Ce travail est consacré au développement de schémas numériques pour approcher les solutions de modèles d'écoulement type “depth averaged”. Dans un premier temps, nous détaillons la construction d'approches Volumes Finis pour le système Shallow Water avec termes sources sur maillages non structurés. En se basant sur une reformulation appropriée des équations, nous mettons en place un schéma équilibré et préservant la positivité de la hauteur d'eau, et suggérons des extensions MUSCL adaptées. La méthode est capable de gérer des topographies irrégulières et exhibe de fortes propriétés de stabilité. L'inclusion des termes de friction fait l'objet d'une analyse poussée, aboutissant à l'établissement d'une propriété type “Asymptotic Preserving” à travers l'amélioration d'un autre récent schéma Volumes Finis. La seconde composante de cette étude concerne les méthodes Elements Finis type Galerkin discontinu. Certaines des idées avancées dans le contexte Volumes Finis sont employées pour aborder le système Shallow Water surmaillages triangulaires. Des résultats numériques sont exposés et la méthode se révèle bien adaptée à la description d'une large variété d'écoulements. Partant de ces observations nous proposons finalement d'exploiter ces caractéristiques pour étendre l'approche à une nouvelle famille d'équations type Green-Nadghi. Des validations numériques sont également proposées pour valider le modèle numérique. / This work is devoted to the development of numerical schemes to approximatesolutions of depth averaged flow models. We first detail the construction of Finite Volume approaches for the Shallow Water system with source terms on unstructured meshes. Based on a suitable reformulation of the equations, we implement a well-balanced and positive preserving approach, and suggest adapted MUSCL extensions. The method is shown to handle irregular topography variations and demonstrates strong stabilities properties. The inclusion of friction terms is subject to a thorough analysis, leading to the establishment of some Asymptotic Preserving property through the enhancement of another recent Finite Volume scheme.The second aspect of this study concerns discontinuous Galerkin Finite Elementmethods. Some of the ideas advanced in the Finite Volume context areemployed to broach the Shallow Water system on triangular meshes. Numericalresults are exposed and the method turns out to be well suited to describe a large variety of flows. On these observations we finally propose to exploit its features to extend the approach to a new family of Green-Nadghi equations. Numerical experiments are also proposed to validate this numerical model.

O presente trabalho teve como objetivo o aprimoramento da transesterificação do óleo de palmiste por rota etílica, por meio da atuação simultânea de lipases de diferentes fontes microbianas, visando a produção de biodiesel com teores residuais de monoacilglicerol (MAG) e diacilglicerol (DAG) dentro dos limites exigidos pela legislação ANP no 45/2014 para biocombustíveis. Para tal propósito, as lipases foram imobilizadas em suporte híbrido sílica-hidroxietilcelulose (SiO2- HEC) e os ensaios foram iniciados em regime descontínuo em reator de tanque agitado, temperatura fixa de 45 °C e razão molar óleo:álcool de 1:8. As lipases de Burkholderia cepacia, Pseudomonas fluorescens e Thermomyces lanuginosus, foram utilizadas de maneira isolada e em associação, com base no conhecimento prévio do bom desempenho destas enzimas para a produção de biodiesel. Conforme a capacidade de atuar em diferentes posições da molécula de triacilglicerol, as associações formaram combi-lipases de mesma especificidade (B. cepacia e P. fluorescens) e de diferente especificidade (B. cepacia e T. lanuginosus), com proporções de cada lipase variando de 75, 50 e 25% em relação ao seu par enzimático. Os melhores resultados foram observados quando utilizadas ambas as combinações em proporções equivalentes. Nestas condições, foram obtidas conversões similares (?98%) e ausência de DAG, com redução da viscosidade cinemática do óleo de palmiste de 30,35 para aproximadamente 4,00 mm2/s. Embora as conversões tenham sido próximas, a combi-lipase de diferente especificidade apresentou menor teor de MAG (1,68%, m/m), sendo escolhida como biocatalisador para o estudo em reatores de leito fixo em regime contínuo. Nesta etapa, foram realizados ensaios para testar os efeitos da razão molar óleo:álcool (1:12, 1:10 e 1:8) e do tempo espacial (16 e 14 h) na conversão, qualidade e produtividade do biodiesel. O melhor desempenho foi apresentado pela razão molar de 1:8 com tempo espacial de 16 h, proporcionando teor em MAG residual de 0,62% (m/m), conversão de 98% e produtividade de 30,9 mmolésteres.gcatalisador -1.h-1. Com relação à qualidade do biodiesel formado em termos de viscosidade cinemática (4,22 mm2/s), massa específica (870 kg/m3) e teor residual de MAG (0,62%, m/m), foi verificada adequação aos parâmetros exigidos pela ANP (3-6 mm2/s, 850-900 kg/m3 e <= 0,7%, m/m, respectivamente). / The objective of the present work was to improve the transesterification of palm kernel oil by ethanolic route through simultaneous action of lipases from different microbial sources, aiming to produce biodiesel with residual levels of monoacylglycerol (MAG) and diacylglycerol (DAG) within the limits required by ANP regulation 45/2014 for biofuels. For this purpose, lipases were immobilized on silica-hydroxyethylcellulose hybrid support (SiO2-HEC) and the assays were first carried out in a stirred tank batch reactor, at fixed temperature of 45 oC and oil -to-alcohol molar ratio of 1:8. The lipases from Burkholderia cepacia, Pseudomonas fluorescens and Thermomyces lanuginosus isolated and in association were used, based on the previous knowledge of the good performance of these enzymes for the biodiesel production. According to the ability to act at different positions of the triacylglycerol molecule, the associations formed combilipases of the same specificity (B. cepacia and P. fluorescens) and different specificities (B. cepacia and T. lanuginosus) at proportion of each lipase ranging from 75, 50 and 25% relative to their enzymatic pair. The best results were attained when both combinations were used at equivalent proportions. Under these conditions, similar conversions (?98%) and absence of DAG were obtained, which was consistent with the kinematic viscosity reduction of the palm kernel oil from 30.35 to 4.00 mm2/ s, approximately. Although similar conversions were attained, the combi-lipase of different specificities provided lower MAG contentes (1.68 wt%), being chosen as a biocatalyst for performing continuous runs in packed-bed reactor. In this step, the effects of the molar ratios oil-to-alcohol (1:12, 1:10 and 1:8) and space-times (16 and 14 h) on biodiesel production, quality and productivity were evaluated. The best performance was achieved by using molar ratio of 1:8 and space-time of 16 h, yielding residual MAG contents of 0.62 wt%, conversion of 98% and productivity of 30.9 mmolester.gcatalyst-1.h-1. The quality of biodiesel produced in terms of kinematic viscosity (4.22 mm2/s), specific mass (870 kg/m3) and residual MAG content (0.62 wt%) was found in accordance of ANP resolution (3-6 mm/ s, 850-900 kg/m3 and <= 0.7 wt%, respectively).

On s'intéresse dans ce mémoire aux équations de la magnétohydrodynamique (MHD) dans des milieux hétérogènes, i.e. dans des milieux pouvant présenter des variations (éventuellement brutales) de propriétés physiques. En particulier, on met ici l'accent sur la résolution des équations de Maxwell dans des milieux avec des propriétés magnétiques inhomogènes. On présentera une méthode non standard pour résoudre ce problème à l'aide d'éléments finis de Lagrange. On évoquera ensuite l'implémentation dans le code SFEMaNS, développé depuis 2002 par J.-L. Guermond, C. Nore, J. Léorat, R. Laguerre et A. Ribeiro, ainsi que les premiers résultats obtenus dans les simulations de dynamo. Nous nous intéresserons par exemple au cas de la dynamo dite de Von Kármán, afin de comprendre l'expérience VKS2. En outre, nous aborderons des cas de dynamo en précession, ou encore le problème de la dynamo au sein d'un écoulement de Taylor-Couette. / We focus on the magnetohydrodynamics (MHD) equations in hetereogeneous media, i.e. media with (possibly brutal) variations on the physical properties. In particular, we are interested in solving the Maxwell equations with discontinuous magnetic properties. We introduce a method that is, to the best of our knowledge, new to solve this problem using only Lagrange Finite Elements. We then discuss its implementation in SFEMaNS, a numerical code developped since 2002 by J.-L. Guermond, C. Nore, J. Léorat, R. Laguerre and A. Ribeiro. We show the results of the first dynamo simulations we have been able to make with this solver. For instance, we present a kinematic dynamo in a VKS setup, as well as some results about dynamo action induced either by a Taylor-Couette flow, or by a precessionnally driven flow.

Ce travail vise à améliorer la description à l'échelle du nanomètre des sols argileux expansifs en utilisant la théorie de la fonctionnelle de densité (DFT). L’eau n’est plus considérée comme un solvant continu mais comme un fluide de molécules polaires individuelles. L'objectif est de reproduire les résultats issus de l'expérience ou de la modélisation numérique tels que la présence de couches d'eau discrètes dans l'espace interfolaire ou la variation de la pression de disjonction avec la distance interfolaire dans le régime de gonflement cristallin. Différents phénomènes physiques de complexité croissante sont successivement étudiés. La taille finie des molécules d'eau est tout d'abord prise en compte en modélisant l'eau comme un fluide de sphères dures traité par la théorie fondamentale de la mesure. La nature polaire du solvant est ensuite implicitement considérée en utilisant un potentiel intermoléculaire de Lennard-Jones pour reproduire les différents types d'interactions de Van der Waals. La nature dipolaire de l'eau est ensuite explicitement modélisée par un fluide dipolaire de sphères dures. Ces deux derniers modèles utilisent une approche perturbative de la théorie de la fonctionnelle de densité dans laquelle les effets de corrélation entre les molécules du fluide sont incorporés. Les ions sont finalement ajoutés afin de compléter la description de la double couche électrique. En vue d'une application au génie civil, l'expression améliorée de la pression de disjonction à l'échelle nanométrique est incluse dans une forme modifiée du principe de Terzaghi appliqué aux argiles expansives non-saturées récemment développée dans notre groupe afin de simuler numériquement le comportement hydro-mécanique des argiles gonflantes lors d’essais d'infiltration d’eau / This work aims at improving the nanoscale description of expansive clayey soils using the Density Functional Theory (DFT). Water is no longer considered as a continuous solvent but as a fluid of individual polar molecules in order to recover existing experimental and modeling results such as the presence of discrete water layers in the interplatelet space or the variation of the disjoining pressure with the interplatelet distance at low hydration level. Different physical phenomena of increasing complexity are successively considered. The finite size of the water molecules is firstly taken into account by modeling water as a Hard Sphere fluid using the Fundamental Measure Theory. The polar nature of the water solvent is then implicitly taken into account through a Lennard-Jones potential averaging the different types of Van der Waals interactions. Next the polar nature of the solvent is explicitly modelized by considering water as a Dipolar Hard Sphere fluid. These two fluid models are studied in the framework of the Density Functional Perturbation Theory in which correlation effects between the fluid molecules are incorporated. Ions are finally added in order to complete the Electrical Double Layer description at the nanoscale. With the objective of an application to civil engineering, the improved expression of the disjoining pressure at the nanoscale is included in a modified form of Terzaghi's effective stress principle for unsaturated expansive clays recently developed by our group in order to numerically simulate the hydro-mechanical behavior of expansive clays during water uptake

Estuda-se o problema de equilíbrio sem força de corpo de uma esfera anisotrópica sob compressão radial uniformemente distribuída sobre o seu contorno no contexto da teoria da elasticidade linear clássica. A solução deste problema prediz o fenômeno inaceitável da auto-intersecção em uma região próxima ao centro da esfera para uma dada faixa de parâmetros materiais. Sob o contexto de uma teoria de minimização do funcional de energia potencial total da elasticidade linear clássica com a restrição de que o determinante do gradiente da função mudança de configuração seja injetivo, este fenômeno é eliminado. Aplicam-se duas formulações do Método dos Elementos Finitos de Galerkin Descontínuo (MEFGD) para obter soluções aproximadas para o problema de equilíbrio da esfera sem restrição. A primeira formulação do MEFGD aproxima diretamente os campos de deslocamento e deformação infinitesimal. A consideração do campo adicional de deformação na formulação do MEFGD aumenta o número de graus de liberdade associados aos nós da malha de elementos finitos e, consequentemente, o custo computacional. Com o objetivo de reduzir o número de graus de liberdade, introduz-se neste trabalho uma formulação alternativa do MEFGD. Nesta formulação, o campo de deformação infinitesimal não é obtido diretamente da inversão do sistema de equações resultante, mas sim por pós-processamento, a partir do campo de deslocamento aproximado. As soluções aproximadas obtidas com ambas as formulações do MEFGD são comparadas com a solução exata do problema sem restrição e com soluções aproximadas obtidas com o Método dos Elementos Finitos de Galerkin Clássico (MEFGC). Ambas as formulações do MEFGD fornecem melhores aproximações para a solução exata do que as aproximações obtidas com o MEFGC. Os erros entre a solução exata e as soluções aproximadas obtidas com a formulação alternativa do MEFGD são um pouco maiores do que os erros correspondentes obtidos com a formulação original do MEFGD. Este aumento nos erros é compensado pelo menor esforço computacional exigido pela formulação alternativa. Este trabalho serve de base para o estudo de problemas com restrição de injetividade utilizando o método de Galerkin descontínuo. / The equilibrium problem without body force of an anisotropic sphere under radial compression that is uniformly distributed on the sphere\'s boundary is investigated in the context of the classical linear elasticity theory. The solution of this problem predicts the unacceptable phenomenon of self-intersection in a vicinity of the center of the sphere for a given range of material parameters. This phenomenon can be eliminated in the context of a theory that minimizes the total potential energy of classical linear elasticity subjected to the restriction that the deformation field be injective. Two formulations of the Finite Element Method using Discontinuous Galerkin (MEFGD) are used to obtain approximate solutions for the unconstrained problem. The first formulation of the MEFGD approximates both the displacement and the strain fields. The consideration of the strain as an additional field in the formulation of the MEFGD increases the number of degrees of freedom associated to the finite elements and, therefore, the computational cost. With the objective of reducing the number of degrees of freedom, an alternative formulation of the MEFGD is introduced in this work. In this formulation, the strain field is not obtained directly from the inversion of the resulting linear system of equations, but from a post-processing calculation using the approximate displacement field. The approximate solutions obtained with both formulations of the MEFGD are compared with the exact solution of the problem without restriction and with approximate solutions obtained with the Finite Element Method using Classical Galerkin (MEFGC). Both formulations of the MEFGD yield better approximations for the exact solution than the approximations obtained with the MEFGC. The errors between the exact solution and the approximate solutions obtained with the alternative formulation of the MEFGD are slightly higher than the corresponding errors obtained with the original formulation of the MEFGD. These errors are compensated by the fact that the alternative formulation requires less computational effort than the computational effort required by the original formulation. This work serves as a basis for the study of problems with the injectivity restriction using the discontinuous Galerkin method.

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.

Der Schwarzkäfer Zophobas rugipes lebt in Höhlen im Dung von Fledermäusen. Die Puppen entwickeln sich in dieser Guanoschicht innerhalb von 9 - 12 Tagen. Sie zeigen während der gesamten Entwicklung den für ruhende Insekten typischen diskontinuierlichen Gasaustausch. Die Umgebungsluft im Guano kann durch Zersetzungsprozesse und Luftabschluss wenig Sauerstoff und viel Kohlendioxid enthalten. Die Puppen müssen daher in der Lage sein, externe Hypoxie oder Hyperkapnie zu tolerieren. Da die Stoffwechselrate zu Beginn und zum Ende des Puppenstadiums relativ hoch ist, ändern sich zusätzlich die internen Anforderungen an den Atemgastransport. Ungünstige Lebensbedingungen und sich im Laufe der Entwicklung ändernde Stoffwechselraten erfordern eine respiratorische und metabolische Anpassung der Puppen. Die vorliegende Arbeit untersucht, welchen Einfluss metabolisch gebildetes und atmosphärisches Kohlendioxid auf den Säure-Basen-Haushalt der Puppen von Zophobas rugipes hat. Untersuchungen des Wassergehalts der Puppen zeigte während der gesamten Entwicklung konstante Werte um 60 %. Die Volumina von HL und Gewebe änderten sich durch Histolyse, Histogenese und Resorption von Exuvialflüssigkeit. Die HL zeigte das für omnivore Insekten charakteristische Ionenmuster mit einem [Na+]-[K+]-Verhältnis von 2,4. [Mg2+] in der HL betrug zu Beginn der Entwicklung 83 meq/l. [Mg2+] und [Cl-] in der HL fielen im Laufe der Entwicklung ab. Protein- und Aminosäurekonzentrationen änderten sich uneinheitlich. Die Nettoladung der Aminosäuren war während des gesamten Puppenstadiums positiv. Von den proteinogenen Aminosäuren fehlten in der HL Aspartat und Methionin. Prolin diente als Energielieferant. Phenyalanin und Tyrosin wurden zu Beginn des Entwicklung bei der Sklerotisierung metabolisiert und später wieder angereichert. Tryptophan wurde zunächst angereichert und zum Ende der Entwicklung zum Aufbau von Ommochromen verwendet. CO2-Kapazitanz und Puffereigenschaften der Kompartimente änderten sich während der gesamten Entwicklung nicht. Die hohe CO2-Kapazitanz der HL spiegelte sich in einer hohen Bikarbonatkonzentration wider. Der in vitro bestimmte Nichtbikarbonatpufferwert (betaNB) betrug 17,0 meq/(l*pH) in der HL und 59,3 meq/(l*pH) im Gewebe. Änderungen des Stoffwechsels während der Entwicklung wurden respiratorisch und nicht durch Anpassung von CO2-Kapazitanz oder betaNB kompensiert. Messung von atmungsabhängigen Änderungen des pH-Werts in der HL erfolgte durch Implantation von pH-Mikro-Glaselektroden an 26 Puppen. Der pH-Wert der HL in vivo betrug 6,65 - 7,11. Die Implantation von pH-Elektroden verursachte eine Erhöhung der Stoffwechselrate und eine Verkürzung der Zyklusdauer. Während der Öffnungsperioden stieg der pH-Wert um etwa 0,01 Einheiten je 100 nmol/g CO2 an. Die Verletzung durch die Implantation verursachte eine metabolische Azidose. Diese Azidose wurde durch den Verlust von Bikarbonat, das als CO2 abgeatmet wurde, respiratorisch kompensiert. Gleichzeitig sank der PCO2 in der HL auf Werte unter 25,8 Torr (3,4 kPa). Eine experimentell induzierte Hyperkapnie wurde metabolisch kompensiert. Als Folge stieg der betaNB der HL auf 37,7 meq/(l*pH). Je höher der in der HL gemessene pH-Wert, desto kürzer waren Zyklusdauer und Dauer der Öffnungsperiode. Dieser Zusammenhang gab Hinweise auf eine Atemregulation durch Wahrnehmung von pH-Wert-Änderungen. / The tenebrionid beetle Zophobas rugipes inhabits caves, living in the dung of bats. The pupal stages develop in 9 to 12 days under a layer of guano. Gas exchange is cyclic and discontinuous during entire pupal development. During development, the atmosphere in the dung may become hypoxic and hypercapnic, extreme environmental conditions to be tolerated by the pupae. Since metabolic rate is relatively high in the beginning and the end of the pupal stage, the pupae have to cope with varying internal respiratory conditions. Extreme environmental conditions and varying metabolic rates have to be compensated by respiratory and metabolic adaptations. This study deals with the effects of metabolic and atmospheric carbon-dioxide on the acid-base-status of pupae of Zophobas rugipes, preceded by an investigation of volume, water-content, and soluble components of haemolmyph and tissue, respectively. Water content of the pupae was rather constant around 60 % during the entire pupal stage. Volumes of haemolymph and tissue changed by histolysis, histogenesis and resorption of exuvial fluid. The ratio between [Na+] and [K+] in the haemolymph (2,4) was typical for omnivorous insects. [Mg2+] in the haemolymph was high in the beginning (83 meq/l), but decreased similar to the pattern for [Cl-] during pupal development. Protein concentration and amino acid concentrations varied irregularly. The sum of amino acid charge was positive. Aspartate and Methionine were not detected in the haemolymph. Proline was used as an energy source. Phenylalanine and Tyrosine were metabolised for sclerotisation in the beginning of the pupal stage and were accumulated during the rest of the development. Tryptophane was accumulated in the beginning of pupal development and was then used as a source for ommochromes. CO2-capacitance and non-bicarbonate buffer-value (betaNB) of haemolymph and tissue did not change during pupal development. They were independent of the changes in concentration of the examined ingredients. The high value of CO2-capacitance was related to a high [HCO3-]. betaNB in vitro was 17,0 meq/(l*pH) in the haemolymph and 59,3 meq/(l*pH) in the tissue. Metabolic changes were compensated by respiratory adjustments rather than by adaptation of CO2-capacitance or betaNB. Respiratory changes in haemolymph-pH were recorded by implantation of pH-micro-glas-electrodes in 26 pupae. Haemolymph-pH in vivo was found to be 6,65 - 7,11. Electrode implantation caused an increase of metabolic rate and diminished the duration of the respiratory cycle. Haemolymph-pH increased during the opening periods with about 0,01 units per 100 nmol/g CO2. Injuring the pupae by implantation of electrodes resulted in a development of metabolic acidosis. This was compensated by buffering action of bicarbonate and expiration of CO2. As a consequence, PCO2 decreased to values lower than 25,8 Torr (3,4 kPa). During elevated atmospheric PCO2, the resulting respiratory acidosis was compensated metabolically. As a consequence, betaNB increased to a value of 37,7 meq/(l*pH). The higher pH in the haemolymph, the shorter was the duration of the respiratory cycle and the opening period. This coincidence is possibly an expression of regulation of respiration by perception of changes in pH.

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.

We prove strong convergence of order 1/4 - E for arbitrarily small E > 0 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.

Mes travaux de thèse portent sur le développement de schémas numériques d'ordre élevé en temps et en espace pour la simulation de propagation des ondes. Nous avons proposé de discrétiser dans un premier temps l'équation des ondes par rapport au temps, en utilisant une technique de type équation modifiée. Puis nous avons utilisé une méthode d'éléments finis de type Galerkine discontinue pour la discrétisation en espace. En modifiant l'ordre de la discrétisation, nous avons construit des schémas tout aussi précis que ceux déjà existants pour un coût de mise en oeuvre très intéressant. Après avoir validé numériquement la nouvelle méthode, nous nous sommes intéressés à sa stabilité ainsi qu'à son adaptivité en temps et en espace. Pour arriver à cela, nous avons dû faire une étude précise de la stabilité de la méthode de Galerkine discontinue et nous avons proposé des améliorations à cette technique entraînant des gains de temps significatifs. / My work consists in developing some high order numerical schemes in time and space for the modeling of the wave propagation. We have proposed to first discretize the wave equation with respect to the time using the so called Modified Equation Technique. Then, we have used a Discontinuous Galerkine Finite Element method for the space discretization. Switching the classical discretization process, we have constructed schemes as accurate as the classical ones with a numerical cost very interesting. After the numerical validation of this method, we have focused on its stability and on its adaptibility in time and space. To reach these objectives, we have performed a stability analysis of the Discontinuous Galerkin method and we have proposed some improvements to this technique which imply very important gain in terms of computationnal time.