dans un nombre donné d'étapes. En considérant des réseaux d'agents modélisés avec des graphes non orientés connectés, nous formulons le problème de la factorisation de la matrice de moyenne et étudions des solutions distribuées à ce problème. Puisque, les appareils communicants doivent apprendre leur environnement avant d'établir des liens de communication, nous suggérons l'utilisation de séquences d'apprentissage afin de résoudre le problème de la factorisation. Ensuite, un algorithme semblable à l'algorithme de rétro-propagation du gradient est proposé pour résoudre un problème d'optimisation non convexe sous contrainte. Nous montrons que tout minimum local de la fonction de coût donne une factorisation exacte de la matrice de moyenne. En contraignant les matrices de facteur à être comme les matrices de consensus basées sur la matrice laplacienne, il est maintenant bien connu que la factorisation de la matrice de moyenne est entièrement caractérisé par les valeurs propres non nulles du laplacien. Par conséquent, la résolution de la factorisation de la matrice de la moyenne de manière distribuée avec une telle contrainte sur la matrice laplacienne, permet d'estimer le spectre de la matrice laplacienne. Depuis le spectre peut être utilisé pour calculer des indices de la robustesse (Nombre d'arbres couvrant et la résistance effective du graphe), la deuxième partie de cette thèse est consacrée à l'évaluation de la robustesse du réseau à travers l'estimation distribuée du spectre du Laplacien. Le problème est posé comme un problème de consensus sous contrainte formulé de deux façons différentes. La première formulation (approche directe) cède à un problème d'optimisation non-convexe résolu de manière distribuée au moyen de la méthode des multiplicateurs de Lagrange. La seconde formulation (approche indirecte) est obtenue après une reparamétrisation adéquate. Le problème est alors convexe et résolu en utilisant l'algorithme du sous-gradient distribué et la méthode de direction alternée de multiplicateurs. En outre, trois cas sont considérés: la valeur moyenne finale est parfaitement connue, bruyant, ou complètement inconnue. Nous fournissons également une façon pour calculer les multiplicités des valeurs propres estimées au moyen d'une programmation linéaire en nombres entiers. L'efficacité des solutions proposées est évaluée au moyen de simulations. Cependant, dans plusieurs cas, la convergence des algorithmes proposés est lente et doit être améliorée dans les travaux futurs. En outre, l'approche indirecte n'est pas évolutive pour des graphes de taille importante car elle implique le calcul des racines d'un polynôme de degré égal à la taille du réseau. Cependant, au lieu d'estimer tout le spectre, il peut être possible de récupérer seulement un petit nombre des valeurs propres, puis déduire des limites significatives sur les indices de la robustesse. / Consensus of Multi-agent systems has received tremendous attention during the last decade. Consensus is a cooperative process in which agents interact in order to reach an agreement. Most of studies are committed to analysis of the steady-state behavior of this process. However, during the transient of this process a huge amount of data is produced. In this thesis, our aim is to exploit data produced during the transient of asymptotic average consensus algorithms in order to design finite-time average consensus protocols, assess the robustness of the graph, and eventually recover the topology of the graph in a distributed way. Finite-time Average Consensus guarantees a minimal execution time that can ensure the efficiency and the accuracy of sophisticated distributed algorithms in which it is involved. We first focus on the configuration step devoted to the design of consensus protocols that guarantee convergence to the exact average in a given number of steps. By considering networks of agents modelled with connected undirected graphs, we formulate the problem as the factorization of the averaging matrix and investigate distributed solutions to this problem. Since, communicating devices have to learn their environment before establishing communication links, we suggest the usage of learning sequences in order to solve the factorization problem. Then a gradient backpropagation-like algorithm is proposed to solve a non-convex constrained optimization problem. We show that any local minimum of the cost function provides an accurate factorization of the averaging matrix. By constraining the factor matrices to be as Laplacian-based consensus matrices, it is now well known that the factorization of the averaging matrix is fully characterized by the nonzero Laplacian eigenvalues. Therefore, solving the factorization of the averaging matrix in a distributed way with such Laplacian matrix constraint allows estimating the spectrum of the Laplacian matrix. Since that spectrum can be used to compute some robustness indices (Number of spanning trees and Effective graph Resistance also known as Kirchoff index), the second part of this dissertation is dedicated to Network Robustness Assessment through distributed estimation of the Laplacian spectrum. The problem is posed as a constrained consensus problem formulated in two ways. The first formulation (direct approach) yields a non-convex optimization problem solved in a distributed way by means of the method of Lagrange multipliers. The second formulation (indirect approach) is obtained after an adequate re-parameterization. The problem is then convex and solved by using the distributed subgradient algorithm and the alternating direction method of multipliers. Furthermore, three cases are considered: the final average value is perfectly known, noisy, or completely unknown. We also provide a way for computing the multiplicities of the estimated eigenvalues by means of an Integer programming. In this spectral approach, given the Laplacian spectrum, the network topology can be reconstructed through estimation of Laplacian eigenvector. The efficiency of the proposed solutions is evaluated by means of simulations. However, in several cases, convergence of the proposed algorithms is slow and needs to be improved in future works. In addition, the indirect approach is not scalable to very large graphs since it involves the computation of roots of a polynomial with degree equal to the size of the network. However, instead of estimating all the spectrum, it can be possible to recover only a few number of eigenvalues and then deduce some significant bounds on robustness indices.