Dans ce travail de thèse a été développé et étudié un nouveau type d'objet semiconducteur magnétique : des boîtes quantiques de CdMnTe insérées dans des nanofils de ZnTe/ZnMgTe constituant une structure de type cœur-coquille. L'objectif était d'étudier la croissance par épitaxie par jets moléculaires et les propriétés fondamentales de ces hétéro-structures complexes. Dans ce but deux aspects principaux ont été abordés : i) la qualité et le contrôle des propriétés structurales, électroniques et magnétiques de ces objets, grâce à une maîtrise de leur croissance et ii) l'obtention d'informations quantitatives locales sur la composition chimique de ces nanostructures inhomogènes. Pour atteindre ces objectifs, nous avons divisé notre étude en quatre étapes. La première étape de ce travail a été concentrée sur l'étude quantitative de la formation des particules d'or servant de catalyseurs à la croissance des nanofils. La seconde étape a porté sur l'analyse des mécanismes de croissance et des paramètres gouvernant la croissance des fils de ZnTe. En particulier deux types de fils ont été observés : des fils cylindriques de structure wurtzite et des fils coniques de structures zinc-blende. Un modèle de croissance guidée par la diffusion a été utilisé pour rendre compte de certains des résultats quantitatifs présentés dans cette partie. La troisième étape a concerné l'insertion de boîtes quantiques de CdMnTe dans des nanofils de structure cœur-coquille ZnTe/ZnMgTe. Une étude préalable des paramètres pertinents influençant les propriétés magnéto-optiques de ces objets, tels que le confinement de la boîte quantique, l'incorporation du Mn et l'anisotropie de contrainte créée par la structure, a été menée. La quatrième et dernière étape de ce travail a porté sur l'interprétation quantitative de mesures d'analyse dispersive en énergie effectuées sur des nanofils de structure cœur-multicoquille. Un modèle géométrique a été proposé, permettant de retrouver la forme, les dimensions et la composition chimique des boîtes quantiques et des coquilles. Cette étude a été couplée à des mesures de caractérisation telles que la cathodo-luminescence, la micro-photo-luminescence et la spectroscopie magnéto-optique effectuées sur le même nanofil. / In this PhD work a novel type of magnetic semiconductor object has been developed: Cd(Mn)Te quantum dots embedded in ZnTe/ZnMgTe core-shell nanowires. The goal was to investigate the growth, by molecular beam epitaxy, and the fundamental properties of these complex heterostructures. For that purpose, two main issues were addressed: i) gaining control of the structural, electronic and magnetic properties of these quantum objects by mastering their growth; and ii) obtaining quantitative local knowledge on the chemical composition of those non-homogeneous nanostructures. To tackle these topics, our research was divided into four stages. The first stage was devoted to perform a quantitative study of the formation process of the Au particles that catalyze the growth of nanowires. The second stage involved the analysis of the mechanisms and parameters governing the growth of ZnTe nanowires. In particular, two different types of nanowires were found: cone-shaped nanowires with the zinc-blende crystal structure and cylinder-shaped nanowires with the hexagonal wurtzite structure. A diffusion-driven growth model is employed to fit some of the quantitative results presented in this part. The third stage focused on the insertion of pure CdTe quantum dots containing Mn ions in the core-shell nanowires. An initial study of the relevant parameters influencing the magneto-optical properties of these objects, such as the quantum dot confinement, the Mn incorporation, and the strain anisotropy, was performed. The four and last stage of this work concerned the quantitative interpretation of Energy-Dispersive X-ray spectroscopy measurements performed on single core-multishell nanowires. A geometrical model was proposed to retrieve the shape, the size and the local composition of the quantum dot insertions and of the multiple layers of the heterostructures. This study was coupled to other complementary characterization measurements on the same nanowire, such as cathodo-luminescence, micro-photo-luminescence and magneto-optical spectroscopy.

Dans ce travail de thèse a été développé et étudié un nouveau type d'objet semiconducteur magnétique : des boîtes quantiques de CdMnTe insérées dans des nanofils de ZnTe/ZnMgTe constituant une structure de type cœur-coquille. L'objectif était d'étudier la croissance par épitaxie par jets moléculaires et les propriétés fondamentales de ces hétéro-structures complexes. Dans ce but deux aspects principaux ont été abordés : i) la qualité et le contrôle des propriétés structurales, électroniques et magnétiques de ces objets, grâce à une maîtrise de leur croissance et ii) l'obtention d'informations quantitatives locales sur la composition chimique de ces nanostructures inhomogènes. Pour atteindre ces objectifs, nous avons divisé notre étude en quatre étapes. La première étape de ce travail a été concentrée sur l'étude quantitative de la formation des particules d'or servant de catalyseurs à la croissance des nanofils. La seconde étape a porté sur l'analyse des mécanismes de croissance et des paramètres gouvernant la croissance des fils de ZnTe. En particulier deux types de fils ont été observés : des fils cylindriques de structure wurtzite et des fils coniques de structures zinc-blende. Un modèle de croissance guidée par la diffusion a été utilisé pour rendre compte de certains des résultats quantitatifs présentés dans cette partie. La troisième étape a concerné l'insertion de boîtes quantiques de CdMnTe dans des nanofils de structure cœur-coquille ZnTe/ZnMgTe. Une étude préalable des paramètres pertinents influençant les propriétés magnéto-optiques de ces objets, tels que le confinement de la boîte quantique, l'incorporation du Mn et l'anisotropie de contrainte créée par la structure, a été menée. La quatrième et dernière étape de ce travail a porté sur l'interprétation quantitative de mesures d'analyse dispersive en énergie effectuées sur des nanofils de structure cœur-multicoquille. Un modèle géométrique a été proposé, permettant de retrouver la forme, les dimensions et la composition chimique des boîtes quantiques et des coquilles. Cette étude a été couplée à des mesures de caractérisation telles que la cathodo-luminescence, la micro-photo-luminescence et la spectroscopie magnéto-optique effectuées sur le même nanofil. / In this PhD work a novel type of magnetic semiconductor object has been developed: Cd(Mn)Te quantum dots embedded in ZnTe/ZnMgTe core-shell nanowires. The goal was to investigate the growth, by molecular beam epitaxy, and the fundamental properties of these complex heterostructures. For that purpose, two main issues were addressed: i) gaining control of the structural, electronic and magnetic properties of these quantum objects by mastering their growth; and ii) obtaining quantitative local knowledge on the chemical composition of those non-homogeneous nanostructures. To tackle these topics, our research was divided into four stages. The first stage was devoted to perform a quantitative study of the formation process of the Au particles that catalyze the growth of nanowires. The second stage involved the analysis of the mechanisms and parameters governing the growth of ZnTe nanowires. In particular, two different types of nanowires were found: cone-shaped nanowires with the zinc-blende crystal structure and cylinder-shaped nanowires with the hexagonal wurtzite structure. A diffusion-driven growth model is employed to fit some of the quantitative results presented in this part. The third stage focused on the insertion of pure CdTe quantum dots containing Mn ions in the core-shell nanowires. An initial study of the relevant parameters influencing the magneto-optical properties of these objects, such as the quantum dot confinement, the Mn incorporation, and the strain anisotropy, was performed. The four and last stage of this work concerned the quantitative interpretation of Energy-Dispersive X-ray spectroscopy measurements performed on single core-multishell nanowires. A geometrical model was proposed to retrieve the shape, the size and the local composition of the quantum dot insertions and of the multiple layers of the heterostructures. This study was coupled to other complementary characterization measurements on the same nanowire, such as cathodo-luminescence, micro-photo-luminescence and magneto-optical spectroscopy.

There is an ever increasing demand for higher spectral usage in wireless communication, radar and imaging systems. Higher spectral efficiency can be achieved using components that are aware of system environment and adapt suitably to the operating conditions. In this regard, radio frequency (RF) signal analysis is of paramount interest. Emergence of dispersive delay networks (DDN) has led to the significant development of microwave analogue-signal processing (ASP) and analysis. DDN causes displacement of spectral components in time domain, relative to the frequency dependant group delay response. The main challenge in the design of DDN in this context is in achieving broad bandwidth with high group delay dispersion (GDD). In this regard, all-pass networks (APN) have been explored as a potential wide-band DDN owing to the possibility of controlling the magnitude of loss characteristics without affecting the dispersion in group delay response. The synthesis procedure of lumped element APN using approximation methods is well known at audio frequencies. Most of these use operational amplifier and cannot be extended directly to RF. There is no generalised closed form analytical procedure at RF for the synthesis of APN with the required GDD. In this regard, this dissertation presents the design and implementation of all-pass networks as wide-band dispersive delay networks at radio frequencies. In this work, we begin by analysing the signal propagation through a DDN with a linear group delay response over a broad bandwidth. It is found that the signal experiences expansion of pulse width, reduction of its peak amplitude and a temporal displacement of the spectral components. Analytical expressions derived help initial synthesis of group delay response required for various ASP applications. As the first step towards implementation at RF, a single stage APN is designed using surface mount devices (SMD). This design approach takes into account practical issues such as parasitic due to mounting pads, available component values, physical dimensions, self-resonance frequency (SRF) and finite Q factor of the components used. Full wave simulation of the design with transmission line pads and components is carried out. This implementation is useful for frequencies up to the component SRF, generally about 5 GHz. This design approach makes the circuit footprint independent of frequency and the performance is limited only by the Q factor of the adopted technology. The Q factor affects the loss characteristics with a negligible effect on group delay response in the frequency band of interest. In order to extend the APN design for high group delay, a novel board level implementation is developed consisting of both lumped SMD components and distributed elements. The implementation results in a lower sensitivity of group delay performance to the commercially specified component value tolerances than the approach using all SMD components. It has been experimentally verified that the measured group delay is 2.4 ns at 1.85 GHz, which is thrice that reported in other approaches. The implementation has a reduced circuit footprint and is attractive in practical applications as it is a single layer micro strip realisation with less complex fabrication procedure and fewer components to assemble. As an extension of this towards wideband cascaded APN, an iterative design procedure is developed to achieve a monotonous group delay response over a broad bandwidth. The approach facilitates cascading of multiple stages of lumped APN with different resonance frequency and peak group delay to obtain linear and non-linear group delay responses with both positive and negative GDD. Circuits with both positive and negative GDD are required for various ASP applications such as compressive receivers and the present approach is unique in obtaining both the responses, not possible with many other RF dispersion techniques. Circuit models have been simulated by cascading transfer function responses of the individual APNs. The design is further extended for SMD implementation. To validate the above approach, a two stage APN is designed in the frequency range [0.5 - 1] GHz for a linear GDD of ±6 ns/GHz. Two negative GDD APNs are further cascaded to obtain a four stage implementation with an overall GDD of -12 ns/GHz. The experimental results are compared with full wave simulations for validation. The design using lumped SMD components has greatly improved the performance in terms of GDD with a reduced circuit footprint and lower insertion loss than previously reported approaches. As practical examples, the ASP modules are experimentally demonstrated using the fabricated APN. Frequency discrimination of two input frequencies with a frequency resolution of 500 MHz is demonstrated. Higher GDD results in higher separation of frequency components in time domain. Pulse compression and magnification is also demonstrated for different wideband LFM input signals. The dispersion effects of amplitude reduction, pulse width expansion and frequency chirping are thereby validated experimentally. In summary, the approaches presented in this dissertation enable the design of wideband all-pass networks to introduce dispersion delays over wide bandwidths, opening up the possibility for their use in analogue signal processing at radio frequencies. Some of these applications have been experimentally demonstrated and validated using time frequency analysis.

Cette thèse est dédiée à l'étude des fluctuations non-linéaires dans les condensats de Bose-Einstein à deux composantes. On présente dans le premier chapitre la dynamique de champ moyen des condensats à deux composantes et les différents phénomènes typiques associés au degré de liberté spinoriel. Dans ce même chapitre, on montre que la dynamique des excitations se sépare en deux modes distincts : un mode dit de densité correspondant au mouvement global des atomes à l'intérieur du condensat et un mode dit de polarisation correspondant à la dynamique relative entre les deux espèces constituant le condensat. Ce calcul est généralisé dans le deuxième chapitre où l'on montre que le mode de polarisation persiste en présence d'un couplage cohérent entre les deux composantes. En particulier on analyse la stabilité modulationnelle du mode en déterminant, à l'aide d'une analyse multi-échelle, la dynamique des excitations non-linéaires. On montre alors que les excitations de polarisation, au contraire des excitations de densité, souffrent d'une instabilité de Benjamin-Feir. Cette instabilité est stabilisée aux grandes impulsions par une résonance onde longue - onde courte. Enfin dans le dernier chapitre, on dérive de façon non-perturbative la dynamique de polarisation proche de la limite de Manakov, dynamique quise révèle être régie par une équation de Landau-Lifshitz sans dissipation. Les équations de Landau-Lifshitz appartiennent à une hiérarchie d'équations intégrables (hiérarchie Ablowitz-Kaup-Newell-Segur) et on étudie les solutions à une phase à l'aide de la méthode d'intégration finite-gap ; on détermine notamment à l'aide de cette méthode un nouveau type de soliton pour les condensats à deux composantes. Finalement, profitant de l'intégrabilité du système, on résout le problème de Riemann à l'aide de la théorie de modulation de Whitham et on montre que les condensats à deux composantes peuvent propager des ondes de raréfaction ainsi que des ondes de choc dispersives ; on décrit notamment la modulation de ces ondes de choc par la propagation d'ondes simples et d'ondes de contact d'invariants de Riemann. / This thesis is devoted to the study of nonlinear fluctuations in two-component Bose-Einstein condensates. In the first chapter we derive the mean field dynamics of two-component condensates and we present the distinctive phenomena associated to the spinorial degree of freedom. In the same chapter, we show that the dynamics of the excitations is divided in two distinct modes: a so-called density mode which corresponds to the global motion of the atoms, and a so-called polarization mode which corresponds to the relative motion between the two species composing the condensate. The computation is generalized in the second chapter in which we demonstrate that the polarization mode remains in presence of a coherent coupling between the two components. In particular we study the modulational stability of the mode and we determine through a multi-scaling analysis the dynamics of non-linear excitations. We show that the excitations of polarization undergo a Benjamin-Feir instability contrary to the density excitations. This instability is then stabilized in the short wavelength regime by a long wave - short wave resonance. Finally in the last chapter, we derive in a non-perturbative way the polarisation dynamics close the Manakov limit.In this limit, the dynamics proves to be governed by a Landau-Lifshitz equation without dissipation. Landau-Lifshitz equations belong to a hierarchy of integrable equations (Ablowitz-Kaup-Newell-Segur hierarchy) and we derive the single-phase solutions thanks to the finite-gap method; in particular we identify a new type of soliton for the two-component Bose-Einstein condensates. Finally, taking advantage of the integrability of the system, we solve the Riemann problem thanks to the Whitham modulation theory and we show that the two-component condensates can propagate rarefaction waves as well as dispersive shockwaves; we describe the modulation of the shockwaves by the propagation of simple waves and contact waves of Riemann invariants.

Currently, existing devices for extracting electrical power from ocean waves all suffer from problems with low efficiency due to a lack of information about the incoming waves in advance. The complex dynamic nonlinear characteristics of the ocean make the prediction of these incoming waves a great challenge. This paper aims to investigate a deterministic short-term wave-by-wave prediction system, that can accurately predict the wave height and timing of the incoming waves, based on measurements from a submerged pressure sensor. The complete prediction process contains three steps, namely reconstruction, assimilation, and prediction. A nonlinear Weakly Dispersive Reconstruction method (WDM) is firstly employed to accurately calculate the surface elevation from the measured pressures. Afterwards, a variational assimilation method is used to convert the time series surface elevation to a spatial wavefield, to obtain initial conditions for the prediction. Lastly, a High Order Spectral Method (HOSM) deterministically predicts the evolution of the 2D irregular wavefield based on the acquired initial conditions. To verify the performance of this proposed prediction system, tests were conducted with data from irregular sea states with varying wave parameters, generated by simulations as well as model experiments in the controlled environment of a wave tank. The results show that the surface elevation can be predicted within 5% from the reference, for a future period of about 10 seconds for wavefields commonly experienced by a wave energy converter. Based on the results, a prediction is possible, but the accuracy heavily depends on the current sea state and the chosen prediction distance.The results have been compared against similar tests made using radar data and proven to be a viable alternative for certain sea states. In conclusion, pressure measurements, as a mean to sample an ocean wavefield, is shown to be a good option when combined with nonlinear reconstruction and prediction methods to assist the power harvesting capabilities of a wave energy converter. / Nuvarande enheter för att extrahera elektrisk energi från havsvågor lider av stora problem med låg effektivitet på grund av brist på information om de inkommande vågorna. Det komplexa ickelinjära dynamiska beteendet hos havsvågor gör förutsägelsen av dem till en stor utmaning. Det här arbetet syftar till att undersöka ett deterministiskt kortsiktigt system för att förutspå våg för våg, som noggrant kan förutspå våghöjd och tidpunkt för de inkommande vågorna, baserat på mätdata från en dränkbar trycksensor. Den kompletta förutsägelseprocessen innehåller tre steg, rekonstruktion, assimilering och förutsägelse. En ickelinjär weakly dispersive reconstruction method används först för att med hög noggrannhet beräkna ythöjningen från det uppmätta trycket. Därefter, används en variational assimilation method för att konvertera en tidsserie av ythöjningen till ett rumsligt vågfält, för att erhålla initialvillkor för förutsägelsen. Slutligen används en High Order Spectral Method för att deterministiskt förutspå utvecklingen av det tvådimensionella oregelbundna vågfältet baserat på de förvärvade initialvillkoren. För att verifiera prestandan av det föreslagna förutsägelsesystemet, så genomfördes tester med data från olika oregelbundna havstillstånd med varierande parametrar, genererade av simuleringar, såväl som modellexperiment utförda i en kontrollerad miljö i form av en vågtank. Resultaten från testerna visar att ythöjningen förutspås inom 5% från referensen, för en period på 10 sekunder framåt i tiden, för vågor som ett vågkraftverk vanligtvis utsätts för. Baserat på resultatet, så är det möjligt att förutspå inkommande vågor, men noggrannheten beror kraftigt på det aktuella havstillståndet och det valda avståndet för förutsägelsen. Resultaten har jämförts mot liknande tester gjorda med radardata och visat sig vara ett genomförbart alternativ för vissa havstillstånd. Sammanfattningsvis visas det att tryckmätningar, som ett medel för att mäta ett havsvågfält, är ett bra alternativ när de kombineras med ickelinjära rekonstruktions- och förutsägelsemetoder för att hjälpa till att öka ett vågkraftverks energigenerering.

The mixing of additives into a plastic is an extremely important step in the plastics industry, necessary for the manufacture of almost every conceivable product. Therefore the costs in developing new products can prove very expensive as the testing is usually carried out using full scale machines, usually using twin screw extruders because they are able to provide good dispersive and distributive mixing. This is particularly important when compounding difficult to disperse additives and nano-additives. What is required is a machine that can replicate the mixing abilities of a twin-screw extruder but on a laboratory scale. There have been attempts by industry to develop smaller machines, such as the Thermo Scientific HAAKE Minilab II Micro Compounder which processes on the scale of 7 cm3 of material volume. This can be too small for some needs and therefore a machine is required to produce material on the 10g to 100g scale. To this end a laboratory mixer of novel design was devised and its mixing performance was assessed using conductive carbon black and compared against the Thermo Scientific HAAKE Minilab II Micro Compounder, a 19 mm co-rotating twin-screw extruder and a 40 mm co-rotating twin-screw extruder. Carbon black was used because mixing performance can be assessed by measuring the minimum carbon loading necessary to induce electrical conductivity. It was found that the minimixer was able to induce electrical conductivity at loading of 5.75% but the comparison with the other machines proved difficult as the achievement of the threshold at which semi-conductivity occurred appeared independent of shear rate and mixing duration.

A computationally efficient, discrete model is presented for transmission line analysis and passive model order reduction of high-speed interconnect systems. The development of this model was motivated by the on-going efforts in chip/package co-design to route a major portion of the on-chip clock and high-speed data buses through the package in order to overcome the bandwidth reduction and delay caused by the high ohmic loss of on-chip wiring. The geometric complexity of the resulting interconnections is such that model order reduction is essential for rapid and accurate signal integrity assessment to support pre-layout design iteration and optimization. The modal network theory of the skin effect in conjunction with the theory of compact differences is used for the development of discrete models for dispersive, multi-conductor interconnects compatible with passive model order reduction algorithms. The passive reduced-order interconnect modeling algorithm, PRIMA, is then used on the resulting discrete model to generate a low-order, multi-port macromodel for interconnect networks. Numerical examples are used to demonstrate the validity and efficiency of the proposed model.

A microextração líquido-líquido dispersiva (DLLME) é uma técnica de preparo de amostra baseada no equilíbrio de distribuição do analito entre a fase doadora (amostra) e a fase aceptora (solvente orgânico) em um sistema ternário de solventes. Foi desenvolvida em 2006 por Rezaee e colaboradores para a determinação de hidrocarbonetos policíclicos aromáticos em amostras de água e por ser uma técnica muito recente,ainda é pouca explorada para o preparo de amostras biológicas. Portanto, o objetivo deste trabalho foi avaliar a DLLME como técnica para a extração da oxibutinina (OXY), fármaco usado para o tratamento da incontinência urinária, e da N-desetiloxibutinina (DEO), seu principal metabólito ativo, em amostras de urina. A análise da OXY e DEO foi realizada por eletroforese capilar (CE), utilizando um capilar de sílica fundida de 50 ?m de diâmetro interno, com comprimento efetivo de 36,5 cm, trietilamina 50 mmol/L, pH 3 como solução de eletrólito, tensão de30 kV, temperatura de 30°C e detecção em 204 nm. Nestas condições o tempo de migração da DEO foi de 7,12 min e da OXY foi de 7,42 min, com resolução de 3,1. O procedimento utilizado para preparo da amostra foi baseado na DLLME, utilizando 5 mL de urina,na qual foi adicionado 2,5% de NaCle cujo pH foi ajustado para 11. O solvente para a extração consistiu de uma mistura de 140 ?L de tetracloreto de carbono (solvente extrator) e 260 ?L de acetonitrila (solvente dispersor), que permaneceram em contato com a amostra pordois minutos. A avaliação das características de desempenho analítico apresentou faixa linear de 90-300 ng/mL para a OXY e 187,5-750ng/mL para a DEO. A recuperação absoluta foi de 71,4 e 60,9% e o limite de quantificação foi de 90 e 187,5 ng/mL para a OXY e DEO, respectivamente. Os estudos de precisão e exatidão apresentaram coeficientes de variação e erros relativos inferiores a 15% e as amostras foram estáveis nos estudos de estabilidade. Portanto, foi possível desenvolver um método rápido, fácil e confiável para analisar e quantificar a OXY e a DEO em amostras de urina por CE, usando a DLLME como técnica de preparo de amostra. / The dispersive liquid-liquid microextraction (DLLME) is a sample preparation technique based on the equilibrium distribution between an extraction solvent and a sample solution in a ternary solvent system. It was developed by Rezaee and co-workers in 2006 for the determination of polycyclic aromatic hydrocarbons in water samples. Until now, for being a very recent technique it was little explored for the analysis of drugs in biological fluids. Therefore, the aim of this work was to evaluate the DLLME as an extraction technique for oxybutynin (OXY), a drug used to treat urinary incontinence, and N-desethyloxybutynin (DEO), its main active metabolite in urine samples. The OXY and DEO\'s analysis was performed by capillary electrophoresis (CE) using a 50 ?m ID fused-silica capillary with an effective length of 36.5 cm with a photodiode array detector set at 204 nm. It made use of triethylamine 50 mmol/L pH 3 as background electrolyte, voltage of +30 kV and temperature of 30°C. Under these conditions the migration time were 7.12 minutes for DEO and 7.42 minutes for OXY, with a resolution of 3.1. The sample preparation procedure was based on DLLME and used 5 mL of urine samples whichionic strength was increased by the addition of 2.5% NaCland pH were adjusted to 11. The extraction mixture consisted of 140 ?L of carbon tetrachloride (extraction solvent) and 260 ?L of acetonitrile (disperser solvent), which remained in contact with the sample for two minutes. The analytical performance\'s evaluation presented linear range of 90-300 ng/mL for OXY and 187.5-750ng/mL for DEO. The absolute recovery were 71.4 and 60.9% and the limit of quantification were 90.0 and 187.5 ng/mL for OXY and DEO, respectively. The accuracy and precision studies showed coefficients of variation and errors below 15% and the samples were stable at stability studies. Therefore, it was possible to develop a fast, reliable and easy method to analyze and quantify OXY and DEO in urine samples by CE, using DLLME as a sample preparation technique.

Na condução por saltos dispersiva, os portadores de carga são caracterizados por tempos de residência não exponenciais. Como uma conseqüência, efeitos hereditários aparecem e o problema deve ser conduzido no espaçõ de Laplace. Distribuições dielétricas conhecidas e algumas outras foram usadas como possíveis funções capazes de descrever o meio desordenado. Um estudo cuidadoso de seus espectros de freqüência foi realizado. O método de inversão de Widder truncado foi desenvolvido para possibilitar a volta do espaço de Laplace para o do tempo real. Dois tipos de problemas práticos foram abordados: condução dispersiva na qual o campo elétrico das cargas móveis pode ser desprezado e o caso de carga espacial para o qual essa aproximação não pode ser feita. Duas configurações de interesse foram escolhidas: decaimento do potencial de superfície de amostras carregadas por descarga corona e a subida do potencial no carregamento por corrente constante. / Dispersive conductive process are characterized by non-exponential residence times of the hopping carrier. As a consequence, hereditary effects appear and the problem must be conducted in the Laplace space. A bunch of known dielectric distributions functions and others were used as possible functions describing the disordered medium. A careful study of their frequency spectrum was carried out. The truncate Widder inversion was developed in order to allow returning from the Lapace to the real time space. Two kind of practical problems were studied: dispersive conduction in which the electric field of the mobile charge may be neglected and the space charge ones when that approximation cannot be made. Two configurations of interest were selected: the corona discharge potential decay and the constant current potentinal build-up.

Dans cette thèse, nous avons voulu exploiter et étendre les outils de simulation à notre disposition pour proposer des méthodes de caractérisation et de prédiction du mélange à différentes échelles. À l'échelle locale d'écoulements macroscopiques, nous avons voulu exploiter les possibilités offertes par le logiciel de simulation 3D éléments finis XimeX® et y apporter des améliorations dans le but d'obtenir un outil d'étude du mélange distributif de particules dans un polymère par extrusion bivis. Nous avons ainsi enrichi la méthode éléments finis existante à l'aide de la bibliothèque éléments finis CimLib© du Cemef pour atteindre une plus grande précision de calcul, puis nous avons testé plusieurs méthodes de lâchers de particules afin de simuler le déplacement de charges dans la matrice polymère au cours du mélange. Nous avons ensuite appliqué quelques méthodes de caractérisations du mélange, dont une inédite, à ces lâchers de particules, et ce dans le cas de plusieurs géométries de vis. À l'échelle de la particule, on s'est intéressé aux mécanismes conduisant à la casse de fibres rigides, telles que les fibres de verre, lors du mélange avec un polymère en extrusion bivis. Nous avons choisi de faire des hypothèses assez importantes afin de simplifier ce problème extrêmement complexe et nous avons proposé une méthode de simulation de l'évolution de la distribution des longueurs de fibres le long de l'écoulement basée sur la conservation de la masse des fibres. Nous avons utilisé comme paramètres de cette simulation les résultats de calcul 1D obtenus par le logiciel Ludovic® qui repose sur des approches de type ALH. Nous avons ensuite comparé quelques résultats de calcul à des distributions de longueurs mesurées sur des échantillons prélevés le long d'une extrudeuse bivis. / In this thesis, we have attempted to use and to extend previously developed simulation tools to propose characterisation and mixing prediction methods at different scales. At a local macroscopic flow scale, we attempted to use the possibilities given by the 3D finite element software XimeX® and to improve it in order to obtain a tool for mixing simulation of filled polymers in twin-screw extruders. Thus we have enriched the existing finite element method using the Cemef finite element library CimLib© in order to achieve a greater computation accuracy. Then we have tested several particle tracking methods to predict the fillers displacement into the matrix during mixing. Furthermore, we have applied several characterisation methods to these particles tracking results for different screw geometries. At the particle scale, we have focused on the mechanisms leading to rigid fibres (such as glass fibres) breakage during mixing with polymer in twin-screw extruders. We have some assumptions in order to simplify this extremely complex problem. We then have proposed a simulation method of the evolution of the fibres length distribution along the flow. This method is based on the fibres mass conservation. We have used the results of the Ludovic® software 1D computations based on lubrication theory as impute parameters for this simulation. Then we have compared some computational results to length distributions measured on experimental samples taken along a twin-screw extruder.