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Terahertz (THz) spectroscopy can potentially be used to probe and characterize inhomogeneous materials, however spectroscopic identification of such materials from spectral features of diffuse returns is a relatively underdeveloped area of study. In this thesis, diffuse THz scattering from granular media is modeled by applying radiative transfer (RT) theory for the first time in THz sensing. Both classical RT theory and dense media radiative transfer (DMRT) theory based on the quasi-crystalline approximation (QCA) are used to calculate diffuse scattered intensity. The numerical solutions of the vector radiative transfer equations (VRTE) were coded and calculated in MATLAB. The diffuse scattered field from compressed Polyethylene (PE) pellets containing steel spheres was measured in both transmission and reflection using a THz time domain spectroscopy (THz-TDS) system. Measurement results showed energy redistribution by granular media due to volume scattering as well as angle dependent spectral features due to Mie scattering. The RT model was validated by successfully reproducing qualitative features observed in experimental results. Diffuse intensity from granular media containing Teflon, lactose sugar, and C4 explosive was then calculated using the RT models. Simulation results showed the amplitude of diffuse intensity is affected by factors such as grain size, fractional volume of grains, thickness of scattering layer, and scattering angles. Spectral features were also observed in the diffuse intensity spectra from media containing grains with THz spectral signatures. The simulation results suggest the possibility of identifying materials from diffuse intensity spectra.

La prédiction de l'émission infrarouge des jets de propulseurs composites aluminisés nécessite principalement trois étapes : le calcul des grandeurs aérothermochimiques du jet, la conversion de ces grandeurs en propriétés optiques (coefficient d'absorption, coefficient de diffusion, fonction de phase) puis la résolution de l'équation de transfert radiatif. Cette thèse,essentiellement consacrée à cette troisième étape, propose de nouvelles voies pour l'application des modèles de bande aux cas de milieux biphasiques et diffusants.D'une part, nous avons étendu ces modèles aux cas de milieux caractérisés par un déséquilibre thermique entre gaz et particules. D'autre part, nous avons proposé une méthode de séparation de la luminance en deux contributions, appelées respectivement non diffusée et diffusée, à partir d'une idée originale de Liu et al. La contribution non diffusée est solution de l'équation de transfert radiatif obtenue en ignorant les effets de la diffusion. Par conséquent, elle peut être résolue par une formulation en modèles de bande. Cette approche permet de réduire les erreurs de corrélations spectrales au seul terme de luminance diffusée.Nous avons montré l'intérêt de ces approches par comparaison avec une résolution de l'équation de transfert radiatif en raie par raie, sur des milieux représentatifs de situations de télédétection de jets. / Prediction of infrared emission of exhaust plumes from aluminized composite rocket, follows mainly three steps : calculating aero-thermo-chemical values in the plume, converting those valuesto optical properties (absorption coefficient, scattering coefficient and phase function) and resolving the radiative transfer equation. This thesis is mostly devoted to this third step, and proposes new ways to use band models on two-phases and scattering media.Firstly, we extended band models to cases with thermic non equilibrium between gas and particles. Secondly, we proposed a method consisting in splitting radiance in two parts, one called un-scattered and the other scattered, from an original idea of Liu et al. The un-scattered part is solution of the radiative transfer equation obtained by ignoring scattering. As a result, the unscattered radiance can be found by using band models. By this approach, errors on spectral correlations are only present on the scattered radiance.We show the interest of thoses approches by comparing them with a line by line resolutionof the radiative transfer equation, on media representative of remote sensing cases of rocket exhaust plumes.

Since the inverse problem in Diffusive Optical Tomography (DOT) is nonlinear and severely ill-posed, only low resolution reconstructions are feasible when noise is added to the data nowadays. The purpose of this thesis is to improve image reconstruction in DOT of the main optical properties of tissues with some novel mathematical methods. We have used the Landweber (L) method, the Landweber-Kaczmarz (LK) method and its improved Loping-Landweber-Kaczmarz (L-LK) method combined with sparsity or with total variation regularizations for single and simultaneous image reconstructions of the absorption and scattering coefficients. The sparsity method assumes the existence of a sparse solution which has a simple description and is superposed onto a known background. The sparsity method is solved using a smooth gradient and a soft thresholding operator. Moreover, we have proposed an improved sparsity method. For the total variation reconstruction imaging, we have used the split Bregman method and the lagged diffusivity method. For the total variation method, we also have implemented a memory-efficient method to minimise the storage of large Hessian matrices. In addition, an individual and simultaneous contrast value reconstructions are presented using the level set (LS) method. Besides, the shape derivative of DOT based on the RTE is derived using shape sensitivity analysis, and some reconstructions for the absorption coefficient are presented using this shape derivative via the LS method.\\Whereas most of the approaches for solving the nonlinear problem of DOT make use of the diffusion approximation (DA) to the radiative transfer equation (RTE) to model the propagation of the light in tissue, the accuracy of the DA is not satisfactory in situations where the medium is not scattering dominant, in particular close to the light sources and to the boundary, as well as inside low-scattering or non-scattering regions. Therefore, we have solved the inverse problem in DOT by the more accurate time-dependant RTE in two dimensions.

[pt] O presente trabalho apresenta um estudo numérico da transferência de energia por radiação e sua interação com as propriedades radiantes cinzas e espectrais dos gases produtos da combustão e da fuligem que são formados em um processo de combustão turbulenta. Assim, utilizam-se sistemas de forno/- queimador que operam em regime de chama não pré-misturada de maneira a avaliar, através da dinâmica dos fluidos computacional (CFD), a influência que exercem os diversos modelos de propriedades radiantes sobre a representação da termoquímica do escoamento reativo. Com o objetivo de identificar as principais características e deficiências que apresentam cada um destes modelos, foram considerados dois cenários. O primeiro, correspondente a um problema de radiação unidimensional de um sistema homogêneo e não isotérmico onde são estudados, modelos de propriedades radiantes (i) disponíveis em um software comercial de CFD e (ii) aqueles que foram implementados neste trabalho. Além disso, foi empregado um código numérico que determina as propriedades radiantes espectrais de gases produtos da combustão e da fuligem através de uma abordagem de banda estreita. Para este fim, este código foi acoplado com o software de CFD. Em seguida, dois queimadores de porte laboratorial são empregados de forma a avaliar a capacidade preditiva dos modelos de propriedades radiantes: o primeiro queima propano gasoso e ar enriquecido com oxigênio e o segundo utiliza querosene líquido e oxigênio como reagentes. Dados experimentais de fluxo de calor radiante e de fração volumétrica da fuligem são utilizados para comparação com os resultados obtidos da simulação. Para ambas as configurações de queimador foi também estudado o modelo de Moss-Brookes para previsão da formação/consumo da fuligem. Os resultados obtidos demonstraram o bom desempenho da maioria dos modelos de propriedades radiantes estudados. Em particular, a abordagem de banda estreita foi o que melhor previu a radiação térmica. Além disso, a sua utilização com o modelo de Moss-Brookes levou à melhor previsão da fração volumétrica da fuligem. / [en] This work presents a numerical study of radiation heat transfer and its interaction with gray and spectral radiation of combustion products and soot that are formed in a turbulent combustion process. Different burner/furnace systems operating in a non-premixed combustion regime were used in order to evaluate, through computational fluid dynamics (CFD), the influence of several radiant properties models. Aiming to identify the key features and shortcomings that exhibit each of these models, two scenarios were considered. The first corresponds to a 1-D radiation problem where radiative properties models of a homogeneous non isothermal system are studied as (i) available CFD commercial software and (ii) those implemented in this work. Moreover, a numerical code was used in order to determine, through a narrow band approach, the spectral radiative properties of soot and combustion products. For this purpose, this code was coupled with the CFD software. Then, two laboratory-scale burners are used to assess the predictive capacity of radiative properties models: the first, burning propane and enriched air oxygen, and the second uses kerosene and oxygen as reactants. Measurements of radiant heat flux and soot volumetric fraction are used for comparison with simulation results. For both configurations, the performance of the Moss-Brookes model for predicting the soot production was also studied. The results of this study demonstrated the good performance of the majority of the radiant properties models studied. Particularly, the narrow band approach was the model that provided the best thermal radiation prediction. Moreover, the combination of the narrow band approach with the Moss-Brookes model lead to the best prediction of soot volume fraction.

Les travaux de la présente thèse portent sur l’estimation d'erreur a posteriori pour les solutions numériques par éléments finis de l'équation des ondes élastiques dans les milieux hétérogènes. Deux types d’estimation ont été développés. Le premier considère directement l’équation élastodynamique et conduit à un nouvel estimateur d'erreur a posteriori explicite en norme L∞ en temps. Les principales caractéristiques de cet estimateur explicite sont l'utilisation de la méthode de résidus et le développement de reconstructions en temps et en espace selon les différentes régularités exigées par les différents termes contribuant à l’obtention d’une borne supérieure. L’analyse numérique de cet estimateur dans le cas des maillages uniformes montre qu’il assure bien une borne supérieure mais avec une propriété asymptotique qui reste à améliorer. Le deuxième type d’estimateur d’erreur est développé dans le contexte de la propagation des ondes à haute fréquence dans des milieux hétérogènes à l’échelle mésoscopique. Il s’agit d’une nouvelle erreur en résidus basée sur l'équation de transfert radiatif, qui est obtenue par un développement asymptotique multi-échelle de l'équation d'onde en utilisant la transformation de Wigner en espace-temps. Les résidus sont exprimés en termes de densités énergétiques calculés dans l’espace des phases pour les solutions d’onde numériques transitoires par éléments finis. L’analyse numérique de cette erreur appliquée aux milieux homogènes et hétérogènes en 1D a permis de valider notre approche. Les champs d’application visés sont la propagation des ondes sismiques dans les milieux géophysiques ou la propagation des ondes ultrasonores dans les milieux polycristallins. / This thesis work deals with a posteriori error estimates for finite element solutions of the elastic wave equation in heterogeneous media. Two different a posteriori estimation approaches are developed. The first one, in a classical way, considers directly the elastodynamic equation and results in a new explicit error estimator in a non-natural L∞ norm in time. Its key features are the use of the residual method and the development of space and time reconstructions with respect to regularities required by different residual operators contributing to the proposed error bound. Numerical applications of the error bound with different mesh sizes show that it gives rise to a fully computable upper bound. However, its effectivity index and its asymptotic accuracy remain to be improved. The second error estimator is derived for high frequency wave propagation problem in heterogeneous media in the weak coupling regime. It is a new residual-type error based on the radiative transfer equation, which is derived by a multi-scale asymptotic expansion of the wave equation in terms of the spatio-temporal Wigner transforms of wave fields. The residual errors are in terms of angularly resolved energy quantities of numerical solutions of waves by finite element method. Numerical calculations of the defined errors in 1D homogeneous and heterogeneous media allow validating the proposed error estimation approach. The application field of this work is the numerical modelling of the seismic wave propagation in geophysical media or the ultrasonic wave propagation in polycrystalline materials.

Esta tesis está centrada en el modelado de la acústica de salas en espacios cerrados mediante el uso de una ecuación de transferencia radiativa y una ecuación de difusión En este trabajo se investiga cómo a través de estos modelos teóricos se pueden simular el campo sonoro en espacios complejos. Recientemente, el modelo de la ecuación de fusión ha sido prppuesto para ser utilizado en el modelado de la acústica de salas con superficies que reflejan el sonido de forma totalmente difusa. Este enfoque del uso de la ecuación de la disusión de sido intensamente investigado en los últimos años, ya que proporciona una alta eficiencia y flexibilidad para simular las distribuciones del campo sonoro en diferentes tipos de salas; sin embargo, sólo se han realizado unas pocas investigaciones con el objetivo de indagar sobre la precisión y las limitaciones de este método alternativo. Por lo tanto, en primer lugar se presenta un modelo basado en la ecuación de transferencia por radiación siendo meta principal el unificar una amplia gama de métodos geométricos de modelado de acústica de salas. Además, esta tesis está especialmente dedicada a establecer las bases y suposiciones que permitan obtener un modelo de difusión acústica como particularización del modelo de transferencia radiativa con el objetivo de conseguir una descripción clara y adecuada de sus ventajas y limitaciones desde el punto de vista teórico. Este trabajo permite enlazar directamente al modelo de la ecuación de difusión con el grupo de métodos de la acústica geométrica reforzando sus características y permitiendo una adecuada comparación con estos métodos ampliamente reconocidos. Una vez realizado este análisis teórico, esta tesis también se dedica a cuestiones relativas a la implementación numérica del modelo acústico de la ecuación de difusión . En este trabajo, se modela el campo sonoro a través de esquemas en diferencias finitas. Los resultados de este estudio proporcionan soluciones simples y practicas que muestran unos requerimientos computacionales bajos tanto de consumo de memoria como de tiempo. / Navarro Ruiz, JM. (2012). Discrete-time modelling of diffusion processes for room acoustics simulation and analysis [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/14861

A novel technique for measuring gas temperature and spectral particle emissivity in high-temperature gas-particle streams is presented. The main application of this optical sensor is to improve the process control of batch unit operations, such as steelmaking furnaces. The spectral emission profile of CO and CO2 and the continuous particle emission in the 3.5 to 5 μm wavelength region was recorded and analyzed in real time with a low-resolution passive sensor. The sensor consisted of light collecting optics, a dispersion element (grating spectrometer) and a 64-pixel pyroelectric array. Wavelength and radiance calibrations were performed. The temperature of the gas-particle medium (Tg+p) followed from the least-squares minimization of the difference between the measured radiance in the 4.56-4.7 μm region –which saturates due to the large CO2 concentrations and path lengths in industrial furnaces– and the corresponding blackbody radiance. Particle emissivity (εp) was calculated at 3.95 μm from an asymptotic approximation of the Radiative Transfer Equation that yields the emerging radiance from a semi-infinite particle cloud. The major source of error in the magnitude of Tg+p and εp could come from particle scattering. Through the method of embedded invariance an expression was developed to estimate the lowering effect of particle size and volume fraction on the saturation of the 4.56-4.7 μm CO2 emission region. An iterative procedure for correcting the values of the gas-particle temperature and particle emissivity was applied to the datasets from the two industrial tests. Results from the measurement campaigns with the infrared sensor prototype at two full-scale furnaces are presented. A proof-of-concept test at a coal-fired boiler for electricity production was followed by more extensive measurements at a Basic Oxygen Furnace (BOF) for steelmaking. The second test provided temperature and particle emissivity profiles for eight heats, which highlighted the simplicity of the technique in obtaining in-situ measurements for modeling studies. Through the analysis of the particle emissivity profile in the BOF and the definition of a new variable –the minimum carbon time– a novel end-point strategy to stop the injection of high-purity oxygen during low-carbon heats in BOF converters was proposed.

A novel technique for measuring gas temperature and spectral particle emissivity in high-temperature gas-particle streams is presented. The main application of this optical sensor is to improve the process control of batch unit operations, such as steelmaking furnaces. The spectral emission profile of CO and CO2 and the continuous particle emission in the 3.5 to 5 μm wavelength region was recorded and analyzed in real time with a low-resolution passive sensor. The sensor consisted of light collecting optics, a dispersion element (grating spectrometer) and a 64-pixel pyroelectric array. Wavelength and radiance calibrations were performed. The temperature of the gas-particle medium (Tg+p) followed from the least-squares minimization of the difference between the measured radiance in the 4.56-4.7 μm region –which saturates due to the large CO2 concentrations and path lengths in industrial furnaces– and the corresponding blackbody radiance. Particle emissivity (εp) was calculated at 3.95 μm from an asymptotic approximation of the Radiative Transfer Equation that yields the emerging radiance from a semi-infinite particle cloud. The major source of error in the magnitude of Tg+p and εp could come from particle scattering. Through the method of embedded invariance an expression was developed to estimate the lowering effect of particle size and volume fraction on the saturation of the 4.56-4.7 μm CO2 emission region. An iterative procedure for correcting the values of the gas-particle temperature and particle emissivity was applied to the datasets from the two industrial tests. Results from the measurement campaigns with the infrared sensor prototype at two full-scale furnaces are presented. A proof-of-concept test at a coal-fired boiler for electricity production was followed by more extensive measurements at a Basic Oxygen Furnace (BOF) for steelmaking. The second test provided temperature and particle emissivity profiles for eight heats, which highlighted the simplicity of the technique in obtaining in-situ measurements for modeling studies. Through the analysis of the particle emissivity profile in the BOF and the definition of a new variable –the minimum carbon time– a novel end-point strategy to stop the injection of high-purity oxygen during low-carbon heats in BOF converters was proposed.

[pt] Estudamos duas classes de equações diferenciais parciais, nomeadamente: uma equação de transferência radiativa e uma equação do calor duplamente não-linear. O primeiro modelo envolve uma equação não-local, na presença de um operador de espalhamento. Estuda-se a boa colocação do problema no semi-plano, no regime peaked. Prova-se um lema de averaging, que produz regularidade interior para o problema, além de regularização fracionária para as derivadas temporais da solução. O segundo conjunto de resultados da tese trata de uma equação de Trudinger com graus de não-linearidade distintos. Aproxima-se este problema pela p-equação do calor e importa-se regularidade da última para a primeira. Como consequência, mostra-se um resultado de regularidade melhorada no contexto não homogêneo. / [en] We consider two classes of partial differential equations. Namely: the radiative transfer equation and a doubly nonlinear model. The former concerns a nonlocal problema, driven by a scattering operator. We study the well-posedness of solutions in the peaked regime, for the half-space. A new averaging lemma yields interior regularity for the solutions and improved fractional regularization for the time derivatives. The second model we examine is a Trudinger equation with distinct nonlinearities degrees. Inspired by ideas launched by L. Caffarelli, we resort to approximation methods and prove improved regularity results for the solutions. The strategy is to relate our equation with p-caloric functions.