The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

In this paper, the property of Curvelet transforms for preconditioning the migration and normal operators is investigated. These operators belong to the class of Fourier integral operators and pseudo-differential operators, respectively. The effect of this preconditioner is shown in term of improvement of sparsity, convergence rate, number of iteration for the Krylov-subspace solver and clustering of singular(eigen) values. The migration operator, which we employed in this work is the common-offset Kirchoff-Born migration.

Dans une première partie, nous proposons une méthodologie innovante pour la comparaison d'images en ingénierie de réservoir. L'objectif est de pouvoir comparer des cubes sismiques obtenus par simulation avec ceux observés sur un champ pétrolier, dans le but de construire un modèle représentatif de la réalité. Nous développons une formulation fondée sur du filtrage, de la classification statistique et de la segmentation d'images. Ses performances sont mises en avant sur des cas réalistes. Dans une seconde partie, nous nous intéressons aux méthodes de recalage d'images utilisées en imagerie médicale pour mettre en correspondance des images. Nous introduisons deux nouveaux modèles de recalage fondés sur l'élasticité non linéaire, où les formes sont appréhendées comme des matériaux de type Saint Venant-Kirchhoff et Ciarlet-Geymonat. Nous justifions théoriquement l'existence de solutions ainsi que la résolution numérique. Le potentiel de ces méthodes est illustré sur des images médicales. / In a first part, we propose an innovative methodology for image matching in the context of reservoir simulation. In order to build a model consistent with data collected on the field, we need to evaluate the error between seismic cubes obtained by simulation and seismic cubes acquired in the oil field. Using image processing tools, we develop a new formulation of the error. The application of this new formulation on synthetic reservoir cases demonstrates its efficiency. In a second part, we address the issue of designing two theoretically well-motivated registration models capable of handling large deformations since they are based on nonlinear elasticity. The shape to be matched are viewed as Ciarlet-Geymonat materials for the first model and as Saint-Venant Kirchhoff materials for the second one. We investigate the efficiency of the proposed matching model for the registration of mouse brain gene expression data to a neuroanatomical mouse atlas.

Dans une première partie, nous proposons une méthodologie innovante pour la comparaison d'images en ingénierie de réservoir. L'objectif est de pouvoir comparer des cubes sismiques obtenus par simulation avec ceux observés sur un champ pétrolier, dans le but de construire un modèle représentatif de la réalité. Nous développons une formulation fondée sur du filtrage, de la classification statistique et de la segmentation d'images. Ses performances sont mises en avant sur des cas réalistes. Dans une seconde partie, nous nous intéressons aux méthodes de recalage d'images utilisées en imagerie médicale pour mettre en correspondance des images. Nous introduisons deux nouveaux modèles de recalage fondés sur l'élasticité non linéaire, où les formes sont appréhendées comme des matériaux de type Saint Venant-Kirchhoff et Ciarlet-Geymonat. Nous justifions théoriquement l'existence de solutions ainsi que la résolution numérique. Le potentiel de ces méthodes est illustré sur des images médicales.

Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications in various branches of engineering and science like : material science ,porous media, study of vibrations of thin structures, composite materials to name a few. There are at present various methods to study homogenization problems (basically asymptotic analysis) and there is a vast amount of literature in various directions. Homogenization arise in problems with oscillatory coefficients, domain with large number of perforations, domain with rough boundary and so on. The latter one has applications in fluid flow which is categorized as oscillating boundaries. In fact ,in this thesis, we consider domains with oscillating boundaries. We plan to study to homogenization of certain optimal control problems with oscillating boundaries. This thesis contains 6 chapters including an introductory Chapter 1 and future proposal Chapter 6. Our main contribution contained in chapters 2-5. The oscillatory domain under consideration is a 3-dimensional cuboid (for simplicity) with a large number of pillars of length O(1) attached on one side, but with a small cross sectional area of order ε2 .As ε0, this gives a geometrical domain with oscillating boundary. We also consider 2-dimensional oscillatory domain which is a cross section of the above 3-dimensional domain. In chapters 2 and 3, we consider the optimal control problem described by the Δ operator with two types of cost functionals, namely L2-cost functional and Dirichlet cost functional. We consider both distributed and boundary controls. The limit analysis was carried by considering the associated optimality system in which the adjoint states are introduced. But the main contribution in all the different cases(L2 and Dirichlet cost functionals, distributed and boundary controls) is the derivation of error estimates what is known as correctors in homogenization literature. Though there is a basic test function, one need to introduce different test functions to obtain correctors. Introducing correctors in homogenization is an important aspect of study which is indeed useful in the analysis, but important in numerical study as well. The setup is the same in Chapter 4 as well. But here we consider Stokes’ Problem and study asymptotic analysis as well as corrector results. We obtain corrector results for velocity and pressure terms and also for its adjoint velocity and adjoint pressure. In Chapter 5, we consider a time dependent Kirchhoff-Love equation with the same domain with oscillating boundaries with a distributed control. The state equation is a fourth order hyperbolic type equation with associated L2-cost functional. We do not have corrector results in this chapter, but the limit cost functional is different and new. In the earlier chapters the limit cost functional were of the same type.