O presente trabalho foi realizado para estudar o efeito sobre a propagação de fraturas em juntas não-persistentes quando existe uma variação da rugosidade nas juntas. Para esta abordagem, foram analisados os modos de coalescência, o ângulo de início das fraturas, a resistência à compressão e deformação de modelos de argamassa contendo juntas não-persistentes e submetidos a estados biaxiais de tensão. Na literatura especializada encontram-se vários trabalhos que estudam o comportamento de juntas lisas não-persistentes. Infelizmente, este tipo de juntas não leva em conta os efeitos da dilatância e do aumento do atrito. Neste estudo, desenvolveu-se um método para produzir juntas rugosas não-persistentes dentro dos moldes de argamassa. Desta forma, conseguiu-se comparar os diferentes modos de ruptura, tanto para as juntas lisas como as rugosas. A configuração geométrica usada foi de 15 juntas com 'alfa' = 54 graus; 'beta' = 60 graus; Lj = Lb = 50mm e d = 25mm. Onde 'alfa' é o ângulo gerado entre o plano de uma junta e o plano formado entre as pontas de juntas não-coplanares, 'beta' é a inclinação da junta com respeito ao plano de tensão maior, Lb denota à distância entre juntas paralelas coplanares, Lj é o comprimento da junta e d é a distância entre juntas paralelas não coplanares. Estes parâmetros mantiveram-se constantes em todos os ensaios, tanto para as juntas lisas (JRC = 0) como as rugosas (JRC = 6,96 e JRC = 12,25). Usando os parâmetros acima mencionados, observou-se que o tipo de ruptura sempre aconteceu por escalonamento. Para as amostras contendo as juntas lisas, JRC = 0, o mecanismo principal de coalescência entre as juntas é a tração. Para estas juntas, os ângulos de início das fraturas, em média, resultaram de 64º e 65º para esquerda e direita, respectivamente. Em média, a resistência a compressão normalizada ('sigma'nor = 'sigma'1 - 'sigma'2 / 'sigma'cs; onde 'sigma'1 e 'sigma'2 são as tensões principais e 'sigma'cs é a resistência média à compressão simples) destes corpos de prova resultou ter o valor mais baixo, 'sigma'nor = 0,52, e a maior deformação, 'épsilon' = 0,0057. No caso das juntas com JRC = 6,7, a coalescência ocorreu tanto por tração como por cisalhamento, descrevendo um caminho ondulante entre as pontas das juntas. O ângulo médio de início das fraturas foi de 40º para o lado esquerdo e 48º para o lado direito. A resistência média normalizada destes corpos a compressão foi de 'sigma'nor = 0,54 e uma deformação de 'épsilon' = 0,0053. Com as juntas com JRC = 12,3, a coalescência também apresentou ambos os mecanismos, tração e cisalhamento, seguindo uma direção inclinada no início e trajetória reta no meio. Os ângulos de início obtidos foram 5º no lado esquerdo e 20º do lado direito. Os valores maiores de resistência média normalizada e o valor médio menor de deformação foram obtidos nestes tipo de juntas, sendo estes de 'sigma'nor = 0,59 e 'épsilon' = 0,0045. Verificou-se então que a rugosidade tem uma grande influência sobre a propagação da fratura, afetando grandemente o modo de coalescência, o ângulo de início de propagação das fraturas e a resistência e deformação total dos corpos de prova / The present experimental study was conducted to investigate the effect of joint roughness on the fracture propagation of models with non persistent joints. For this approach the parameters investigated are : coalescence, the crack initiation angle, the compressive strength and deformation of the mortar samples containing non-persistent rough joints under biaxial loading. There are many works in specialized literature that study the behavior of non-persistent smooth joints, unfortunately, this kind of approach does not take into account the effect of the dilation and the increase of friction due to the joint roughness. In this study, a new method was developed to produce non-persistent rough joints inside the mortar models. With this method it was possible to compare the different paths of rupture generated for the smooth and for the rough joints. Each sample had 15 joints with 'alfa' = 54º; 'beta' = 60º; Lj = Lb = 50mm and d = 25mm. Where 'alfa' is the formed angle between the joint plane and the plane generated by two non coplanar joint tips, 'beta' is the joint inclination angle with the principal plane stress, Lb is the distance between coplanar joints, Lj is the length of the joint, d is the distance between two non-coplanar joints. These parameters remained constant in all the tests; the only variation permitted was in the joint roughness : from smooth joints (JRC = 0) to rough joints (JRC = 6,96 and JRC = 12,25). Using the mentioned parameters before it was always obtained the stepping failure. For the samples containing smooth joints, JRC = 0, the main mechanism of coalescence is tension. For these joints the average crack initiation angles, had resulted of 64º and 65º for left and right side, respectively. The average normalized compression strength ('sigma'nor = 'sigma'1 - 'sigma'2 / 'sigma'cs; where 'sigma'1 and 'sigma'2 are the principal stresses and 'sigma'cs is the average compression strength) of these tests resulted to have the lowest value, 'sigma'nor = 0,52, and the highest deformation, 'épsilon' = 0,0057. In the case of joints with JRC = 6,7; the mechanisms of coalescence are tension and shear, growing in a waving path between the joint tips. The average crack initiation angle was of 40º for the left side and 48º for the right side of the joint. The average normalized compression strength of these tests was of 'sigma'nor = 0,54 and deformation 'épsilon' = 0,0053. With joints having JRC = 12,3; the coalescence also presents both mechanisms, tension and shear, following a direction inclined in the beginning and a straight line in the middle of the way. The crack initiation angles had been : 5º in the left side and 20º of the right side. The highest values of average normalized strength resistant and the lowest average value of deformation were found in this type of joint, being of 'sigma'nor = 0,59 e 'épsilon' = 0,0045 respectively. With this approach, it was verified that the joint roughness influence the fracture propagation, affecting the coalescence, the crack initiation angle, the resistance and total deformation of the tested specimens

Dans cette thèse, la Méthode des Points Matériels (MPM) est étendue à l’approximation de Galerkin Discontinue (DG) et appliquée aux problèmes hyperboliques en mécanique des solides. La méthode résultante (DGMPM) a pour objectif de suivre précisément les ondes dans des solides subissant de fortes déformations et dont les modèles constitutifs dépendent de l’histoire du chargement. A la croisée des méthodes de types éléments finis et volumes finis, la DGMPM s’appuie sur une grille de calcul arbitraire dans laquelle des flux sont calculés au moyen de solveurs de Riemann approximés sur les arêtes entre les éléments. L’intérêt de ce type de solveurs est qu’ils permettent l’introduction de la structure caractéristique des solutions des équations aux dérivées partielles hyperboliques directement dans le schéma numérique. Les analyses de stabilité et de convergence ainsi que l’illustration de la méthode sur des simulations de problèmes unidimensionnels et bidimensionnels montrent que le schéma numérique permet d’améliorer le suivi des ondes par rapport à la MPM. Par ailleurs, un deuxième objectif poursuivi dans cette thèse consiste à caractériser la réponse des solides élastoplastiques à des sollicitations dynamiques en deux dimensions en vue d’améliorer la résolution numérique de ces problèmes. Bien qu’un certain nombre de travaux aient déjà été menés dans cette direction, les problèmes étudiés se limitent à des cas particuliers. Un cadre unifié pour l’étude de la propagation d’ondes simples dans les solides élastoplastiques en déformations et contraintes plane est proposé dans cette thèse. Les trajets de chargement suivis à l’intérieur de ces ondes simples sont de plus analysés. / In this thesis, the material point method (MPM) is extended to the discontinuous Galerkin approximation (DG) and applied to hyperbolic problems in solid mechanics. The resulting method (DGMPM) aims at accurately following waves in finite-deforming solids whose constitutive models may depend on the loading history. Merging finite volumes and finite elements methods, the DGMPM takes advantage of an arbitrary computational grid in which fluxes are evaluated at element faces by means of approximate Riemann solvers. This class of solvers enables the introduction of the characteristic structure of the solutions of hyperbolic partial differential equations within the numerical scheme. Convergence and stability analyses, along with one and two-dimensional numerical simulations,demonstrate that this approach enhances the MPM ability to track waves. On the other hand, a second purpose has been followed: it consists in identifying the response of two-dimensional elastoplastic solids to dynamic step-loadings in order to improve numerical results on these problems. Although some studies investigated similar questions, only particular cases have been treated. Thus,a generic framework for the study of the propagation of simple waves in elastic-plastic solids under plane stress and plane strain problems is proposed in this thesis. The loading paths followed inside those simple waves are further analyzed.

Os biolubrificantes têm incrementado progressivamente a sua importância sobre os lubrificantes derivados do petróleo devido às rigorosas regulamentações governamentais, o esgotamento das reservas de petróleo e especialmente pelo alto impacto e efeito tóxico dos óleos petroquímicos no ambiente. Os ésteres de óleos naturais podem ser usados como biolubrificantes e são obtidos por transesterificação dos triacilgliceróis com álcoois superiores. A transesterificação enzimática de óleos com álcoois metílico e etílico é um processo muito estudado para a produção de biodiesel, porém outros ésteres podem ser obtidos a partir de aceptores de acila de tamanho de cadeias carbônicas maiores, tais como os álcoois butílico e isoamílico ou misturas de diversos álcoois como o subproduto resultante destilação do bioetanol (óleo fúsel). Neste contexto, o presente trabalho de tese teve como objetivo a obtenção de ésteres com potencial lubrificante por transesterificação enzimática de óleo de palmiste com álcoois superiores. Os ensaios foram efetuados em regime descontínuo (reator de tanque agitado) e em regime contínuo (reator de leito empacotado) utilizando como biocatalisadores as lipases de Burkholderia cepacia e Pseudomonas fluorescens imobilizadas em suportes híbridos de SiO2-?CD e SiO2-HEC numa temperatura fixa de 45°C. Foram testados os efeitos da razão molar óleo: álcool etílico, butílico, isoamílico e óleo fúsel simulado (mistura de álcoois) (1:4 a 1:12), tempos de reação em batelada (24h a 72h) e tempos espaciais em fluxo contínuo (4 a 14h) na conversão, produtividade e a qualidade dos ésteres. Os resultados mostraram bom desempenho das lipases e conversões totais foram alcançadas. No entanto, foi possível observar o efeito do tamanho da cadeia do aceptor de acila, no excesso requerido e no tempo de reação, obtendo-se os melhores resultados para o processo descontínuo com razões molares de 1:6 e 72h para álcool etílico, 1:6 e 48h para ésteres butílicos, 1:4 e 48h para álcool isomílico e óleo fúsel simulado. No processo contínuo, o melhor desempenho foi determinado para razões molares de 1:8 e tempo espacial de 10h para etanol, 1:6 e 8h para butanol, 1:4 com 6h e 8h para isoamílico e óleo fúsel simulado, respectivamente. Em termos gerais, produtividades mais elevadas foram atingidas em regime de fluxo contínuo e especificamente com álcool de isoamila e óleo fúsel (111,10 e 130,18 mg de éster.gcatalisador-1.h-1). Com relação à qualidade dos produtos obtidos nas reações que forneceram elevadas conversões foi constatado baixos teores de monoacilgliceróis (<=1%) e ausência de diacilgliceróis. As viscosidades cinemáticas a 40 °C, confirmaram o elevado grau de transesterificação do óleo de palmiste modificando a viscosidade inicial do óleo de 30,13 mm2.s-1 para valores na faixa entre 3 a 6 mm2.s-1. O índice de viscosidade variou entre 114 e 150 e a estabilidade oxidativa (período de indução) entre 22 e 37 min (9 e 20 h, método Rancimat). Os resultados obtidos foram bastante satisfatórios e contribuíram para o estabelecimento de condições reacionais e operacionais para a produção enzimática de ésteres com potencial uso como lubrificantes, tanto em regime descontínuo como contínuo utilizando óleo de palmiste e álcoois e misturas de álcoois superiores. / Biolubricants have progressively increased their importance on oil-based lubricants due to stringent government regulations, the depletion of oil reserves and especially the high impact and toxic effect of petrochemical oils on the environment. Natural fatty acid alkyl esters can be used as biolubricants and are obtained by transesterification of triacylglycerols with higher alcohols. The enzymatic transesterification of oils with methyl and ethyl alcohols is a much-studied process for the production of biodiesel. However, other esters may be obtained using higher chain acyl acceptors such as butyl and isoamyl alcohols or mixtures thereof as the fusel oil, resulting from the production of bioethanol. In this context, the present thesis aimed to obtain esters with lubricating potential by enzymatic transesterification of palm kernel oil with higher alcohols. Transesterification runs were performed under batch mode (stirred reactor) and continuous flow (packed bed reactor) using as biocatalysts the lipases from Burkholderia cepacia and Pseudomonas fluorescens immobilized on hybrid matrixes SiO2-?CD and SiO2-HEC at 45 °C. The effects of oil to ethyl, butyl, isoamyl alcohol and synthetic fusel oil (1: 4 to 1:12) molar ratios, batch reaction times (24h to 72h) and special times (4 to 14 h) were tested in the conversion, productivity and quality of final esters. The results showed good lipase performance and 100% bulk conversions were achieved. However, it was possible to observe the effect of the acyl acceptor chain on the required excess and on the reaction time, obtaining the best results for batch process with molar ratios of 1: 6 and 72 h for ethyl alcohol, 1: 6 and 48 h for butyl, 1: 4 and 48 h for isoamyl alcohol and synthetic fusel oil. In general terms, better productivities were obtained under continuous flow, particularly with isoamyl alcohol and fusel oil (111.10 and 130.18 mg of ester.g catalyst-1.h-1). Regarding the product quality, low monoacylglycerol contents (<=1% ) and absence of diacylglycerols were found in products obtained under the best reaction conditions. The kinematic viscosities at 40 °C confirmed the high degree of transesterification of palm kernel oil by modifying its initial viscosity from 30.13 mm2 s -1 to a value in the range of 3 to 6 mm2 s -1, the viscosity index between 114 and 150 and an oxidative stability (induction period) between 22 and 37 min (9 and 20 h, Rancimat method). The results obtained were very satisfactory and contributed to the establishment of reactional and operational conditions for the enzymatic production of esters with potential use as lubricants both in discontinuous and continuous flow mode using palm kernel oil and alcohols and mixtures of higher alcohols.

A sacarose é uma matéria-prima, cuja produção é considerada ecologicamente correta, sendo o Brasil seu maior produtor e exportador. O dissacarídeo pode ser convertido, através de um processo multienzimático, em substâncias de maior valor agregado: frutose e ácido glicônico, as quais são importadas pelo Brasil, tendo amplo uso nos setores químico, farmacêutico e alimentício. A conversão foi feita através da ação da invertase, glicose oxidase e catalase, utilizando os reatores descontínuo e contínuo. No procedimento utilizando reator descontínuo, o tempo de residência é igual para reagentes, produtos e catalisador. Neste caso as enzimas foram adicionadas seqüencialmente, em um primeiro momento, e na segunda etapa foram adicionadas simultaneamente. Os parâmetros de partida, a saber, concentração inicial de sacarose, pH, temperatura e atividades enzimáticas, foram testados em diferentes quantidades no intuito de encontrar a mistura inicial mais eficiente na conversão do substrato. No procedimento contínuo, utilizou-se reator com membrana, da marca MILLIPORE®, que permite integrar em uma única etapa a conversão catalítica, a separação/concentração do produto e a recuperação do biocatalisador. A temperatura foi controlada por circulação de água, tendo acoplado uma bomba peristáltica (para controlar a vazão de alimentação do substrato) e um sistema de pressurização. O reator operou com membrana de ultrafiltração (corte molecular = 100 kDa) e foi mantido sob agitação constante. Os parâmetros de partida, neste reator, foram fixados de acordo com os valores otimizados no reator descontínuo com o emprego simultâneo das enzimas. / Sucrose is produced in large amount in Brazil, being a worldwide commercialized commodity. However, it can be converted into more valuable products such as fructose and gluconic acid, both used largely in the chemical, pharmaceutical and food industry. Conversion occurred through the action of invertase, glucose oxidase and catalase, using the discontinuous and continuous reactors. In the batch reactor, the residence time is equal to reactants, products and catalyst. In this case, enzymes were added sequentially, at first, and in the second step were added simultaneously. Boot parameters, initial sucrose concentration, pH, temperature and enzyme activities were tested in different amounts in order to find the most efficient initial mixture to the conversion of the substrate. In continuous process, we used the membrane reactor, MILLIPORE®, which allows for one-step catalytic conversion, the separation / concentration of the product and recovery of the biocatalyst. The temperature was controlled by circulation of water, coupled with a peristaltic pump (to control the feed flow of the substrate) and a pressurization system. The reactor was operated with ultrafiltration membrane (molecular cutoff = 100 kDa) and was kept under constant agitation. The initial parameters in this reactor were set according to the values optimized in the batch reactor with the simultaneous use of enzymes.

Les structures mécaniques utilisées de nos jours ne cessent d’évoluer en utilisant des matériaux composites ou à gradient fonctionnel afin de répondre aux enjeux de résistance accrue, allégement de la structure et amélioration des performances. Ceux-ci nécessitent un contrôle adéquat de leur état de santé afin de s’assurer de l’intégrité de la structure. L’utilisation des ondes guidées ultrasonores fournit un moyen efficace et rapide d’inspection sur de longues distances. Néanmoins, ces ondes présentent certaines caractéristiques complexes qui rendent la tâche très difficile. L’utilisation d’outils d’analyse tels que les modèles numériques constitue un grand atout pour ce type d’application. Dans ce contexte, l’objectif de cette de thèse est le développement d’un outil de modélisation performant, permettant d’étudier la propagation des ondes guidées ultrasonores avec une grande précision et une faible consommation de ressources et de temps de calculs. De ce fait, l’intérêt est porté sur des méthodes numériques d’ordres élevés dont les propriétés de convergence sont beaucoup améliorées que les méthodes classiques. En particulier, la méthode semi-analytique éléments finis de Galerkin discontinue pour la détermination des courbes de dispersion des ondes guidées est développée. La méthode est applicable aux structures planes et cylindriques fabriquées de matériaux isotropes, anisotropes et hétérogènes (à gradient fonctionnel de propriétés). Une étude comparative sur l’analyse des performances de ces méthodes est effectuée. Celle-ci a démontré la capacité de la méthode à modéliser la propagation des ondes guidées ultrasonores dans des guides d’ondes à section arbitraire avec des performances prometteuses par rapport à la méthode des éléments finis classique. / The mechanical structures used today are constantly evolving using composite or functionally gradient materials to meet the challenges of increased strength, lightening the structure and improving performance. These require adequate control of their state of health to ensure the integrity of the structure. The use of Ultrasound Guided Waves (UGW) provides an efficient and fast way of inspection over long distances. Nevertheless, these waves have some complex features that make the task very difficult. The use of analysis tools such as numerical models is a great asset for this type of application. In this context, the objective of this thesis is the development of a powerful modeling tool, allowing to study the propagation of UGWs with a great precision, less computational time and consumption of resources. Accordingly, we are interested in higher order numerical methods whose convergence properties are much improved than the classical methods. In particular, a semi-analytical discontinuous Galerkin finite element method (SADG-FE) is developped for the determination of the dispersion properties of guided waves in arbitrary cross-section waveguides. The method is applicable to plates and cylindrical structures made of isotropic, anisotropic heterogeneous (functionally graded) materials. The performance analysis of these methods and their comparisons are performed with respect to the models based on the classical finite element method. The results demonstrated the ability of the proposed method to model the propagation of ultrasounic guided waves in arbitrary section waveguides with promising performance over the conventional finite element method.

La réduction des nuisances sonores est un enjeu permanent pour les acteurs de l’aéronautique. L’optimisation de la réduction de bruit apportée par les traitements acoustiques tapissant la nacelle des réacteurs turbofan passe par une caractérisation précise des matériaux employés dans l’environnement aéroacoustique d’utilisation, qui met en jeu un écoulement rasant de vitesse importante combiné à de forts niveaux sonores. L’objectif de cette thèse est de développer une méthode inverse pour la détermination de l’impédance acoustique de liners soumis à un écoulement rasant, basée sur des mesures non intrusives du champ de vitesse acoustique au-dessus du matériau par Vélocimétrie Laser Doppler (LDV). L’impédance de liner est obtenue par minimisation de l’écart entre le champ de vitesse acoustique mesuré et le champ simulé numériquement en résolvant les équations d’Euler linéarisées bidimensionnelles harmoniques, discrétisées par un schéma Galerkin discontinu. Le gradient de la fonction objectif minimisée est calculé via la résolution, à chaque itération, des équations directes et adjointes. Une première étape de validation du solveur est effectuée sur des cas-tests académiques, puis sur des cas expérimentaux impliquant des mesures de pression acoustique en paroi rigide opposée au liner. Dans un second temps, la méthode est appliquée à des mesures de vitesse acoustique obtenues par LDV dans le banc B2A de l’ONERA en l’absence d’écoulement. La dernière étape consiste à prendre en compte l’effet d’un écoulement rasant de profil cisaillé. Les impédances identifiées à partir de mesures LDV en présence d’écoulement ont notamment permis de gagner en compréhension sur les phénomènes d’absorption intervenant dans le banc B2A. / While aircraft noise constraints become increasingly stringent, efficient duct treatment of turbofan engines requires an accurate knowledge of liner impedance with grazing flow at high acoustic levels. This thesis aims at developing an impedance eduction method in the presence of grazing flow. The inverse process is based on acoustic velocity fields acquired by Laser Doppler Velocimetry (LDV) above the liner. The liner acoustic impedance is obtained by minimization of the distance between the measured acoustic velocity field and the simulated one. Computations rely on the resolution of the 2D linearized Euler equations in the harmonic domain, spatially discretized by a discontinuous Galerkin scheme. The gradient of the objective function is achieved by the resolution, at each iteration on the liner impedance, of the direct and adjoint equations. The solver is first validated on academic test cases, then on experimental results of acoustic pressure measurements at the rigid wall opposite the liner. Secondly the method is applied to acoustic velocity measurements obtained by LDV above the liner without flow, in the ONERA B2A test bench. The last step consists in taking into account the effects of a sheared grazing flow. The impedances educed from LDV measurements in the presence of flow namely allowed to gain insight into the absorption phenomena occuring in the B2A test bench.

The primary intention with this Doctoral thesis is to fillin the knowledge gaps and raise the level of understandingregarding the different metal dusting mechanisms in general andexplain the process in detail for high alloyed materials.Considerable effort is put into identifying the driving forcesand elucidating the diffusional processes in metal dusting. The results are based on a series of long-term laboratory exposures of stainless steels and high-performance commercial alumina-forming Fe- and Ni-base alloys in synthesis gasmixtures, plus a separate shorter study on ultra pure iron. ANi-base alloy was also investigated after a two years field exposure in a methanol plant. Post exposure metallographic examinations and analysis aswell as thermodynamic calculations were made in order toidentify and describe the operating metal dusting mechanisms.Two main mechanisms were previously used to explain metaldusting, one on the basis of decomposition of metastable carbides (Type I) the other on graphite formation (TypeII). A new metal dusting mechanism has been identified in this Thesis which appears on high alloyed steels and Ni-base alloys,an active corrosion induced by carbon and oxygen, denoted TypeIII. Both the mechanisms and the type of corrosion products were consistent with the thermodynamic conditions of the material under the influence of a carbon and oxygen gradient.It was shown that this mechanism not only accelerates the metaldusting process, in fact, it determines the overall metaldusting kinetics on stainless steels and Ni-base alloys. Another feature, which may occur at temperatures where metalbulk and even static grain boundary diffusion is too slow forexplaining the metal dusting corrosion process, was identifiedon a Ni-base alloy. It involves a fast growing cellular structure with discontinuous precipitated carbides whichprovides fast metal dusting kinetics by the Type IIImechanism. A Type IV metal dusting mechanism, continued fragmentationby graphitization until nano-sized particles are formed andcatalyse carbon nanotube formation is also described. Thesteady state process and the driving force for metal dusting onpure iron was identified and described. With these additional processes it is now possible to extendour understanding of the metal dusting processes to a widerange of engineering alloys. / QC 20100825

This thesis is concerned with the development of numerical techniques to simulate compressible multi-phase flows, in particular a high-accuracy numerical approach with mesh adaptivity. The Discontinuous Galerkin (DG) method was chosen as the framework for this work for being characterized for its high-order of accuracy -thus low numerical diffusion- and being compatible with mesh adaptivity due to its locality. A DG solver named DiGGIT (Discontinuous Galerkin at the Georgia Institute of Technology) has been developed and several aspects of the method have been studied. The Local Discontinuous Galerkin (LDG) method -an extension of DG for equations with high-order derivatives- was extended to solve multiphase flows using Diffused Interface Methods (DIM). This multi-phase model includes the convection of the volume fraction, which is treated as a Hamilton-Jacobi equation. This is the first study, to the author's knowledge, in which the volume fraction of a DIM is solved using the DG and the LDG methods. The formulation is independent of the Equation of State (EOS) and it can differ for each phase. This allows for a more accurate representation of the different fluids by using cubic EOSs, like the Peng-Robinson and the van der Waals models. Surface tension is modeled with a new numerical technique appropriate for LDG. Spurious oscillations due to surface tension are common to all the capturing schemes, and this new approach presents oscillations comparable in magnitude to the most common schemes. The moment limiter (ML) was generalized for non-uniform grids with hanging nodes that result from adaptive mesh refinement (AMR). The effect of characteristic, primitive, or conservative decomposition in the limiting stage was studied. The characteristic option cannot be used with the ML in multi-dimensions. In general, primitive variable decomposition is a better option than with conservative variables, particularly for multiphase flows, since the former type of decomposition reduces the numerical oscillations at material discontinuities. An additional limiting technique was introduced for DIM to preserve positivity while minimizing the numerical diffusion, which is especially important at the interface. The accuracy-preserving total variation diminishing (AP-TVD) marker for ``troubled-cell' detection, which uses an averaged-derivative basis, was modified to use the Legendre polynomial basis. Given that the latest basis is generally used for DG, the new approach avoids transforming to the averaged-derivative basis, what results in a more efficient technique. Furthermore, a new error estimator was proposed to determine where to refine or coarsen the grid. This estimator was compared against other estimator used in the literature and it showed an improved performance. In order to provide equal order of accuracy in time as in space, the commonly used 3rd-order TVD Runge-Kutta (RK) scheme in the DG method was replaced in some cases by the Spectral Deferred Correction (SDC) technique. High orders in time were shown to only be required when the error in time is significant. For instance, convection-dominated compressible flows require for stability a time step much smaller than is required for accuracy, so in such cases 3rd-order TVD RK resulted to be more efficient than SDC with higher orders. All these new capabilities were included in DiGGIT and have provided a generalized approach capable of solving sub- and super-critical flows at sub- and super-sonic speeds, using a high-order scheme in space and time, and with AMR. Canonical test cases are presented to verify and validate the formulation in one, two, and three dimensions. Finally, the solver is applied to practical applications. Shock-bubble interaction is studied and the effect of the different thermodynamic closures is assessed. Interaction between single-drops and a wall is simulated. Sticking and the onset of splashing are observed. In addition, the solver is used to simulate turbulent flows, where the high-order of accuracy clearly shows its benefits. Finally, the methodology is challenged with the simulation of a liquid jet in cross flow.

Die Z-Transformation ist ein wichtiges Werkzeug für diskontinuierliche Regelungen. Ein wenig beachteter Transformationsweg führt über die Berechnung von Residuen. Alle wichtigen Besonderheiten wie Mehrfachpole, Sprungfähigkeit, komplexe Pole oder Zeitverschiebung unterhalb der Abtastzeit (modifizierte Z-Transformation) können einbezogen werden. Die Vorgabe von Reihenabbruchkriterien oder das Auffinden von Summenformeln ist nicht notwendig. Der Weg ist prinzipiell für manuelle und maschinelle Berechnungen einsetzbar. Die Vorgehensweise wird durch drei ausführliche Beispiele verdeutlicht. / The Z-transformation is an important tool for the control of discontinuous systems. A seldom considered transformation way uses the residue computation. All relevant fea-tures as for instance multiple poles, process with feedthrough, complex poles or delay less than the sampling time (so called modified Z-transformation) may be included. There is no truncation criterion or search for a sum formula necessary. This way is always applicable for manual as well as for computer-aided computations. Three detailed examples demonstrate the use of the formulas.

In this study we tested whether the prevalence or synaptic distribution of NMDA receptor subunits would be altered in the brain of the MeCP2-null mouse model of Rett syndrome. Detergent resistant membranes (DRMs) and post-synaptic densities (PSDs) were isolated from the synaptic membranes treated with TritonX-100, and resolved by sucrose density gradient centrifugation. Immunoblot analysis of the resulting density gradient fractions revealed that the relative distribution of the different NMDA receptor subunits between the DRM fractions, soluble fractions, and insoluble postsynaptic density fractions was preserved in the MeCP2-null brain. However, analysis of the overall NMDA receptor subunit prevalence within these fractions revealed a significant decrease in the expression of the NR1 and NR2A subunits, but not the NR2B subunit, in the MeCP2-null brain. The preservation of distribution of NMDAR subunits to the synaptic membranes, together with the decrease in NR1 and NR2A prevalence, suggest an imbalance in equilibrium between the mature and the immature synapses in a mouse model of Rett syndrome.