Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.

The numerics of hyperbolic conservation laws, e.g., the Euler equations of gas dynamics, shallow water equations and MHD equations, is non-trivial due to the convective terms being highly non-linear and equations being coupled. Many numerical methods have been developed to solve these equations, out of which central schemes and upwind schemes (such as Flux Vector Splitting methods, Riemann solvers, Kinetic Theory based Schemes, Relaxation Schemes etc.) are well known. The majority of the above mentioned schemes give rise to very dissipative solutions. In this thesis, we propose novel low dissipative numerical algorithms for some hyperbolic conservation laws representing fluid flows. Four different and independent numerical methods which give low diffusive solutions are developed and demonstrated. The first idea is to regulate the numerical diffusion in the existing dissipative schemes so that the smearing of solution is reduced. A diffusion regulator model is developed and used along with the existing methods, resulting in crisper shock solutions at almost no added computational cost. The diffusion regulator is a function of jump in Mach number across the interface of the finite volume and the average Mach number across the surface. The introduction of the diffusion regulator makes the diffusive parent schemes to be very accurate and the steady contact discontinuities are captured exactly. The model is demonstrated in improving the diffusive Local Lax-Friedrichs (LLF) (or Rusanov) method and a Kinetic Scheme. Even when employed together with accurate methods of Roe and Osher, improvement in solutions is demonstrated for multidimensional problems. The second method, a Central Upwind-Biased Scheme (CUBS), attempts to reorganize a central scheme such that information from irrelevant directions is largely reduced and the upwind biased information is retained. The diffusion co-efficient follows a new format unlike the use of maximum characteristic speed in the Local Lax-Friedrichs method and the scheme results in improved solutions of the flow features. The grid-aligned steady contacts are captured exactly with the reorganized format of diffusion co-efficient. The stability and positivity of the scheme are discussed and the procedure is demonstrated for its ability to capture all the features of solution for different flow problems. Another method proposed in this thesis, a Central Rankine-Hugoniot Solver, attempts to integrate more physics into the discretization procedure by enforcing a simplified Rankine-Hugoniot condition which describes the jumps and hence resolves steady discontinuities very accurately. Three different variants of the scheme, termed as the Method of Optimal Viscosity for Enhanced Resolution of Shocks (MOVERS), based on a single wave (MOVERS-1), multiple waves (MOVERS-n) and limiter based diffusion (MOVERS-L) are presented. The scheme is demonstrated for scalar Burgers equation and systems of conservation laws like Euler equations, ideal Magneto-hydrodynamics equations and shallow water equations. The new scheme uniformly improves the solutions of the Local Lax-Friedrichs scheme on which it is based and captures steady discontinuities either exactly or very accurately. A Grid-Free Central Solver, which does not require a grid structure but operates on any random distribution of points, is presented. The grid-free scheme is generic in discretization of spatial derivatives with the location of the mid-point between a point and its neighbor being used to define a relevant coefficient of numerical dissipation. A new central scheme based on convective-pressure splitting to solve for mid-point flux is proposed and many test problems are solved effectively. The Rankine-Hugoniot Solver, which is developed in this thesis, is also implemented in the grid-free framework and its utility is demonstrated. The numerical methods presented are solved in a finite volume framework, except for the Grid-Free Central Solver which is a generalized finite difference method. The algorithms developed are tested on problems represented by different systems of equations and for a wide variety of flow features. The methods presented in this thesis do not need any eigen-structure and complicated flux splittings, but can still capture discontinuities very accurately (sometimes exactly, when aligned with the grid lines), yielding low dissipative solutions. The thesis ends with a highlight on the importance of developing genuinely multidimensional schemes to obtain accurate solutions for multidimensional flows. The requirement of simpler discretization framework for such schemes is emphasized in order to match the efficacy of the popular dimensional splitting schemes.

No description available.

Dynamic optimization methods have become increasingly important over the last years in economics. Within the dynamic optimization techniques employed, optimal control has emerged as the most powerful tool for the theoretical economic analysis. However, there is the need to advance further and take account that many dynamic economic processes are, in addition, dependent on some other parameter different than time. One can think of relaxing the assumption of a representative (homogeneous) agent in macro- and micro-economic applications allowing for heterogeneity among the agents. For instance, the optimal adaptation and diffusion of a new technology over time, may depend on the age of the person that adopted the new technology. Therefore, the economic models must take account of heterogeneity conditions within the dynamic framework.This thesis intends to accomplish two goals. The first goal is to analyze and revise existing environmental policies that focus on defining the optimal management of natural resources over time, by taking account of the heterogeneity of environmental conditions. Thus, the thesis makes a policy orientated contribution in the field of environmental policy by defining the necessary changes to transform an environmental policy based on the assumption of homogeneity into an environmental policy which takes account of heterogeneity. As a result the newly defined environmental policy will be more efficient and likely also politically more acceptable since it is tailored more specifically to the heterogeneous environmental conditions. Additionally to its policy orientated contribution, this thesis aims making a methodological contribution by applying a new optimization technique for solving problems where the control variables depend on two or more arguments --- the so-called two-stage solution approach ---, and by applying a numerical method --- the Escalator Boxcar Train Method --- for solving distributed optimal control problems, i.e., problems where the state variables, in addition to the control variables, depend on two or more arguments.Chapter 2 presents a theoretical framework to determine optimal resource allocation over time for the production of a good by heterogeneous producers, who generate a stock externalit and derives government policies to modify the behavior of competitive producers in order to achieve optimality. Chapter 3 illustrates the method in a more specific context, and integrates the aspects of quality and time, presenting a theoretical model that allows to determine the socially optimal outcome over time and space for the problem of waterlogging in irrigated agricultural production. Chapter 4 of this thesis concentrates on forestry resources and analyses the optimal selective-logging regime of a size-distributed forest.

Φαινόμενα άντλησης με ή χωρίς βαλβίδες εξετάζονται πειραματικά και θεωρητικά μέσω κυλινδρικών εύκαμπτων αγωγών. Το φαινόμενο της άντλησης ρευστού χωρίς βαλβίδες μελετάται πειραματικά σε κλειστό βρόχο αποτελούμενο από δύο αγωγούς, έναν εύκαμπτο και έναν άκαμπτο. Αναπτύσσεται μη μηδενική μέση χρονικά παροχή ρευστού όταν διεγείρεται τμήμα του εύκαμπτου αγωγού σε συγκεκριμένες συχνότητες και πλάτη διέγερσης. Η διέγερση επιτυγχάνεται μέσω συμπίεσης και αποσυμπίεσης του εύκαμπτου αγωγού από έναν κατάλληλο παλινδρομικό μηχανισμό. Εξετάζονται τέσσερις παράμετροι επιρροής του φαινομένου, η συχνότητα, το μήκος, το πλάτος και η θέση της διέγερσης. Καταγράφονται τα σήματα μέτρησης της παροχής στο μέσον του άκαμπτου αγωγού, οι τιμές της στατικής πίεσης στα άκρα του άκαμπτου αγωγού και η κατακόρυφη μετατόπιση της πλάκας συμπίεσης. Επιπλέον, προσδιορίζεται η παραμόρφωση της εγκάρσιας διατομής του ελαστικού αγωγού στην περιοχή της διέγερσης, κατά τη συμπίεση και αποσυμπίεσή του για διάφορα πλάτη διέγερσης. Τα αποτελέσματα φανερώνουν την ανάπτυξη ροής προς μία κατεύθυνση με την αύξηση της συχνότητας διέγερσης. Η ροή αυτή μεγιστοποιείται όταν η συχνότητα διέγερσης ταυτίζεται με την ιδιοσυχνότητα του υδραυλικού κυκλώματος. Η μέση χρονικά παροχή αυξάνει καθώς το σημείο διέγερσης απομακρύνεται από το μέσον του εύκαμπτου αγωγού και επίσης με την αύξηση του πλάτους ή του μήκους διέγερσης. Θεωρητικά το φαινόμενο της άντλησης χωρίς βαλβίδες μελετάται μέσω της ανάπτυξης ενός κατάλληλου ψευδο-μονοδιάστατου μοντέλου που επιλύεται αριθμητικά, θεωρώντας ξανά κλειστό βρόχο ενός εύκαμπτου και ενός άκαμπτου αγωγού. Οι εξισώσεις του μοντέλου διαμορφώνονται με την ολοκλήρωση των εξισώσεων ροής (συνέχειας και ορμής) επί της εγκάρσιας διατομής του κλειστού βρόχου, θεωρώντας αξονοσυμμετρική ροή ασυμπίεστου ρευστού με σταθερό ιξώδες. Χρησιμοποιείται επίσης μία καταστατική εξίσωση που σχετίζει την αναπτυσσόμενη πίεση με την μεταβαλλόμενη εγκάρσια διατομή του βρόχου, έχοντας υποθέσει λεπτά ελαστικά τοιχώματα αγωγών με γραμμικές παραμορφώσεις. Επιλύεται αριθμητικά μη γραμμικό σύστημα μερικών διαφορικών εξισώσεων υπερβολικού τύπου, μέσω τριών αριθμητικών σχημάτων: Lax-Wendroff, MacCormack, και Dispersion Relation Preserving (DRP), το οποίο παρουσιάζει και την υψηλότερη ακρίβεια. Οι τρεις άγνωστες συναρτήσεις που υπολογίζονται στο χώρο και το χρόνο είναι η εγκάρσια διατομή του κλειστού κυκλώματος, η αναπτυσσόμενη εσωτερική πίεση του ρευστού και η ταχύτητά του. Σε κάποιο σημείο του εύκαμπτου αγωγού η περιοδική διέγερση προκαλεί κατευθυνόμενη ροή του ρευστού υπό συγκεκριμένες συνθήκες. Όταν η διέγερση απομακρύνεται από το μέσον του εύκαμπτου αγωγού, αναπτύσσεται διαφορά φάσης μεταξύ των κυματομορφών της πίεσης στα σημεία σύνδεσης των δύο αγωγών. Η κυματομορφή της πίεσης που προηγείται είναι αυτή που διαμορφώνεται στο σημείο σύνδεσης των δύο αγωγών που είναι πιο κοντά στη διέγερση. Με αύξηση του πλάτους ή του μήκους του διεγειρόμενου τμήματος του κλειστού κυκλώματος, η μέση χρονικά παροχή αυξάνει και μεγιστοποιείται στην ιδιοσυχνότητα του συστήματος. Μεταβάλλοντας τη συχνότητα διέγερσης στο πεδίο μακριά της συχνότητας συντονισμού, εμφανίζονται τοπικά ακρότατα της συνάρτησης της μέσης χρονικά παροχής με τη συχνότητα, τα οποία αναδεικνύουν τον περίπλοκο χαρακτήρα του φαινομένου της άντλησης χωρίς βαλβίδες. Τα αποτελέσματα του μοντέλου παρουσιάζουν την ίδια συστηματικότητα με τα αντίστοιχα του πειράματος, διατηρώντας τα περισσότερα χαρακτηριστικά και τάσεις στις μεταβολές. Κατά το πρώιμο στάδιο κύησης του εμβρύου το αίμα κυκλοφορεί προς μία κατεύθυνση στο πρωταρχικό κυκλοφορικό σύστημα του εμβρύου, παρότι οι βαλβίδες απουσιάζουν. Το παραπάνω θεωρητικό μοντέλο επιλύεται με αριθμητικά δεδομένα από τη φυσιολογία του εμβρύου, γι’ αυτό το πρώιμο στάδιο κύησης, χρησιμοποιώντας τη μέθοδο DRP 4ης τάξης ακρίβειας στο χώρο και το χρόνο. Το μέγεθος της μέσης παροχής του αίματος εξαρτάται από τους εμβρυϊκούς καρδιακούς παλμούς και το βαθμό συστολής του αρχέγονου καρδιακού σωλήνα. Η αντλητική ικανότητα του κυκλοφορικού συστήματος του εμβρύου εκφράζεται με τη μέση παροχή αίματος ως συνάρτηση των καρδιακών παλμών και του βαθμού συστολής του αρχέγονου καρδιακού σωλήνα. Το φαινόμενο της άντλησης με βαλβίδες μελετάται πειραματικά μέσω ενός ανατάξιμου εύκαμπτου αγωγού, ο οποίος συμπιέζεται από ένα μηχανισμό δίχρονης περισταλτικής αντλίας. Μία πρότυπη συσκευή έχει σχεδιαστεί και κατασκευαστεί, ώστε να αναλυθεί η συμπεριφορά και να εξαχθούν οι χαρακτηριστικές καμπύλες της δίχρονης περισταλτικής αντλίας. Περισταλτικές αντλίες αυτού του τύπου χρησιμοποιούνται στην ιατρική σε εφαρμογές παρεντερικής διατροφής, άντλησης του αίματος και ειδικότερα σε έγχυση φαρμάκων. Για την κατασκευή της πρότυπης αντλίας, σχεδιάστηκε και κατασκευάστηκε ένας καινοτομικός μηχανισμός εκκεντροφόρου άξονα, ο οποίος επιτυγχάνει σταθερό ρυθμό έγχυσης. Η πειραματική διάταξη αποτελείται από δύο δεξαμενές υπερχείλισης που συνδέονται μέσω ενός σωλήνα ελαστικού σιλικόνης. Το όλο σύστημα πληρώνεται με αποσταγμένο νερό και η άντληση επιτυγχάνεται από τη μία δεξαμενή στην άλλη με κατάλληλη προοδευτική συμπίεση ενός τμήματος του ελαστικού αγωγού μέσω του μηχανισμού της αντλίας. Η παροχή μετράται ζυγίζοντας τη δεξαμενή κατάθλιψης, η οποία είναι τοποθετημένη σε δυναμοκυψέλη γι’ αυτό το σκοπό. Για χαμηλές συχνότητες λειτουργίας η έγχυση είναι σχεδόν ομαλή χωρίς πάλμωση. Επίσης, η παροχή εξαρτάται κυρίως από τη συχνότητα περιστροφής του άξονα της αντλίας και μεγιστοποιείται γύρω από την ιδιοσυχνότητα της συσκευής. / Valveless and valvate pumping phenomena are investigated experimentally and theoretically through cylindrical distensible tubes. The phenomenon of valveless pumping is studied experimentally in a loop consisting of two tubes, a soft and a hard one filled with salted water. A non zero mean flow-rate is established via a reciprocating flat plate mechanism compressing and decompressing a portion of the flexible tube with a controllable frequency and depth of compression. Four parameters of the problem were examined, namely the frequency of the oscillating plate, its length, the depth of compression and the location where the tube is compressed. Four signals were simultaneously recorded, namely the flow-rate at the mid length of the hard tube, the static pressure at the tube’s ends and the displacement of the oscillating plate. Also, the tube cross-sectional area was measured versus the displacement of the oscillating plate for various values of the maximum depth of compression. Analysis of the obtained data showed that a unidirectional flow is established increasing the frequency of compression and it maximizes when the compression frequency coincides with the natural frequency of the hydraulic loop. The mean value of the flow-rate increases when the point of compression moves far from the mid length of the flexible tube, when the length of the reciprocating plate increases and when the depth of compression increases. Additionally, the development of a theoretical model of valveless pumping and its numerical solution is presented, applied for the case of the closed hydraulic loop, consisting of a flexible and a rigid tube. The integration of the governing flow equations (continuity and momentum), over the tube cross-sectional area results in a quasi-one-dimensional unsteady model, considering axisymmetric flow of incompressible fluid with constant viscosity. There was also used a constitutive state equation, relating pressure and cross-sectional area, and assuming that the deformations of the thin-walled tubes are purely elastic. A system of nonlinear partial differential equations of the hyperbolic type is solved numerically, employing three finite difference schemes: Lax-Wendroff, MacCormack, and Dispersion Relation Preserving (DRP), the last being the most accurate one. Three functions in time and space are calculated, the cross-sectional area of the closed loop, the building up internal pressure and the velocity of the fluid inside the loop. A periodic compression and decompression of the flexible tube causes a unidirectional flow, under certain conditions. When the excitation takes place far from the midlength of the flexible tube, a phase difference between the pressures at the two edges of each tube is developed, being in advance the one that is closer to the excitation area. Increasing the tube occlusion or the length of the excited part of the loop the mean flow rate increases and maximizes at the natural frequency of the loop. Varying the excitation frequency both above and below the resonance frequency, local flow rate extremes appear, manifesting the complex character of the valveless pumping phenomenon. The simulated results maintain most of the characteristics found in the experiment. During early embryonic life, blood circulates in one direction through the primitive circulatory system, in spite of the complete lack of valves. The above mathematical model described the coordinated fashion of the blood circulation in the circulatory system of the embryo. The one-dimensional model is analysed numerically and solved with the DRP scheme, which is of fourth order accurate in time and space. The mean blood flow-rate depends on the embryonic heart rate and the contraction grade of the primordial heart tube. The pumping activity of the embryo circulatory system is shown by presenting the mean blood flow-rate as a function of embryonic heart rate for several contraction grades of the primordial heart tube. Furthermore, the phenomenon of valvate pumping is studied experimentally through a resilient tube, compressed by a two-cycle peristaltic pump mechanism. A prototype device was designed and manufactured in order to analyze the behaviour and reveal the characteristic curves of such a pump. This kind of pump can be used in medicine for nutrition, pumping blood and especially for drug infusion therapies. Concerning the manufacturing of this prototype device, an innovative mechanism was applied, regarding the camshaft of the pump, in order to achieve constant infusion flow-rate in time. The experimental set-up consists of two rigid overflow vessels filled with distilled water, communicating via a silicone rubber tube. Pumping is achieved from one vessel to the other by inducing a progressive deformation (shrinkage) on a segment of the silicone rubber tube through the pump. The flow-rate is measured by weighing the fluid-receiver vessel, which is placed on a single point load-cell platform. At low pumping frequencies the flow-rate is almost steady. Also it is shown that the flow-rate is mainly dependent on the rotating frequency of the pump and maximizes when the excitation frequency coincides with the natural frequency of the device.

[pt] Esta tese propõe um método meshfree adaptativo de advecção para problemas de fluxo bifásico de fluidos incompressíveis e imiscíveis em meios porosos heterogêneos tridimensionais. Este método se baseia principalmente na combinação do método Semi-Lagrangeano adaptativo com interpolação local meshfree usando splines poliharmônicas como funções de base radial. O método proposto é uma melhoria e uma extensão do método adaptativo meshfree AMMoC proposto por Iske e Kaser (2005) para modelagem 2D de reservatórios de petróleo. Inicialmente este trabalho propõe um modelo em duas dimensões, contribuindo com uma melhoria significativa no cálculo do Laplaciano, utilizando os métodos meshfree de Hermite e Kansa. Depois, o método é ampliado para três dimensões (3D) e para um meio poroso heterogêneo. O método proposto é testado com o problema de five spot e os resultados são comparados com os obtidos por sistemas bem conhecidos na indústria de petróleo. / [en] This thesis proposes an adaptive meshfree advection method for two-phase flow problems of incompressible and immiscible fluids through three-dimensional heterogeneous porous media. This method is based mainly on a combination of adaptive semi-Lagrangian method with local meshfree interpolation using polyharmonic splines as radial basis functions. The proposed method is an improvement and extension of the adaptive meshfree advection scheme AMMoC proposed by Iske and Kaser (2005) for 2D oil reservoir modeling. Initially this work proposes a model in two dimensions, contributing to a significant improvement in the calculation of the Laplacian, using the meshfree methods of Hermite and Kansa. Then, the method is extended to three dimensions (3D) and a heterogeneous porous medium. The proposed method is tested with the five spot problem and the results are compared with those obtained by well-known systems in the oil industry.

Les Processus Markoviens Déterministes par Morceaux (PDMP) ont été introduits dans la littérature par M.H.A Davis comme une classe générale de modèles stochastiques. Les PDMP forment une famille de processus markoviens qui décrivent une trajectoire déterministe ponctuée par des sauts aléatoires. Dans une première partie, les PDMP sont utilisés pour calculer des probabilités d'événements redoutés pour un cas-test de la fiabilité dynamique (le réservoir chauffé) par deux méthodes numériques différentes : la première est basée sur la résolution du système différentieldécrivant l'évolution physique du réservoir et la seconde utilise le calcul de l'espérancede la fonctionnelle d'un PDMP par un système d'équations intégro-différentielles.Dans la seconde partie, nous proposons une méthode numérique pour approcher lafonction valeur du problème d'arrêt optimal pour un PDMP. Notre approche estbasée sur la quantification de la position après saut et le temps inter-sauts de lachaîne de Markov sous-jacente au PDMP, et la discréetisation en temps adaptée à latrajectoire du processus. Ceci nous permet d'obtenir une vitesse de convergence denotre schéma numérique et de calculer un temps d'arrêt ε-optimal. / Piecewise Deterministic Markov Processes (PDMP's) have been introduced inthe literature by M.H.A. Davis as a general class of stochastics models. PDMP's area family of Markov processes involving deterministic motion punctuated by randomjumps. In a first part, PDMP's are used to compute probabilities of top eventsfor a case-study of dynamic reliability (the heated tank system) with two di#erentmethods : the first one is based on the resolution of the differential system giving thephysical evolution of the tank and the second uses the computation of the functionalof a PDMP by a system of integro-differential equations. In the second part, wepropose a numerical method to approximate the value function for the optimalstopping problem of a PDMP. Our approach is based on quantization of the post-jump location and inter-arrival time of the Markov chain naturally embedded in thePDMP, and path-adapted time discretization grids. It allows us to derive boundsfor the convergence rate of the algorithm and to provide a computable ε-optimalstopping time.

Avec l’avènement de la prochaine génération de télescope de plus de 30m de diamètre, il devient primordial de réduire le coût des observations et d’améliorer leur rendement scientifique. De plus il est essentiel de construire ces instruments sur des sites disposant d’une qualité optique maximale. J’ai donc essayé, au cours de ma thèse, de développer un outil fiable, facile d’utilisation et économique permettant de satisfaire ces exigences. J’ai donc utilisé le modèle de prévision météorologique Weather Research and Forecasting et le modèle de calcul de la turbulence optique Trinquet-Vernin pour prédire, plusieurs heures à l’avance, les conditions optiques du ciel tout au long de la nuit. Cette information permettrait d’améliorer la gestion du programme d’observation, appelée "flexible scheduling", et ainsi de réduire les pertes dues à la variation des conditions atmosphériques. Les résultats obtenus et les améliorations apportées au modèle WRF-TV lui permettent de présenter un bon accord entre les mesures et les prévisions ce qui est prometteur pour une utilisation réelle. Au delà de cette gestion, nous avons voulu créer un moyen d’améliorer la recherche et le test de sites astronomiquement intéressants. Nous avons donc définit un paramètre de qualité qui prend en compte les conditions météorologiques et optiques. Ce paramètre a été testé au-dessus de l’île de La Palma aux Canaries et a montré que l’Observatorio del Roque de los Muchachos est situé au meilleur emplacement de l’île. Enfin nous avons créé une routine d’automatisation du modèle WRF-TV afin d’avoir un outil opérationnel fonctionnant de manière autonome. / With the next generation of extremely large telescope having mirror with a diameter larger than 30m, it becomes essential to reduce the cost of observations and to improve their scientific efficiency. Moreover it is fundamental to build these huge infrastructures in location having the best possible optical quality. The purpose of my thesis is to bring a solution easier and more economical than before. I used the Weather Research and Forecasting (WRF) model and the Trinquet-Vernin parametrization, which computes the values of the optical turbulence, to forecast a couple of hours in advance the evolution of the sky optical quality along the coming night. This information would improve the management of observation program, called "flexible scheduling", and thereby reduce losses due to the atmospheric variations. Our results and improvements allow the model us WRF-TV to have a good agreement between previsions and in-situ measurements in different sites, which is promising for a real use in an observatory. Beyond the flexible scheduling, we wanted to create a tool to improve the search for new sites or site testing for already existing sites. Therefore we defined a quality parameter which takes into account meteorological conditions (wind, humidity, precipitable water vapor) and optical conditions (seeing, coherence time, isoplanatic angle). This parameter has been tested above La Palma in Canary island showing that the Observatorio del Roque de los Muchachos is located close to the best possible location of the island. Finally we created an automated program to use WRF-TV model in order to have an operational tool working routinely.

Cette thèse a pour objet d'étude les méthodes numériques d'approximation de la densité de probabilité associée à des variables aléatoires admettant des distributions composées. Ces variables aléatoires sont couramment utilisées en actuariat pour modéliser le risque supporté par un portefeuille de contrats. En théorie de la ruine, la probabilité de ruine ultime dans le modèle de Poisson composé est égale à la fonction de survie d'une distribution géométrique composée. La méthode numérique proposée consiste en une projection orthogonale de la densité sur une base de polynômes orthogonaux. Ces polynômes sont orthogonaux par rapport à une mesure de probabilité de référence appartenant aux Familles Exponentielles Naturelles Quadratiques. La méthode d'approximation polynomiale est comparée à d'autres méthodes d'approximation de la densité basées sur les moments et la transformée de Laplace de la distribution. L'extension de la méthode en dimension supérieure à $1$ est présentée, ainsi que l'obtention d'un estimateur de la densité à partir de la formule d'approximation. Cette thèse comprend aussi la description d'une méthode d'agrégation adaptée aux portefeuilles de contrats d'assurance vie de type épargne individuelle. La procédure d'agrégation conduit à la construction de model points pour permettre l'évaluation des provisions best estimate dans des temps raisonnables et conformément à la directive européenne Solvabilité II. / This PhD thesis studies numerical methods to approximate the probability density function of random variables governed by compound distributions. These random variables are useful in actuarial science to model the risk of a portfolio of contracts. In ruin theory, the probability of ultimate ruin within the compound Poisson ruin model is the survival function of a geometric compound distribution. The proposed method consists in a projection of the probability density function onto an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Families with Quadratic Variance Function. The polynomiam approximation is compared to other numerical methods that recover the probability density function from the knowledge of the moments or the Laplace transform of the distribution. The polynomial method is then extended in a multidimensional setting, along with the probability density estimator derived from the approximation formula. An aggregation procedure adapted to life insurance portfolios is also described. The method aims at building a portfolio of model points in order to compute the best estimate liabilities in a timely manner and in a way that is compliant with the European directive Solvency II.

Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.