The diffusive gradient in thin films technique (DGT) was used to measure concentration of labile metal-species (Cu, Ni, Pb) in the waste water from Faculty of Chemistry, Brno University of Technology.

6-mercaptopurine was joined by diazotation and copulation reactions on Iontosorb AV. Presence of thiol groups in modified resin was showed by infrared spectrometry. Amount of thiol groups was determined by iodometric titration. Resin gel was preparated from modified resin and agarose and both of them were tested for mercury determination by DGT technique.

In the time period from November to April of the academic year 2007/2008 presence of mercury and its forms was monitored in the waste waters of Faculty of Chemistry, VUT in Brno. The level of mercury was determined as total mercury with help of the atomic absorption spectrometry method and in available forms by diffusive gradient in thin film technique.

The theoretical part of this doctoral thesis deals with determination of mercury and its species in aquatic systems. Special attention is paid to the use in situ sampling technique diffusive gradients in thin films technique (DGT) and its development. Current resin gels used for determination of mercury by DGT technique Duolite GT-73, Chelex-100 and Spheron-Thiol are described. Moreover, new types of resin gels including Iontosorb AV modified by imidazole or 6-mercaptopurine and commercially available titanium dioxide. Preparations of resin gels and their basic tests in model solution according to DGT Research are described. Mercury accumulation in relation to time and basic recovery test were tested and capacity of resins was determined. All tested resins meet the requirements of basic DGT Research tests and relative standard deviations of mercury in recovery tests were lower than 10 %. The sorption capacity of resins varied from 1,5 to 6 µmol.l-1 and decreased in following order: Duolite GT-73 > ISAV-IM > Chelex-100 > Spheron-Thiol > TiO2 > ISAV-MP. Mercury sorption on resins was investigated under conditions similar to those in natural waters. It was found that the ionic strength commonly occurring in natural waters does not affect the determination of mercury. The presence of chlorides significantly affects the determination of mercury using DGT with titanium dioxide and therefore this sorbent can not be recommended for the determination of mercury in sea waters. The accumulated amount of mercury, depending on the pH shows that all the sorbents can be used in natural waters with pH in the range form 4 to 8. Mercury sorption is most affected by the presence of humic acids, especially at ion-exchange resins containing other than thiol functional groups. The exception is titanium dioxide for which physical sorption of humic acid metal complexes is typical. Cadmium and copper in model solutions in the molar balance of the excess mostly influenced the sorption of mercury on Chelex-100 and Spheron-Thiol resins. After laboratory tests, the DGT units with studied sorbents were used for the determination of mercury in natural waters of South Moravia (Svratka, Jihlava and Svitava river). Mercury concentration determined using DGT units containing Duolite GT-73 resin was comparable to the total dissolved concentration of mercury in river water provided by direct determination using AAS technique. Order of magnitude smaller concentrations than the total dissolved mercury concentration were found using DGT containing Spheron-Thiol and ISAV-MP resins. These sorbents are probably able to capture only mercury present in the form of labile complexes. This can be used for speciation analysis if more DGT units with different resins are deployed together. Subtracting the measured DGT Spheron-Thiol or ISAV-MP concentrations from the DGT Duolite GT-73 concentration, information about the amount of mercury present in the form of stabile complexes can be obtained. The amount of mercury determined after application of DGT units containing ISAV-IM, Chelex 100 or TiO2 can probably represent the mercury fraction bound in even weaker complexes than fraction determined by Spheron-Thiol and ISAV-MP DGT.

Dans cette étude, nous analysons les conséquences mécaniques des transformations de phase diffusives, particulièrement la plasticité de transformation ou TRIP (TRansformation Induced Plasticity) ainsi que le comportement élasto-viscoplastique. Cette plasticité de transformation, explicable par le mécanisme de Greenwood-Johnson, est souvent décrite avec le modèle de Leblond qui fait l'hypothèse d'un comportement élastoplastique. Dans ce modèle comme dans la majorité des analyses expérimentales et des modélisations (analytiques, par éléments finis, FFT ou encore champ de phase), une des hypothèses principales est de ne pas prendre en compte le caractère visqueux du comportement. Or plusieurs études récentes montrent que le comportement des deux phases (parente et produite) peut être très sensible au taux de déformation imposé, particulièrement à haute température. D'où l'intérêt de développer une modélisation rendant compte des effets visqueux présents lors de certaines transformations. Pour ce faire, nous adoptons une modélisation numérique où le comportement de chaque phase est décrit par une loi élasto-viscoplastique à écrouissage mixte associée à la loi de Norton ; la cinétique de transformation est imposée et le problème d'interactions mécaniques entre phases est traité par la méthode des éléments finis. D'une part, la contribution de la viscosité au TRIP est quantifiée pour différents taux de déformation imposés durant la transformation de phase. D'autre part, l'effet du taux de transformation (configuration arbitraire) sur la prédiction du TRIP est évalué et caractérisé. Une extension des modèles existants (à cinétique périodique et aléatoire) est proposée. Elle consiste d'abord à étudier et évaluer l'effet de la morphologie de germe ainsi que l'anisotropie de croissance sur la prédiction du TRIP. Ensuite, une amélioration avec un modèle anisotherme, basé sur des mesures expérimentales existantes, a été introduite. Elle consiste principalement à tenir compte de la variation des propriétés mécaniques en fonction de la température. Les analyses montrent que la prise en compte de la viscosité peut conduire à des effets importants sur la prédiction du TRIP par rapport aux résultats obtenus avec un modèle élastoplastique classique. Elles montrent en particulier, en configuration anisotherme, une amélioration de la prédiction du TRIP mesuré expérimentalement lors de la transformation perlitique d'un acier 100Cr6 [Tahimi, 2012]. Cette étude permet par ailleurs de dégager des tendances évidentes dans les relations entre le TRIP et l'histoire de la transformation : chargement mécanique et cinétique de transformation, morphologie des germes et anisotropie de croissance. Ces résultats pourront contribuer à l'élaboration d'un modèle analytique simple prenant en compte la viscosité. / In this study, the mechanical consequences of phase transformations in steel, particularly, the TRansformation Induced Plasticity TRIP as well as the elasto-viscoplastic behavior has been analyzed. This transformation plasticity, due to the Greenwood-Johnson mechanism, is often described with the model of Leblond with the assumption of an elastoplastic behavior. Moreover, in the majority of experimental analysis or numerical finite elements modeling FEM or phase field modeling PFM, the viscous criteria were not considered. However, several recent studies have demonstrated that both phases (parent and product) show high strain-rate sensitivity at elevated temperatures. Hence, the principal interests using the FEM modeling to extend these main reference models of [Leblond, 89] and [Taleb-Sidoroff, 2003], with taking into account the viscous effects, which are present during some phase transformations, especially at high temperatures. To do this, the behavior of each phase is described by an elasto-viscoplastic law with mixed hardening associated to the Norton law. The transformation kinetics is imposed and the problem of mechanical interactions between phases is processed by the finite element method. On the one hand, the contribution from viscosity to TRIP was quantified for different strain-rate during phase transformation. On the other hand, the effect of an arbitrarily-set of transformation-rate in the FEM simulations was evaluated and characterized. An extension of the existing models (for periodic and random kinetics) is proposed. It consists at first in studying and in evaluating the effect of both the morphology of nuclei and the growth anisotropy, on the prediction of TRIP. Then, an improvement with non-isothermal model, based on existing experimental measures, was introduced. It consists mainly in taking into account the variation of the mechanical properties of the mixture of both phases, according to the temperature. The predictions show that in such cases, the consideration of the viscosity can lead to major changes of the estimated TRIP compared with results obtained from a classic plastic model. Also, the prediction of TRIP can be significantly influenced by the choice of the morphology of germs and by the type of growth: isotropic or anisotropic. These improvements, particularly with the non-isothermal configuration, show a good agreement with experimental measures of TRIP on the 10006 steel during pearlite phase transformation [Tahimi, 2012]. This study allows besides, releasing obvious trends in the relations between the TRIP and the history of the phase transformation: mechanical loading and kinetics of transformation, morphology of nuclei and growth anisotropy. These results can contribute to the elaboration of a simple analytical model taking into account the viscous criteria.

Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.

Dans cette thèse, nous rapportons l'évolution temporelle du premier et du troisième ordre de la diffusion magnétique d'un film CoTb amorphe après une excitation femtoseconde. Ces résultats sont obtenus en appliquant une diffusion résonnants de rayons X aux petits angles au seuil d'absorption magnétique de Co M3 via des expériences de pompe sonde répétitives. Une différence de comportement entre le premier et le troisième ordre de diffusion a été observée après 3,5 ps, où une seconde baisse de l'intensité du troisième ordre apparaît. En utilisant des modèles appropriés, nous montrons que cette différence est due à une augmentation de la largeur de la paroi du domaine séparant deux domaines opposés. Nous supposons que cet élargissement de la paroi est généré par une variation de l'anisotropie uniaxiale hors plan due au réchauffement thermique du réseau par l'impulsion laser femtoseconde. Cette interprétation est vérifiée en mesurant l’anisotropie uniaxiale en fonction de la température de chauffage en effectuant des mesures statiques SQUID-VSM. / In this thesis, we report the time evolution of first and third order of magnetic scattering from an amorphous CoTb film after a femtosecond excitation. These results are obtained by applying a resonant small angle X ray scattering at the Co magnetic absorption edge M3 via a repetitive pump probe experiments. Difference in behaviours between the first and third scattering orders was observed after 3.5 ps where a second drop of the third order intensity appears. Using suitable models, we show that this difference is due to an increase of the domain wall width separating two opposite domains. We suppose that this wall broadening is generated by the variation of the out of plane uniaxial anisotropy due to the thermal heating of the lattice by the femtosecond laser pulse. This interpretation is verified by following the uniaxial anisotropy as function of the heating temperature by doing static SQUID-VSM measurements

No description available.

Les études menées permettent d’étendre la méthodologie de commande H∞ aux modèles décrits par des équations différentielles faisant intervenir des ordres de dérivation non entiers. Deux approches sont proposées. La première consiste à réécrire le modèle non entier comme un modèle entier incertain afin de pouvoir utiliser les méthodes de commande H∞ développées pour les modèles entiers. La seconde approche consiste à développer des conditions LMI spécifiques aux modèles non entiers à partir de leur pseudo représentation d’état. Ces deux approches sont appliquées à l’isolation vibratoire d’un pont. / The general theme of the work enables to extend H∞ control methodology to fractional order models. Two approaches are proposed. The first one consists in rewriting the fractional order model as an uncertain integer order model in order to use existing H∞ control methods for integer order models. The second approach consists in developing specific LMI conditions for fractional order models based on their pseudo state space representation. These two approaches are applied to the vibratory isolation of a bridge.

Les travaux de cette thèse s'inscrivent dans le domaine des équations aux dérivées partielles et sont liés à la problématique des changements d'échelle dans le contexte de la cinétique des gaz. En effet, sachant qu'il existe plusieurs niveaux de description pour un gaz, on cherche à relier les différentes échelles associées dans un cadre où une part d'aléa intervient. Dans une première partie, on établit la dérivation rigoureuse de l'équation de Boltzmann linéaire sans cut-off en partant d'un système de particules interagissant via un potentiel à portée infinie en partant d'un équilibre perturbé.La deuxième partie traite du passage d'un modèle BGK stochastique avec champ fort à une loi de conservation scalaire avec forçage stochastique. D'abord, on établit l'existence d'une solution au modèle BGK considéré. Sous une hypothèse additionnelle, on prouve alors la convergence vers une formulation cinétique associée à la loi de conservation avec forçage stochastique.Au cours de la troisième partie, on quantifie dans le cas à vitesses discrètes le défaut de régularité dans les lemmes de moyenne et on établit un lemme de moyenne stochastique dans ce même cas. On applique alors le résultat au cadre de l'approximation de Rosseland pour établir la limite diffusive associée à ce modèle.Enfin, on s'intéresse à l'étude numérique du modèle de Uchiyama de particules carrées à quatre vitesses en dimension deux. Après avoir adapté les méthodes de simulation développées dans le cas des sphères dures, on effectue une étude statistique des limites à différentes échelles de ce modèle. On rejette alors l'hypothèse d'un mouvement Brownien fractionnaire comme limite diffusive / The work of this thesis belongs to the field of partial differential equations and is linked to the problematic of scale changes in the context of kinetic of gas. Indeed, knowing that there exists different scales of description for a gas, we want to link these different associated scales in a context where some randomness acts, in initial data and/or distributed on all the time interval. In a first part, we establish the rigorous derivation of the linear Boltzmann equation without cut-off starting from a particle system interacting via a potential of infinite range starting from a perturbed equilibrium. The second part deals with the passage from a stochastic BGK model with high-field scaling to a scalar conservation law with stochastic forcing. First, we establish the existence of a solution to the considered BGK model. Under an additional assumption, we prove then the convergence to a kinetic formulation associated to the conservation law with stochastic forcing. In the third part, first we quantify in the case of discrete velocities the defect of regularity in the averaging lemmas. Then, we establish a stochastic averaging lemma in that same case. We apply then the result to the context of Rosseland approximation to establish the diffusive limit associated to this model.Finally, we are interested into the numerical study of Uchiyama's model of square particles with four velocities in dimension two. After adapting the methods of simulation which were developed in the case of hard spheres, we carry out a statistical study of the limits at different scales of this model. We reject the hypothesis of a fractional Brownian motion as diffusive limit