In dieser Arbeit werden stochastische Charakteristiken der Lösung parabolischer Differentialgleichungen mit zufälligen Neumann-Randbedingungen mit Hilfe der Finite-Elemente-Methode angegeben. Dabei wird der Berechnung der Korrelations- bzw. Varianzfunktion besondere Bedeutung beigemessen. Das stochastische Randanfangswertproblem wird durch Anwendung von FEM-Techniken durch ein System gewöhnlicher Differentialgleichungen mit stochastischen inhomogenen Termen approximiert. Die Modellierung der stochastischen Eingangsparameter durch epsilon-korrelierte Felder gestattet Entwicklungen der Lösungscharakteristiken nach der Korrelationslänge. Numerische Beispiele enthalten den Vergleich zwischen analytischen Ergebnissen und Simulationsresultaten.

In dieser Arbeit werden parabolische Randanfangswertprobleme mit zufälliger Anfangs- und Neumann-Randbedingung betrachtet. Die zufälligen Einflußgrößen werden dabei als epsilon-korrelierte, zufällige Felder modelliert. Das Hauptinteresse liegt auf der Berechnung stochastischer Kenngrößen der auf Basis der Finite-Elemente Methode erhaltenen Lösung des Randanfangswertproblems. Für die Korrelationsfunktion der Lösung wird eine Entwicklung nach der Korrelationslänge sowie eine explizite Berechnung für spezielle Typen der Vernetzung vorgestellt. Anhand von numerischen Beispielen werden abschließend die auf den verschiedenen Wegen erhaltenen Varianzen mit der einer simulierten Lösung verglichen.

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The ATLAS detector at CERN's Large Hadron Collider has been instrumental in scientific discoveries,including the Higgs particle. As part of the High Luminosity (HL) upgrade, the current Inner Detector (ID) isbeing replaced by the new IInner Tracker (ITk), and Uppsala University is collaborating with industrypartner NOTE to produce around 700 modules for the ITk. The production process involves gluing hybridsto sensors using a glue robot, which currently lacks a complete metrology system needed to verify thegeometry of produced items. This project aims to integrate a Micro Epsilon ILD1900 laser sensor with theglue robot to enable accurate measurements in the z-axis. In order to reach this goal, a few differenttasks had to be completed. These included creating a measurement API to enable the utilisation of thelaser sensor, recommending modifications to the glue robot syringe and camera holder in order to holdthe laser sensor, performing validation tests of the laser sensor's measuring capability, developing a lasersensor mount for a mock-up glue robot used during the validation process and developing a holder for aUSB/RS422 converter necessary for communication with the laser sensor. As a result of the project, themeasurement API was successfully created and utilised, appropriate modifications to the syringe holderwere made, validation tests were conducted though deemed insufficient due to limitations of the setup,and, finally, the laser sensor mount for the mock-up glue robot and the USB/RS422 holder weresuccessfully designed and produced.

Firstly, an existing thermodynamic model for the predicting of martensite start temperature of commercial steels has been improved to include more elements such as N, Si, V, Mo, Nb, W, Ti, Al, Cu, Co, B, P and S and their corresponding composition ranges for Martensitic transformation. The predicting ability of the existing model is improved considerably by critical assessment of different binary and ternary systems i.e. CALPHAD approach which is by wise selection of experimental data for optimization of the interaction parameters. Understanding the degree of variation in multi-component commercial alloys, various ternary systems such as Fe-Ni-X and Fe-Cr-X are optimized using both binary and ternary interaction parameters. The large variations between calculated and the experimental values are determined and reported for improvements in thermodynamics descriptions.Secondly, model for the prediction of Epsilon martensite start temperature of some commercial steels and shape memory alloys is newly introduced by optimizing Fe-Mn, Fe-Mn-Si and other Fe-Mn-X systems considering the commercial aspects in the recent development of light weight steels alloyed with Al and Si.Thirdly, the effect of prior Austenite grain size (pAGS) on martensite start temperature is introduced into the model in the form of non-chemical contribution which will greatly influence the Gibbs energy barrier for transformation. A serious attempt has been made to describe the dependency of transition between lenticular and thin-plate martensite morphologies on the refinement of prior Austenite grain size.Finally, the model is validated using a data-set of 1500 commercial and novel alloys. Including the newly modified thermodynamic descriptions for the Fe-based TCFE9 database by Thermo-Calc software AB, the model has the efficiency to predict the martensite start temperature of Multi-component alloys with an accuracy of (±) 35 K. The model predictability can be further improved by critical assessment of thermodynamic factors such as stacking faults and magnetism in Fe-Mn-Si-Ni-Cr systems.

This work evaluates whether the branch of Reynolds Averaging in Computational Fluid Dynamics can be used to, based on real field measurements, find the source of the measured gas in question. The method to do this is via the adjoint to the Reynolds Averaged Scalar Transport equation, explained and derived herein. Since the Inverse is only as good as the main equation, forward runs are made to evaluate the turbulence model. Reynolds Averaged Navier Stokes is solved in a domain containing 4 cubes in a 2x2 grid, generating a velocity field for said domain. The turbulence model in question is a union of two modifications to the standard two equation k-ε model in order to capture blunt body turbulence but also to model the atmospheric boundary layer. This field is then inserted into the Reynolds Averaged Scalar Transport equation and the simulation is compared to data from the Environmental Flow wind tunnel in Surrey. Finally the adjoint scalar transport is solved, both for synthetic data that was generated in the forward run, but also for the data from EnFlo. It was discovered that the turbulent Schmidt number plays a major role in capturing the dispersed gas, three different Schmidt numbers were tested, the standard 0.7, the unconventional 0.3 and a height dependent Schmidt number. The widely accepted value of 0.7 did not capture the dispersion at all and gave a huge model error. As such the adjoint scalar transport was solved for 0.3 and a height dependent Schmidt number. The interaction between measurements, the real source strength (which is not used in the adjoint equation, but needed to find the source) and the location of the source is intricate indeed. Over estimation and under estimation of the forward model may cancel out in order to find the correct source, with the correct strength. It is found that Reynolds Averaged Computational fluid dynamics may prove useful in source term estimation. / Detta arbete utvärderar hurvida Reynolds medelvärdesmodellering inom flödessimuleringar kan användas till att finna källan till en viss gas baserat på verkliga mätningar ute i fält. Metoden går ut på att använda den adjungerade ekvationen till Reynolds tidsmedlade skalära transportekvationen, beskriven och härledd häri. Då bakåtmodellen bygger på framåtmodellen, måste såleds framåtmodellen utvärderas först. Navier-Stokes ekvationer med en turbulensmodell löses i en domän, innehållandes 4 kuber i en 2x2 orientering, för vilken en hastighetsprofil erhålles. Turbulensmodellen som användes är en union av två olika k-ε modeller, där den ena fångar turbulens runt tröga objekt och den andra som modellerar atmosfäriska gränsskiktet. Detta fält används sedan i framåtmodellen av skalära transportekvationen, som sedan jämförs med körningar från EnFlo windtunneln i Surrey. Slutligen testkörs även den adjungerade ekvationen, både för syntetiskt data genererat i framåtkörningen men även för data från EnFlo tunneln. Då det visade sig att det turbulenta Schmidttalet spelar stor roll inom spridning i det atmosfäriska gränsskiktet, gjordes testkörningar med tre olika Schmidttal, det normala 0.7, det väldigt låga talet 0.3 samt ett höjdberoende Schmidttal. Det visade sig att det vanligtvis använda talet 0.7 inte alls lyckas fånga spridningen tillfredställande och gav ett stort modellfel. Därför löstes den adjungerade ekvationen för 0.3 samt för ett höjdberoende Schmidttal. Interaktionen mellan mätningar, den riktiga källstyrkan (som är okänd i den adjungerade ekvationen) samt källpositionen är onekligen intrikat. Över- samt underestimationer av framåtmodellen kan ta ut varandra i bakåtmodellen för att finna rätt källa, med rätt källstyrka. Det ter sig som Reynolds turbulensmodellering mycket möjligt kan användas inom källtermsuppskattning.

Der Schwerpunkt der vorliegenden Arbeit liegt auf Methoden zur Lösung nichtlinearer Optimierungsprobleme mit der Anforderung, jedes globale Optimum garantiert zu finden und mit einer im Voraus festgesetzten Genauigkeit zu approximieren. Eng verbunden mit dieser deterministischen Optimierung ist die Berechnung von Schranken für den Wertebereich einer Funktion über einem gegebenen Hyperquader. Verschiedene Ansätze, z. B. auf Basis der Intervallarithmetik, werden vorgestellt und analysiert. Im Besonderen werden Methoden zur Schrankengenerierung für multivariate ganz- und gebrochenrationale Polynome mit Hilfe der Darstellung in der Basis der Bernsteinpolynome weiterentwickelt. Weiterhin werden in der Arbeit schrittweise die Bausteine eines deterministischen Optimierungsverfahrens unter Verwendung der berechneten Wertebereichsschranken beschrieben und Besonderheiten für die Optimierung polynomialer Aufgaben näher untersucht. Die Analyse und Bearbeitung einer Aufgabenstellung aus dem Entwicklungsprozess für Fahrzeuggetriebe zeigt, wie die erarbeiteten Ansätze zur Lösung nichtlinearer Optimierungsprobleme die Suche nach energieeffizienten Getrieben mit einer optimalen Struktur unterstützen kann. Kontakt zum Autor: [Nachname] [.] [Vorname] [@] gmx [.] de

Des ligands diketimines porteurs de substituants N-benzyl, N-9-anthrylmethyl et N-mesitylmethyl (nacnacBnH, nacnacAnH, and nacnacMesH) ont été synthétisés par condensation d’une amine et d’acétyl acétone ou son monoacétal d’éthylène glycol. La chlorination de la position 3 a été effectuée à l’aide de N-chlorosuccinimide conduisant à la formation des ligands ClnacnacBnH et ClnacnacAnH. Cette même position 3 a également été substituée par un groupement succinimide par lithiation du nacnacBnH, suivi de la réaction avec le N-chlorosuccinimide (3-succinimido-nacnacBnH). Les ligands N-aryl nacnacippH et nacnacNaphH (ipp = 2-isopropylphenyl, Naph = 1-naphthyl) ont été préparés selon les procédures reportées dans la littérature. La réaction de ces ligands avec Zn(TMSA)2 (TMSA = N(SiMe3)2) conduit à la formation des complexes nacnacAnZn(TMSA) et ClnacnacBnZn(TMSA). La protonation avec l’isopropanol permet l’obtention des complexes nacnacAnZnOiPr et ClnacnacBnZnOiPr. La réaction avec Mg(TMSA)2 permet quant à elle la formation des complexes nacnacAnMg(TMSA), nacnacMesMg(TMSA), ClnacnacBnMg(TMSA) et ClnacnacAnMg(TMSA). La protonation subséquente à l’aide du tert-butanol permet l’obtention du nacnacMesMgOtBu et du ClnacnacBnMgOtBu, alors que l’on observe uniquement une décomposition avec les ligands possédant des substituants N-anthrylmethyl. La réaction de ces diketimines avec Cu(OiPr)2 conduit aux dimères hétéroleptiques [nacnacBnCu(μ-OiPr)]2 et [3-Cl-nacnacBnCu(μ-OiPr)]2 lors de l’usage des ligands stériquement peu encombrés. Lors de l’utilisation de ligands plus encombrés, la stabilisation du complexe hétéroleptique par dimérisation n’est plus possible, conduisant, par un échange de ligand, à la formation des complexes homoleptiques Cu(nacnacipp)2 et Cu(nacnacNaph)2. Les complexes homoleptiques Cu(nacnacBn)2 et Cu(3-succinimido-nacnacBn)2 ont été obtenus à partir des ligands N-benzyl. Les ligands encore plus encombrés tels que nacnacAnH, nacnacMesH ou ceux comportant des substituants N-methylbenzyl ne présentent alors plus de réactivité avec le Cu(OiPr)2. La plupart des complexes ont été caractérisés par Diffraction des Rayons X. Les complexes homoleptiques ainsi que ceux de TMSA sont monomériques, alors que ceux formés à partir d’alkoxides se présentent sous forme de dimères à l’état solide. Tous les complexes d’alkoxides ainsi que les nacnacAnMg(TMSA)/BnOH et ClnacnacAnMg(TMSA)/BnOH présentent une réactivité modérée à haute en matière de polymérisation du rac-lactide (90% de conversion en 30 secondes à 3 heures). Le nacnacAnZnOiPr permet la synthèse d’un polymère hautement hétérotactique (Pr = 0.90) quand le ClnacnacBnMgOtBu/BnOH génère un polymère isotactique à -30°C (Pr = 0.43). Tous les autres catalyseurs produisent des polymères atactiques avec une légère tendance hétérotactique (Pr = 0.48 – 0.55). Les complexes hétéroleptiques [nacnacBnCu(μ-OiPr)]2 et [3-Cl-nacnacBnCu(μ-OiPr)]2 se révèlent être de très bons catalyseurs pour la polymérisation du rac-lactide présentant une conversion complète du monomère à température ambiante, en solution, en 0,5 à 5 minutes. Le [nacnacBnCu(μ-OiPr)]2 est actif en présence ou absence d’isopropanol, agissant comme agent de transfert de chaine à haute activité (k2 = 32 M–1•s–1) dans le dichlorométhane. Dans l’acétonitrile, le THF, le dichloromethane et le toluène, [nacnacBnCu(μ-OiPr)]2 conduit à une étroite polydispersité, possédant respectivement des kobs = 2.4(1), 5.3(5), 3.6-4.4 and 10(1) min–1. Aucune réaction parasite, telle qu’une trans-esterification, une épimerisation ou une décomposition du catalyseur, n’a été observée. Les complexes homoleptiques en présence d’alcool libre semblent présenter un équilibre avec une petite quantité de leurs équivalents hétéroleptiques, permettant une polymérisation complète, en moins de 60 min, à température ambiante. Tous les catalyseurs de cuivre présentent un haut contrôle de la polymérisation avec une polydispersité égale ou inférieure à 1.1. Les polymères obtenus sont essentiellement atactiques, avec une légère tendance à l’hétérotacticité à température ambiante et -17°C. Le [nacnacBnCu(μ-OiPr)]2 polymérise également la -butyrolactone (BL), l’-caprolactone (CL) et la -valerolactone (VL) avec des constantes respectivement égales à kobs = 3.0(1)•10–2, 1.2–2.7•10–2, et 0.11(1) min–1. Les homopolymères présentent une étroite polydispersité d’approximativement 1.1. Les polymérisations par addition séquentielle ont mis en évidence une trans-estérification (non observée dans les homopolymérisations) si BL ou CL sont introduits après un bloc lactide. / Diketimine ligands bearing N-benzyl, N-9-anthrylmethyl and N-mesitylmethyl substituents (nacnacBnH, nacnacAnH, and nacnacMesH) were prepared from condensation of amine with either acetyl acetone or its ethylene glycol monoketal. Chlorination of the 3-position was achieved using N-chlorosuccinimide, yielding ClnacnacBnH and ClnacnacAnH. The 3-position was also substituted by succinimido by lithiation of nacnacBnH followed by reaction with N-chlorosuccinimide (3-succinimido-nacnacBnH). N-aryl ligands nacnacippH and nacnacNaphH (ipp = 2-isopropylphenyl, Naph = 1-naphthyl) were prepared from literature. The ligands were reacted with Zn(TMSA)2 (TMSA = N(SiMe3)2) to yield nacnacAnZn(TMSA) and ClnacnacBnZn(TMSA). Protonation with isopropanol gave nacnacAnZnOiPr and ClnacnacBnZnOiPr. Reaction of the diketimines with Mg(TMSA)2 afforded nacnacAnMg(TMSA), nacnacMesMg(TMSA), ClnacnacBnMg(TMSA) and ClnacnacAnMg(TMSA). Subsequent protonation with tert-butanol produced nacnacMesMgOtBu and ClnacnacBnMgOtBu, but only decomposition was observed with N-anthrylmethyl substituents. Reaction of the diketimines with Cu(OiPr)2 yielded the heteroleptic [nacnacBnCu(μ-OiPr)]2 and [3-Cl-nacnacBnCu(μ-OiPr)]2 when using sterically undemanding ligands. When sterically more demanding diketimines were used, stabilization of the heteroleptic complex by dimerization was not possible, resulting in the formation of the homoleptic complexes Cu(nacnacipp)2 and Cu(nacnacNaph)2 by ligand exchange. Homoleptic complexes were also prepared with N-benzyl ligands, i. e. Cu(nacnacBn)2 and Cu(3-succinimido-nacnacBn)2. Even bulkier ligands such as nacnacAnH, nacnacMesH or N-methylbenzyl substituents failed to react with Cu(OiPr)2. Most complexes were characterized by single crystal X-ray diffraction. TMSA complexes and homoleptic complexes were monomeric, alkoxide complexes were dimeric in the solid state. All alkoxide complexes, as well as nacnacAnMg(TMSA)/BnOH and ClnacnacAnMg(TMSA)/BnOH were moderately to highly active in rac-lactide polymerization (90% conversion in 30 sec to 3 h). nacnacAnZnOiPr produced highly heterotactic polymer (Pr = 0.90), ClnacnacBnMgOtBu/BnOH produced slightly isotactic polymer at –30 °C (Pr = 0.43), all other catalysts produced atactic polymers with a slight heterotactic bias (Pr = 0.48 – 0.55). Heteroleptic complexes [nacnacBnCu(μ-OiPr)]2 and [3-Cl-nacnacBnCu(μ-OiPr)]2 are very highly active rac-lactide polymerization catalysts, with complete monomer conversion at ambient temperature in solution in 0.5 – 5 min. [nacnacBnCu(μ-OiPr)]2 specifically polymerized in the presence or absence of isopropanol as a chain-transfer reagent with very high activity (k2 = 32 M–1•s–1), in methylene chloride. While in acetonitrile, THF, dichloromethane and toluene has a kobs = 2.4(1), 5.3(5), 3.6-4.4 and 10(1) min–1, respectively. [nacnacBnCu(μ-OiPr)]2 yields narrow polydispersities and no evidence of side reactions such as transesterification, epimerization or catalyst decomposition. The homoleptic complexes in the presence of free alcohol, seem to be in equilibrium with small amounts of the respective heteroleptic complex, which are sufficient to complete polymerization in less than 60 min at room temperature. All Cu catalysts show high control of polymerization with polydispersities of 1.1 and below. The obtained polymers were essentially atactic, with a slight heterotactic bias at ambient temperature and at –17 °C. [nacnacBnCu(μ-OiPr)]2 polymerizes -butyrolactone (BL), -caprolactone (CL) and -valerolactone (VL) with rate constants of kobs = 3.0(1)•10–2, 1.2–2.7•10–2, and 0.11(1) min–1, respectively. Homopolymers showed narrow polydispersities of appr. 1.1. Sequential addition polymerizations showed evidence for transesterification (not seen in homopolymerizations) if BL or CL are introduced after a lactide block.

To avoid the large amount of damage that floods can cause, spillway tunnels are used to control water levels. To ensure the safety of water transportation through spillway tunnels, the behaviour of the water throughout the tunnel is important to know. Physical experiments are time consuming and expensive, hence CFD simulations are a profitable option for investigating the performance of the spillway tunnel. In this project, simulations of water flow in a spillway tunnel were executed. A three dimensional model of the spillway tunnel in Zipingpu Water Conservancy Project was created in the software ANSYS Gambit. A coarse, middle and fine mesh with both hexahedral- and tetrahedral elements were also created for the model in ANSYS Gambit. The meshes were imported to ANSYS Fluent where the simulations, and a convergence analysis were made. The water flow was set to be described by the Reynolds-Averaged Navier-Stokes model, using the pressure solver, k-epsilon model and the VOF model. Physical experiments had previously been performed, and the simulated results were compared to these, in an attempt to find the parameters to replicate the experimental results to the greatest extent possible. The inlet velocity of the tunnel was known and the inlet boundary was set as a velocity inlet. The ceiling of the tunnel was set as a pressure inlet, the floor and walls were set as wall, and the outlet was set as pressure outlet. The simulated results showed similar behavior as the experimental results, but all differed from the experimental results. The grid convergence index, estimating the results' dependency on the mesh was 6.044 %. The flow was analyzed, and where the flow had unfavorable characteristics, such as a high cavitation number, the geometry of the spillway was altered in ANSYS Gambit to investigate if an improved geometry for the spillway tunnel could be found. The water flow in the revised geometry was simulated in ANSYS Fluent, and results showing flow with lower cavitation numbers was found.

Este trabalho tem como finalidade obter condições de recuperar e purificar a pró-toxina épsilon e uma protease produzida pelo Clostridium perfringens através do uso da técnica de extração líquido-líquido em sistema de duas fases aquosas (SDFA) para utilização na produção de vacinas. A aplicação do sistema de duas fases aquosas é proposta como alternativa para a purificação, pois permite a separação e análise de partículas biológicas. Esta técnica é aconselhável para purificação em larga escala pela possibilidade de partição seletiva com altos rendimentos, além de apresentar uma boa relação custo-benefício. Foram construídas as curvas binodais que foram utilizadas para análise da composição dos sistemas de duas fases aquosas formados por polietileno glicol e citrato de sódio, como também a extração e recuperação da pró-toxina épsilon e da protease produzidas por Clostridium perfringens. As curvas binodais foram construídas utilizando PEG 400, 550, 1000, 1500, 3350 e 8000 em diferentes valores de pH (6,0; 6,5; 7,0; 7,5 e 8,0) e água para formação do sistema. Também foram construídas curvas na presença de caldo clarificado em substituição à água. Foi avaliada ainda a estabilidade da pró-toxina épsilon, antes da extração, e da protease antes e após a extração, frente às variações de pH e temperatura. Um planejamento experimental ('2pot.8-3') foi usado para avaliar a influência das variáveis concentração e massa molar do PEG, concentração de citrato, pH, concentração de NaCl, fator de diluição do extrato, temperatura e massa total do sistema na extração da pró-toxina épsilon. A partição de uma protease presente no meio fermentado de C. perfringens foi estudada através do uso de três planejamentos experimentais completos (dois do tipo '2pot.4' e um do tipo '2pot.3') que avaliaram a influência das variáveis concentração e massa molar do PEG, concentração de citrato e pH. Três variáveis-resposta foram obtidas (aumento de pureza, coeficiente de partição e recuperação da enzima). Os resultados atingidos foram: coeficiente de partição de 0,57, aumento de pureza de 4,2 com uma recuperação de 131% da atividade enzimática na fase superior do sistema. O sistema de extração que proporcionou as melhores condições de extração foi constituído por: PEG 10000 (g/mol) e concentração de 22% (m/m), concentração de citrato de 8% (m/m) e pH 8,5. A protease permaneceu estável (durante 48 h), mesmo após a extração, nas temperaturas de 5°C e 25°C e nos valores de pH de 6,0 a 9,0. / The purpose of this work is to obtain best conditions of recovery and purification of proteins (epsilon prototoxin and a protease) produced by Clostridium perfringens through the use of the liquid-liquid extraction by aqueous two-phases systems (ATPS). The application of these systems is proposed as alternative for protein purification, because it allows the separation and analysis of biological particles. This technique is advisable process purification applied to large scale since it provides a selective partition with high yields, and good cost-benefit ratio. The binodal curves were constructed and used to determine the system composition based on polyethylene glicol and citrate concentrations. The binodal curves were built by using PEG 400, 550, 1000, 1500, 3350 and 8000 g/mol at different pH values (6.0; 6.5; 7.0; 7.5 and 8.0). The curves were, initially, built in the presence of water and, later, with clarified fermented broth. The differences in the curve profiles (water versus broth) helped to explain the phase separation behaviour. The stability, as a function of pH and temperature, of the epsilon prototoxin was evaluated before the extraction, while the stability of the protease was evaluated before and after the extraction. An experimental design ('2pot.8-3') was used to evaluate the influence of the following variables on epsilon prototoxin extraction: concentration and molar mass of PEG, citrate concentration and NaCl concentrations, pH, dilution factor of the extract, temperature and total mass of the system. However, the partition of the protease was studied through the use of the three full different experimental designs (two of the type '2pot.4', and one of the type '2pot.3') that evaluated the influence of the following variables: concentration and molar mass of PEG, citrate concentration and pH. Three parameter responses were obtained: purification factor; coefficient partition; and recovery yield of the enzyme. The results were satisfactory: partition coefficient = 0.57, purification factor = 4.2; yield = 131%. The extraction conditions which provided the best results were: molar mass of PEG 10000 (g/mol); concentration of PEG of 22% (w/w); concentration of citrate of 8% (w/w); and pH 8.5. The protease was stable (during 48h), even after the extraction, in the temperatures of 5°C and 25°C, and at pH values of from 6.0 to 9.0.