In recent years, the discontinuous Galerkin (DG) method has been successfully applied to solving hyperbolic conservation laws. Due to its compactness, high order accuracy, and versatility, the DG method has been extensively applied to convection-diffusion problems. In this dissertation, a numerical package, texttt{PHORCE}, is introduced to solve a number of convection-diffusion problems in neutral fluids and plasmas. Unstructured grids are used in order to randomize grid errors, which is especially important for complex geometries. texttt{PHORCE} is written in texttt{C++} and fully parallelized using the texttt{MPI} library. Memory optimization has been considered in this work to achieve improved efficiency. DG algorithms for hyperbolic terms are well studied. However, an accurate and efficient diffusion solver still constitutes ongoing research, especially for a nodal representation of the discontinuous Galerkin (NDG) method. An affine reconstructed discontinuous Galerkin (aRDG) algorithm is developed in this work to solve the diffusive operator using an unstructured NDG method. Unlike other reconstructed/recovery algorithms, all computations can be performed on a reference domain, which promotes efficiency in computation and storage. In addition, to the best of the authors' knowledge, this is the first practical guideline that has been proposed for applying the reconstruction algorithm on a nodal discontinuous Galerkin method. TVB type and WENO type limiters are also studied to deal with numerical oscillations in regions with strong physical gradients in state variables. A high-order positivity-preserving limiter is also extended in this work to prevent negative densities and pressure. A new interface tracking method, mass of fluid (MOF), along with its bound limiter has been proposed in this work to compute the mass fractions of different fluids over time. Hydrodynamic models, such as Euler and Navier-Stokes equations, and plasma models, such as ideal-magnetohydrodynamics (MHD) and two-fluid plasma equations, are studied and benchmarked with various applications using this DG framework. Numerical computations of Rayleigh-Taylor instability growth with experimentally relevant parameters are performed using hydrodynamic and MHD models on planar and radially converging domains. Discussions of the suppression mechanisms of Rayleigh-Taylor instabilities due to magnetic fields, viscosity, resistivity, and thermal conductivity are also included. This work was partially supported by the US Department of Energy under grant number DE-SC0016515. The author acknowledges Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this work. URL: http://www.arc.vt.edu / Doctor of Philosophy / High-energy density (HED) plasma science is an important area in studying astrophysical phenomena as well as laboratory phenomena such as those applicable to inertial confinement fusion (ICF). ICF plasmas undergo radial compression, with an aim of achieving fusion ignition, and are subject to a number of hydrodynamic instabilities that can significantly alter the implosion and prevent sufficient fusion reactions. An understanding of these instabilities and their mitigation mechanisms is important allow for a stable implosion in ICF experiments. This work aims to provide a high order accurate and robust numerical framework that can be used to study these instabilities through simulations. The first half of this work aims to provide a detailed description of the numerical framework, texttt{PHORCE}. texttt{PHORCE} is a high order numerical package that can be used in solving convection-diffusion problems in neutral fluids and plasmas. Outstanding challenges exist in simulating high energy density (HED) hydrodynamics, where very large gradients exist in density, temperature, and transport coefficients (such as viscosity), and numerical instabilities arise from these region if there is no intervention. These instabilities may lead to inaccurate results or cause simulations to fail, especially for high-order numerical methods. Substantial work has been done in texttt{PHORCE} to improve its robustness in dealing with numerical instabilities. This includes the implementation and design of several high-order limiters. An novel algorithm is also proposed in this work to solve the diffusion term accurately and efficiently, which further enriches the physics that texttt{PHORCE} can investigate. The second half of this work involves rigorous benchmarks and experimentally relevant simulations of hydrodynamic instabilities. Both advection and diffusion solvers are well verified through convergence studies. Hydrodynamic and plasma models implemented are also validated against results in existing literature. Rayleigh-Taylor instability growth with experimentally relevant parameters are performed on both planar and radially converging domains. Although this work is motivated by physics in HED hydrodynamics, the emphasis is placed on numerical models that are generally applicable across a wide variety of fields and disciplines.

The availability of high performance computing clusters has allowed scientists and engineers to study more challenging problems. However, new algorithms need to be developed to take advantage of the new computer architecture (in particular, distributed memory clusters). Since the solution of linear systems still demands most of the computational effort in many problems (such as the approximation of partial differential equation models) iterative methods and, in particular, efficient preconditioners need to be developed. In this study, we consider application of incomplete LU (ILU) preconditioners for finite element models to partial differential equations. Since finite elements lead to large, sparse systems, reordering the node numbers can have a substantial influence on the effectiveness of these preconditioners. We study two implementations of the ILU preconditioner: a stucturebased method and a threshold-based method. The main emphasis of the thesis is to test a variety of breadth-first ordering strategies on the convergence properties of the preconditioned systems. These include conventional Cuthill-McKee (CM) and Reverse Cuthill-McKee (RCM) orderings as well as strategies related to the physical distance between nodes and post-processing methods based on relative sizes of associated matrix entries. Although the success of these methods were problem dependent, a number of tendencies emerged from which we could make recommendations. Finally, we perform a preliminary study of the multi-processor case and observe the importance of partitioning quality and the parallel ILU reordering strategy. / Master of Science

Dans cette thèse, nous étudions les fonctions propres de l'opérateur de Laplace-Beltrami - ou simplement laplacien - sur une surface fermée, c'est-à-dire une variété riemannienne lisse, compacte et sans bord de dimension 2. Ces fonctions propres satisfont l'équation $\Delta_g \phi_\lambda + \lambda \phi_\lambda = 0$ et les valeurs propres forment une suite infinie. L'ensemble nodal d'une fonction propre du laplacien est celui de ses zéros et est d'intérêt depuis les expériences de plaques vibrantes de Chladni qui remontent au début du 19ème siècle et, plus récemment, dans le contexte de la mécanique quantique. La taille de cet ensemble nodal a été largement étudiée ces dernières années, notamment par Donnelly et Fefferman, Colding et Minicozzi, Hezari et Sogge, Mangoubi ainsi que Sogge et Zelditch. L'étude de la croissance de fonctions propres n'est pas en reste, avec entre autres les récents travaux de Donnelly et Fefferman, Sogge, Toth et Zelditch, pour ne nommer que ceux-là. Notre thèse s'inscrit dans la foulée du travail de Nazarov, Polterovich et Sodin et relie les propriétés de croissance des fonctions propres avec la taille de leur ensemble nodal dans l'asymptotique $\lambda \nearrow \infty$. Pour ce faire, nous considérons d'abord les exposants de croissance, qui mesurent la croissance locale de fonctions propres et qui sont obtenus à partir de la norme uniforme de celles-ci. Nous construisons ensuite la croissance locale moyenne d'une fonction propre en calculant la moyenne sur toute la surface de ces exposants de croissance, définis sur de petits disques de rayon comparable à la longueur d'onde. Nous montrons alors que la taille de l'ensemble nodal est contrôlée par le produit de cette croissance locale moyenne et de la fréquence $\sqrt{\lambda}$. Ce résultat permet une reformulation centrée sur les fonctions propres de la célèbre conjecture de Yau, qui prévoit que la mesure de l'ensemble nodal croît au rythme de la fréquence. Notre travail renforce également l'intuition répandue selon laquelle une fonction propre se comporte comme un polynôme de degré $\sqrt{\lambda}$. Nous généralisons ensuite nos résultats pour des exposants de croissance construits à partir de normes $L^q$. Nous sommes également amenés à étudier les fonctions appartenant au noyau d'opérateurs de Schrödinger avec petit potentiel dans le plan. Pour de telles fonctions, nous obtenons deux résultats qui relient croissance et taille de l'ensemble nodal. / In this thesis, we study eigenfunctions of the Laplace-Beltrami operator - or simply the Laplacian - on a closed surface, i.e. a two dimensional smooth, compact Riemannian manifold without boundary. These functions satisfy $\Delta_g \phi_\lambda + \lambda \phi_\lambda = 0$ and the eigenvalues form an infinite sequence. The nodal set of a Laplace eigenfunction is its zero set and is of interest since the vibrating plates experiments of Chladni at the beginning of the 19th century as well as, more recently, in the context of quantum mechanics. The size of the nodal sets has been largely studied recently, notably by Donnelly and Fefferman, Colding and Minicozzi, Hezari and Sogge, Mangoubi as well as Sogge and Zelditch.The study of eigenfunction growth is also an active topic, with the recent works of Donnelly and Fefferman, Sogge, Toth and Zelditch to name only a few. Our thesis follows the work of Nazarov, Polterovich and Sodin and links growth and nodal sets of eigenfunctions in the asymptotic $\lambda \nearrow \infty$. To do so, we first consider growth exponents, which measure the local growth of eigenfunctions via their uniform norm. The average local growth of an eigenfunction is built by averaging growth exponents defined on small disks of wavelength like radius over the whole surface. We show that the size of the nodal set is controlled by the product of this average local growth with the frequency $\sqrt{\lambda}$. This result allows a function theoretical reformulation of the famous conjecture of Yau, which predicts that the size of the nodal set grows like the frequency. Our work also strengthens the common intuition that an eigenfunction behaves in many ways like a polynomial of degree $\sqrt{\lambda}$. We then generalize our results to growth exponents built upon $L^q$ norms. We are also led to study functions belonging to the kernel of Schrödinger operators with small potential in the plane. For such functions, we obtain two results linking growth and size of nodal sets.

L'objectif de ce mémoire est de démontrer certaines propriétés géométriques des fonctions propres de l'oscillateur harmonique quantique. Nous étudierons les domaines nodaux, c'est-à-dire les composantes connexes du complément de l'ensemble nodal. Supposons que les valeurs propres ont été ordonnées en ordre croissant. Selon un théorème fondamental dû à Courant, une fonction propre associée à la $n$-ième valeur propre ne peut avoir plus de $n$ domaines nodaux. Ce résultat a été prouvé initialement pour le laplacien de Dirichlet sur un domaine borné mais il est aussi vrai pour l'oscillateur harmonique quantique isotrope. Le théorème a été amélioré par Pleijel en 1956 pour le laplacien de Dirichlet. En effet, on peut donner un résultat asymptotique plus fort pour le nombre de domaines nodaux lorsque les valeurs propres tendent vers l'infini. Dans ce mémoire, nous prouvons un résultat du même type pour l'oscillateur harmonique quantique isotrope. Pour ce faire, nous utiliserons une combinaison d'outils classiques de la géométrie spectrale (dont certains ont été utilisés dans la preuve originale de Pleijel) et de plusieurs nouvelles idées, notamment l'application de certaines techniques tirées de la géométrie algébrique et l'étude des domaines nodaux non-bornés. / The aim of this thesis is to explore the geometric properties of eigenfunctions of the isotropic quantum harmonic oscillator. We focus on studying the nodal domains, which are the connected components of the complement of the nodal (i.e. zero) set of an eigenfunction. Assume that the eigenvalues are listed in an increasing order. According to a fundamental theorem due to Courant, an eigenfunction corresponding to the $n$-th eigenvalue has at most $n$ nodal domains. This result has been originally proved for the Dirichlet eigenvalue problem on a bounded Euclidean domain, but it also holds for the eigenfunctions of a quantum harmonic oscillator. Courant's theorem was refined by Pleijel in 1956, who proved a more precise result on the asymptotic behaviour of the number of nodal domains of the Dirichlet eigenfunctions on bounded domains as the eigenvalues tend to infinity. In the thesis we prove a similar result in the case of the isotropic quantum harmonic oscillator. To do so, we use a combination of classical tools from spectral geometry (some of which were used in Pleijel’s original argument) with a number of new ideas, which include applications of techniques from algebraic geometry and the study of unbounded nodal domains.

Les maladies rares sont définies en Europe par une prévalence inférieure à 1/2 000 cas et représentent plus de 7000 entités différentes dont 80% sont d’origine génétique. La majorité est de début pédiatrique. J’ai réalisé l’étude de cas familiaux rares avec récurrence dans la fratrie de cardiopathies congénitales avec hétérotaxie (défaut de latéralité gauche/droite) d’une part, et de mort subite cardiaque inexpliquée chez le nourrisson ou en période néonatale d’autre part. La stratégie d’identification de gène par séquençage de l’exome au sein de ces familles dans l’hypothèse d’une transmission autosomique récessive a permis d’identifier trois gènes et d’en étudier deux sur le plan fonctionnel dans différents modèles : 1) Perte de fonction de MMP21 et malformations cardiaques congénitales par anomalie de latéralité embryonnaire. MMP21 code pour une métallopeptidase matricielle dont nous démontrons le rôle très spécifique au niveau du nœud embryonnaire sur un modèle poisson zèbre et souris. Ceci ouvre de nouvelles perspectives dans la compréhension des mécanismes moléculaires qui sous-tendent la mise en place de l’asymétrie gauche/droite chez la plupart des vertébrés. De manière intéressante, alors que tous les mammifères ont le cœur latéralisé à gauche, tous n’ont pas un gène MMP21 codant. Il existe donc plusieurs voies de signalisation de l’asymétrie gauche/droite chez les vertébrés. 2) Mutations hypomorphes de PPA2 et mort subite cardiaque chez le nourrisson. PPA2 code pour une pyrophosphatase mitochondriale et les données chez la levure ont montré que la fonction de cette enzyme était essentielle au fonctionnement mitochondrial. Nous décrivons une nouvelle présentation clinique de maladie mitochondriale responsable de décès par arrêt cardiaque inattendu chez le nourrisson. 3) Perte de fonction de PLCD3 et cardiomyopathie foudroyante par apoptose et nécrose diffuse des cardiomyocytes en période néonatale. Ce résultat nécessite encore d’être confirmé par l’identification d’autres cas mais la fonction de la protéine et des données chez la souris sont des arguments majeurs en faveur de la causalité du gène. Au total, ces travaux sont déterminants à la fois sur le plan clinique dans le cadre du conseil génétique pour les familles concernées et sur le plan fondamental en éclairant les mécanismes biologiques de mise en place de l’axe gauche-droit au cours du développement embryonnaire avec MMP21, sur le rôle essentiel de PPA2 dans la mitochondrie et sur celui de PLCD3 dans la survie des cardiomyocytes en postnatal. / Rare diseases are defined in Europe by a prevalence of less than 1/2,000 individuals and represent more than 7,000 different diseases of which 80% are genetic. Most have a paediatric onset. My project involved the study of rare cardiac disorders in familial cases with recurrence in siblings, focusing on congenital heart disease in the context of heterotaxia (laterality defects) and sudden unexpected death due to cardiac arrest in infancy and the neonatal period. Whole exome sequencing was used as a tool for disease gene discovery in these families with the hypothesis of autosomal recessive inheritance. This strategy led to the identification of 3 novel disease genes. I performed functional validation for two of these genes in different models, confirming their involvement in each disease. 1) Loss of function of MMP21 and cardiac malformations due to left-right patterning defects during embryonic development. MMP21 encodes a metallopeptidase for which I demonstrated a highly specialized role in the generation of left-right asymmetry at the node using zebrafish. This gives new insight into the molecular mechanisms at the origin of left-right asymmetry in vertebrates. Interestingly, all mammals have a left-sided heart, but some species have lost the Mmp21 gene, indicating that there are different pathways leading to left-right determination in vertebrates. 2) Hypomorphic mutations in PPA2 cause sudden cardiac arrest in infants. PPA2 is a nuclear gene encoding the mitochondrial pyrophosphatase and using a yeast model we showed that this enzyme is essential for the mitochondrial energy transducing system and biogenesis. I described a novel clinical spectrum for a mitochondrial disease responsible for unexpected cardiac arrest in infancy. 3) PLCD3 loss of function and fatal cardiomyopathy by cardiomyocyte apoptosis and necrosis in neonates. Exome sequencing in one familial case with 2 siblings presenting fatal cardiomyopathy led to the identification of compound heterozygous mutations in PLCD3, a gene previously implicated in a similar pathology in a mouse model. Identification of further cases with mutations in this gene will be needed in order to confirm the role of PLCD3 in the disease. In total, these studies are crucial from a clinical point of view for the genetic counseling of the affected families and they contribute to the elucidation of biological mechanisms of embryonic development and left-right determination (MMP21), mitochondrial function (PPA2) and post-natal cardiomyocyte survival (PLCD3).

France Télécom possède des armoires de télécommunication dont la puissance est limitée à cause de la dissipation thermique des équipements actifs qui entraîne une augmentation de leur température interne. La puissance des équipements limite le nombre de clients qu'il est possible de connecter aux services des réseaux à hauts débits. En plus de cette contrainte, les armoires sont soumises à des effets liés au climat (ensoleillement) qui peuvent être sévères et difficiles à maîtriser. Ceci nécessite l’intégration de systèmes de refroidissement permettant de maintenir la température des composants en dessous de la limite imposée (55°C). C’est dans cet objectif que ce travail de thèse a été mené au sein du laboratoire FEMTO-ST en collaboration avec le service R&D de France Télécom à Lannion. Le refroidissement par changement de phase est favorisé pour maintenir la température de fonctionnement du système stable et pour être utilisé dans les systèmes à haute densité de puissance. Les boucles diphasiques sont des systèmes de refroidissement pour le contrôle thermique et fonctionnent passivement sans pompage mécanique du fluide caloporteur. Après une étude bibliographique sur les boucles de refroidissement diphasiques et leurs applications, on a constaté que les boucles thermosiphons sont particulièrement adaptées aux applications où le faible coût, l'efficacité énergétique et la fiabilité d’entretien sont souhaités. Cette étude a été conduite en suivant un cahier de charge proposé par France Télécom qui consiste à : (i) développer un modèle numérique permettant de modéliser les transferts échangés entre l’armoire de télécommunication et le milieu ambiant, (ii) mener une étude expérimentale en vue de concevoir une boucle thermosiphon pour le refroidissement d’armoires de télécommunication.Le mémoire de cette thèse montre la limitation des systèmes de refroidissement classiques utilisant des écoulements d’air en convection forcée ou autre fluides sans changement de phase. Un modèle numérique est développé afin de permettre la prédiction des températures à l’entrée des boitiers chauffants pour différentes conditions climatiques. Le choix est porté sur l’utilisation d’une modélisation par réseau nodal. La modélisation est effectuée en tridimensionnel et en régime transitoire. Nous avons également modélisé le rayonnement solaire auquel est soumise l’armoire de télécommunication. Le modèle développé a été validé en effectuant une comparaison entre les résultats issus de la modélisation et ceux obtenus à partir des expériences menées au laboratoire et à la plateforme CLIMA chez France Télécom. Les essais sont effectués en régime transitoire en imposant une puissance électrique et en faisant varier la température ambiante ou la densité de flux thermique solaire. L’ensemble des résultats obtenus ont permis de constituer une base de données. Le deuxième objectif fixé dans le cadre de ce travail de thèse est la conception d’un système de refroidissement sous forme d’une boucle thermosiphon. La contrainte principale qui a guidée cette conception était le fait que la boucle doit refroidir l’armoire et assurer une température d’air à l’entrée des équipements inférieure à la limite imposée par la norme ETSI. Ceci nous a mené à concevoir un prototype de boucle thermosiphon dont la puissance thermique qu’il doit dissiper est imposée. On a montré que ce prototype permet de dissiper des puissances thermiques allant jusqu’à 470 W en utilisant une petite charge de npentane. Nous avons effectué des essais sur le refroidissement du prototype d’armoire de télécommunication en utilisant la boucle thermosiphon légèrement modifiée. On montre que les performances thermiques obtenues en utilisant un mode de refroidissement en boucle thermosiphon sont meilleures. Les boucles thermosiphons semblent intéressantes pour un refroidissement passif de matériels déployés dans un réseau de télécommunication... / France Telecom owns telecommunication cabinets whose power is limited because of the heat dissipation of active devices which leads to increased internal temperature. Power equipment limits the number of clients that can connect to networks services with high data rates. In addition to this constraint, the cabinets are subject to climate-related impacts (sunlight) that can be severe and difficult to master. This requires the integration of cooling systems to maintain the temperature of components below the limit (55 ° C). It is with this aim that this work was conducted in the laboratory Femto-ST in collaboration with the R & D department of France Telecom in Lannion.Cooling the phase change is promoted to maintain the operating temperature of the stable and system for use in systems with high power density. The loops are two-phase cooling systems for thermal control and operate passively without mechanical pumping of the coolant.After a literature review on two-phase cooling loops and their applications, it was found that the thermosyphon loops are particularly suitable for applications where low cost, energy efficiency and reliability maintenance are desired. This study was conducted by following a set of specifications proposed by France Telecom which involves: (i) develop a numerical model to model transfers exchanged between the cabinet and the telecommunications environment, (ii) conduct an experimental study to design a thermosyphon loop for cooling telecommunication cabinets.The memory of this thesis shows the limitation of conventional cooling systems using air flow forced convection or other fluids without phase change. A numerical model is developed to enable the prediction of temperatures at the inlet of heated enclosures for different climatic conditions. The choice is focused on the use of a nodal network modeling. The modeling is done by three-dimensional and transient. We also modeled the solar radiation, which applies to the telecommunications closet. The developed model was validated by comparison between the results of modeling and those obtained from experiments in the laboratory and platform CLIMA at France Telecom. The tests are performed by imposing transient electrical power and varying the temperature or heat flux density solar. All the results obtained allowed to establish a database.The second goal as part of this thesis is the design of a cooling system as a thermosyphon loop. The main constraint has guided this design was that the loop needs to cool the cabinet and provide air temperature at the inlet of the equipment below the limit imposed by the ETSI. This led us to design a prototype of thermosyphon loop with a heat output that must be dissipated is imposed. We showed that this prototype is used to dissipate the heat ratings up to 470 W using a small load of npentane.We conducted tests on the prototype cooling telecommunication cabinet using slightly modified thermosyphon loop. We show that the thermal performance obtained by using a cooling mode loop thermosyphon are better. Thermosyphon loops seem interesting for passive cooling of equipment deployed in a telecommunications network. Indeed, being able to use an air conditioning system independent and requires no energy should be promoted in a reduction of overall energy consumption.

Orientador: José Roberto Sanches Mantovani / Resumo: Neste trabalho propõe-se o desenvolvimento de uma ferramenta computacional para o planejamento da operação de curto prazo de sistemas de distribuição com geração distribuída (GD) considerando uma abordagem probabilística. Uma modelagem sequencial formulada com base na perspectiva das companhias de distribuição (DisCos) é proposta. As decisões operacionais da DisCo são inicialmente otimizadas no estágio de operação day-ahead (DA) e, então, na operação real-time (RT). A operação DA visa maximizar a diferença entre a energia vendida aos consumidores e as compras realizadas no mercado de eletricidade atacadista e da GD, ou seja, os lucros. No estágio RT, busca-se a minimização dos ajustes necessários para acomodar os desvios das quantidades previstas no planejamento DA. Modelos de cargas dependentes de tensão e restrições relacionadas à demanda são explicitamente formulados. A rede é representada através de equações de fluxo de potência AC completo. Propõe-se ainda a incorporação de um mecanismo para precificação nodal de potência reativa. Os modelos resultantes são caracterizados como programas de otimização matemática multiperíodo de grande porte não lineares e não convexos com variáveis contínuas e discretas. Um algoritmo pseudodinâmico baseado na meta-heurística Busca Tabu (BT) é proposto para solução do problema resultante de maneira eficaz, sem linearizações. Os resultados obtidos para alimentadores de distribuição de 69 e 135 barras ilustram a eficiência da metodologia pro... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor

Submitted by MARCEL CHUMA CERBANTES null (marcel.chuma@gmail.com) on 2017-04-16T19:19:19Z No. of bitstreams: 1 phd_dissertation_marcel_chuma_cerbantes.pdf: 2683152 bytes, checksum: bb2fddaeed33cb6c6ee2f902e3624178 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-04-18T17:43:20Z (GMT) No. of bitstreams: 1 chumacerbantes_m_dr_ilha.pdf: 2683152 bytes, checksum: bb2fddaeed33cb6c6ee2f902e3624178 (MD5) / Made available in DSpace on 2017-04-18T17:43:20Z (GMT). No. of bitstreams: 1 chumacerbantes_m_dr_ilha.pdf: 2683152 bytes, checksum: bb2fddaeed33cb6c6ee2f902e3624178 (MD5) Previous issue date: 2017-03-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho propõe-se o desenvolvimento de uma ferramenta computacional para o planejamento da operação de curto prazo de sistemas de distribuição com geração distribuída (GD) considerando uma abordagem probabilística. Uma modelagem sequencial formulada com base na perspectiva das companhias de distribuição (DisCos) é proposta. As decisões operacionais da DisCo são inicialmente otimizadas no estágio de operação day-ahead (DA) e, então, na operação real-time (RT). A operação DA visa maximizar a diferença entre a energia vendida aos consumidores e as compras realizadas no mercado de eletricidade atacadista e da GD, ou seja, os lucros. No estágio RT, busca-se a minimização dos ajustes necessários para acomodar os desvios das quantidades previstas no planejamento DA. Modelos de cargas dependentes de tensão e restrições relacionadas à demanda são explicitamente formulados. A rede é representada através de equações de fluxo de potência AC completo. Propõe-se ainda a incorporação de um mecanismo para precificação nodal de potência reativa. Os modelos resultantes são caracterizados como programas de otimização matemática multiperíodo de grande porte não lineares e não convexos com variáveis contínuas e discretas. Um algoritmo pseudodinâmico baseado na meta-heurística Busca Tabu (BT) é proposto para solução do problema resultante de maneira eficaz, sem linearizações. Os resultados obtidos para alimentadores de distribuição de 69 e 135 barras ilustram a eficiência da metodologia proposta. / In this work, we propose a solution solution procedure for the short-term operation planning of distribution systems with distributed generation (DG) considering a probabilistic approach. A sequential formulation based on the distribution company's (DisCo's) perspective is presented. The DisCo’s operational decisions are optimized first in a day-ahead (DA) operation stage, and then in real-time (RT). The DA operation maximizes the difference between the energy sold to customers and the purchases from the wholesale electricity market and distributed generators. In RT, the objective is to minimize the adjustments that are required to accommodate deviations from forecasted quantities. The voltage-sensitiveness of power load injections and demand related constraints are explicitly formulated. The network is modeled using full ac power flow equations. In addition, a nodal-based reactive power pricing mechanism is proposed to be incorporated in the formulation. The resulting models are characterized as large-scale non-linear non-convex mathematical programs with continuous and discrete variables. A pseudo-dynamic Tabu Search (TS)-based solution algorithm is used to tackle the problem in an effective manner, without linearizations. Numerical results from the 69-bus and 135-bus distribution test feeders illustrate the performance of the proposed approach. / FAPESP: 2013/13070-7 / FAPESP: 2014/22314-0

Ce mémoire de thèse traite de l’analyse, l’intensification et l’optimisation du transfert thermique convectif dans les échangeurs à plaques et ailettes à pas décalés utilisés notamment dans le domaine automobile comme refroidisseurs d’air de suralimentation. Deux approches complémentaires sont abordées dans cette étude : des simulations numériques visant à l’analyse fine locale des caractéristiques de l’écoulement et des mécanismes de transfert, et une modélisation de type nodale permettant une caractérisation globale des performances thermo-aérauliques. Sur la gamme de Reynolds considérée différentes modélisations de la turbulence sont mises en œuvre et comparées. Ainsi des simulations aux grandes échelles (LES) permettent de qualifier des simulations de type RANS classiquement utilisées jusque-là : de fortes différences tant au niveau structuration de l’écoulement qu’au niveau performances globales sont ainsi mises en évidence selon le régime d’écoulement considéré. La mise au point d’un modèle nodal est ensuite abordée dans le but de mener des optimisations de géométries d’échangeurs non-conventionnels à pas décalés. Les différents scénarii d’optimisation considérés montrent l’intérêt de cette approche autorisant l’évaluation d’un nombre élevé de configurations géométriques. Dans une dernière partie une nouvelle géométrie innovante permettant de générer des tourbillons longitudinaux sur ce type d’ailettes est proposée et étudiée. / This thesis deals with the analysis, intensification and optimization of convective heat transfer in offset strip fins (OSF) heat exchangers used, for example, in the automotive field as water-cooled charge air coolers. Two complementary approaches are carried out in this study: CFD simulations to perform local fine analysis of the flow characteristics and transfer mechanisms, and a nodal type modeling allowing calculation of global aerothermal performance. Over the range of Reynolds numbers considered, different turbulence modeling approaches are implemented and compared: Large Eddy Simulations (LES) and RANS simulations which are usually used. The qualification of the RANS models shows that strong differences, both in the flow structure and at the overall performance evaluation level, may beobserved, depending on the flow regime considered. Then the development of a nodal model is presented. It aims at carrying out rapid optimization of geometries of unconventional OSF heat exchangers. The various optimization scenarios considered show the interest of this approach allowing the evaluation of a large number of geometric configurations. In a last part, an innovative new geometry that generates longitudinal vortices on this type of fins is proposed and studied.

In den letzten Jahren führte die Verbindung zwischen Topologie und kondensierter Materie zur Entdeckung vieler interessanter und exotischer elektronischer Effekte. Während sich die Forschung anfangs auf elektronische Systeme mit einer Bandlücke wie den topologischen Isolator konzentrierte, erhalten in letzter Zeit topologische Halbmetalle viel Aufmerksamkeit. Das bekannteste Beispiel sind Weyl-Halbmetalle, die an beliebigen Punkten in der Brillouin-Zone lineare Kreuzungen von nicht entarteten Bändern aufweist. An diese Punkte ist eine spezielle Quantenzahl namens Chiralität gebunden, die die Existenz von Weyl-Punktpaaren erzwingt. Diese Paare sind topologisch geschützt und wirken als Quellen und Senken der Berry-Krümmung, einem topologischen Feld im reziproken Raum. Diese Berry-Krümmung steht in direktem Zusammenhang mit dem anomalen Hall-Effekt, der die Entstehung einer Querspannung aus einem Längsstrom in einem magnetischen Material beschreibt. Analog existiert auch der anomale Nernst-Effekt, bei dem der longitudinale Strom durch einen thermischen Gradienten ersetzt wird. Dieser Effekt ermöglicht die Umwandlung von Wärme in elektrische Energie und ist zudem stark an die Berry-Krümmung gebunden. In dieser Arbeit werden die anomalen Transporteffekte zunächst in fundamentalen Modellsystemen untersucht. Hier wird eine Kombination aus analytischen und numerischen Methoden verwendet, um Quantisierungen sowohl des Hall- und Nernst- als auch des thermischen Hall-Effekts in zweidimensionalen Systemen mit und ohne externen Magnetfeldern zu zeigen. Eine Erweiterung in drei Dimensionen zeigt eine Quasi-Quantisierung, bei der die Leitfähigkeiten Werte der jeweiligen zweidimensionalen Quanten skaliert durch charakteristische Wellenvektoren annehmen. Im nächsten Schritt werden verschiedene Mechanismen zur Erzeugung starker Berry-Krümmung und damit großer anomaler Hall- und Nernst-Effekte sowohl in Modellsystemen als auch in realen Materialien untersucht. Dies ermöglicht die Identifizierung und Isolierung vielversprechender Effekte in den einfachen Modellen, in denen wichtige Merkmale untersucht werden können. Die Ergebnisse können dann auf die realen Materialien übertragen werden, wo die jeweiligen Effekte erkennbar sind. Hier werden sowohl Weyl-Punkte als auch Knotenlinien in Kombination mit Magnetismus als vielversprechende Eigenschaften identifiziert und Materialrealisierungen in der Klasse der Heusler-Verbindungen vorgeschlagen. Diese Verbindungen sind eine sehr vielseitige Materialklasse, in der unter anderem auch magnetische topologische Metalle zu finden sind. Um ein tieferes Verständnis der anomalen Transporteffekte zu erhalten sowie Faustregeln für Hochleistungsverbindungen abzuleiten, wurde eine High-Throughput-Rechnung von magnetisch-kubischen Voll-Heusler-Verbindungen durchgeführt. Diese Berechnung zeigt die Bedeutung von Spiegelebenen in magnetischen Materialien für große anomale Hall- und Nernst-Effekte und zeigt, dass einige der Heusler-Verbindungen die höchsten bisher berichteten Literaturwerte bei diesen Effekten übertreffen. Auch andere interessante Effekte im Zusammenhang mit Weyl-Punkten werden untersucht. Beim bekannten Weyl-Halbmetall NbP weisen die Weyl-Punkte aufgrund der hohen Symmetrie des Kristalls eine hohe Entartung auf. Die Anwendung von einachsigem Zug reduziert jedoch die Symmetrien und hebt damit die Entartungen auf. Eine theoretische Untersuchung zeigt, dass die Weyl-Punkte bei einachsigem Zug energetisch verschoben werden und, was noch wichtiger ist, dass sie bei realistischen Werten das Fermi-Niveau durchschreiten. Dies macht NbP zu einer vielversprechenden Plattform, um die Weyl-Physik weiter zu untersuchen. Die theoretischen Ergebnisse werden mit experimentellen Messungen von Shubnikov-de-Haas-Oszillationen unter einachsigem Zug kombiniert und es wird eine gute Übereinstimmung mit den theoretischen Ergebnissen gefunden. Als erster Schritt in Richtung neuer Berechnungsmethoden wird die Idee eines Weyl-Halbmetall-basierten Chiralitätsfilters für Elektronen untersucht. An der Grenzfläche zweier Weyl-Halbmetalle kann in Abhängigkeit von den genauen Weyl-Punktparametern nur eine Chiralität übertragen werden. Hier wird ein effektives geometrisches Modell erstellt und zur Untersuchung realer Materialgrenzflächen eingesetzt. Während im Allgemeinen eine Filterwirkung möglich erscheint, zeigten die untersuchten Materialien keine geeignete Kombination. Hier können weitere Studien mit Fokus auf magnetische Weyl-Halbmetalle oder Multifold-Fermion-Materialien durchgeführt werden.:List of publications Preface 1. Theoretical background 1.1. Berry curvature and Weyl semimetals 1.1.1. From the adiabatic evolution to the Berry phase 1.1.2. From the Berry phase to the Berry curvature 1.1.3. Topological phases of condensed matter 1.1.4. Weyl semimetals 1.1.5. Dirac semimetals 1.1.6. Nodal line semimetals 1.2. Density-functional theory 1.2.1. Born-Oppenheimer approximation 1.2.2. Hohenberg-Kohn theorems 1.2.3. Kohn-Sham formalism 1.2.4. Exchange-correlation functional 1.2.5. Pseudopotentials 1.2.6. Basis functions 1.2.7. VASP 1.3. Tight-binding Hamiltonian from Wannier functions 1.3.1. Wannier functions 1.3.2. Constructing Wannier functions from DFT 1.3.3. Generating a Wannier tight-binding Hamiltonian 1.3.4. Necessity of the tight-binding Hamiltonian 1.4. Linear response theory 1.4.1. General introduction to linear response 1.4.2. Anomalous Hall effect 1.4.3. Anomalous Nernst effect 1.4.4. Anomalous thermal Hall effect 1.4.5. Common features of anomalous transport effects 1.4.6. Symmetry considerations for Berry curvature related transport effects 1.4.7. Magneto-optic Kerr effect 1.4.8. About the efficiency of the calculations 2. (Quasi-)Quantization in the Hall, thermal Hall, and Nernst effects 2.1. Quantization with an external magnetic field 2.1.1. Two-dimensional case 2.1.2. Three-dimensional case 2.2. Quantization without an external field 2.2.1. Two-dimensional case 2.2.2. Three-dimensional case . 2.3. A remark on the spin Hall effect 2.4. A remark on the quasi-quantization of the three-dimensional conductivities 2.5. Conclusions 3. Understanding anomalous transport 3.1. Anomalous transport without a net magnetic moment 3.1.1. Toy model 3.1.2. Ti2MnAl and related compounds 3.2. Large Berry curvature enhancement from nodal line gapping 3.2.1. Toy model 3.2.2. Fe2MnP and related compounds 3.2.3. Co2MnGa 3.3. Topological features away from the Fermi level and the anomalous Nernst effect 3.3.1. Toy model . 3.3.2. Co2FeGe and Co2FeSn 3.4. Conclusions 4. Heusler database calculation 4.1. Workflow 4.2. Importance of mirror planes 4.3. The right valence electron count 4.4. Correlation between anomalous Hall and Nernst effects 4.5. Selected special compounds 4.6. Conclusions 5. NbP under uniaxial strain 5.1. NbP and its symmetries 5.2. The influence of strain on the electronic structure 5.2.1. Shifting of the Weyl points 5.2.2. Splitting of the Fermi surfaces 5.3. Comparison with experimental results 5.4. Conclusions 6. A tunable chirality filter 6.1. Concept 6.2. Geometrical simplification and expansion for more Weyl points 6.3. Material selection 6.3.1. Workflow 6.3.2. Results for NbP and TaAs 6.3.3. Results for Ag2Se and Ag2S 6.4. Conclusions and perspective . Summary and outlook A. Numerical tricks A.1. Hamiltonian setup at several k points at once A.2. Precalculating prefactors B. Derivation of the conductivity (quasi-)quanta B.1. Two dimensions B.1.1. General formula and necessary approximations B.1.2. Useful integrals B.1.4. Quantized thermal Hall effect B.1.5. Quantized Nernst effect B.1.6. Flat bands and the Nernst effect B.2. Three dimensions B.2.1. General formula B.2.2. Three-dimensional electron gas B.2.3. Three-dimensional Weyl semimetal C. Heusler database tables D. Details on the NbP strain calculations E. Details on the geometrical matching procedure References List of abbreviations List of Figures List of Tables Acknowledgements Eigenständigkeitserklärung / In recent years, the connection between topology and condensed matter resulted in the discovery of many interesting and exotic electronic effects. While in the beginning, the research was focused on gapped electronic systems like the topological insulator, more recently, topological semimetals are getting a lot of attention. The most well-known example is the Weyl semimetal, which hosts linear crossings of non-degenerate bands at arbitrary points in the Brillouin zone. Tied to these points there is a special quantum number called chirality, which enforces the existence of Weyl point pairs. These pairs are topologically protected and act as sources and sinks of the Berry curvature, a topological field in reciprocal space. This Berry curvature is directly connected to the anomalous Hall effect, which describes the emergence of a transverse voltage from a longitudinal current in a magnetic material. Analogously, there also exists the anomalous Nernst effect, where the longitudinal current is replaced by a thermal gradient. This effect allows for the conversion of heat into electrical energy and is also strongly tied to the Berry curvature. In this work, the anomalous transport effects are at first studied in fundamental model systems. Here, a combination of analytical and numerical methods is used to reveal quantizations in both the Hall, the Nernst, and the thermal Hall effects in two-dimensional systems with and without external magnetic fields. An expansion into three dimensions shows a quasi-quantization, where the conductivities take values of the respective two-dimensional quanta scaled by characteristic wavevectors. In the next step, several mechanisms for the generation of strong Berry curvature and thus large anomalous Hall and Nernst effects are studied in both model systems and real materials. This allows for the identification and isolation of promising effects in the simple models, where important features can be studied. The results can then be applied to the real materials, where the respective effects can be recognized. Here, both Weyl points and nodal lines in combination with magnetism are identified as promising features and material realizations are proposed in the class of Heusler compounds. These compounds are a very versatile class of materials, where among others also magnetic topological metals can be found. To get a deeper understanding of the anomalous transport effects as well as to derive guidelines for high-performance compounds, a high-throughput calculation of magnetic cubic full Heusler compounds was carried out. This calculation reveals the importance of mirror planes in magnetic materials for large anomalous Hall and Nernst effects and shows that some of the Heusler compounds outperform the highest so-far reported literature values in these effects. Also other interesting effects related to Weyl points are investigated. In the well-known Weyl semimetal NbP, the Weyl points have a high degeneracy due to the high symmetry of the crystal. However, the application of uniaxial strain reduces the symmetries and therefore lifts the degeneracies. A theoretical investigation shows, that the Weyl points are moved in energy under uniaxial strain and, more importantly, that at reasonable strain values they cross the Fermi level. This renders NbP a promising platform to further study Weyl physics. The theoretical results are combined with experimental measurements of Shubnikov-de Haas oscillations under uniaxial strain and a good agreement with the theoretical results is found. As a first step in the direction of new ways of computation, an idea of a Weyl semimetal based chirality filter for electrons is investigated. At the interface of two Weyl semimetals, depending on the exact Weyl point parameters, it is possible to transmit only one chirality. Here, an effective geometrical model is established and employed for the investigation of real material interfaces. While in general, a filtering effect seems possible, the investigated materials did not show any suitable combination. Here, further studies can be made with the focus on either magnetic Weyl semimetals of multifold-fermion materials.:List of publications Preface 1. Theoretical background 1.1. Berry curvature and Weyl semimetals 1.1.1. From the adiabatic evolution to the Berry phase 1.1.2. From the Berry phase to the Berry curvature 1.1.3. Topological phases of condensed matter 1.1.4. Weyl semimetals 1.1.5. Dirac semimetals 1.1.6. Nodal line semimetals 1.2. Density-functional theory 1.2.1. Born-Oppenheimer approximation 1.2.2. Hohenberg-Kohn theorems 1.2.3. Kohn-Sham formalism 1.2.4. Exchange-correlation functional 1.2.5. Pseudopotentials 1.2.6. Basis functions 1.2.7. VASP 1.3. Tight-binding Hamiltonian from Wannier functions 1.3.1. Wannier functions 1.3.2. Constructing Wannier functions from DFT 1.3.3. Generating a Wannier tight-binding Hamiltonian 1.3.4. Necessity of the tight-binding Hamiltonian 1.4. Linear response theory 1.4.1. General introduction to linear response 1.4.2. Anomalous Hall effect 1.4.3. Anomalous Nernst effect 1.4.4. Anomalous thermal Hall effect 1.4.5. Common features of anomalous transport effects 1.4.6. Symmetry considerations for Berry curvature related transport effects 1.4.7. Magneto-optic Kerr effect 1.4.8. About the efficiency of the calculations 2. (Quasi-)Quantization in the Hall, thermal Hall, and Nernst effects 2.1. Quantization with an external magnetic field 2.1.1. Two-dimensional case 2.1.2. Three-dimensional case 2.2. Quantization without an external field 2.2.1. Two-dimensional case 2.2.2. Three-dimensional case . 2.3. A remark on the spin Hall effect 2.4. A remark on the quasi-quantization of the three-dimensional conductivities 2.5. Conclusions 3. Understanding anomalous transport 3.1. Anomalous transport without a net magnetic moment 3.1.1. Toy model 3.1.2. Ti2MnAl and related compounds 3.2. Large Berry curvature enhancement from nodal line gapping 3.2.1. Toy model 3.2.2. Fe2MnP and related compounds 3.2.3. Co2MnGa 3.3. Topological features away from the Fermi level and the anomalous Nernst effect 3.3.1. Toy model . 3.3.2. Co2FeGe and Co2FeSn 3.4. Conclusions 4. Heusler database calculation 4.1. Workflow 4.2. Importance of mirror planes 4.3. The right valence electron count 4.4. Correlation between anomalous Hall and Nernst effects 4.5. Selected special compounds 4.6. Conclusions 5. NbP under uniaxial strain 5.1. NbP and its symmetries 5.2. The influence of strain on the electronic structure 5.2.1. Shifting of the Weyl points 5.2.2. Splitting of the Fermi surfaces 5.3. Comparison with experimental results 5.4. Conclusions 6. A tunable chirality filter 6.1. Concept 6.2. Geometrical simplification and expansion for more Weyl points 6.3. Material selection 6.3.1. Workflow 6.3.2. Results for NbP and TaAs 6.3.3. Results for Ag2Se and Ag2S 6.4. Conclusions and perspective . Summary and outlook A. Numerical tricks A.1. Hamiltonian setup at several k points at once A.2. Precalculating prefactors B. Derivation of the conductivity (quasi-)quanta B.1. Two dimensions B.1.1. General formula and necessary approximations B.1.2. Useful integrals B.1.4. Quantized thermal Hall effect B.1.5. Quantized Nernst effect B.1.6. Flat bands and the Nernst effect B.2. Three dimensions B.2.1. General formula B.2.2. Three-dimensional electron gas B.2.3. Three-dimensional Weyl semimetal C. Heusler database tables D. Details on the NbP strain calculations E. Details on the geometrical matching procedure References List of abbreviations List of Figures List of Tables Acknowledgements Eigenständigkeitserklärung