Pas de résumé / The level set method was introduced by Osher & Sethian (1988) as a general technique to capture moving interfaces. It has been used to study crystal growth, to simulate water and fire for computer graphics applications, to study two-phase flows and in many other fields. The wellknown problem of the level set method is the following: if the flow velocity is not constant, the level set scalar may become strongly distorted. Thus, the numerical integration may suffer from loss of accuracy. In level set methods, this problem is remedied by the reinitialization procedure, i.e. by reconstruction of the level set function in a way to satisfy the eikonal equation. We propose an alternative approach. We modify directly the level set equation by embedding a source term. The exact expression of this term is such that the eikonal equation is automatically satisfied. Furthermore on the interface, this term is equal to zero. In the meantime, the advantage of our approach is this: the exact expression of the source term allows for the possibility of derivation of its local approximate forms, of first-and-higher order accuracy. Compared to the extension velocity method, this may open the simplifications in realization of level set methods. Compared to the standard approach with the reinitialization procedure, this may give the economies in the number of level set re-initializations, and also, due to reduced number of reinitializations, one may expect an improvement in resolution of zero-set level. Hence, the objective of the present dissertation is to describe and to assess this approach in different test cases.

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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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