Le travail de la thèse concerne l'étude de quelques problèmes inverses par différents approches mathématiques. Dans la première partie, nous considérons le problème inverse géométrique consistant à retrouver une fissure ou cavité(s) inconnue à partir de mesures sur le bord d'un domaine plan. Nous traitons ce problème par des techniques d'approximation rationnelle et méromorphe dans le plan complexe. Nous étudions un autre problème inverse consistant à estimer l'aire d'une cavité. Nous donnons une majoration explicite de l'aire de la cavité. Cette majoration est basée sur une estimation de croissance dans l'espace de Hardy­-Sobolev de la couronne. Nous appliquons également cette estimation pour donner la vitesse de comvergence d'un schéma d'ïnterpolation d'une fonction de l'espace de Hardy-Sobolev de la couronne. Dans la deuxième partie, nous considérons d'abord le problème inverse d'identification des paramètres de Lamé en élasticité linéaire. Nous transformons ce problème en un problème de minimisation et nous exhibons quelques exemples numériques. Nous considérons également le problème inverse d'identification d'une inclusion correspondant à une discontinuité de la conductivité. Nous utilisons la méthode du gradient topologique pour une première approximation et ensuite la méthode du gradient classique pour identifier plus précisément celles-ci. Enfin, nous étudions un problème inverse d'identification d'une inclusion en élasticité linéaire. Nous utilisons le gradient de forme pour retrouver numériquement des inclusions elliptiques. / This work concerns the study of some inverse problems by different mathematical approaches. ln the first part, we consider the geometrical inverse problem. related to the identification of an unknown crack or inclusion(s) by boundary measurements. We treat this problem by technique of rational and meromorphic approximation in the complex plane. We study another inverse problem, namely estimating the area of a cavity. We derivive an explicit upper bound on the area of the cavity. We also aplly this estimation, to find an upper bound on the rate of convergence of a recovery interpolation schema in the Hardy-Sobolev space of an annulus. ln the second part. we first consider the inverse problem of recovering the Lamé parameters in linear elasticity from boundary measurements. we perform numerical experiments. We also consider the inverse problem or identification of an inclusion corresponding to a discontinuity of the conductivity. We use the method of the topological gradient to obtain a first estimate on the location of one or several inclusions and then, we use the method of the classical gradient to identify more precisely these. Finally. in the context of shape optimization, we study the inverse problem of identification of an inclusion in linear elasticity. We calculate the shape gradient of a functional of Kohn-Vogelius type, minmax of a lagrangian with respect to the parameter of deformation. We use this gradient to numerically flnd elliptic inclusions

L'objectif de l'optimisation de forme d'une pompe générique de fond de puits est de maximiser le gain de pression par unité de longueur de la pompe, en redessinant ses aubes et son moyeu, tout en respectant un certain nombre de contraintes géométriques. On génère la représentation de la géométrie 3D de la pompe grâce à des B-splines paramétriques cubiques 2D. Pour l'optimisation on utilise une méthode de gradient classique. On emploie Fluent, un logiciel de modélisation de mécanique des fluides "boîte noire" et on procède par conséquent à un calcul de gradient incomplet de la fonction coût. Pour cela on écrit l'expression analytique exacte du gradient à l'aide d'une formule d'intégration sur les bords variables puis on ne prend en compte que les termes que l'on peut calculer ou déterminer numériquement. Les termes généralement écartés sont les dérivées des solutions de l'équation d'état par rapport au déplacement d'un point de contrôle. On a d'abord développé un code d'optimisation pour le moyeu de la pompe seul, sans aubages, et on présente les résultats obtenus. On utilise une méthode d'optimisation sans contrainte et on prend en compte par réduction du problème des contraintes d'égalité linéaires. On constate qu'après une première phase de décroissance, la fonction coût ne converge pas vers un minimum. On propose alors quelques tests de façon à analyser ce résultat. Parmi ceux-là, l'emploi des différences finies confirme que le gradient incomplet n'est pas systématiquement une direction de descente. Enfin quelques pistes sont évoquées pour l'expliquer. / The aim of the optimization of a well-pump is to maximize the pressure gain per length unit in the pump by designing its blades and hub, while taking into account some geometrical constraints. The 3D representation of the geometry of the pump is generated thanks to 2D parametric and cubic B-splines. We lead the optimization with a classical gradient method. Fluent, a computational fluid dynamics (CFD) "black box" software, is used and therefore we chose to compute an incomplete gradient of the cost function. We calculate the exact analytical expression of the gradient thanks to an integration formula on variable boundaries. Only the terms we can calculate or compute numerically are then kept. The terms we generally omit are the derivatives of the solutions of the state equations with respect to the displacement of the control points. An optimization program for the single hub of the pump has first been developed and we present its results. We use an optimization method without constraints though linear equality constraints are taken into account by reducing the problem. After a first decreasing phase, the cost function does not converge to a minimum value. We suggest some tests so as to analyze this result. Among these, the use of finite differences confirms that the incomplete gradient is not systematically a descent direction. Some ideas are finally given in order to explain this phenomenon.

When using Stochastic Gradient Descent (SGD) to train Artificial Neural Networks, gradient variance comes from two sources: differences in the weights of the network when each batch gradient is estimated and differences between the input values in each batch. Some architectural traits, like skip-connections and batch-normalization, allow much deeper networks to be trained by reducing each type of variance and improving the conditioning of the network gradient with respect to both the weights and the input. It is still unclear to which degree each property is responsible for these dramatic stability improvements when training deep networks. This thesis summarizes previous findings related to gradient conditioning in each case, demonstrates efficient methods by which each can be measured independently, and investigates the contribution each makes to the stability and speed of SGD in various architectures as network depth increases.

No description available.

abstract: Electrophoretic exclusion is a counter-flow gradient focusing method that simultaneously separates and concentrates electrokinetic material at a channel entrance utilizing electric and fluid velocity fields. However, its effectiveness is heavily dependent on the non-uniform field gradients about the entrance. This work assesses the capability of electrophoretic exclusion to capture and enrich small molecules and examines the channel entrance region both quantitatively and qualitatively to better understand the separation dynamics for future design. A flow injection technique is used to experimentally evaluate electrophoretic exclusion of small molecules. Methyl violet, a cationic dye, and visible spectroscopy are used to monitor flow and electrophoretic dynamics at the entrance region resulting in successful capture and simultaneous enrichment of methyl violet at the channel interface. Investigation of the entrance region is performed using both experiment data and finite element analysis modeling to assess regional flow, electric fields, diffusion, convection, and electrophoretic migration. Longitudinal fluid velocity and electric field gradient magnitudes near the channel entrance are quantified using Particle Tracking Velocimetry (PTV) and charged fluorescent microspheres. Lateral studies using rhodamine 123 concentration monitoring agree qualitatively with simulation results indicating decreased gradient uniformity for both electric and fluid velocity fields closer to the channel wall resulting in a localized concentration enhancement at lower applied voltages than previously observed or predicted. Resolution interrogation from both a theoretical assessment and simulation construct demonstrate resolution improvement with decreased channel width and placement of an electrode directly at the interface. Simulation resolution predictions are in general agreement with early experimental assessments, both suggesting species with electrophoretic mobilities as similar as 10-9 m2/(Vs) can be separated with the current design. These studies have helped evolve the understanding of the interface region and set the foundation for further interface developments. / Dissertation/Thesis / Doctoral Dissertation Chemistry 2015

In this thesis a church named Hamrånge, located North of the town Gävle in Sweden, has been studied. In this church thermal comfort is a problem that need to be considered. There is poor insulation and air leakage in the building envelope. And appearance doesn't allow to add any additional insulation, becauce people want to keep its original appearance. In cold weather the church is heated by bench heaters and radiators through direct electicity. / Energy system

University of Macau / Faculty of Science and Technology. / Department of Civil and Environmental Engineering

In the past, the oil and gas industry has typically used the single gradient system to drill wells offshore. With this system the bottom hole pressure was controlled by a mud column extending from the drilling rig to the bottom of the wellbore. This mud column was used to achieve the required bottom hole pressure. But, as the demand for oil and gas increased, the industry started exploring for oil and gas in deep waters. Because of the narrow margin between the pore and fracture pressures it is somewhat difficult to reach total depth with the single gradient system. This led to the invention of the dual gradient system. In the dual gradient method, heavy density fluid runs from the bottom hole to the mudline and a low density fluid from the mudline to the rig floor so as to maintain the bottom hole pressure. Several methods have been developed to achieve the dual gradient drilling principle. For this research project, we paid more attention to the liquid lift, dual gradient drilling (riser dilution method). This method of achieving dual gradient drilling was somewhat different from the others, because it does not utilize elaborate equipment and no major changes are made on the existing drilling rigs. In this thesis the technical feasibility of using the liquid lift method over the other methods of achieving dual gradient drilling was determined. A computer program was developed to simulate the wellbore hydraulics under static and dynamic conditions, injection rate and base fluid density required to dilute the riser fluid and finally, u-tubing phenomena. In this thesis we also identified some problems associated with the liquid lift method and recommendations were made on how these problems can be eliminated or reduced. Emphases were placed on the effect of u-tubing, injection rate of base fluid at the bottom of the riser and well control issues facing this system.

In the past, the oil and gas industry has typically used the single gradient system to drill wells offshore. With this system the bottom hole pressure was controlled by a mud column extending from the drilling rig to the bottom of the wellbore. This mud column was used to achieve the required bottom hole pressure. But, as the demand for oil and gas increased, the industry started exploring for oil and gas in deep waters. Because of the narrow margin between the pore and fracture pressures it is somewhat difficult to reach total depth with the single gradient system. This led to the invention of the dual gradient system. In the dual gradient method, heavy density fluid runs from the bottom hole to the mudline and a low density fluid from the mudline to the rig floor so as to maintain the bottom hole pressure. Several methods have been developed to achieve the dual gradient drilling principle. For this research project, we paid more attention to the liquid lift, dual gradient drilling (riser dilution method). This method of achieving dual gradient drilling was somewhat different from the others, because it does not utilize elaborate equipment and no major changes are made on the existing drilling rigs. In this thesis the technical feasibility of using the liquid lift method over the other methods of achieving dual gradient drilling was determined. A computer program was developed to simulate the wellbore hydraulics under static and dynamic conditions, injection rate and base fluid density required to dilute the riser fluid and finally, u-tubing phenomena. In this thesis we also identified some problems associated with the liquid lift method and recommendations were made on how these problems can be eliminated or reduced. Emphases were placed on the effect of u-tubing, injection rate of base fluid at the bottom of the riser and well control issues facing this system.

In the past, the oil and gas industry has typically used the single gradient system to drill wells offshore. With this system the bottom hole pressure was controlled by a mud column extending from the drilling rig to the bottom of the wellbore. This mud column was used to achieve the required bottom hole pressure. But, as the demand for oil and gas increased, the industry started exploring for oil and gas in deep waters. Because of the narrow margin between the pore and fracture pressures it is somewhat difficult to reach total depth with the single gradient system. This led to the invention of the dual gradient system. In the dual gradient method, heavy density fluid runs from the bottom hole to the mudline and a low density fluid from the mudline to the rig floor so as to maintain the bottom hole pressure. Several methods have been developed to achieve the dual gradient drilling principle. For this research project, we paid more attention to the liquid lift, dual gradient drilling (riser dilution method). This method of achieving dual gradient drilling was somewhat different from the others, because it does not utilize elaborate equipment and no major changes are made on the existing drilling rigs. In this thesis the technical feasibility of using the liquid lift method over the other methods of achieving dual gradient drilling was determined. A computer program was developed to simulate the wellbore hydraulics under static and dynamic conditions, injection rate and base fluid density required to dilute the riser fluid and finally, u-tubing phenomena. In this thesis we also identified some problems associated with the liquid lift method and recommendations were made on how these problems can be eliminated or reduced. Emphases were placed on the effect of u-tubing, injection rate of base fluid at the bottom of the riser and well control issues facing this system.