The numeric simulation of magnetic field of selected samples is made and resuled is compared with MRI measurement.

Numeric simulation welding of the turbine vane and rotor - master’s thesis is ordered by the Siemens Industrial Turbomachinery ltd. company. Simulation welding is done in program SYSWELD. Used welding materials are X22CrMoV12-1 (turbine vane), 30CrMoNiV5-11 (rotor), TOPCORE 838 B (additional material). These are temperature-resistant and fire-resistant welding materials. The SYSWELD program works on the principle of finite elements method. By SYSWELD is done the evaluation of temperature and stress fields and material structure after welding. Here is a part , which deals with computations of welding crevices.

The master´s diploma thesis elaborated as the master's degree M-STG Manufacturing Technology solves surfacing problems in the simulations of surfacing turbine rotors pinot pins. The work was seen as a preparatory work before the real surfacing. Topic commissioned by Siemens Industrial Turbomachinery Ltd. For welding plates test has been used the method of SAW and the base material was identical to turbine rotor material, X22CrMoV 12-1. Additional material was Fluxocord 42. Simulations were carried out in programs SYSWELD and Visual - WELD. The output of the simulation software are temperature and stress fields, material structures and creations of the CCT diagrams at the base material, filler material, and mixed area.

Thesis (M.Ed. (Mathematics Education)) -- University of Limpopo, 2019 / Alignment between content standards, instruction, assessment and learning materials assists in achieving the intended content in the classroom. The purpose of this study was to explore the alignment between Senior Phase Mathematics Content Standards (SPMCS) and numeric and geometric patterns’ workbook activities. The problem was that teachers sometimes use the Department of Basic Education’s workbooks interchangeably with textbooks, while their purpose is to supplement textbooks and provide worksheets for the learners. The alignment status of the Department of Basic Education (DBE) senior phase mathematics’ workbooks could not be found in the literature. Mixed methods research and document analysis were employed to explore the status of alignment between SPMCS and DBE workbook activities on Numeric and Geometric Patterns (NGP). This was aimed at highlighting the status of alignment in terms of the content structure and the alignment indices through the use of alignment model of Webb (1997) and of Porter (2002). The findings of this study revealed that the alignment between SPMCS and DBE workbook activities on NGP in terms of the categorical concurrence, depth of knowledge consistency and range of knowledge correspondence ranges from ‘acceptable’ to ‘full’ level of agreement. However, content beyond the scope of the content standards was found in Grade 7 and Grade 8 DBE workbook activities on NGP. The computed alignment indices for Grade 7, Grade 8 and Grade 9 range from moderate to strong alignment. Besides, weak and strong discrepancies were identified, which need to be addressed to improve the content structure of the DBE workbooks. This study recommends two alignment models to explore the alignment between educational components for comprehensive results and complementation. In addition, studies such as this should be conducted to enhance the quality in developing assessments in future. KEY CONCEPTS Alignment; assessment; content standards; learning materials; workbooks; numeric patterns and geometric patterns.

Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2019 / Alignment between content standards, instruction, assessment and learning materials assists in achieving the intended content in the classroom. The purpose of this study was to explore the alignment between Senior Phase Mathematics Content Standards (SPMCS) and numeric and geometric patterns’ workbook activities. The problem was that teachers sometimes use the Department of Basic Education’s workbooks interchangeably with textbooks, while their purpose is to supplement textbooks and provide worksheets for the learners. The alignment status of the Department of Basic Education (DBE) senior phase mathematics’ workbooks could not be found in the literature. Mixed methods research and document analysis were employed to explore the status of alignment between SPMCS and DBE workbook activities on Numeric and Geometric Patterns (NGP). This was aimed at highlighting the status of alignment in terms of the content structure and the alignment indices through the use of alignment model of Webb (1997) and of Porter (2002). The findings of this study revealed that the alignment between SPMCS and DBE workbook activities on NGP in terms of the categorical concurrence, depth of knowledge consistency and range of knowledge correspondence ranges from ‘acceptable’ to ‘full’ level of agreement. However, content beyond the scope of the content standards was found in Grade 7 and Grade 8 DBE workbook activities on NGP. The computed alignment indices for Grade 7, Grade 8 and Grade 9 range from moderate to strong alignment. Besides, weak and strong discrepancies were identified, which need to be addressed to improve the content structure of the DBE workbooks. This study recommends two alignment models to explore the alignment between educational components for comprehensive results and complementation. In addition, studies such as this should be conducted to enhance the quality in developing assessments in future. KEY CONCEPTS Alignment; assessment; content standards; learning materials; workbooks; numeric patterns and geometric patterns.

Användargränssnitt är en viktig del av kommunikationen mellan människor och maskin. Tidigare så kallat människa-datorinteraktion var baserad på användning av hålkort vid kommunikation med datorer, detta ändrades under andra halvan av 1900-talet. Där användningen av det grafiska användargränssnittet och kommandoradsgränssnitt började ta över. I dag finns det flera olika sorters användargränssnitt till flera olika maskiner och enheter, bland annat touch-gränssnittet som används till alla våra smarttelefon. Touch-gränssnittet ansågs som något lättanvänt och gav möjligheter till andra gränssnitt i detta fält. Ett av dem är det haptiska gränssnittet som ger användaren möjligheten att ändra data direkt i verkligheten, inte digitalt.I denna studie presenterar vi ett påtagligt gränssnitt (tangible interface) i form av ett interaktivt blixtlås. Syftet med denna studie är att använda en teknisk uppfinning med ett så kallat Tangible interface för att samla in data i form av en skala och sedan jämföra den med en numerisk skala representerad på papper. Ett experiment användes vid insamlingen av data, den var baserad på två sorters enkäter, det ena var pappersbaserad, medan den andra var baserad på det interaktiva blixtlåset. Hela experimentet avslutades med en utvärdering. Resultatet från experimentet visade att skillnaderna mellan en numerisk skala i form av papper inte skilde sig åt så mycket från det interaktiva blixtlåset. / User Interfaces are necessary for us when communicating with the machines. Early human-computer interactions were based upon the usage of puncture card to communicate with the computer, that later transformed into Graphical User Interfaces and Command Line Interfaces during the latter half of the 20th century. Today there are a lot of different kinds of interfaces for various types of devices, such as the touch interface for our smartphones. Due to the ease and possibilities of using the touch, further development in this area has been desired. An interface that gives the user the possibility to manipulate data in real life, is called a haptic interface. In this paper an interactive zipper is presented as a tangible interface that is part of the haptic interface. The study focuses on how a technological invention with a tangible interface can be used to gather feedbacks in the form of a numeric scale and how it compares to a numeric scale presented on paper. An experiment based on two questionnaires was used to gather the feedbacks, one was paper-based and the other based upon the interactive zipper, and it ended with an evaluation of the interactive zipper. The results showed that there are not any big differences between the numeric scale presented on paper compared to the interactive zipper.

As part of a continued research project for the Utah Water Research Laboratory and the State of Utah, a study of flow measurement devices is being conducted throughout the state. Initially the project included only measurement devices associated with high-risk dams, but has since been broadened to any measurement structure of interest for water users in the state. The physical dimensions, relative elevations, and flow accuracy were documented for each included device. After visiting sixteen sites, it was found that fourteen of the measuring devices had incorrect geometries. Of these fourteen, thirteen of them were originally Parshall flumes. A large percentage of Parshall flumes with geometry inaccuracies was also found from previous data collected for this project. One reoccurring issue was that the flumes had not been well maintained and had damage to the walls or floor. Some of these Parshall flumes did not have a diverging downstream section and are referred to as Montana flumes. In these cases, a standard Parshall rating curve was used to determine flow where it did not apply. Some of the flumes that were tested operated regularly under submerged conditions, and no adjustments were made for submergence. The objective of this research is to determine if Montana flumes (Parshall flumes without a diverging section) operate similarly to fully constructed Parshall flumes under both free-flow and submerged conditions. Laboratory tests were performed in the Utah Water Research Laboratory to determine corrections for submergence. Flow 3D, a computational fluid dynamics (CFD) software program, was also used to develop corrections for a submerged Montana flume. The laboratory results were compared to the computational fluid dynamics results. By using Flow 3D, a reliable numerical process was developed to determine the flow rate in a submerged Montana flume in an effort to expand the results to other seized flumes.

Cette thèse propose trois contributions aux preuves mathématiques assistées par ordinateur. On s'intéresse non seulement aux preuves reposant sur le calcul, mais aussi aux preuves formelles, qui sont àla fois produites et vérifiées à l'aide d'un logiciel appelé assistant à la preuve.Dans la première partie, nous illustrons le thème de l'expérimentation au service de la preuve en nous intéressant au problème de la complexité des algorithmes de multiplication matricielle. Cette question a historiquement été posée de manière de plus en plus abstraite: les approches modernes ne construisent pas d'algorithmes explicites mais utilisent des résultats théoriques pour améliorer la borne inférieure sur la célèbre constante oméga. Nous sommes revenus à une approche plus pratique en essayant de programmer certains des algorithmes impliqués par ces résultats théoriques. Cette approche expérimentale a révélé un motif inattendu dans des algorithmes existants. Alors que ces algorithmes contiennent une nouvelle variable epsilon dont la présence est réputée les rendre impraticables pour des tailles de matrices raisonnables, nous avons découvert que nous pouvions construire des algorithmes de multiplication matricielle en parallèle sans epsilon avec une complexité asymptotique qui peut théoriquement battre l'algorithme de Strassen pour les multiplications. Un sous-produit de cette exploration est un outil symbolique en Ocaml qui peut analyser, composer et exporter des algorithmes de multiplication matricielle. Nous pensons aussi qu'il pourrait être utilisé pour construire de nouveaux algorithmes pratiques de multiplication matricielle.Dans la deuxième partie, nous décrivons une preuve formelle de l'irrationalité de la constante zeta(3), en suivant la démonstration historique due à Apéry. L'étape cruciale de cette preuve est d'établir que deux suites de nombres rationnels satisfont une surprenante récurrence commune. Il est en fait possible de "découvrir"cette récurrence en utilisant des algorithmes symboliques, et leurs implémentations existantes dans un système de calcul formel. De fait,ce travail constitue un exemple d'une approche dite sceptique de la démonstration formelle de théorèmes, dans lequel des calculs sont principalement réalisés par un logiciel efficace de calcul formel puis vérifiés formellement dans un assistant à la preuve. Incidemment, ce travail questionne la valeur des certificats de télescopage créatif comme preuves complètes d'identités. Cette preuve formelle est également basée sur de nouvelles bibliothèques de mathématiques,formalisées pour ses besoins. En particulier, nous avons formalisé et simplifié une étude du comportement asymptotique de la suite ppcm(1,.., n). Ce travail est conduit dans l'assistant à la preuve Coq et prolonge les bibliothèques Mathematical Components.Dans la dernière partie, nous présentons une procédure qui calcule les approximations d'une classe d'intégrales propres et impropres tout en produisant simultanément un preuve formelle Coq de la correction du résultat de ce calcul. Cette procédure utilise une combinaison d'arithmétique d'intervalles et d'approximations polynomiales rigoureuses de fonctions. Ce travail utilise crucialement les possibilités de calculer efficacement à l'intérieur de la logique sous-jacente au système Coq. Il s'agit d'une extension de la bibliothèque CoqInterval d'approximation numérique d'une classe d'expressions réelles. Sa mise en œuvre a également donné lieu à des extensions de la bibliothèque Coquelicot d'analyse réelle, notamment pour améliorer le traitement des intégrales impropres. Nous illustrons l'intérêt de cet outil et ses performances en traitant des exemples standards mais non triviaux de la littérature, sur lesquels d'autres outils se sont en certains cas révélés incorrects. / This thesis proposes three contributions to computer-aidedmathematical proofs. It deals, not only with proofs relying oncomputations, but also with formal proofs, which are both produced andverified using a piece of software called a proof assistant.In the first part, we illustrate the theme of experimentation at theservice of proofs by considering the problem of the complexity ofmatrix multiplication algorithms. This problem has historically beenapproached in an increasingly abstract way: modern approaches do notconstruct algorithms but use theoretical results to improve the lowerbound on the famous omega constant. We went back to a more practicalapproach by attempting to program some of the algorithms implied bythese theoretical results. This experimental approach reveals anunexpected pattern in some existing algorithms. While these algorithmscontain a new variable epsilon whose presence is reputed to renderthem inefficient for the purposes of reasonable matrix sizes, we havediscovered that we could build matrix multiplication algorithms inparallel without epsilon's with an asymptotic complexity which cantheoretically beat Strassen's algorithm in terms of the number ofmultiplications. A by-product of this exploration is a symbolic toolin Ocaml which can analyze, compose and export matrix multiplicationalgorithms. We also believe that it could be used to build newpractical algorithms for matrix multiplication.In the second part, we describe a formal proof of the irrationality ofthe constant zeta (3), following the historical demonstration due toApéry. The crucial step of this proof is to establish that twosequences of rational numbers satisfy a suprising commonrecurrence. It is in fact possible to "discover" this recurrence usingsymbolic algorithms, and their existing implementations in a computeralgebra system. In fact, this work is an example of a skepticalapproach to the formal proof of theorems, in which computations aremainly accomplished by an efficient computer algebra program, and thenformally verified in a proof assistant. Incidentally, this workquestions the value of creative telescoping certificates as completeproofs of identities. This formal proof is also based on newmathematical libraries, which were formalised for its needs. Inparticular, we have formalized and simplified a study of theasymptotic behaviour of the sequence lcm(1,..., n). This work isdeveloped in the Coq proof assistant and extends the MathematicalComponents libraries.In the last part, we present a procedure which computes approximationsof a class of proper and improper integrals while simultaneouslyproducing a Coq formal proof of the correction of the result of thiscomputation. This procedure uses a combination of interval arithmeticand rigorous polynomial approximations of functions. This work makescrucial use of the possibility to efficiently compute inside Coq'slogic. It is an extension of the CoqInterval library providingnumerical approximation of a class of real expressions. Itsimplementation has also resulted in extensions to the Coquelicotlibrary for real analysis, including a better treatment of improperintegrals. We illustrate the value of this tool and its performanceby dealing with standard but nontrivial examples from the literature,on which other tools have in some cases been incorrect.

Le développement récent du transport ferroviaire a conduit à une forte augmentation du trafic durant la dernière décennie, augmentation qui devrait sepoursuivre dans la décennie à venir avec les futurs développements de ce mode de transport. L'augmentation du trafic se traduit pour l'infrastructure par une augmentation des sollicitations subies par les voies ferrées. La qualité des voies ferrées est garante de la performance du mode de transport ferroviaire,mais également de la sécurité des matériels roulants et des usagers de l'infrastructure. Conserver la qualité du réseau ferré est donc une priorité pour les gestionnaires d'infrastructures ferroviaires. Le ballast ferroviaire a pour rôle de répartir les efforts induits par la circulation des trains et d'assurer la bonne géométrie de l'infrastructure. La surveillance de la dégradation du ballast est donc primordiale pour assurer la qualité del'infrastructure.L'objectif de cette thèse est de proposer un outil numérique permettant d'anticiper la dégradation et le comportement d'une infrastructure ferroviaire sous trafic. Cet outil doit permettre de simuler efficacement lecomportement du ballast ferroviaire sous un grand nombre de cycles de chargements mobiles.Une première partie détaille la composition des infrastructures ferroviaires, précise les rôles du ballast et identifie les grandes lignes de son comportement.Il est fait le choix d'utiliser une méthode de représentation du ballast par élément fini et un modèle de comportement élastoplastique. Le ballast est alors traité comme un géomatériau continu répondant à des lois de comportementélastoplastique.Dans une seconde partie, les bases de la modélisation élastoplastique sont rappelées. Puis, plusieurs modèles de comportement issus de la littérature et comportant des éléments intéressants sont identifiés et étudiés.Dans une troisième partie, un nouveau modèle de comportement frottant compactant est proposé. Il est composé d’un critère nouveau et d'une loi d'écoulement originale. Enfin, le modèle est complété par la prise encompte, de la dégradation du matériau via une diminution de l'angle de frottement interne.Dans une quatrième partie, les méthodes stationnaires sont rappelées. Ces méthodes sont spécifiquement développées pour la modélisation des problèmes incluant des charges en mouvement. Les différents algorithmes sont implémentés àl'aide d'un code de calcul développé dans le logiciel Matlab et à l'aide du logiciel d'éléments finis COMSOL Multiphysics. En particulier, la méthode stationnaire à double échelle de temps, qui est un développement nouveau, permet la modélisation rapide d'un grand nombre de cycles de chargements et la prise en compte des effets d'usure du matériau.Dans une dernière partie, les deux principaux modèles tridimensionnels utilisés sont présentés. Sur un faible nombre de cycles de chargements, divers résultats sont établis selon les différents modèles de comportement utilisé. Sur un très grand nombre de cycles de chargements, les résultats obtenus montrent l'évolution des déformations irréversibles de la structure et de la dégradation du matériau. / Recent development in rail transportation has led traffic increasing during last decade, an increase which should continue in next decade due to the future developments of railway transport. Traffic growing induces infrastructure's solicitation increasing. Railways quality is warrant of rail transport performance, but also ensure security of the rolling stock and safety of the infrastructure users. Maintaining quality of the rail network is major priority for railway infrastructure managers. Purpose of rail ballast is to distribute load of the moving trains and to ensure track geometry. Monitoring of ballast degradation is therefore essential to ensure the quality of the infrastructure.The aim of this thesis is to develop a numerical tool to anticipate the degradation and behaviour of a railway infrastructure under traffic. This tool is intended to effectively simulate the behaviour of railway ballast under numerous mobile loads cycles.A first part details the composition of railway infrastructures, specifies roles of the ballast and identifies the main lines of its behaviour.Choice is made to use finite element method to represent the ballast and an elastic-plastic behaviour model. The ballast is then treated as a continuous geomaterial responding to elastic-plastic behaviour. Therefore, in a second part, the basics of elastic-plastic modelling are exposed. Then, several existing behaviours models which present interesting elements are identified and studied.In a third part, a new behaviour model, called "frottant-compactant" is presented. It is composed with a new criterion and an original flow rule. Finally, the model is completed by taking account of materials degradation via internal friction angle decreasing.In a fourth part, the steady-states methods are exposed. These methods are specifically developed for modelling problems including moving loads. Different algorithms are implemented using Matlab coding software and using the finites elements method software COMSOL Multiphysics. Principally, the double time-scale steady-state method, newly developed, allow rapid modelling of numerous loading cycles and representation of material wear effects.In a final part, the two three-dimensional models used are presented. On a few loading cycles, various results are established depending on different behaviour models. On a very large number of load cycles, the results obtained show the evolution of plastic strains in the structure and the degradation of the material.

Les matériaux cimentaires sont les plus utilisés dans les ouvrages du génie civil. Que ce soit dans les domaines de l'habitation, des transports ou bien encore de l'énergie, ils sont utilisés massivement et doivent faire face à un environnement varié et parfois agressif. Le béton, particulièrement lorsqu'il est armé, est un matériau qui de part son fonctionnement est amené à fissurer. Outre l'aspect visuel qui peut attirer l'attention des utilisateurs, la fissuration impacte, en premier lieu la résistance mécanique mais aussi la durabilité de l'ouvrage. Une meilleure caractérisation de cette fissuration (quantité, trajet, tortuosité) est donc un enjeu majeur. Pour répondre à cette problématique, il est nécessaire de prédire le comportement à long terme des ouvrages. Néanmoins, cette tâche reste ardue. La grande hétérogénéité du matériau combinée aux sollicitations multiples (thermique, chimique, hydrique, mécanique) rend l'œuvre complexe. Si on s'intéresse plus spécifiquement aux sollicitations hydriques, on constate que toute structure tend à s'équilibrer avec son milieu ambiant entraînant un phénomène de dessiccation. L'objectif de ce travail de thèse est de prendre en compte les effets de cette dessiccation dans la détermination des propriétés mécaniques et du comportement macroscopique des ouvrages en béton (à l'échelle de l'échantillon de laboratoire) afin de mettre en place un cadre de modélisation éléments finis prédictif prenant en compte la dessiccation et les phénomènes associés. Conventionnellement, lorsque les propriétés mécaniques du béton sont caractérisées, les contraintes internes ne sont pas considérées et les phénomènes de dessiccation ne sont pas pris en compte. Néanmoins, le gradient hydrique entre la surface et le cœur d'une structure en béton peut mener à un état de contrainte hétérogène et engendrer une micro-fissuration conséquente. Dans certains cas (durabilité, étanchéité), ce phénomène peut-être d'une importance majeure. Bien qu'il semble remarquable, l'impact du séchage et de la micro-fissuration sur les propriétés mécaniques n'est que peu étudié. De plus, les résultats obtenus sont parfois contradictoires ce qui ne permet pas de dégager de consensus. Il est notable que dans la description du phénomène, trois facteurs prépondérants peuvent être dégagés. L'un d'eux, la pression capillaire, améliore la résistance du matériau et les deux autres, le gradient hydrique ainsi que l'incompatibilité de déformation entre la pâte et les granulats, vont diminuer les caractéristiques mécaniques à long terme. Peu d'études comparent l'influence de la dessiccation sur les propriétés mécaniques en mettant en regard les résultats obtenus suivant les différentes méthodes de caractérisations standards. Ce travail de thèse développe, des campagnes expérimentales investiguant les effets de la dessiccation sous humidité relative, température et temps de dessiccation variés. Il se poursuit par la mise en place du cadre de simulation numérique s'appuyant sur les expériences réalisées. Ces dernières sont modélisées mécaniquement en tenant compte du processus de dessiccation. La prise en compte du retrait de dessiccation, du développement du fluage propre et de dessiccation ainsi que l'apport de la pression capillaire permet de retrouver les résultats expérimentaux mécaniques. De ces simulations mécaniques, des faciès et des ouvertures de fissure sont extraits du modèle continu en se basant sur la théorie de la bande de fissuration. Enfin, des outils d'identification sont développés dans ce cadre afin de déterminer les propriétés des différents modèles numériques. / Cementitious materials are the most used material in civil engineering fields. Whether in the areas of housing, transport or energy, they are used heavily and have to face a varied and sometimes aggressive environment. Concrete, especially when it is reinforced, is a material which by its operation is caused to crack. In addition to the visual aspect that can attract the attention of users, cracking impacts, primarily the mechanical strength but also the durability of the structure. A better characterization of this cracking (quantity, path, tortuosity) is therefore a major issue.To answer this problem, it is necessary to predict the long-term behavior of structures. Nevertheless, this task remains arduous. The great heterogeneity of the material combined with multiple stresses (thermal, chemical, hydric, mechanical) makes the work complex. If one is interested more specifically in the hydric solicitations, one finds that any structure tends to equilibrate with its environment causing a phenomenon of drying.The aim of this thesis is to take into account the effects of drying on the mechanical properties and the macroscopic behavior of concrete structures (at the laboratory sample scale) in order to set up a predictive finite element modelling framework taking into account drying and associated phenomena. Conventionally, when the mechanical properties of concrete are characterized, internal stresses are not considered and drying phenomena are not taken into account. Nevertheless, the hydric gradient between the surface and the core of a concrete structure can lead to a state of heterogeneous stress and generate a consequent micro-cracking. In some cases (durability, tightness), this phenomenon may be of major importance.Although it seems remarkable, the impact of drying and micro-cracking on mechanical properties is poorly studied. In addition, the results obtained are sometimes contradictory which does not allow to reach consensus. It is notable that in the description of the phenomenon, three overriding factors can be identified. One of them, the capillary pressure, improves the resistance of the material and the two others, the water gradient as well as the incompatibility of deformation between the paste and the aggregates, will decrease the mechanical characteristics in the long term.Few studies compare the influence of desiccation on mechanical properties by comparing the results obtained using different standard characterization methods. This thesis work develops experimental campaigns investigating the effects of drying under relative humidity, temperature and drying time varied. It continues with the implementation of the numerical simulation framework based on the experiments carried out.These are modelled mechanically taking into account the drying process. Taking into account the withdrawal of desiccation, the development of clean creep and desiccation as well as the contribution of the capillary pressure makes it possible to recover the experimental mechanical results. These mechanical simulations, facies and crack openings are extracted from the continuous model based on the crack band theory. Finally, identification tools are developed in this context to determine the properties of different numerical models.