Le soudage hybride arc / laser représente une solution adéquate à l'assemblage de tôles d'acier de forte épaisseur. La présence d'une source laser en amont de la torche MIG permet d'accroître la productivité du procédé tout en assurant une excellente qualité de la soudure. Cependant la phénoménologie complexe de ce procédé multiphysique n'est pas encore totalement maîtrisée, ce qui motive le développement d'outils de simulation numérique. La présente étude s'est déroulée dans le cadre d'un projet multipartenaires "SISHYFE" (ANR Matériaux et Procédés).Dans ce but un modèle éléments finis 3D non stationnaire a été développé. Construit à partir de l'approche level set, il est en mesure de simuler un procédé multi-passes de soudage hybride arc / laser. Il a été développé autour de quatre principaux axes. (1) Une modélisation plus réaliste de l'apport de chaleur a conduit à la définition d'un nouveau modèle basé sur le rayonnement thermique pour décrire la source MIG. (2) Grâce au couplage entre l'intégration de termes source de matière et de chaleur dans les équations de conservation et l'actualisation de l'interface gaz / métal, le modèle proposé est capable de simuler le développement d'un cordon de soudure. (3) L'intégration d'une modélisation des écoulements du bain de fusion dans une approche level set a été évaluée et son impact sur la distribution thermique dans le métal analysé. (4) La simulation de la formation des contraintes pendant et après soudage a été possible grâce à l'adaptation d'un solveur thermomécanique.La modélisation finale a permis de simuler une configuration industrielle de soudage hybride arc / laser multi-passes. Des mesures expérimentales effectuées par les partenaires du projet "SISHYFE" ont été utilisées afin d'évaluer le modèle et d'éprouver sa capacité à reproduire l'expérience. / Hybrid arc / laser welding represents the solution for high thickness steel sheets assembly. The laser heat source added to the MIG torch improves the process productivity while respecting quality standards. Nevertheless, the phenomenology of the process remains complex and not totally understood. This is the thrust for the development of numerical simulation. The present study has been carried out as part of the "SISHYFE" Material and Process ANR project.For that purpose, a new non stationary 3D finite element model has been developed. Based on the level set approach, it allows to simulate a multipass hybrid arc/ laser welding process. The work focused on four research axes. (1) A more representative model of the plasma heat source has been defined, based on thermal radiation. (2) The coupling of a material and a heat source term integrated in the conservation equations and the update of the level set gas / metal interface is able to correctly model the formation of the weld bead. (3) The integration of a fluid flow model within the level set approach has been evaluated and its impact on thermal distribution analyzed. (4) The stress formation during and after the process has been modeled through the adaptation of a thermo-mechanical solver to the previous modeling in a level set framework.In the end, the developed model has shown to be able to simulate an industrial multi-pass hybrid arc / laser welding process. Experimental measurements provided by the project partners have been used to evaluate the model and to assess its abilities to reproduce experimental features.

In this thesis, I survey 11 approximation algorithms for unweighted set cover problem. I have also implemented the three algorithms and created a software library that stores the code I have written. The algorithms I survey are: 1. Johnson's standard greedy; 2. f-frequency greedy; 3. Goldsmidt, Hochbaum and Yu's modified greedy; 4. Halldorsson's local optimization; 5. Dur and Furer semi local optimization; 6. Asaf Levin's improvement to Dur and Furer; 7. Simple rounding; 8. Randomized rounding; 9. LP duality; 10. Primal-dual schema; and 11. Network flow technique. Most of the algorithms surveyed are refinements of standard greedy algorithm.

Consider the random set system (Formula presented.), where (Formula presented.) and Ajselected with probabilityp=pn}. A set H⊆[n] is said to be a hitting set for (Formula presented.). The second moment method is used to exhibit the sharp concentration of the minimal size of H for a variety of values of p.

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A homework set for learning the International Phonetic Alphabet. Both reading and writing the IPA are used. Note that these .doc files use the old SILDoulos IPA93 font. The set includes the problem set and answer key. / This collection consists of learning objects developed for use in courses offered by the Department of Linguistics. Learning objects include lectures, presentations, quizzes, activities, and more. Access to this collection is restricted to authorized faculty and instructors. For access to this collection, please contact Dr. Amy Fountain, Department of Linguistics, avf@email.arizona.edu.

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L’optimisation des transferts de chaleur est un enjeu de recherche important pour améliorer les performances des systèmes énergétiques, notamment des échangeurs de chaleur. Cette optimisation peut s’appuyer sur différents leviers, comme le choix du régime d’écoulement, ou la modification de la géométrie de l’échangeur. C’est sur ce deuxième angle que nous avons travaillé au cours de cette thèse, en proposant une méthode d’optimisation topologique. Le nombre de paramètres impliqués dans cette méthode est important (plusieurs milliers). Une méthode à gradient est donc employée. Le calcul du gradient de la fonction de coût en fonction des paramètres de design est facilité par l’emploi d’une méthode adjointe. Le problème direct est résolu à l’aide de la méthode de Lattice Boltzmann (LBM). L’implémentation aisée des conditions aux limites dans l’algorithme LBM est un bénéfice pour l’optimisation topologique. De plus, la formulation de la LBM est explicite et hautement parallélisable, notamment sur les cartes graphiques (GPU), utilisées au cours de cette thèse. Ensuite le domaine d’optimisation est composé de fluide et de solide. Leur distribution est définie par une fonction Level- Set (LSF). Cette fonction est continue et le contour zéro définit précisément l’interface fluide/solide. La méthode d’optimisation développée a été testée et validée pour différents objectifs (minimisation de la température moyenne, maximisation de l’échange de chaleur) et contraintes (limitation des pertes de charges, porosité fixée). / Heat transfer enhancement is an important research area to improve the efficiency of energy systems, especially for heat exchangers. There are different ways of optimizing such systems as the choice of flow regime or the modification on the fluid channels geometry. This thesis is focused on the latter option with the development of a topology optimization method. The number of design parameters involved in this technique is important (several thousands) so a gradient-based method is employed. The calculation of the cost function gradient with respect to the design variables is done with an adjoint-state method. The forward problem is solved with the Lattice Boltzmann Method (LBM). The simple implementation of the LBM boundary conditions is an interesting feature for topology optimization. The LBM algorithm is also highly parallelizable and GPU cards have been used in this thesis to obtain fast computational times. The efficiency of the LBM is important because the forward problem must be solved at each optimization step. Then, the optimization domain is composed of either solid of fluid elements. This material distribution is defined by a Level-Set Function (LSF). This is a continuous function in which the zero contour defines the fluid/solid interface, allowing an accurate description of both domains. The proposed optimization method has been tested for different objectives (minimization of the mean temperature, maximization of heat transfer rate) and constraints (pressure drops limitation, fixed porosity).

A significant limitation of the conventional level set method in topology optimization is that it can not create new holes in the design domain. Therefore, the topological derivative approach is proposed to overcome this problem. In this part of the thesis, we investigated the use of the topological derivative in combination with the level set method for topology optimization of solid structures. The topological derivative can indicate the appropriate location to create new holes so that the strong dependency of the optimal topology on the initial design can be alleviated. We also develop an approach to evolve the level set function by replacing the gradient item with a Delta function in the standard Hamilton-Jacobi equation. We find that this handling can create new holes in the solid domain, grow a structure from an empty domain, and improve the convergence rate of the optimization process. The success of our approach is demonstrated by several numerical examples. / Following those methods some numerical implementation issues are discussed, and numerical examples of 2D structural topology optimization problems of minimum compliance design are given and combined with a comparative study where the efficiency, convergence and accuracy of the present methods are highlighted. Finally, conclusions are given. / In the second part of this thesis, we implement another variational level set method, the piecewise constant level set (PCLS) method. This method was first proposed by Lie-Lysaker-Tai in the interface problem field for such tasks as image segmentation and denoising problems. In this approach, by defining a piecewise density function over the whole design domain, the sensitivity of the objective function in respect to the design variable, the level set surface, can be explicitly obtained. Thus, the piecewise density function can be viewed as a bridge establishing the relationship between the implicit level set function and the performance function defined on the design domain. This proposed method retains the advantages of the implicit level set representation, such as the capability of the interface to develop sharp corners, break apart and merge together in a flexible manner. Because the PCLS method is implemented by an implicit iteration differential scheme rather than solving the Hamilton-Jacobi equation, it is not only free of the CFL condition and the reinitialization scheme, but it is also easy to implement. These favorable properties lead to a great timesaving advantage over the conventional level set method. Two other meaningful advantages are the natural nucleation property with which the proposed PCLS method need not incorporate any artificial nucleation scheme and the dependence of the initial design is greatly alleviated. / In the third part of this thesis, we apply a parametric scheme by combining the conventional level set method with radial basis functions (RBFs). This method is introduced because the conventional level set function has no analytical form then the entire design domain must be made discrete in an artificial manner using a rectilinear grid for level set processing - often through a distance transform. The classical level set method for structural topology optimization requires a careful choice of an upwind scheme, extension velocity and a reinitialization algorithm. With the versatile tool, RBF, the original problem can be converted to a parametric optimization problem. Therefore, the costly Hamilton-Jacobi PDE solving procedure can be easily replaced by a standard gradient method or another mature conventional optimization method in the parameter space such as MMA, OC, mathematic programming and so on. / Keywords: structural optimization, level set method, topological derivative, radial basis functions, piecewise constant level set method. (Abstract shortened by UMI.) / The concept of structural optimization has been more and more widely accepted in many engineering fields during the past several decades, because the optimization can result in a much more reasonable and economical structure design with even less material consumption. / Wei Peng. / "June 2007." / Adviser: Yu Michael Wang. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0640. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 166-180). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.