Nous considérons la simulation numérique des écoulements de fluides viscoélatiques. Développant une approximation en temps par la méthode des directions alternées, nous proposons un algorithme entièrement nouveau permettant de découpler le calcul des contraintes de celui des vitesses. D'ordre deux en temps, cette méthode permet de plus le calcul rapide des solutions stationnaires. L'éléments à divergence nulle de Thomas-Raviart est utilisé pour les vitesses, et celui de Lesaint-Raviart pour les contraintes. La méthode est appliquée au problème de l'écoulement de fluides du type Oldroyd dans une contraction brusque (problème de la marche).

L'Anisotropie de Susceptibilité Magnétique (ASM) est maintenant une technique bien éprouvée qui permet de détecter rapidement et précisément l'orientation préférentielle des minéraux d'une roche même faiblement déformée. Lorsque plusieurs marqueurs magnétiques interagissent, il est nécessaire de coupler l'ASM à des études de minéralogie magnétique qui préciseront la nature des marqueurs, et à d'autres types de mesure d'anisotropie. Sont étudiées ici : l'anisotropie de susceptibilité anhystérétique et l'anisotropie de susceptibilité en champ fort. L'application de ces différentes techniques à des marno-calcaires des chaînes subalpines des Alpes françaises, principalement ceux des Terres Noires (Jurassique supérieur), et dans une moindre mesure, ceux du Crétacé inférieur, permet d'élargir le champ d'investigation habituel de ces méthodes magnétiques: on détecte des linéations magnétiques parallèles au cisaillement-transport de la couverture subalpine et qui n'ont pas d'homologues microstructuraux: sur le terrain . on précise les sous-fabriques qui correspondent à l'enregistrement des différents évènements de l'histoire de la déformation par la matrice argileuse et les grains de titanomagnétites ; l'évolution de la déformation finie se traduit par une évolution des paramètres d'anisotropie magnétique. Ces résultats magnétiques peuvent être intégrés dans un modèle d'évolution de l'arc alpin occidental caractérisé par des mouvements de translation et de rotation des blocs crustaux. L'étude de l'aimantation rémanente naturelle des terres Noires permet de retrouver des aimantations primaires du Jurassique supérieur qui présentent un double intérêt : celui de définir la direction du pôle Jurassique supérieur et celui de préciser les rotations possibles de certaines unités de l'arc alpin pendant sa tectogénèse.

Les calculs de réactivité constituent une brique fondamentale dans la simulation des coeurs des réacteurs nucléaires. Ceux-ci conduisent à la résolution de problèmes aux valeurs propres généralisées via l'algorithme de la puissance inverse. A chaque itération, on est amené à résoudre un système linéaire de manière approchée via un algorithme d'itérations imbriquées. Il est difficile de traiter les modélisations très fines avec le solveur développé à EDF, au sein de la plate-forme Cocagne, en raison de la consommation mémoire et du temps de calcul. Au cours de cette thèse, on étudie une méthode de décomposition de domaine de type Schur dual. Plusieurs placements de l'algorithme de décomposition de domaine au sein du système d'itérations imbriquées sont envisageables. Deux d'entre eux ont été implémentés et les résultats analysés. Le deuxième placement, utilisant les spécificités des éléments finis de Raviart-Thomas et de l'algorithme des directions alternées, conduit à des résultats très encourageants. Ces résultats permettent d'envisager l'industrialisation de la méthodologie associée.

<p>Traffic planning in a modern congested society is an important and time consuming procedure. Finding fast algorithms for solving traffic problems is therefore of great interest for traffic planners allover the world. </p><p>This thesis concerns solving the fixed demand traffic assignment problem (TAP) on a number of different transportation test networks. TAP is solved using the Frank-Wolfe algorithm and the shortest path problems that arise as subproblems to the Frank-Wolfe algorithm are solved using the network simplex algorithm. We evaluate how a number of existing pricing strategies to the network simplex algorithm performs with TAP. We also construct a new efficient pricing strategy, the Bucket Pricing Strategy, inspired by the heap implementation of Dijkstra's method for shortest path problems. This pricing strategy is, together with the actual use of the network simplex algorithm, the main result of the thesis and the pricing strategy is designed to take advantage of the special structure of TAP. In addition to performing tests on the conventional Frank-Wolfe algorithm, we also test how the different pricing strategies perform on Frank-Wolfe algorithms using conjugate and bi-conjugate search directions. </p><p>These test results show that the updating shortest path calculations obtained by using the network simplex outperforms the non-updating Frank-Wolfe algorithms. Comparisons with Bar-Gera's OBA show that our implementation, especially together with the bucket pricing strategy, also outperforms this algorithm for relative gaps down to 10E-6.</p>

Traffic planning in a modern congested society is an important and time consuming procedure. Finding fast algorithms for solving traffic problems is therefore of great interest for traffic planners allover the world. This thesis concerns solving the fixed demand traffic assignment problem (TAP) on a number of different transportation test networks. TAP is solved using the Frank-Wolfe algorithm and the shortest path problems that arise as subproblems to the Frank-Wolfe algorithm are solved using the network simplex algorithm. We evaluate how a number of existing pricing strategies to the network simplex algorithm performs with TAP. We also construct a new efficient pricing strategy, the Bucket Pricing Strategy, inspired by the heap implementation of Dijkstra's method for shortest path problems. This pricing strategy is, together with the actual use of the network simplex algorithm, the main result of the thesis and the pricing strategy is designed to take advantage of the special structure of TAP. In addition to performing tests on the conventional Frank-Wolfe algorithm, we also test how the different pricing strategies perform on Frank-Wolfe algorithms using conjugate and bi-conjugate search directions. These test results show that the updating shortest path calculations obtained by using the network simplex outperforms the non-updating Frank-Wolfe algorithms. Comparisons with Bar-Gera's OBA show that our implementation, especially together with the bucket pricing strategy, also outperforms this algorithm for relative gaps down to 10E-6.

This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps. The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one. The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed. We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space. / The articles are note published due to copyright rextrictions.

Over the last 25 years, interior-point methods (IPMs) have emerged as a viable class of algorithms for solving various forms of conic optimization problems. Most IPMs use a modified Newton method to determine the search direction at each iteration. The system of equations corresponding to the modified Newton system can often be reduced to the so-called normal equation, a system of equations whose matrix ADA' is positive definite, yet often ill-conditioned. In this thesis, we first investigate the theoretical properties of the maximum weight basis (MWB) preconditioner, and show that when applied to a matrix of the form ADA', where D is positive definite and diagonal, the MWB preconditioner yields a preconditioned matrix whose condition number is uniformly bounded by a constant depending only on A. Next, we incorporate the results regarding the MWB preconditioner into infeasible, long-step, primal-dual, path-following algorithms for linear programming (LP) and convex quadratic programming (CQP). In both LP and CQP, we show that the number of iterative solver iterations of the algorithms can be uniformly bounded by n and a condition number of A, while the algorithmic iterations of the IPMs can be polynomially bounded by n and the logarithm of the desired accuracy. We also expand the scope of the LP and CQP algorithms to incorporate a family of preconditioners, of which MWB is a member, to determine an approximate solution to the normal equation. For the remainder of the thesis, we develop a new preconditioning strategy for solving systems of equations whose associated matrix is positive definite but ill-conditioned. Our so-called adaptive preconditioning strategy allows one to change the preconditioner during the course of the conjugate gradient (CG) algorithm by post-multiplying the current preconditioner by a simple matrix, consisting of the identity matrix plus a rank-one update. Our resulting algorithm, the Adaptive Preconditioned CG (APCG) algorithm, is shown to have polynomial convergence properties. Numerical tests are conducted to compare a variant of the APCG algorithm with the CG algorithm on various matrices.

Clinicians are becoming increasingly aware of the effect of various pathologies on the characteristics of saccadic eye movements. As such, an efficient and non-invasive means of measuring eye-movement in a clinical environment is of interest to many. The aim of this thesis is to investigate the clinical application of a non-invasive eye movement recording technique as a part of a clinical examination. Eye movements were measured using an IRIS 6500 infrared limbal eye tracker, which we customized for the direct recording of oblique eye movements as well as horizontal and vertical. Firstly, the eye-tracker itself was assessed. Visually normal observers made saccadic eye movements to a 10' stimulus in eight directions of gaze. Primary (ANOVA) and secondary analyses (mean error less than 5%) resulted in acceptance that averaging four measurements would give a representative measurement of saccadic latency, peak velocity, amplitude and duration. Test-retest results indicated that this technique gives statistically (± 1.96*STDEVDifference) repeatable responses. Several factors that could potentially influence clinically based measures of eye-movements were examined. These included, the effect of ageing, viewing distances, dioptric blur and cataract. The results showed that saccadic latency and duration are significantly (p < 0.05) longer in older (60-89 years) observers compared to younger (20-39 years). Peak velocity and amplitude were not significantly affected by the age of the observer. All saccadic parameters (SP) were significantly affected by direction (Chapter 5). The compact nature of this eye movement methodology is obtainable since there is no significant effect on viewing distance (300 cm vs. 49 cm) (Chapter 6). There is also no significant effect of dioptric blur (up to +LOODS) on any of the four SP. In contrast, a higher level of defocus (+3.O ODS) has a larger probability of interfering with the measurements of peak velocity and duration (Chapter 7). Saccadic eye-movements were also recorded whilst normally sighted subjects wore cataract simulation goggles. The results suggested that the presence of dense cataract introduces significant increases in saccadic latencies and durations. No effect was found on the peak velocities and amplitudes. The effect of amblyopia on SP was also investigated in order to examine if this methodology is able to detect normal from abnormal responses (i.e. increased saccadic latencies). This set of data (Chapter9 ) showed that using IRIS 6500, longer than normal latencies may be recorded from the amblyopic eye but no consistent effect was found for the other SP (peak velocity, amplitude, duration). Overall, the results of this thesis demonstrate that the IRIS 6500 eye-tracker has many desirable elements (it is non-invasive; comfortable for the observers and gives repeatable and precise results in an acceptable time) that would potentially make it a useful clinical tool as a part of a routine examination.

Ce travail porte sur l'étude de l'environnement électromagnétique dans une chambre réverbérante à brassage mécanique de modes. Les chambres réverbérantes constituent un outil fondamental pour réaliser des mesures de compatibilité électromagnétique. Leur étude se focalise généralement sur les propriétés statistiques de la puissance du champ stationnaire. Cependant, d'autres études de ce champ stationnaire ont été faites sous un autre angle qui consiste à utiliser la décomposition en spectre d'ondes planes pour décrire ce champ. Les méthodes d'estimation spectrale à haute résolution constituent un outil puissant pour identifier les directions d'arrivée d'ondes planes. Ces méthodes réputées puissantes sont paramétriques, elles requièrent la connaissance a priori du nombre d'ondes planes à séparer. Une méthode complète basée sur le critère MDL (Minimum Description Length) pour l'estimation d'ordre et de l'algorithme MUSIC (MUltiple SIgnal Classification) a été codée pour l'estimation du nombre, des directions d'arrivée, des amplitudes et des phases des ondes planes. L'adaptation de l'estimateur du spectre d'ondes planes à l'environnement de la chambre réverbérante, qui est un milieu à forte corrélation, nécessite l'utilisation de la technique de lissage spatial pour décorréler les fronts d'onde. La simulation du fonctionnement de la chambre réverbérante par la méthode numérique FDTD (Finite Difference Time Domain) a permis d'avoir les cartographies du champ électrique pour réaliser l'étude de la variation du spectre angulaire par rotation du brasseur mettant en évidence l'effet du mouvement du brasseur sur les directions d'arrivée des ondes et sur leurs puissances respectives. Ce travail se termine par une étude statistique des directions d'arrivée et des amplitudes des ondes planes de la décomposition

The work describes historical development of esotherics and its related fields. It tracks the history line back to the ancient cultures that lay the grounds for the New Age understanding of magic as well as astrology and tarot. It studies the Middle Ages and the present when new religions not only came to existence but they also have made great development since.