Systems of Differential-Algebraic Equations Encountered in the Numerical Modeling of High-Temperature Superconductors

RÉSUMÉ L’objectif principal de ce mémoire est d’étudier les systèmes d’Équations Différentielles et Algébriques (EDA) qui apparaissent lors de la modélisation numérique d'équipements électriques supraconducteurs à Haute Température Critique (HTC). Ces systèmes d’équations ainsi que le comportement non linéaire des matériaux supraconducteurs sont possiblement responsables des difficultés rencontrées lors de simulations numériques de ces appareillages. Dans la littérature, beaucoup d’attention a été portée aux problèmes liés à la nonlinéarité des matériaux, mais, au meilleur de notre connaissance, aucune étude des systèmes d'équations différentielles et algébriques n'a été répertoriée. Ainsi, il est essentiel d’approfondir nos connaissances à leur sujet dans le cadre de la simulation numérique d’équipements supraconducteurs à HTC. Dans ce document, nous présentons une revue de la théorie des supraconducteurs de type I et de type II. Cette revue nous permet de bien comprendre le potentiel des supraconducteurs à HTC en électrotechnique. Ces derniers se démarquent notamment par leur capacité à opérer en fort champ et par leur température critique élevée. Nous discutons que la simulation numérique d’équipements supraconducteurs permet de les optimiser à faible coût en améliorant certaines caractéristiques d'opération tel que les pertes en courant alternatif. Ensuite, nous présentons les principaux modèles physiques utilisés pour modéliser les équipements supraconducteurs. Plus précisément, nous décrivons un modèle 1-D utilisant une formulation en flux magnétique. Ce modèle est relativement simple mais son équation aux dérivées partielles possède une solution analytique connue. Ce modèle est donc utile pour s’introduire à la discipline et vérifier une méthode numérique implémentée dans un code. Puis, nous présentons des modèles 2-D et 3-D qui utilisent la formulation en champs magnétique. Ces modèles sont une meilleure approximation de la réalité que le modèle 1-D. Ils peuvent notamment considérer des matériaux de différentes natures et géométries. Cependant, ils sont plus complexes. Finalement, nous présentons un modèle qui utilise la formulation en potentiel vecteur magnétique sous sa forme intégrale. Ce modèle peut tenir compte d’effets 3-D en utilisant la bonne définition pour l’intégrale du potentiel vecteur. Nous présentons deux méthodes numériques pour discrétiser les équations des modèles physiques dans l'espace, soit la Méthode des Éléments Finis (MEF) et la Méthode Semi-Analytique (MSA). Nous montrons que la MEF est utilisée pour discrétiser une forme faible des équations à l'aide d'une approximation discrète de la solution sur un maillage constitué d'éléments. Nous introduisons deux types d'éléments: les éléments finis nodaux et les éléments d'arrête (edge elements). Finalement, nous présentons brièvement la MSA qui est utilisée pour discrétiser dans l'espace les équations de la formulation en potentiel vecteur magnétique sous sa forme intégrale. Cette méthode consiste à trouver une expression analytique reliant des champs et des potentiels aux termes sources sur une certaine discrétisation puis à résoudre le système d'équations résultant numériquement. Il s’agit d’une méthode à collocation par point.----------ABSTRACT The main objective of this thesis is to study the systems of Differential-Algebraic Equations (DAE) encountered in the numerical modeling of electrical devices made of High-Temperature Superconductors (HTS). These systems of equations and the nonlinear behavior of HTS are possibly responsible for the difficulties faced when simulating HTS devices. In the literature, much attention is paid to the issues related to the nonlinearity of HTS but, to the best of our knowledge, there is no in-depth study of the problems related to the systems of DAE. Consequently, it is essential to improve our knowledge about those systems, in the context of HTS modeling. In this document, we review the theory of type I and type II superconductors. This review is useful to understand the potential of HTS materials for power engineering applications. Their potential is mainly due to their ability to operate in strong fields and their high critical temperatures. We discuss that numerical simulation can be used to optimize HTS devices at low cost, by improving some quantities of interest, e.g.\ AC losses. We introduce the main physical models used for the modeling of HTS devices. We describe a 1-D model based on a magnetic flux density formulation. This model is relatively simple but has a known analytical solution for a nonlinear HTS problem. It is convenient to use as an introduction to the methodology used in this thesis and to verify a code. Then, we introduce a 2-D and a 3-D model based on a magnetic field formulation. These models provide a better representation of the reality than the 1-D model. They can consider materials with different properties and complex geometries. However, they are more complicated than the 1-D model. Finally, we review a model based on a magnetic vector potential formulation in integral form (A-V). This model can take into account 3-D effects by using the proper definition for the magnetic vector potential integral. We summarize two numerical methods to discretize the equations of the physical models in space, i.e.\ the Finite Element Method (FEM) and the Semi-Analytical Method (SAM). The FEM is used to discretize a weak form of the equations of the models using a discrete approximation of the solution over a mesh made of geometrical elements. We introduce two types of elements: nodal elements and edge elements. Then, we review the SAM, a numerical method used to discretize the equations of the magnetic vector potential formulation in integral form. It is a collocation method. We introduce systems of DAE. These systems of equations are obtained after discretizing the equations of the physical models in space. We discuss that the mathematical structure of a system of DAE can be described by a notion called the index. The index is the number of derivation required for a system of DAE to become a system of Ordinary Differential Equations (ODEs). We note that systems of DAE of index 2 in Hessenberg form are recurrent in variational problems. Subsequently, we discuss three strategies to discretize systems of DAE in time, i.e.\ direct discretization, reduction of the index and reformulation into semi-explicit form. The direct discretization strategy consists in applying directly an implicit time integration scheme to a system of DAE without reducing its index. In most cases, this yields a system of nonlinear equations. The reduction of index consists in reducing the index of the system of DAE and then reassess its structure. Systems of DAE of index 0 can be reformulated into a semi-explicit form and then discretized using an explicit method. We introduce two time transient solvers that use the direct discretization strategy, i.e. Differential-Algebraic System SoLver (DASSL) and Implicit Differential-Algebraic Solver (IDAS)

Développement d'une cellule de conductivité hydraulique permettant d'évaluer l'anisotropie des tills compactés du nord québécois

Les tills compactés sont largement utilisés comme noyau des barrages en remblai dans le Nord québécois. La mise en place en différentes couches successives laisse présager un rapport d’anisotropie (rK) de la perméabilité différent de l’unité. Différents montages expérimentaux sont disponibles dans la littérature pour évaluer l’anisotropie de la conductivité hydraulique sur plusieurs types de sols. Toutefois, ces méthodes présentent deux principaux désavantages : i) le rapport d’anisotropie est évalué sur deux échantillons distincts et ii) la procédure expérimentale peut potentiellement remanier l’échantillon par des manipulations hasardeuses. Dans l’objectif d’améliorer la caractérisation du rapport d’anisotropie des tills compactés, un nouveau perméamètre cubique a été conçu. Cette nouvelle cellule permet de quantifier le paramètre rK dans le domaine saturé ou quasi-saturé, et ce sans démanteler la cellule. Successivement, une percolation verticale et une horizontale sont effectuées sur un même échantillon. Une procédure spéciale a été développée afin de limiter l’écoulement dans les pierres poreuses inactives, i.e. parallèles à l’écoulement. Une solution de gélatine bovine qui est solide à une température inférieure à 30°C est utilisée afin de sceller ces pierres inactives. De l’eau chaude à 60°C permet de chasser cette gélatine sans démanteler la cellule. Un nouvel essai de perméabilité peut ainsi être effectué sur le même échantillon, mais selon une autre direction. Le nouveau perméamètre et la procédure ont permis d’évaluer l’effet de la mise en place et de la teneur en pierre sur rK. Pour une analyse dans le domaine quasi-saturé, le rapport d’anisotropie varie de 3 à 7 pour une mise en place du côté sec de la courbe Proctor. Pour le côté humide, le rapport d’anisotropie est près de l’unité. Cependant, la procédure développée pour des conditions saturées devrait être utilisée pour confirmer ces résultats. En conclusion, un outil intéressant a été conçu pour quantifier le rapport d’anisotropie des tills compactés, une problématique importante pour l’analyse des barrages en remblai. Mots clés: perméabilité, anisotropie, perméamètre cubique, tills compactés, barrage en remblaiCompacted tills are widely use as core of embankment dams in northern Quebec. It is expected that placement method in successive layers may result in a permeability anisotropy different from unity. Various experimental techniques are available to assess the permeability anisotropy for different types of materials. However, these methods have two principal disadvantages: i) the anisotropy rapport is evaluated on separate samples and ii) the experimental procedure could potentially disturb the sample by inappropriate manipulations. In order to improve the characterization of the anisotropy rapport of compacted tills, a new square cell was built. This new cell is able to quantify the anisotropy rapport in both states, saturated and almost saturated conditions. The permeability under vertical and horizontal flow is assessed on a single sample and a new experimental procedure has been developed to minimize preferential seepage paths along the porous stones. Injection of bovine gelatin is used to temporarily seal the porous stones perpendicular to the flow path (unused). Continuous hot water flow is used to extract the gelatin once the permeability testing is done. This new device and procedure have been successfully tested to evaluate the effect of placing method and stone content on the permeability anisotropy of compacted tills. For an analysis in quasi-saturated state, the anisotropy rapport is greater than 3 or 7 for a dry compaction. On the wet side, the anisotropy rapport is close to one. However, the procedure developed in the saturated condition should be used to confirm these results. In conclusion, this project has helped to build a useful tool to quantify the anisotropy rapport of tills, an important issue in the evaluation of embankment dams. Key words: permeability, anisotropy, square permeability cell, compacted tills, embankment dam

Far-and mid-infrared properties of carbon layers elaborated by plasma sputtering

International audienceThe far-and mid-infrared reflectivity spectra of two carbon layers deposited on pure (100) silicon substrates by DC magnetron sputtering were investigated at room temperature in the 10-5000 cm-1 wavenumber range. Their structural and textural features were also studied by combining Raman spectroscopy, Field Emission Scanning Electron Microscopy (FESEM), High Resolution Transmission Electron Microscopy (HRTEM), X-Ray Reflectivity (XRR) and Rutherford Backscattering Spectroscopy (RBS). The set of results was used to discuss afterwards the influence of the texture on the infrared properties at varying length scale. Thereby, the two layers were found to be heterogeneous as assessed by RBS, XRR and FESEM and their thicknesses had been measured by XRR and FESEM. The information on the structural organization and " crystallite " size was given by Raman spectroscopy. The influence of both the textural and structural parameters on the measured infrared reflectivity spectra was discussed. Finally, a methodology was proposed to recover the intrinsic index of refraction and the intrinsic index of absorption of each layer

Sib1, Sib2, and Sib3 proteins are required for ferrichrome-mediated cross-feeding interaction between Schizosaccharomyces pombe and Saccharomyces cerevisiae

Although Saccharomyces cerevisiae is unable to produce siderophores, this fungal organism can assimilate iron bound to the hydroxamate-type siderophore ferrichrome (Fc) produced and secreted by other microbes. Fc can enter S. cerevisiae cells via Arn1. Unlike S. cerevisiae, Schizosaccharomyces pombe synthesizes and secretes Fc. The sib1+ and sib2+ genes encode, respectively, a Fc synthetase and an ornithine-N5-oxygenase, which are required for Fc production. When both genes were expressed in S. pombe, cross-feeding experiments revealed that S. cerevisiae fet3Δ arn1-4Δ cells expressing Arn1 could grow in the vicinity of S. pombe under low-iron conditions. In contrast, deletion of sib1+ and sib2+ produced a defect in the ability of S. pombe to keep S. cerevisiae cells alive when Fc is used as the sole source of iron. Further analysis identified a gene designated sib3+ that encodes an N5-transacetylase required for Fc production in S. pombe. The sib3Δ mutant strain exhibited a severe growth defect in iron-poor media, and it was unable to promote Fc-dependent growth of S. cerevisiae cells. Microscopic analyses of S. pombe cells expressing a functional Sib3-GFP protein revealed that Sib3 was localized throughout the cells, with a proportion of Sib3 being colocalized with Sib1 and Sib2 within the cytosol. Collectively, these results describe the first example of a one-way cross-feeding interaction, with S. pombe providing Fc that enables S. cerevisiae to grow when Fc is used as the sole source of iron

Genome analysis of the necrotrophic fungal pathogens Sclerotinia sclerotiorum and Botrytis cinerea

Sclerotinia sclerotiorum and Botrytis cinerea are closely related necrotrophic plant pathogenic fungi notable for their wide host ranges and environmental persistence. These attributes have made these species models for understanding the complexity of necrotrophic, broad host-range pathogenicity. Despite their similarities, the two species differ in mating behaviour and the ability to produce asexual spores. We have sequenced the genomes of one strain of S. sclerotiorum and two strains of B. cinerea. The comparative analysis of these genomes relative to one another and to other sequenced fungal genomes is provided here. Their 38–39 Mb genomes include 11,860–14,270 predicted genes, which share 83% amino acid identity on average between the two species. We have mapped the S. sclerotiorum assembly to 16 chromosomes and found large-scale co-linearity with the B. cinerea genomes. Seven percent of the S. sclerotiorum genome comprises transposable elements compared t

Epistatic Roles of E2 Glycoprotein Mutations in Adaption of Chikungunya Virus to Aedes Albopictus and Ae. Aegypti Mosquitoes

Between 2005 and 2007 Chikungunya virus (CHIKV) caused its largest outbreak/epidemic in documented history. An unusual feature of this epidemic is the involvement of Ae. albopictus as a principal vector. Previously we have demonstrated that a single mutation E1-A226V significantly changed the ability of the virus to infect and be transmitted by this vector when expressed in the background of well characterized CHIKV strains LR2006 OPY1 and 37997. However, in the current study we demonstrate that introduction of the E1-A226V mutation into the background of an infectious clone derived from the Ag41855 strain (isolated in Uganda in 1982) does not significantly increase infectivity for Ae. albopictus. In order to elucidate the genetic determinants that affect CHIKV sensitivity to the E1-A226V mutation in Ae. albopictus, the genomes of the LR2006 OPY1 and Ag41855 strains were used for construction of chimeric viruses and viruses with a specific combination of point mutations at selected positions. Based upon the midgut infection rates of the derived viruses in Ae. albopictus and Ae. aegypti mosquitoes, a critical role of the mutations at positions E2-60 and E2-211 on vector infection was revealed. The E2-G60D mutation was an important determinant of CHIKV infectivity for both Ae. albopictus and Ae. aegypti, but only moderately modulated the effect of the E1-A226V mutation in Ae. albopictus. However, the effect of the E2-I211T mutation with respect to mosquito infections was much more specific, strongly modifying the effect of the E1-A226V mutation in Ae. albopictus. In contrast, CHIKV infectivity for Ae. aegypti was not influenced by the E2-1211T mutation. The occurrence of the E2-60G and E2-211I residues among CHIKV isolates was analyzed, revealing a high prevalence of E2-211I among strains belonging to the Eastern/Central/South African (ECSA) clade. This suggests that the E2-211I might be important for adaptation of CHIKV to some particular conditions prevalent in areas occupied by ECSA stains. These newly described determinants of CHIKV mosquito infectivity for Ae. albopictus and Ae. aegypti are of particular importance for studies aimed at the investigation of the detailed mechanisms of CHIKV adaptations to its vector species

The regulation and deregulation of Wnt signaling by PARK genes in health and disease

Wingless/Int (Wnt) signaling pathways are signal transduction mechanisms that have been widely studied in the field of embryogenesis. Recent work has established a critical role for these pathways in brain development, especially of midbrain dopaminergic neurones. However, the fundamental importance of Wnt signaling for the normal function of mature neurones in the adult central nervous system has also lately been demonstrated by an increasing number of studies. Parkinson's disease (PD) is the second most prevalent neurodegenerative disease worldwide and is currently incurable. This debilitating disease is characterized by the progressive loss of a subset of midbrain dopaminergic neurones in the substantia nigra leading to typical extrapyramidal motor symptoms. The aetiology of PD is poorly understood but work performed over the last two decades has identified a growing number of genetic defects that underlie this condition. Here we review a growing body of data connecting genes implicated in PD--most notably the PARK genes--with Wnt signaling. These observations provide clues to the normal function of these proteins in healthy neurones and suggest that deregulated Wnt signaling might be a frequent pathomechanism leading to PD. These observations have implications for the pathogenesis and treatment of neurodegenerative diseases in general

Genomic analysis of the necrotrophic fungal pathogens Sclerotinia sclerotiorum and Botrytis cinerea

This is the final version of the article. Available from the publisher via the DOI in this record.Sclerotinia sclerotiorum and Botrytis cinerea are closely related necrotrophic plant pathogenic fungi notable for their wide host ranges and environmental persistence. These attributes have made these species models for understanding the complexity of necrotrophic, broad host-range pathogenicity. Despite their similarities, the two species differ in mating behaviour and the ability to produce asexual spores. We have sequenced the genomes of one strain of S. sclerotiorum and two strains of B. cinerea. The comparative analysis of these genomes relative to one another and to other sequenced fungal genomes is provided here. Their 38-39 Mb genomes include 11,860-14,270 predicted genes, which share 83% amino acid identity on average between the two species. We have mapped the S. sclerotiorum assembly to 16 chromosomes and found large-scale co-linearity with the B. cinerea genomes. Seven percent of the S. sclerotiorum genome comprises transposable elements compared to <1% of B. cinerea. The arsenal of genes associated with necrotrophic processes is similar between the species, including genes involved in plant cell wall degradation and oxalic acid production. Analysis of secondary metabolism gene clusters revealed an expansion in number and diversity of B. cinerea-specific secondary metabolites relative to S. sclerotiorum. The potential diversity in secondary metabolism might be involved in adaptation to specific ecological niches. Comparative genome analysis revealed the basis of differing sexual mating compatibility systems between S. sclerotiorum and B. cinerea. The organization of the mating-type loci differs, and their structures provide evidence for the evolution of heterothallism from homothallism. These data shed light on the evolutionary and mechanistic bases of the genetically complex traits of necrotrophic pathogenicity and sexual mating. This resource should facilitate the functional studies designed to better understand what makes these fungi such successful and persistent pathogens of agronomic crops.The Sclerotinia sclerotiorum genome project was supported by the USDA Cooperative State Research, Education and Extension Service (USDA-NRI 2004). Sclerotinia sclerotiorum ESTs were funded by a grant to JA Rollins from USDA specific cooperative agreement 58-5442-4-281. The genome sequence of Botrytis cinerea strain T4 was funded by Genoscope, CEA, France. M Viaud was funded by the “Projet INRA Jeune-Equipe”. PM Coutinho and B Henrissat were funded by the ANR to project E-Tricel (grant ANR-07-BIOE-006). The CAZy database is funded in part by GIS-IBiSA. DM Soanes and NJ Talbot were partly funded by the UK Biotechnology and Biological Sciences Research Council. KM Plummer was partially funded by the New Zealand Bio-Protection Research Centre, http://bioprotection.org.nz/. BJ Howlett and A Sexton were partially funded by the Australian Grains Research and Development Corporation, www.grdc.com.au. L Kohn was partially funded by NSERC Discovery Grant (Natural Sciences and Engineering Research Council of Canada) - Grant number 458078. M Dickman was supported by the NSF grant MCB-092391 and BARD grant US-4041-07C. O Yarden was supported by BARD grant US-4041-07C. EG Danchin obtained financial support from the European Commission (STREP FungWall grant, contract: LSHB - CT- 2004 - 511952). A Botrytis Genome Workshop (Kaiserslautern, Germany) was supported by a grant from the German Science Foundation (DFG; HA1486) to M Hahn

The App-Runx1 Region Is Critical for Birth Defects and Electrocardiographic Dysfunctions Observed in a Down Syndrome Mouse Model

Down syndrome (DS) leads to complex phenotypes and is the main genetic cause of birth defects and heart diseases. The Ts65Dn DS mouse model is trisomic for the distal part of mouse chromosome 16 and displays similar features with post-natal lethality and cardiovascular defects. In order to better understand these defects, we defined electrocardiogram (ECG) with a precordial set-up, and we found conduction defects and modifications in wave shape, amplitudes, and durations in Ts65Dn mice. By using a genetic approach consisting of crossing Ts65Dn mice with Ms5Yah mice monosomic for the App-Runx1 genetic interval, we showed that the Ts65Dn viability and ECG were improved by this reduction of gene copy number. Whole-genome expression studies confirmed gene dosage effect in Ts65Dn, Ms5Yah, and Ts65Dn/Ms5Yah hearts and showed an overall perturbation of pathways connected to post-natal lethality (Coq7, Dyrk1a, F5, Gabpa, Hmgn1, Pde10a, Morc3, Slc5a3, and Vwf) and heart function (Tfb1m, Adam19, Slc8a1/Ncx1, and Rcan1). In addition cardiac connexins (Cx40, Cx43) and sodium channel sub-units (Scn5a, Scn1b, Scn10a) were found down-regulated in Ts65Dn atria with additional down-regulation of Cx40 in Ts65Dn ventricles and were likely contributing to conduction defects. All these data pinpoint new cardiac phenotypes in the Ts65Dn, mimicking aspects of human DS features and pathways altered in the mouse model. In addition they highlight the role of the App-Runx1 interval, including Sod1 and Tiam1, in the induction of post-natal lethality and of the cardiac conduction defects in Ts65Dn. These results might lead to new therapeutic strategies to improve the care of DS people