A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

Des travaux scientifiques récents ont ouvert de nouveaux champs d’application aux traitements mécaniques tels que le grenaillage. Il a été montré que de tels traitements, réalisés avant un traitement de nitruration à la surface d’alliage ferreux, permettaient d’abaisser les températures de traitement et d’augmenter significativement les cinétiques de diffusion. Nous avons entrepris de tester les performances de cette combinaison de traitements mécanique et thermochimique sur des aciers inoxydables et des alliages à base nickel austénitiques. Des essais ont été réalisés à partir d’une technique de grenaillage mécanique appelée « Surface Mechanical Attrition Treatment » (SMAT). Des billes en métal ou en céramique sont introduites dans l’enceinte et mises en mouvement par la sonotrode. Les billes percutent et introduisent donc une déformation plastique à la surface des échantillons. Après cette étape, les échantillons subissent un traitement thermochimique de nitruration assisté plasma. La comparaison des résultats obtenus après nitruration sur des échantillons traités mécaniquement avec ceux n’ayant pas été pré-traités mécaniquement a permis de quantifier les effets des traitements combinés. Les analyses par diffraction des rayons X, les mesures de microdureté, les observations au microscope optique/électronique à balayage/électronique en transmission, les analyses de texture par EBSD (Electron BackScatered Diffraction) et la mesure des profils de concentration en azote par SIMS (Secondary Ion Mass Spectrometry) et SDL (Spectroscopie à Décharge Luminescente) ont montré l’importance de la nature de la couche transformée mécaniquement sur la diffusion de l’azote / Recent scientific work has opened new fields of application to mechanical treatments such as shot blasting or peening. Indeed, it has been shown that this treatment, performed before a nitriding treatment on the surface of ferrous alloy, lowers processing temperatures and significantly increases the diffusion kinetics. We undertook to test this combination of mechanical and thermochemical treatments on stainless steels and nickel-based alloys. The mechanical treatments were done by Surface Mechanical Attrition Treatment (SMAT). This method is implemented in a box where metal or ceramic balls were introduced and set in motion by an ultrasound system in order to impact the surface of the pieces. The treated samples were then nitrided at low temperature by using a remote plasma. The comparison of the results obtained after nitriding treatments on mechanically treated samples and those not mechanically treated allows quantifying the effects of the combined treatments. Analyses by X-ray diffraction, microhardness measurement, observations by optical and scanning and transmission electron microscopy, texture analysis by EBSD (Electron Diffraction BackScatered) and measurement of nitrogen concentration profiles by SIMS (Secondary Ion Mass Spectrometry) show the importance of the nature of the deformed layer

<p>U ovoj doktorskoj disertaciji izloženi su rezultati&nbsp;analize eksperimentalno i teorijski dobijene&nbsp;raspodele gustine naelektrisanja dva derivata&nbsp;tiosemikarbazida, 4-metil-3-tiosemikarbazida&nbsp;(MeTSC) i 4-metil-3-tiosemikarbazon 2-piridinformamida (TSC4). &nbsp;Analiza&nbsp;eksperimentalno dobijene gustine naelektrisanja je&nbsp;zasnovana&nbsp; na preciznim &nbsp;podacima dobijenim&nbsp;difrakcijom rendgenskog zračenja visoke&nbsp;rezolucije. Teorijska istraživanja bazirana su na&nbsp;teorijskim strukturnim faktorima dobijenim&nbsp;primenom programa CRYSAL09 polazeći od&nbsp;geometrije&nbsp; molekula određene nakon multipol&nbsp;utačnjavanja eksperimentalno dobijene gustine&nbsp;naelektrisanja. Za opisivanje eksperimentalne i&nbsp;teorijske ukupne elektronske gustine kori&scaron;ćen je&nbsp;Hansen-Coppens-ov multipol-model.&nbsp; Takođe je&nbsp;urađena i topolo&scaron;ka analizahemijskih veza i&nbsp;interakcija &nbsp;i ispitivana su elektrostatička svojstva&nbsp;atoma sumpora.</p><p>Analizom eksperimentalne gustine&nbsp;naelektrisanja kristalnih struktura MeTSC i TSC4&nbsp;uočeno je da deformaciona gustina slobodnih&nbsp;elektronskih parova S atoma ima &nbsp;oblik torusa, da&nbsp;je unutar njega raspodela elektronske gustine&nbsp;nehomogena i da položaj samog torusa može biti&nbsp;ortogonalan (SalTSC) ili pod uglom (MeTSC,&nbsp;<br />TSC4).&nbsp; Na osnovu raspodele deformacione&nbsp;gustine i elektrostatičkog potencijala, kao &nbsp;i na&nbsp;osnovu topolo&scaron;ke analize ukupne eksperimentalne&nbsp;gustine naelektrisanja &rho;_ktv&nbsp; i njenog Laplasijana &nabla;²&rho;_ktv zaključeno je da atom sumpora ima izrazitu&nbsp;fleksibilnost i sposobnost da prilagodi svoju&nbsp;elektronsku gustinu slobodnih elektronskih &nbsp;parova&nbsp;prostornom rasporedu donornih grupa koje&nbsp;učestvuju u interakcijama sa S akceptorom.&nbsp; U&nbsp;kristalnim strukturama MeTSC i TSC4 utvrđeno&nbsp;je da S atom istovremeno gradi četiri, odnosno&nbsp;prosečno &scaron;est međumolekulskih interakcija.</p><p>U cilju upotpunjavanja eksperimentalnih&nbsp;rezultata analizirana je teorijski dobijena gustina&nbsp;naelektrisanja oba molekula, a zatim su ispitivane&nbsp;karakteristike sumpora kao akceptora i to u&nbsp;sistemima različite složensti polazeći od&nbsp;izolovanih monomera, preko izdvojenih dimer do&nbsp;kristalnogokruženja. Ovom analizom je utvrđeno&nbsp;da se simultanim angažovanjem S atoma u vi&scaron;e&nbsp;interakcija ne umanjuje njegova akceptorska&nbsp;sposobnost.</p><p>Vodonične vezekoje uključuju S akceptor su&nbsp;ispitivane sa aspekta &nbsp;energijskih svojstava dimera&nbsp;koji suprisutni u MeTSCi TSC4, kaoi u dodatno&nbsp;konstruisanim&nbsp; sistemima&nbsp; MeTSC/MeOH&nbsp; i&nbsp;aceton/MeOH. Energijske&nbsp; karakteristike&nbsp; su&nbsp;proučavane u pogledu elektrostatičke energije&nbsp;interakcije (E_es) i kohezione energije(E_coh). Za&nbsp;<br />dva odabrana&nbsp; MeTSC/MeOH i aceton/MeOH&nbsp;sistema je primenjena metoda &nbsp;kuplovanih klastera&nbsp;kao&scaron;to&nbsp; je&nbsp;<em> ab initio</em>&nbsp; CCSD(T)&nbsp; metod.&nbsp; Za&nbsp;MeTSC/MeOH sistem je &nbsp;urađena potpuna&nbsp;optimizacija i za tako dobijenu ravnotežnu&nbsp;geometriju je izračunata energija sistema&nbsp;∆E_CCSD(T),CBS.</p> / <p>In this dissertation the analysis of the experimental and theoretically obtained electron &nbsp;density of two derivatives of thiosemicarbasides, 4-methyl-3-thiosemicarbaside (MeTSC) and 4-methyl-3-thiosemikabazone 2-piridinformamide (TSC4) are presented.&nbsp; The analysis of experimentally obtained electron density is based on &nbsp;accurate X-ray diffraction data of high resolution. Theoretically calculated electron densities are obtained from periodic quantum mechanical calculation using CRYSTAL09 and the accurate structural parameters from high resolution X-ray&nbsp;experiment. For the description of the theoretical and experimental electron density the Hansen-Coppens multipol model was used. Further topological analysis of chemical bonds and interactions was performed in order to explain the electrostatic properties of sulfur.</p><p>In this work it has been observed that in the experimentally obtained electron density of the MeTSC and TSC4 crystal structures, the deformational electron density of sulfur free electron pairs forms a toroidal shape. Further, this torus is not homogeneously filled but shows pronounced local accumulations and its position can be either orthogonal (like in SalTSC) or tilted (MeTSC, TSC4). Based on the distribution of the&nbsp;deformational electron&nbsp; density and electrostatic potential, as well as the topological analysis of the total electron density &rho;_ktv and its Laplasian &nabla;²&rho;_ktv&nbsp;it can be concluded that the S atom has a remarkable flexibility and ability to adapt his deformation electron density of free electron pairs into toruses corresponding to the position of donor groups surrounding him. In the crystal structures of MeTSC and TSC4 it was determined that the S atom participates in four and six interactions, respectively.</p><p>In order to supplement&nbsp; the experimentally obtained results a theoretically calculated electron density of both molecules (MeTSC and TSC4) was performed and the properties of the S atom as a hydrogen acceptor have been studied. The analysis was &nbsp;performed on systems of various complexity, starting with isolated monomers, then on &nbsp;dimers and up to the whole crystal packing. From this work it has been concluded that &nbsp;the acceptor capabilities of the S atom are not diminished with the increasing number &nbsp;of interactions.&nbsp;&nbsp;&nbsp;&nbsp;</p><p>The hydrogen bonding involving thioureido S&nbsp;acceptor is also investigated in terms of the energetic properties of the MeTSC and TSC4 dimers existing in the crystal structure, and additional MeTSC/MeOH and acetone/MeOH systems. Energetic features were thoroughly studied through electrostatic interactions energies (E_es) and &nbsp;cohesive energies (E_coh). For two selected MeTSC/MeOH and acetone/MeOH systems an ab initio approach&nbsp;employing the coupled-cluster singles and doubles augmented by a perturbational correction for connected triple excitations (CCSD(T)) method were applied. Finaly, for MeTSC/MeOH system full geometry optimization was &nbsp;performed and for resulting equilibrium geometry the energy of the system (∆E_CCSD(T),CBS) was calculated.</p>

La méthode d'intégration produit a été proposée pour résoudre des équations linéaires de Fredholm de deuxième espèce singulières dont la solution exacte est régulière, au moins continue. Dans ce travail on adapte cette méthode à des équations dont la solution est juste intégrable. On étudie également son extension au cas non linéaire posé dans l'espace des fonctions intégrables. Ensuite, on propose une autre manière de mettre en oeuvre la méthode d'intégration produit : on commence par linéariser l'équation par une méthode de type Newton puis on discrétise les itérations de Newton par la méthode d'intégration produit / The product integration method has been proposed for solving singular linear Fredholm equations of the second kind whose exact solution is smooth, at least continuous. In this work, we adapt this method to the case where the solution is only integrable. We also study the nonlinear case in the space of integrable functions. Then, we propose a new version of the method in the nonlinear framework : we first linearize the eqaution by a Newton type method and then discretize the Newton iterations by the product integration method

This dissertation develops adaptive hp-Finite Element (FE) technology and a parallel sparse direct solver enabling the accurate modeling of the absorption of Electro-Magnetic (EM) energy in the human head. With a large and growing number of cell phone users, the adverse health effects of EM fields have raised public concerns. Most research that attempts to explain the relationship between exposure to EM fields and its harmful effects on the human body identifies temperature changes due to the EM energy as the dominant source of possible harm. The research presented here focuses on determining the temperature distribution within the human body exposed to EM fields with an emphasis on the human head. Major challenges in accurately determining the temperature changes lie in the dependence of EM material properties on the temperature. This leads to a formulation that couples the BioHeat Transfer (BHT) and Maxwell equations. The mathematical model is formed by the time-harmonic Maxwell equations weakly coupled with the transient BHT equation. This choice of equations reflects the relevant time scales. With a mobile device operating at a single frequency, EM fields arrive at a steady-state in the micro-second range. The heat sources induced by EM fields produce a transient temperature field converging to a steady-state distribution on a time scale ranging from seconds to minutes; this necessitates the transient formulation. Since the EM material properties depend upon the temperature, the equations are fully coupled; however, the coupling is realized weakly due to the different time scales for Maxwell and BHT equations. The BHT equation is discretized in time with a time step reflecting the thermal scales. After multiple time steps, the temperature field is used to determine the EM material properties and the time-harmonic Maxwell equations are solved. The resulting heat sources are recalculated and the process continued. Due to the weak coupling of the problems, the corresponding numerical models are established separately. The BHT equation is discretized with H¹ conforming elements, and Maxwell equations are discretized with H(curl) conforming elements. The complexity of the human head geometry naturally leads to the use of tetrahedral elements, which are commonly employed by unstructured mesh generators. The EM domain, including the head and a radiating source, is terminated by a Perfectly Matched Layer (PML), which is discretized with prismatic elements. The use of high order elements of different shapes and discretization types has motivated the development of a general 3D hp-FE code. In this work, we present new generic data structures and algorithms to perform adaptive local refinements on a hybrid mesh composed of different shaped elements. A variety of isotropic and anisotropic refinements that preserve conformity of discretization are designed. The refinement algorithms support one- irregular meshes with the constrained approximation technique. The algorithms are experimentally proven to be deadlock free. A second contribution of this dissertation lies with a new parallel sparse direct solver that targets linear systems arising from hp-FE methods. The new solver interfaces to the hierarchy of a locally refined mesh to build an elimination ordering for the factorization that reflects the h-refinements. By following mesh refinements, not only the computation of element matrices but also their factorization is restricted to new elements and their ancestors. The solver is parallelized by exploiting two-level task parallelism: tasks are first generated from a parallel post-order tree traversal on the assembly tree; next, those tasks are further refined by using algorithms-by-blocks to gain fine-grained parallelism. The resulting fine-grained tasks are asynchronously executed after their dependencies are analyzed. This approach effectively reduces scheduling overhead and increases flexibility to handle irregular tasks. The solver outperforms the conventional general sparse direct solver for a class of problems formulated by high order FEs. Finally, numerical results for a 3D coupled BHT with Maxwell equations are presented. The solutions of this Maxwell code have been verified using the analytic Mie series solutions. Starting with simple spherical geometry, parametric studies are conducted on realistic head models for a typical frequency band (900 MHz) of mobile phones. / text

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Cette thèse étudie des problèmes liés aux treillis des sous-groupes quantiques et la caractérisationdes actions ergodiques et des états idempotents d’un groupe quantique compact.Elle consiste en 3 parties. La première partie présente des résultats préliminaires sur lesgroupes quantiques localement compacts, les sous-groupes quantiques normaux ainsi queles actions ergodiques et les états idempotents. La seconde partie étudie l’analogue quantiquede la règle de modularité de Dedekind et de l’analogue quantique des théorèmesd’isomorphisme de Noether ainsi que leur conséquences comme le théorème de raffinementde Schreier, et le théorème Jordan-Hölder. Cette partie s’inspire du travail de recherche deShuzhouWang sur l’analogue quantique du troisième théorème d’isomorphisme de Noetherpour les groupes quantiques compacts ainsi que le travail récent de Kasprzak, Khosraviet Soltan sur l’analogue quantique du premier théorème d’isomorphisme de Noether pourles groupes quantiques localement compacts. Dans la troisième partie, nous caractérisonsles états idempotents du groupe quantique compact O−1(2) en s’appuyant sur la caractérisationde ses actions ergodiques plongeables. Cette troisième partie est dans la lignedes travaux fait par Franz, Skalski et Tomatsu pour les groupes quantiques compactsUq(2), SUq(2) et SOq(3). Nous classifions au préalable les actions ergodiques et les actionsergodiques plongeables du groupe quantique compact O−1(2).Les travaux présentés dans cette thèse se basent sur deux articles de l’auteur et al.Le premier s’intitule “Fundamental isomorphism theorems for quantum groups” et a étéaccepté pour publication dans Expositionae Mathematicae et le second est intitulé “Ergodicactions and idempotent states of O−1(2)” et est en cours de finalisation pour être soumis. / This thesis studies problems linked to the lattice of quantum subgroups and characterizationof ergodic actions and idempotent states of a compact quantum group. It consistsof three parts. The first part present some preliminary results about locally compactquantum groups, normal quantum subgroups, ergodic actions and idempotent states. Thesecond part studies the quantum analog of Dedekind’s modularity law, Noether’s isomorphismtheorem and their consequences as the Schreier refinement theorem and theJordan-Hölder theorem. This part completes the work of Shuzhou WANG on the quantumanalog of the third isomorphism theorem for compact quantum group and the recentwork of Kasprzak, Khosravi and Soltan on the quantum analog of the first Noether isomorphismtheorem for locally compact quantum groups. In the third part, we characterizeidempotent states of the compact quantum group O−1(2) relying on the characterizationof embeddable ergodic actions. This third part is in the sequence of the seminal works ofFranz, Skalski and Tomatsu for the compact quantum groups Uq(2), SUq(2) and SOq(3).We classify in advance the ergodic actions and embeddable ergodic actions of the compactquantum group O−1(2).This thesis is based on two papers of the author and al. The first one is entitled“Fundamental isomorphism theorems for quantum groups” which have been accepted forpublication in Expositionae Mathematicae and the second one is entitled “Ergodic actionsand idempotent states of O−1(2)” and is being finalized for submission.

Cette thèse est une contribution à la théorie économique sur trois aspects: la dynamique de prix dans les marchés financiers avec asymétrie d’information, la mise à jour des croyances et les raffinements d'équilibre dans les jeux de signaux, et l'introduction de l'ambiguïté dans la théorie du prix limite. Dans le chapitre 2, nous formalisons un jeu d'échange à somme nulle entre un secteur mieux informé et un autre qui l'est moins, pour déterminer de façon endogène, la dynamique du prix sous-jacent. Dans ce modèle, joueur 1 est informé de la conjoncture (L) mais est incertain de la croyance de joueur 2, car ce dernier est seulement informé à travers un message (M) qui est lié à cette conjoncture. Si L et M sont indépendants, alors le processus de prix sera une Martingale Continue à Variation Maximale (CMMV) et joueur 1 peut disposer de cet avantage informationnel. Par contre, si L et M ne sont pas indépendants, joueur 1 ne révèlera pas son information pendant le processus, et il ne bénéficiera donc pas de son avantage en matière d'information. Dans le chapitre 3, je propose une définition de l'équilibre de Test d'hypothèse (HTE) pour des jeux de signaux généraux, avec des joueurs non-Bayésiens qui sont soumis à une règle de mise à jour selon le modèle de vérification d'hypothèse caractérisé par Ortoleva (2012). Un HTE peut être différent d'un équilibre séquentiel de Nash en raison d'une incohérence dynamique. Par contre, dans le cas où joueur 2 traite seulement un message à probabilité nulle comme nouvelle inespérée, un HTE est un raffinement d'équilibre séquentiel de Nash et survit au critère intuitif dans les jeux de signaux généraux mais pas inversement. Nous fournissons un théorème d'existence qui couvre une vaste classe de jeux de signaux qui sont souvent étudiés en économie. Dans le chapitre 4, j'introduis l’ambiguïté dans un modèle d'organisation industrielle classique, dans lequel l'entreprise déjà établie est soit informée de la vraie nature de la demande agrégée, soit soumise à une incertitude mesurable classique sur la conjoncture, tandis qu'un éventuel nouvel arrivant fait face à une incertitude a la Knight (ambiguïté) concernant cette conjoncture. Je caractérise les conditions sou lesquelles le prix limite émerge en équilibre, et par conséquent l'ambigüité diminue la probabilité d'entrée. L'analyse du bien-être montre que le prix limite est plus nocif dans un marché où la demande escomptée est plus élevée que dans un autre où celle-ci est moindre. / This thesis contributes to the economic theory literature in three aspects: price dynamics in financial markets with asymmetric information belief updating and equilibrium refinements in signaling games, and introducing ambiguity in limit pricing theory. In chapter 2, we formulate a zero-sum trading game between a better informed sector and a less 1nformed sector to endogenously determine the underlying price dynamics. In this model, player 1 is informed of the state (L) but is uncertain about player 2's belief about the state, because player 2 is informed through some message (M) related to the state. If L and M are independent, then the price proces s will be a Continuous Martingale of Maximal Variation (CMMV), and player 1 can benefit from his informational advantage. However, if L and M are not independent, player 1 will not reveal his information during the trading process, therefore, he does not benefit from his informational advantage. In chapter 3, I propose a definition of Hypothesis Testing Equilibrium (HTE) for general signaling games with non-Bayesian players nested, by an updating rule according to the Hypothesis Testing model characterized by Ortoleva (2012). An HTE may differ from a sequential Nash equilibrium because of dynamic inconsistency. However, in the case in which player 2 only treats a zero-probability message as an unexpected news, an HTE is a refinement of sequential Nash equilibrium and survives the intuitive Critenon in general signaling games but not vice versa. We provide an existence theorem covering a broad class of signaling games often studied in economics. In chapter 4, I introduce ambiguity in a standard industry organization model, in which the established firm is either informed of the true state of aggregate demand or is under classical measurable uncertainty about the state, while the potential entrant is under Knightian uncertainty (ambiguity) about the state. I characterize the conditions under which limit pricing emerges in equilibria, and thus ambiguity decreases the probability of entry. Welfare analysis shows that limit pricing is more harmful in a market with higher expected demand than in a market with lower expected demand.