O espalhamento eletromagnético por uma esfera com propriedades ópticas e raio arbitrários, conhecido como espalhamento de Lorenz-Mie, ou por um cilindro circular infinito, pode ser resolvido analiticamente e é comumente tratado dentro da abordagem de espalhadores dielétricos. Na região óptica, tanto meio circundante quanto partícula espalhadora possuem o mesmo valor de permeabilidade magnética. A ausência do magnetismo nessa região do espectro torna o índice de refração relativo entre os meios interno e externo ao espalhador homogêneo equivalente ao respectivo índice de impedância óptica. Em regiões espectrais de micro-ondas ou radiofrequências, entretanto, materiais ferro- e ferrimagnéticos podem exibir valores absolutos de permeabilidade magnética extremamente elevados, reduzindo então a impedância óptica em comparação ao valor correspondente de índice de refração relativo. Uma característica marcante vinculada ao magnetismo no centro espalhador é que pequenas partículas comparadas com o comprimento de onda (parâmetros de tamanho na região de Rayleigh) podem apresentar grandes seções de choque de extinção a despeito de suas pequenas seções de choque geométricas. Isso torna possível, fisicamente, a presença de picos de ressonância morfológica na energia eletromagnética interna ao centro espalhador mesmo na região de parâmetros de tamanho inferiores à unidade. Em especial, mostramos que essa energia eletromagnética possui, no regime de fraca absorção, uma relação funcional simples com o comprimento de onda incidente e a seção de choque de absorção da partícula espalhadora, independentemente do formato geométrico da mesma. No espalhamento por uma coleção de partículas magnéticas, a velocidade de transporte de energia pode ser estimada a partir da energia eletromagnética média que é armazenada no interior de um centro espalhador isolado. Dessa maneira, a validade da relação universal que encontramos entre o fator de aumento da energia eletromagnética interna ao centro espalhador e sua correspondente seção de choque de absorção (no regime de baixa absorção óptica) implica na possibilidade de estimarmos de maneira simples a velocidade de transporte de energia em um meio desordenado. Um resultado decorrente dessa aproximação é que mesmo na região de Rayleigh a velocidade de transporte de energia em um meio magnético desordenado é drasticamente reduzida, levando, por conseguinte, à redução do coeficiente de difusividade dos fótons no meio. O estudo analítico e numérico da energia eletromagnética armazenada por uma esfera e por um cilindro magnéticos irradiados por ondas planas homogêneas são os temas em foco nesta dissertação de Mestrado. / Electromagnetic scattering by a sphere with arbitrary optical properties and radius, known as the Lorenz-Mie scattering, or by an infinite right circular cylinder can be solved analytically and is widely treated in the approach of dielectric scatterers. In the optical range, both embedding medium and scattering particle have the same magnetic permeability. The absence of magnetism in this spectral range leads to the equivalence between the relative refraction and impedance indices associated with the scatterers. However, in microwave or radio-frequency ranges, ferro- and ferrimagnetic materials can exhibit extremely huge values of magnetic permeability, which reduce the optical impedance in comparison to the corresponding value of relative refraction index. One striking feature associated with the magnetism in the scatterer is that particles smaller than the wavelength (Rayleigh size region) can present large extinction cross sections in despite of their small geometric cross sections. This becomes physically possible the presence of morphology-dependent resonances in the electromagnetic energy within the scatterer even in size parameters region smaller than unity. In particular, we show that this time-averaged electromagnetic energy has, in the weak absorption regime, a simple functional relation with the incident wavelength and the scatterer absorption cross section which does not depend on the shape of the scatterer. In the multiple scattering regime, the energy-transport velocity can be estimated from the time-averaged electromagnetic energy stored in a single scatterer. Thereby, the validity of the universal relation between the internal energy-enhancement factor and the absorption cross section respective to an arbitrary scattering center (in the weak absorption regime) implies that the energy-transport velocity in disordered media can be evaluated in a simple way. From this approximation, we obtain that even in the Rayleigh size region the energy-transport velocity in disordered magnetic media is dramatically reduced, which consequently leads to a reduction of the diffusion coefficient of the photons. The analytical and numerical studies of the time-averaged electromagnetic energy within magnetic isotropic spheres and cylinders irradiated by plane waves are our aim in this Master\'s degree dissertation.

Le couple zéolite/H2O, qui présente une densité énergétique importante et remplit les conditions d’innocuité requises pour un système de stockage de chaleur pour l’habitat, est mis en œuvre dans réacteur modulaire à lit fixe. Un modèle monodimensionnel de transferts couplés de masse et de chaleur dans un lit fixe de grains de zéolite parcourus par un flux d'air humide été élaboré. Ce dernier a été conçu de façon à pouvoir intégrer rapidement des données sur de nouvelles générations de matériaux et coupler le réacteur à d’autres modèles : bâtiment/sous-station/quartier. L'étape de validation expérimentale montre que le modèle permet une estimation satisfaisante de l'autonomie, la durée d'amorçage et la puissance moyenne fournie en phase de décharge ainsi que la durée de charge. Ce modèle est donc un bon outil de dimensionnement et de pilotage du réacteur. L'analyse de sensibilité a montré que l'amélioration des prévisions du modèle requiert une évaluation plus précise de la chaleur complémentaire de sorption et de la porosité du lit. Après avoir estimé les besoins de chauffage d'une maison BBC deux dimensionnements ont été proposés afin d'effacer soit l'hyper-pointe de 18h - 20h soit la semaine la plus froide. Si la première stratégie aboutit à un système de stockage plus compact, la seconde permet de réduire le nombre de cycles marche/arrêt. Pour un îlot de 50 maisons BBC, la notion de foisonnement est considérée lors de l'estimation des besoins en chauffage pendant la semaine la plus froide. La phase de charge du système de stockage se ferait par le biais de la chaleur fatale récupérée dans l'industrie. Pour des stratégies d'effacement similaires (semaine la plus froide en hiver), un volume équivalent de 544 litres par maison dans l'îlot suffit pour répondre aux besoins de chauffage à Nancy contre 580 litres pour une maison BBC seule. / Heat storage systems for residential house heating could contribute to smoothing the load curve and would help prevent the use of the most polluting power plants or electricity imports during consumption peaks. Thermochemical heat storage systems are suitable for the intended application since they have high energy densities and low thermal losses. This thesis focuses on the design of an adsorption heat storage system that would be used to shed the load curve of the heating device of a house or residential district during the winter peak consumption periods. The zeolite/H2O pair, which has interesting features such as a high energy density and meets the conditions of safety required for a heat storage system for housing, is implemented in a modular fixed bed reactor. A 1D pseudo-homogeneous model was developed in order to simulate the performance of a fixed bed of zeolite during the adsorption and desorption of water. The latter was designed so as to facilitate the integration of data on new generations of materials and model couplings. The need to obtain data on the sorption properties of the zeolite/H2O pair to have reliable simulation results has been demonstrated, particularly at low partial pressures of water vapor and under the operating conditions selected. The experimental validation phase shows that the pseudo-homogeneous model provides a satisfactory estimate of criteria such as the autonomy, the responsiveness and the average power delivered during the discharging phase and the charging time. The model is thus a good sizing and management tool of the reactor. A sensitivity analysis, with the method of Morris, showed that improved model estimates require a more accurate assessment of the additional heat of sorption and porosity of the bed. After assessing the heating needs of the LEB house with a thermal model of the latter in cold climate conditions, two heat storage reactors were sized in order to shed the heating system's load curve either between 6 and 8pm or during the coldest week of the year. While the first strategy results in a more compact storage system, the second makes it possible to reduce the number of on/off cycles. The need for predictive control for monitoring the storage system was highlighted. As for the residential district of 50 LEB houses, diversity is considered when estimating the heating needs of the latter during the coldest week in Nancy. The heat source during the charging phase of the container would be industrial waste heat. During the coldest week, two sizings are suggested. For similar load shedding strategies, the comparison of the equivalent storage volume per house in the district with the storage volume for a single house serves highlights the importance of taking into account diversity. In order to meet the heating needs in Nancy, an equivalent volume of 544 liters per house in the district is sufficient whereas 580 liters are needed for a LEB house.

Les simulations hydrodynamiques pour la physique de haute densité d'énergie ainsi que pour la fusion par confinement inertiel exigent une description détaillée de flux d'énergie. Le mécanisme principal est le transport électronique, qui peut être un phénoméne non local qui doit être décrit avec des modèles de Fokker-Planck, stationnaires et simplifiés dans les codes hydrodynamiques à grande échelle. Mon travail thèse est consacré au développement d'un nouveau modèle de transport non local basé sur l'utilisation d'une méthode de fermeture entropique pour la résolution des premiers moments de l'équation de Fokker-Planck agrémentée d'un opérateur de collision dédié. Une telle fermeture permet une bonne résolution des fortes anisotropies de la fonction de distribution électronique dans les régimes où le développement d'instabilités électrostatiques à petite échelle le requiert. Ce modèle aux moments (M1) est comparé avec succès au modèle de Schurtz, Nicolaï et Busquet (SNB), référent dans le domaine du transport électronique non local. Ce modèle, basé sur l'hypothèse d'une faible anisotropie de la fonction de distribution sous-jacente induisant une relation de fermeture polynomiale (P1), utilise un opérateur de collision simplifié dont nous avons proposé une amélioration. Après avoir considéré plusieurs configurations typiques de transport de chaleur, nous avons montré que le modèle M1 ultidimensionnel peut prendre naturellement en compte des effets d'un plasmas magnétisés sur le transport électronique. De plus, ce modèle permet de calculer des fonctions de distribution utiles aux études cinétiques comme la stabilité du plasma dans la zone de transport. Nous confirmons avec notre modèle que le transport d'énergie électronique peut fortement modifier l'amortissement des ondes de Langmuir et des ondes acoustiques ; contrairement aux modèles non locaux simplifiés, M1 décrit les modifications de la fonction de distribution et l'amortissement des ondes du plasma. La structure du modèle permet également de prendre en compte naturellement des champs magnétiques autogénérés, qui jouent un rôle crucial dans des simulations multidimensionnelles. Ces champs magnétiques pourraient également être étudiés pour concentrer l'énergie dans les schémas d'ignition. Enfin, nous montrons que le modèle M1 reproduit les résultats de la théorie locale élaborée par Braginskii pour tous les niveau de magnétisation et propose de nouveaux résultats pour le régime non local. Ce travail constitue une première validation de l'utilisation des fermetures entropiques, dans les régimes de faibles anisotropies, qui va s'ajouter aux tests dans les régimes fortement anisotropes. / Hydrodynamic simulations in high-energy-density physics and inertial con nement fusion require a detailed description of energy uxes. The leading mechanism is the electron transport, which can be a nonlocal phenomenon that needs to be described with quasistationary and simplified Fokker-Planck models in large scale hydrodynamic codes. My thesis is dedicated to the development of a new nonlocal transport model based on a fast-moving-particles collision operator and on a first moment Fokker-Planck equation, simplified with an entropic closure relation. Such a closure enables a better description of the electron distribution function in the limit of high anisotropies, where small scale electrostatic instabilities could be excited. This new model, so called M1, is successfully compared with the well known nonlocal electron transport model proposed by Schurtz, Nicolaï and Busquet, using different collision operators, and with the reduced Fokker-Planck model, based on a small-anisotropies polynomial closure relation (P1). Several typical configurations of heat transport are considered. We show that the M1 entropic model may operate in two and three dimensions and is able to account for electron transport modifications in external magnetic fields. Moreover, our model enables to compute realistic electron distribution functions, which can be used for kinetic studies, as for the plasma stability in the transport zone. It is demonstrated that the electron energy transport may strongly modify damping of Langmuir and ion acoustic waves, while the simplified nonlocal transport models are not able to describe accurately the modifications of the distribution function and plasma wave damping. The structure of the M1 model allows to naturally take into account self-generated magnetic fields, which play a crucial role in multidimensional simulations. Moreover, magnetic fields could also be used for the focusing of energetic particles in alternative ignition schemes. The M1 model reproduces the results of the local transport theory in plasma, developed by Braginskii, in a broad range of degrees of magnetization and predicts new results in the nonlocal regime. This work constitutes a first validation of the entropic closure assumption in the weakly-anisotropic regime. It can be added to the existing tests, in the strongly-anisotropic regimes.

<p>Modeling microbial inactivation has a great influence on the optimization, control and design of food processes. In the area of food safety, modeling is a valuable tool for characterizing survival curves and for supporting food safety decisions. The modeling of microbial behavior is based on the premise that the response of the microbial population to the environment factors is reproducible. And that from the past, it is possible to predict how these microorganisms would respond in other similar environments. Thus, the use of mathematical models has become an attractive and relevant tool in the food industry.</p> <p>This research provides tools to relate the inactivation of microorganisms of public health importance with processing conditions used in nonisothermal and non-thermal food processing technologies. Current models employ simple approaches that do not capture the realistic behavior of microbial inactivation. This oversight brings a number of fundamental and practical issues, such as excessive or insufficient processing, which can result in quality problems (when foods are over-processed) or safety problems (when foods are under-processed). Given these issues, there is an urgent need to develop reliable models that accurately describe the inactivation of dangerous microbial cells under more realistic processing conditions and that take into account the variability on microbial population, for instance their resistance to lethal agents. To address this urgency, this dissertation focused on mathematical models, combined mathematical tools with microbiological science to develop models that, by resembling realistic and practical processing conditions, can provide a better estimation of the efficacy of food processes. The objective of the approach is to relate the processing conditions to microbial inactivation. The development of the modeling approach went through all the phases of a modeling cycle from planning, data collection, formulation of the model approach according to the data analysis, and validation of the model under different conditions than those that the approach was developed.</p> <p>A non-linear ordinary differential equation was used to describe the inactivation curves with the hypothesis that the momentary inactivation rate is not constant and depends on the instantaneous processing conditions. The inactivation rate was related to key process parameters to describe the inactivation kinetics under more realistic processing conditions. From the solution of the non-linear ordinary differential equation and the optimization algorithm, safety inferences in the microbial response can be retrieved, such as the critical lethal variable that increases microbial inactivation. For example, for nonisothermal processes such as microwave heating, time-temperature profiles were modeled and incorporated into the inactivation rate equation. The critical temperature required to increase the microbial inactivation was obtained from the optimization analysis. For non-thermal processes, such as cold plasma, the time-varying concentration of reactive gas species was incorporated into the inactivation rate equation. The approach allowed the estimation of the critical gas concentration above which microbial inactivation becomes effective. For Pulsed Electric Fields (PEF), the energy density is the integral parameter that groups the wide range of parameters of the PEF process, such as the electric field strength, the treatment time and the electrical conductivity of the sample. The literature has shown that all of these parameters impact microbial inactivation. It has been hyphothesized that the inactivation rate is a function of the energy density and that above a threshold value significant microbial inactivation begins. </p> <p>The differential equation was solved numerically using the Runge-Kutta method (<i>ode45</i> in MATLAB ®). The<i> lsqcurvefit</i> function in MATLAB ® estimated the kinetic parameters. The approach to model microbial inactivation, whether when samples were subjected to nonisothermal or to non-thermal food processes, was validated using data published in the literature and/or in other samples and treatment conditions. The modeling approaches developed by this dissertation are expected to assist the food industry in the development and validation process to achieve the level of microbial reduction required by regulatory agencies. In addition, it is expected to assist the food industry in managing food safety systems through support food safety decision-making, such as the designation of the minimal critical parameter that may increase microbial inactivation. Finally, this dissertation will contribute in depth to the field of food safety and engineering, with the ultimate outcome of having a broad and highly positive impact on human health by ensuring the consumption of safe food products.</p>

Dans ce manuscrit de thèse, nous nous intéressons à la description des noyaux atomiques composés d’un nombre impair de nucléons dans la méthode dite de la fonctionnelle énergiede la densité (EDF). Plus précisément, nous présentons et appliquons dans le cas de ces noyaux,des extensions à cette méthode : (i) la projection sur les bons nombres quantiques, (ii) le mélange de configurations à travers la méthode des coordonnées génératrices (GCM), qui permettent deprendre en compte dans nos calculs des corrélations de type « au-delà du champ moyen » entre les nucléons constituant le noyau. De telles extensions n’avaient jusqu’alors été employées, dansleurs versions les plus générales, qu’aux noyaux ayant à la fois un nombre pair de neutrons etde protons, et nous nous proposons donc de démontrer leurs applicabilités également dans le cas des noyaux impairs. Dans la première partie de ce travail, nous présentons le formalisme mathématique de la méthode EDF, en mettant tout particulièrement l’accent sur le traitement des symétries dans cette approche. Dans la seconde partie du manuscrit, nous appliquons notre modèle au cas du noyau de 25Mg et analysons les résultats sous différents angles (ex : précision numérique des résultats, convergence du mélange de configurations, comparaison avec les données expérimentales connues). Les premiers résultats obtenus dans ce travail de thèse sontencourageants et démontrent l’intérêt de notre approche pour les calculs théoriques de structure nucléaire. / In this work, we are interested in the treatment of odd-mass atomic nuclei in energydensity functional (EDF) models. More precisely, the goal of this thesis is to develop and to applyto odd-mass nuclei, the theoretical extensions of the EDF method that are: (i) the projectiontehnique, and (ii) the configuration mixing by the generator coordinate method (GCM). Thesetwo extensions are part of the so-called multi-reference energy density functional (MR-EDF)formalism and allow for taking into account, within an EDF context, the "beyond-mean-field"correlations between the nucleons forming the nucleus. Until now, the MR-EDF formalism hasbeen applied, in its full-fledged version, only to the calculation of even-even nuclei. In this thesis,we want to demonstrate the applicability of such a model also for the description of odd-massnuclei. In the first part of this thesis, we describe the theoretical formalism of the EDF models,giving particular attention to the treatment of symmetries within our approach. In the secondpart of the manuscript, we apply our model to the nucleus 25Mg and investigate different aspectsof the method (e.g. numerical accuracy, convergence of the configuration mixing, comparison toknown experimental data). The results obtained in this work are encouraging and demonstratethe potential of our approach for theoretical nuclear structure calculations.

Ο χαρακτηρισμός της ποιότητας των χυτών κραμάτων αλουμινίου , γίνεται μέχρι σήμερα μέσω του χαρακτηρισμού της ποιότητας της μικροδομής, μετρήσεων σκληρότητας και πειραμάτων κρούσης και σε μικρότερο βαθμό, δοκιμών εκφυλισμού. Στην παρούσα διατριβή, προτείνεται ένας νέος εμπειρικός δείκτης για τον ποσοτικοποιημένο χαρακτηρισμό της ποιότητας χυτών κραμάτων αλουμινίου. Ο προτεινόμενος δείκτης αξιολογεί την ποιότητα ενός υλικού από την πλευρά του μηχανικού που σχεδιάζει ένα κατασκευαστικό στοιχείο και επομένως την αξιολογεί ως την ικανότητα του υλικού για μηχανικές επιδόσεις. Για την αξιολόγηση αυτή ο προτεινόμενος δείκτης συνεκτιμά την αντοχή και την ολκιμότητα του υλικού σε εκφυλισμό. Παράλληλα, για το χαρακτηρισμό της ποιότητας, ο δείκτης παίρνει υπόψη τη δυσθραυσότητα του υλικού καθώς και τη διασπορά των μηχανικών ιδιοτήτων του υλικού. Η διατύπωση του δείκτη στηρίχτηκε σε έναν ευρείας έκτασης πειραματικό χαρακτηρισμό της μηχανικής συμπεριφοράς σε εφελκυσμό καθώς και της μικροδομής των κυριότερων αεροπορικών χυτών κραμάτων αλουμινίου σε συνάρτηση με τη μεταβολή α) της χημικής σύστασης, β) του ρυθμού στερεοποίησης και γ) της θερμικής κατεργασίας αυτών καθώς και στη διατύπωση εμπειρικών συναρτήσεων για την εξάρτηση των μηχανικών ιδιοτήτων των κραμάτων που εξετάστηκαν από τις παραπάνω μεταβολές των παραμέτρων χύτευσης. Προκειμένου να διευκολυνθεί η αξιοποίηση του δείκτη, διατυπώθηκαν απλουστευμένες προσεγγιστικές εκφράσεις που επιτρέπουν τον υπολογισμό του από δεδομένα των απλών πειραμάτων της σκληρομέτρησης και της κρούσης. Τέλος προτάθηκε μεθοδολογία δημιουργίας χαρτών ποιότητας με βάση τον προταθέντα δείκτη για την υποστήριξη της επιλογής υλικού όταν είναι γνωστές οι απαιτήσεις σε μηχανικές επιδόσεις συγκεκριμένων κατασκευαστικών στοιχείων. / Quality evaluation of cast aluminum alloys is currently made mainly by means of the met- allographic characterization of the alloy’s niicrostructure, hardness measurements, impact tests and, to a lesser extend, tensile tests, are involved, as well. Yet, the overall decision is not a straight forward procedure, relies heavily on the experience of the quality engineer and involves an appreciable amount of subjective judgment. In the present Thesis, a new empirical quality index for the quantitative evaluation of the quality of cast aluminum alloys is introduced. The proposed index evaluates quality which is regarded as the ability of a material for mechanical performance. The index evaluates the quality of a cast alloy on the basis of a balance between the material’s tensile strength and ductility with regard also to the material’s toughness. In the proposed index the scatter in mechanical properties is also accounted. The formulation of the index has been based on an extensive experimental characterization of the tensile behavior and the microstructural features of the main aircraft aluminum cast alloys by varying chemical composition, solidification rate and artificial aging treat- ment. To facilitate the wide spread use of the index, simplified approximate expressions of the index have been formulated as well. These expressions allow for the calculation of the proposed quality index based on hardness measurements and impact test results. The index has been also exploited to devise quality maps, which may be used to support material selection with regard to the mechanical properties required by the design office for a certain application.

Ion irradiation of tetrahedral amorphous carbon (ta-C) thin films induces a carbon phase transformation from the electrically insulating sp3 hybridization into the conducting sp2 hybridization. In this work, a detailed study on the electrical resistivity and the microstructure of areas, irradiated with several ion species at 30 keV energy is presented. Continuous ion bombardment yields a drastic drop of the resistivity as well as significant structural modifications of the evolving sp2 carbon phase. It is shown that the resistivity lowering can be attributed to the degree of graphitization in the film. Furthermore, the structural ordering processes are correlated with the ion deposited energy density. It is therefore revealed that the ion-induced phase transformation in ta-C films is a combination of sp3-to-sp2 conversion of carbon atoms and ion-induced ordering of the microstructure into a more graphite-like arrangement. All experiments were done with focused ion beam (FIB) systems by applying FIB lithography of electrical van-der-Pauw test structures. FIB lithography on ta-C layers is presented as a fast and easy technique for the preparation of electrically active micro- and nanostructures in an insulating carbon matrix.

Nos efforts se sont portés sur des fluorophosphates de structure TAVORITE de formule LiMPO4F (M = V, Fe, Ti) et LiVPO4O qui, comparés à d’autres familles structurales de phosphates tels que Li3M2(PO4)3 (NASICON) ou LiFePO4(OH) (Tavorite) possèdent d’excellentes densités d’énergie théorique comme matériaux d’électrodes dans des accumulateurs au Li. Des méthodes de synthèse reproductibles, par voie céramique en tubes scellés et/ou ionothermale (synthèse à basse température), ont été mises au point dans ce travail. Les matériaux ainsi préparés ont été caractérisés en détail par magnétométrie, par RMN et surtout par diffraction des rayons X et des neutrons. Les structures cristallines ont ainsi pu être déterminées ainsi que les mécanismes d’insertion/extraction du Li+, via de nombreuses études par diffraction X insitu lors de la charge/décharge des accumulateurs. / This work focused on TAVORITE-based fluorophosphates LiMPO4F (M = V, Fe, Ti) and LiVPO4O which, when compared with other phosphate structural families such as Li3V2(PO4)3 (NASICON) or LiFePO4(OH) (Tavorite), possess superior energy density as electrode materials for Li batteries. Reproducible synthesis procedures were developed through “classical” ceramic routes in sealed containers and/or low temperature ionothermal reaction. The obtained materials were characterized by magnetometry, solid state NMR and heavily by X-Ray and Neutron diffraction. The crystal structures of all the materials were determined, as well as the mechanisms of Li+ insertion/extraction through insitu X-Ray diffraction during electrochemical charge/discharge of the batteries.

O espalhamento eletromagnético por uma esfera com propriedades ópticas e raio arbitrários, conhecido como espalhamento de Lorenz-Mie, ou por um cilindro circular infinito, pode ser resolvido analiticamente e é comumente tratado dentro da abordagem de espalhadores dielétricos. Na região óptica, tanto meio circundante quanto partícula espalhadora possuem o mesmo valor de permeabilidade magnética. A ausência do magnetismo nessa região do espectro torna o índice de refração relativo entre os meios interno e externo ao espalhador homogêneo equivalente ao respectivo índice de impedância óptica. Em regiões espectrais de micro-ondas ou radiofrequências, entretanto, materiais ferro- e ferrimagnéticos podem exibir valores absolutos de permeabilidade magnética extremamente elevados, reduzindo então a impedância óptica em comparação ao valor correspondente de índice de refração relativo. Uma característica marcante vinculada ao magnetismo no centro espalhador é que pequenas partículas comparadas com o comprimento de onda (parâmetros de tamanho na região de Rayleigh) podem apresentar grandes seções de choque de extinção a despeito de suas pequenas seções de choque geométricas. Isso torna possível, fisicamente, a presença de picos de ressonância morfológica na energia eletromagnética interna ao centro espalhador mesmo na região de parâmetros de tamanho inferiores à unidade. Em especial, mostramos que essa energia eletromagnética possui, no regime de fraca absorção, uma relação funcional simples com o comprimento de onda incidente e a seção de choque de absorção da partícula espalhadora, independentemente do formato geométrico da mesma. No espalhamento por uma coleção de partículas magnéticas, a velocidade de transporte de energia pode ser estimada a partir da energia eletromagnética média que é armazenada no interior de um centro espalhador isolado. Dessa maneira, a validade da relação universal que encontramos entre o fator de aumento da energia eletromagnética interna ao centro espalhador e sua correspondente seção de choque de absorção (no regime de baixa absorção óptica) implica na possibilidade de estimarmos de maneira simples a velocidade de transporte de energia em um meio desordenado. Um resultado decorrente dessa aproximação é que mesmo na região de Rayleigh a velocidade de transporte de energia em um meio magnético desordenado é drasticamente reduzida, levando, por conseguinte, à redução do coeficiente de difusividade dos fótons no meio. O estudo analítico e numérico da energia eletromagnética armazenada por uma esfera e por um cilindro magnéticos irradiados por ondas planas homogêneas são os temas em foco nesta dissertação de Mestrado. / Electromagnetic scattering by a sphere with arbitrary optical properties and radius, known as the Lorenz-Mie scattering, or by an infinite right circular cylinder can be solved analytically and is widely treated in the approach of dielectric scatterers. In the optical range, both embedding medium and scattering particle have the same magnetic permeability. The absence of magnetism in this spectral range leads to the equivalence between the relative refraction and impedance indices associated with the scatterers. However, in microwave or radio-frequency ranges, ferro- and ferrimagnetic materials can exhibit extremely huge values of magnetic permeability, which reduce the optical impedance in comparison to the corresponding value of relative refraction index. One striking feature associated with the magnetism in the scatterer is that particles smaller than the wavelength (Rayleigh size region) can present large extinction cross sections in despite of their small geometric cross sections. This becomes physically possible the presence of morphology-dependent resonances in the electromagnetic energy within the scatterer even in size parameters region smaller than unity. In particular, we show that this time-averaged electromagnetic energy has, in the weak absorption regime, a simple functional relation with the incident wavelength and the scatterer absorption cross section which does not depend on the shape of the scatterer. In the multiple scattering regime, the energy-transport velocity can be estimated from the time-averaged electromagnetic energy stored in a single scatterer. Thereby, the validity of the universal relation between the internal energy-enhancement factor and the absorption cross section respective to an arbitrary scattering center (in the weak absorption regime) implies that the energy-transport velocity in disordered media can be evaluated in a simple way. From this approximation, we obtain that even in the Rayleigh size region the energy-transport velocity in disordered magnetic media is dramatically reduced, which consequently leads to a reduction of the diffusion coefficient of the photons. The analytical and numerical studies of the time-averaged electromagnetic energy within magnetic isotropic spheres and cylinders irradiated by plane waves are our aim in this Master\'s degree dissertation.

La hiérarchisation de la puissance injectée par des sources acoustiques dans une cavité d'avion telle qu'un cockpit, en vol, revêt un caractère majeur dans le but d'en réduire le bruit intérieur. Afin de répondre à ce besoin, la nécessité de considérer la cavité dans son ensemble à l'aide d'une méthode globale se révèle importante. Au cours de cette thèse, une méthode d'identification basée sur une méthode énergétique locale, appelée MES pour Méthode Energétique Simplifiée, est utilisée. En connaissant la géométrie de la cavité, ainsi que l'absorption des matériaux qui la composent, elle permet de déterminer la puissance rayonnée par les différentes sources acoustiques à l'intérieur de la cavité, à l'aide de mesures d'intensité tridimensionnelle, et de densité d'énergie acoustique totale. Afin de tester la méthode dans un cas réel, mesurer ces quantités énergétiques s'avère alors nécessaire. Une sonde acoustique est donc conçue, fabriquée, testée et enfin validée. Basée sur quatre mesures de pressions réalisées autour d'une sphère rigide à l'aide de microphones électrostatiques déportés, elle permet de mesurer la pression et le vecteur vitesse particulaire au centre de la sphère, et d'en déduire alors l'intensité 3D et la densité d'énergie totale. Un démonstrateur est ensuite construit pour réaliser des essais. Il s'agit d'une maquette de cockpit basée sur celui de l'A380. Différents essais acoustiques et vibro-acoustiques permettent alors de démontrer la capacité de l'association formée par la méthode d'identification et la sonde à déterminer la puissance injectée par les différentes sources dans des conditions acoustiques plus ou moins sévères, avec une précision de l'ordre de 2dB. Le post-traitement à l'aide de la MES des flux acoustiques rayonnés ainsi déterminés permet également de reconstruire le champ acoustique dans la cavité, ainsi que de séparer les différentes contributions en des points d'intérêt tels que les têtes pilote et copilote. / Organizing into a hierarchy the power injected by acoustic sources inside an aircraft cavity such as a cockpit, in flight conditions, appears as a crucial stage in orcier to reduce interior noise. To address this need, considering the whole cavity with a global method turns out to be essential. In this work, an identification method based on a local energy method called MES for Simplified Energy Method is used. With the cavity geometry and the absorption characteristics of the materials inside, the method is capable of retrieving the acoustic power radiated by the sources within the cavity from three dimensional intensity vector and energy density measurements. To assess the method in a real test case, measuring these previous energy quantities turns out to be necessary. Thus, an acoustic probe is designed, manufactured, tested and to finish validated. Based on four pressure measurements performed around a hard sphere with remote pre-amplified microphones, the multi-sensor probe is able to compute the pressure and the particle velocity vector at the center of the sphere, and then obtain the 3D intensity, and the total acoustic energy density. A cockpit mock-up based on the A380 cockpit geometry is manufactured to perform tests. Several acoustic and vibro-acoustic tests carried out in the mock-up show the capability of the association composed of the identification method and the probe to extract the acoustic power radiated by the sources, in more or less harsh acoustic conditions, with accuracy close to 2dB. Post-processing the computed injected power allows to reconstruct the acoustic field inside the cavity, and to separate the different sources contributions for sorne points of interest such as the pilot or copilot heads.