On retrouve dans la nature un nombre impressionnant de matériaux semi-transparents tels le marbre, le jade ou la peau, ainsi que plusieurs liquides comme le lait ou les jus. Que ce soit pour le domaine cinématographique ou le divertissement interactif, l'intérêt d'obtenir une image de synthèse de ce type de matériau demeure toujours très important. Bien que plusieurs méthodes arrivent à simuler la diffusion de la lumière de manière convaincante a l'intérieur de matériaux semi-transparents, peu d'entre elles y arrivent de manière interactive. Ce mémoire présente une nouvelle méthode de diffusion de la lumière à l'intérieur d'objets semi-transparents hétérogènes en temps réel. Le coeur de la méthode repose sur une discrétisation du modèle géométrique sous forme de voxels, ceux-ci étant utilisés comme simplification du domaine de diffusion. Notre technique repose sur la résolution de l'équation de diffusion à l'aide de méthodes itératives permettant d'obtenir une simulation rapide et efficace. Notre méthode se démarque principalement par son exécution complètement dynamique ne nécessitant aucun pré-calcul et permettant une déformation complète de la géométrie. / We find in nature several semi-transparent materials such as marble, jade or skin, as well as liquids such as milk or juices. Whether it be for digital movies or video games, having an efficient method to render these materials is an important goal. Although a large body of previous academic work exists in this area, few of these works provide an interactive solution. This thesis presents a new method for simulating light scattering inside heterogeneous semi-transparent materials in real time. The core of our technique relies on a geometric mesh voxelization to simplify the diffusion domain. The diffusion process solves the diffusion equation in order to achieve a fast and efficient simulation. Our method differs mainly from previous approaches by its completely dynamic execution requiring no pre-computations and hence allowing complete deformations of the geometric mesh.

Das globale Klimasystem ist ein ausgesprochen komplexes und hochgradig nichtlineares System mit einer Vielzahl von Einflüssen und Interaktionen zwischen Variablen und Parametern. Komplementär zu der Beschreibung des Systems mit globalen Klimamodellen, kann Klima anhand der Interaktionsstruktur des Gesamtsystems durch Netzwerke beschrieben werden. Statt Details so genau wie möglich zu modellieren, werden hier Zeitreihendaten verwendet um zugrundeliegende Strukturen zu finden. Die Herausforderung liegt dann in der Interpretation dieser Strukturen. Um mich der Frage nach der Interpretation von Netzwerkmaßen zu nähern, suche ich nach einem allgemeinen Zusammenhang zwischen Eigenschaften der Netzwerktopologie und Eigenschaften des zugrundeliegenden physikalischen Systems. Dafür werden im Wesentlichen zwei Methoden entwickelt, die auf der Analyse von Temperaturentwicklungen gemäß der Advektions-Diffusions-Gleichung (ADE) basieren. Für die erste Methode wird die ADE mit offenen Randbedingungen und δ-peak Anfangsbedingungen gelöst. Die resultierenden lokalen Temperaturprofile werden verwendet um eine Korrelationsfunktion und damit ein Netzwerk zu definieren. Diese Netzwerke werden analysiert und mit Klimanetzen aus Daten verglichen. Die zweite Methode basiert auf der Diskretisierung der stochastischen ADE. Die resultierende lineare, stochastische Rekursionsgleichung wird verwendet um eine Korrelationsmatrix zu definieren, die nur von der Übergangsmatrix und der Varianz des stochastischen Störungsterms abhängt. Ich konstruiere gewichtete und ungewichtete Netzwerke für vier verschiedene Fälle und schlage Netzwerkmaße vor, die zwischen diesen Systemen zu unterscheiden helfen, wenn nur das Netzwerk und die Knotenpositionen gegeben sind. Die präsentierten Rekonstruktionsmethoden generieren Netzwerke, die konzeptionell und strukturell Klimanetzwerken ähneln und können somit als "proof of concept" der Methode der Klimanetzwerke, sowie als Interpretationshilfe betrachtet werden. / The earth’s climate is an extraordinarily complex, highly non-linear system with a multitude of influences and interactions between a very large number of variables and parameters. Complementary to the description of the system using global climate models, in recent years, a description based on the system’s interaction structure has been developed. Rather than modelling the system in as much detail as possible, here time series data is used to identify underlying large scale structures. The challenge then lies in the interpretation of these structures. In this thesis I approach the question of the interpretation of network measures from a general perspective, in order to derive a correspondence between properties of the network topology and properties of the underlying physical system. To this end I develop two methods of network construction from a velocity field, using the advection-diffusion-equation (ADE) for temperature-dissipation in the system. For the first method, the ADE is solved for δ-peak-shaped initial and open boundary conditions. The resulting local temperature profiles are used to define a correlation function and thereby a network. Those networks are analysed and compared to climate networks from data. Despite the simplicity of the model, it captures some of the most salient features of climate networks. The second network construction method relies on a discretisation of the ADE with a stochastic term. I construct weighted and unweighted networks for four different cases and suggest network measures, that can be used to distinguish between the different systems, based on the topology of the network and the node locations. The reconstruction methods presented in this thesis successfully model many features, found in climate networks from well-understood physical mechanisms. This can be regarded as a justification of the use of climate networks, as well as a tool for their interpretation.

The convective drying of thin layers of multicomponentliquid mixtures into an inert gas, and the influence ofdifferent process controlling mechanisms on drying selectivityis studied. Drying experiments under gas-phase-controlledconditions are performed by low intensity evaporation, fromfree liquid surfaces, of ternary mixtures without non-volatilesolutes. Liquid-side-controlled experiments are carried out bydrying a multicomponent polymeric solution containing twovolatile components, one non-volatile polymer and an optionalnonvolatile softening substance. Mathematical models to describe gas- andliquid-side-controlled drying based on interactive diffusion inboth liquid and gas phases as the main mechanisms for masstransfer are developed. For gas-phase-controlled drying, astability analysis of the ordinary differential equations thatdescribes the evaporation process is performed. Isothermal andnon-isothermal drying processes are considered in batch andcontinuous modes. The mathematical model to describe thecomposition profiles during batch drying of the polymeric film,considering liquid resistance, is solved numerically. Due tothe lack of experimental data, properties for this polymericsystem are estimated by using established methods. Ananalytical solution of the diffusion equation, by assuming anisothermal drying process and a constant matrix ofmulticomponent diffusion coefficients is developed. For thecontinuous case, liquid-side resistance is studied by modellingevaporation of a multicomponent falling liquid film into aninert gas including indirect heating. The results of the gas-phase-controlled model are in goodagreement with experimental results. For the polymeric film,the agreement is only qualitative since the model does notaccount for a membrane that develops on the film surface. Thestability analysis permits the prediction of trajectories andfinal state of a liquid mixture in a gas-phase-controlleddrying process. For isothermal evaporation of ternary mixturesinto pure gas, the solutions are trajectories in the phaseplane represented by a triangular diagram of compositions. Thepredicted ternary dynamic azeotropic points are unstable orsaddle. On the other hand, binary azeotropes are stable whenthe combination of the selectivities of the correspondingcomponents is negative. In addition, pure component singularpoints are stable when they are contained within theirrespective isolated negative selectivity zones. Undernon-isothermal conditions, maximum temperature valuescharacterise stable azeotropes. Incremental loading of the gaswith one or more of the components leads to a node-saddlebifurcation, where a saddle azeotrope and a stable azeotropecoalesce and disappear. For continuous drying, the singularpoints are infinite and represent dynamic equilibrium pointswhose stability is mainly dependent on the ratio of inletgas-to-liquid flow rates. As long as the process isgas-phasecontrolled, these results also apply to a porous solidcontaining a liquid mixture. In general, liquid-side control makes the drying processless selective but it is difficult to maintain this conditionduring the whole process. Under the influence of its owndynamics, a process starting as liquid-side-controlled tendstowards a gas-phase-controlled process. The presence ofnon-volatile components and indirect heating may delay thisdevelopment. Considering the evolution of the processcontrolling steps and its influence on selectivity, a modelaimed at describing the complete trajectory of a drying orevaporation process must include the coexistence of allrelevant mechanisms. Keywords:ternary mixture, falling film, diffusionequation, gas-phase control, liquid-phase control, selectivity,stability analysis, polymeric solution, evaporation, azeotrope,batch drying, continuous drying.

During the development of multicellular organisms, organs grow to well-defined shapes and sizes. The proper size and patterning of tissues are ensured by signaling molecules as e.g. morphogens. Secreted from a restricted source, morphogens spread into the adjacent target tissue where they form a graded concentration profile. Upon binding of the morphogens to receptors on the cell surfaces, the morphogenetic signal is transduced inside the cell via the phosphorylation of transcription factors, which subsequently regulate the expression of different target genes. Thus, cell fates are determined by the local concentration of such morphogens. In this work, we investigate three key aspects of morphogenetic signaling processes in growing tissues. First, we study the mechanics of tissue growth via cell division and cell death. We examine the rearrangements of cells on large scales and times by developing a continuum theory which describes the growing tissue as an active complex fluid. In our description we include anisotropic stresses generated by oriented cell division, and we show that average cellular trajectories exhibit anisotropic scaling behaviors. Our description is used to study experimentally measured shape changes of the developing wing disk of the fruit fly Drosophila melanogaster. Second, we focus on the spreading of morphogens in growing tissues. We show that the flow field of cell movements due to oriented cell division and cell death causes a drift term in the morphogen transport equation, which captures the stretching and dilution of the concentration profile. Comparing our theoretical results to recent experiments in the Drosophila wing disk, we find that the transport of the morphogen Dpp is mainly intracellular. We moreover show that the decay length of the Dpp gradient increases during development as a result of changing degradation rate and diffusion coefficient, whereas the drift of molecules due to growth is negligible. Thus growth does not affect the decay length of the gradient, but the decay length of the gradient might affect the tissue growth rate as discussed in this work. Finally, we develop a microscopic theoretical description of the intracellular transduction machinery of morphogenetic signals within an individual cell. Our description captures the kinetics of the trafficking of proteins between different cellular compartments in response to receptor-bound signaling molecules. Analyzing experimental data at the Drosophila neuromuscular junction, we show that the morphogenetic signaling is modulated by synaptic signaling via neuronal action potentials.

<p>The convective drying of thin layers of multicomponentliquid mixtures into an inert gas, and the influence ofdifferent process controlling mechanisms on drying selectivityis studied. Drying experiments under gas-phase-controlledconditions are performed by low intensity evaporation, fromfree liquid surfaces, of ternary mixtures without non-volatilesolutes. Liquid-side-controlled experiments are carried out bydrying a multicomponent polymeric solution containing twovolatile components, one non-volatile polymer and an optionalnonvolatile softening substance.</p><p>Mathematical models to describe gas- andliquid-side-controlled drying based on interactive diffusion inboth liquid and gas phases as the main mechanisms for masstransfer are developed. For gas-phase-controlled drying, astability analysis of the ordinary differential equations thatdescribes the evaporation process is performed. Isothermal andnon-isothermal drying processes are considered in batch andcontinuous modes. The mathematical model to describe thecomposition profiles during batch drying of the polymeric film,considering liquid resistance, is solved numerically. Due tothe lack of experimental data, properties for this polymericsystem are estimated by using established methods. Ananalytical solution of the diffusion equation, by assuming anisothermal drying process and a constant matrix ofmulticomponent diffusion coefficients is developed. For thecontinuous case, liquid-side resistance is studied by modellingevaporation of a multicomponent falling liquid film into aninert gas including indirect heating.</p><p>The results of the gas-phase-controlled model are in goodagreement with experimental results. For the polymeric film,the agreement is only qualitative since the model does notaccount for a membrane that develops on the film surface. Thestability analysis permits the prediction of trajectories andfinal state of a liquid mixture in a gas-phase-controlleddrying process. For isothermal evaporation of ternary mixturesinto pure gas, the solutions are trajectories in the phaseplane represented by a triangular diagram of compositions. Thepredicted ternary dynamic azeotropic points are unstable orsaddle. On the other hand, binary azeotropes are stable whenthe combination of the selectivities of the correspondingcomponents is negative. In addition, pure component singularpoints are stable when they are contained within theirrespective isolated negative selectivity zones. Undernon-isothermal conditions, maximum temperature valuescharacterise stable azeotropes. Incremental loading of the gaswith one or more of the components leads to a node-saddlebifurcation, where a saddle azeotrope and a stable azeotropecoalesce and disappear. For continuous drying, the singularpoints are infinite and represent dynamic equilibrium pointswhose stability is mainly dependent on the ratio of inletgas-to-liquid flow rates. As long as the process isgas-phasecontrolled, these results also apply to a porous solidcontaining a liquid mixture.</p><p>In general, liquid-side control makes the drying processless selective but it is difficult to maintain this conditionduring the whole process. Under the influence of its owndynamics, a process starting as liquid-side-controlled tendstowards a gas-phase-controlled process. The presence ofnon-volatile components and indirect heating may delay thisdevelopment. Considering the evolution of the processcontrolling steps and its influence on selectivity, a modelaimed at describing the complete trajectory of a drying orevaporation process must include the coexistence of allrelevant mechanisms.</p><p><b>Keywords:</b>ternary mixture, falling film, diffusionequation, gas-phase control, liquid-phase control, selectivity,stability analysis, polymeric solution, evaporation, azeotrope,batch drying, continuous drying.</p>

Many physical problems lead to boundary value problems for partial differential equations, which can be solved with the finite element method. In order to construct adaptive solution algorithms or to measure the error one aims at reliable a posteriori error estimators. Many such estimators are known, as well as their theoretical foundation. Some boundary value problems yield so-called anisotropic solutions (e.g. with boundary layers). Then anisotropic finite element meshes can be advantageous. However, the common error estimators for isotropic meshes fail when applied to anisotropic meshes, or they were not investigated yet. For rectangular or cuboidal anisotropic meshes a modified error estimator had already been derived. In this paper error estimators for anisotropic tetrahedral or triangular meshes are considered. Such meshes offer a greater geometrical flexibility. For the Poisson equation we introduce a residual error estimator, an estimator based on a local problem, several Zienkiewicz-Zhu estimators, and an L_2 error estimator, respectively. A corresponding mathematical theory is given.For a singularly perturbed reaction-diffusion equation a residual error estimator is derived as well. The numerical examples demonstrate that reliable and efficient error estimation is possible on anisotropic meshes. The analysis basically relies on two important tools, namely anisotropic interpolation error estimates and the so-called bubble functions. Moreover, the correspondence of an anisotropic mesh with an anisotropic solution plays a vital role. AMS(MOS): 65N30, 65N15, 35B25

On retrouve dans la nature un nombre impressionnant de matériaux semi-transparents tels le marbre, le jade ou la peau, ainsi que plusieurs liquides comme le lait ou les jus. Que ce soit pour le domaine cinématographique ou le divertissement interactif, l'intérêt d'obtenir une image de synthèse de ce type de matériau demeure toujours très important. Bien que plusieurs méthodes arrivent à simuler la diffusion de la lumière de manière convaincante a l'intérieur de matériaux semi-transparents, peu d'entre elles y arrivent de manière interactive. Ce mémoire présente une nouvelle méthode de diffusion de la lumière à l'intérieur d'objets semi-transparents hétérogènes en temps réel. Le coeur de la méthode repose sur une discrétisation du modèle géométrique sous forme de voxels, ceux-ci étant utilisés comme simplification du domaine de diffusion. Notre technique repose sur la résolution de l'équation de diffusion à l'aide de méthodes itératives permettant d'obtenir une simulation rapide et efficace. Notre méthode se démarque principalement par son exécution complètement dynamique ne nécessitant aucun pré-calcul et permettant une déformation complète de la géométrie. / We find in nature several semi-transparent materials such as marble, jade or skin, as well as liquids such as milk or juices. Whether it be for digital movies or video games, having an efficient method to render these materials is an important goal. Although a large body of previous academic work exists in this area, few of these works provide an interactive solution. This thesis presents a new method for simulating light scattering inside heterogeneous semi-transparent materials in real time. The core of our technique relies on a geometric mesh voxelization to simplify the diffusion domain. The diffusion process solves the diffusion equation in order to achieve a fast and efficient simulation. Our method differs mainly from previous approaches by its completely dynamic execution requiring no pre-computations and hence allowing complete deformations of the geometric mesh.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-06-11T23:25:51Z No. of bitstreams: 1 RUBENS MACIEL MIRANDA PINHEIRO – TESE (PPGEP) 2017.pdf: 3597155 bytes, checksum: c7a82fbab15a4a78e7d7a4dfdee185c5 (MD5) / Made available in DSpace on 2018-06-11T23:25:51Z (GMT). No. of bitstreams: 1 RUBENS MACIEL MIRANDA PINHEIRO – TESE (PPGEP) 2017.pdf: 3597155 bytes, checksum: c7a82fbab15a4a78e7d7a4dfdee185c5 (MD5) Previous issue date: 2017-03-03 / Objetivou-se com este trabalho avaliar o processo difusivo na desidratação osmótica , seguida de secagem em estufa, de melão cortado em formato de cubo com ênfase na modelagem matemática, análises físico-química e sensorial do produto obtido. As cinéticas características do processo de desidratação osmótica e da secagem em estufa são descritas por meio de dois modelos matemáticos que usam soluções analíticas da equação de difusão, em coordenadas cartesianas, com condição de contorno de primeiro e terceiro tipo. Às soluções analíticas foram acoplados algoritmos de otimização propostos neste trabalho, escritos na linguagem FORTRAN, que se baseiam na remoção ótima de pontos experimentais, visando-se à determinação dos parâmetros termofísicos para a descrição das cinéticas de absorção de sacarose e de remoção de água do melão. Foram realizados testes comparativos entre os otimizadores desenvolvidos com os resultados obtidos por outros softwares, os quais também utilizam as condições de contorno de primeiro (Prescribed) e terceiro tipo (Convective). Esta comparação possibilitou analisar a capacidade dos otimizadores propostos de encontrar os valores ótimos nos processos de transferência de massa. Adicionalmente, os cubos de melões desidratados foram submetidos à avaliação físico-química, pelas determinações de atividade de água, acidez, pH, açucares, cinzas, cor e firmeza, bem como, a avaliação sensorial pelos testes de aceitação e intenção de compra. Os dados foram obtidos em experimentos de desidratação osmótica de melão (cortados em pedaços de 10 mm de aresta) usando soluções osmodesidratante com teor de sólidos solúveis totais de 25, 45 e 65 ºBrix . A secagem posterior foi realizada em estufa, nas temperaturas de 50, 60 e 70 ºC. Os resultados indicaram que os otimizadores propostos têm capacidade para obter os parâmetros necessários ao estudo proposto neste trabalho. Constatou-se, através dos valores obtidos para o coeficiente de transferência convectiva, número de Biot e indicadores estatísticos que a condição de contorno mais adequada para descrever o processo que rege a transferência de massa é a condição de terceiro tipo. Verificou-se, através da análise sensorial, que a amostra com maior aceitação pelos provadores foi aquela submetida a desidratação osmótica na concentração de 65 ºBrix e secagem posterior na temperatura de 50 ºC, sendo que as maiores concentrações de sacarose e temperaturas de secagem favoreceram maior remoção da água, todavia as amostras submetidas às maiores temperaturas complementares apresentaram maior escurecimento enzimático. Todas as amostras apresentaram atividades de água dentro dos valores considerados microbiologicamente seguros após a secagem em estufa. / The present study makes an assessment of the diffusive process used in osmotic dehydration of melon sliced into cubes following kiln-drying based on mathematical modeling, considering the physicochemical and sensory properties of the product. The kinetic features of both osmotic dehydration and kiln-drying are described by means of two mathematical models using the analytical solution of the diffusion equation in conjunction with Cartesian coordinates of the first and third kind boundary conditions. In the present work, optimization algorithms have been correlated to analytical solutions. These algorithms were written in FORTRAN based on the optimum removal of experimental points so as to determine the thermophysical parameters with the purpose of describingthe melon solid absorption kinetics and moisture removal.Comparative tests have been conducted between the optimizers implemented for the present study. These were based on the results obtained by other software which also uses contour conditions of the first type (Prescribed) and the third type (Convective). As a result, it waspossible to analyze the efficiency of the proposed optimizers to determine the optimal values along mass transfer processes. In addition, the dehydrated melon cubes were submitted to physicochemical evaluation, considering water activity, acidity, pH, sugars, ash, color and firmness. They were also submitted to sensory evaluati on as determined bythe acceptance tests and purchase intention.The data were obtained via experiments conducted on the osmotic dehydration of melons (cut into pieces of 10 mm) using osmodesidratant solutions with total soluble solid contents of 25, 45 and 65 ºBrix. The drying was done in an oven at temperatures of 50, 60 and 70 ºC. Results demonstrated that the proposed optimizers can provide the necessary parameters for the study proposed in the present work. It has been verified, considering the values obtained for the convective transfer coefficient, Biot number and for the statistical indicators that the most adequate contour condition to describe the process governing mass transfer is that of the third kind condition. The sensorial analysis has also revealed that the sample with the greater acceptance by the testers was the one that underwe nt osmotic dehydration ata 65 ºBrix concentration and subsequent drying at a temperature of 50 ºC, considering as well that higher concentrations of sucrose and drying temperatures favored better water removal. However, the samples submitted to higher complementary temperatures displayed greater enzymatic browning. All samples have exhibited, after oven drying, water activities within values considered microbiologically safer.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.