In these diploma thesis magnetically ordered materials are studied with the prospect of their application in spintronics. Specifically, we investigated metallic alloy FeRh, which undergoes a magnetic phase transition from antife- romagnetic phase to feromagnetic one around 100◦ C. This phenomenon can be readily used in memory devices. Laser spectroscopy is used as a nondestructive method without need of any electrical contacts. Magnetic properties of FeRh are studied by magnetooptical effects including quadratic magnetic linear dichroism. The measured polarization rotations are of the order of miliradians, therefore, the detection is realized by an optical bridge. At first, we concentrated on discrimina- ting of various magnetooptical effects from each other. The second part is focused on the phase transition induced by different means. Firstly, by heating the whole sample, secondly by illuminating the sample locally by continuous laser.

Dans la première partie de cette thèse nous traitons l’écoulement diphasique compositionnel, partiellement miscible et compressible en milieux poreux. Déplacement d'une phase par un autre est analysé. Nous examinons les mélanges non idéals, la pression est variable, et les concentrations de phase, la densité et la viscosité sont les fonctions de la pression. Le processus est décrit par le problème de Riemann qui admet des solutions discontinues. Nous avons développé une méthode numérique-analytique de solution pour déterminer les paramètres à tous les chocs avant résoudre les équations de flux. Cette méthode est basée sur la séparation de thermodynamique et hydrodynamique, proposée dans [Oladyshkin, Panfilov 2006] et qui était inapplicable à problème de Riemann, en raison de manque des conditions d’Hugoniot. Dans cette thèse, nous avons construit les conditions supplémentaires d'Hugoniot. Dans la deuxième partie, nous examinons l'écoulement diphasique lors que les zones monophasique apparaissent, dans cette zone, le fluide est sur/sous-saturés et les équations diphasique dégénèrent.Nous avons proposé de décrire les zones diphasique et sur/sous-saturés avec un système uniforme des équations diphasique classique en étendant le concept de saturation d'être négatif et supérieur à un. Physiquement, cela signifie que les états monophasiques sont considérés comme des états diphasiques consistant une phase imaginaire avec la saturation négative. Une telle extension de la saturation exige développement des conditions de consistance qui sont fait dans cette thèse.La dernière partie est consacrée ensuite à étendre le modèle HT-split pour le cas d’écoulement triphasique compositionnel. Nous avons obtenu le modèle asymptotique, dans lequel la thermodynamique et l'hydrodynamique sont séparées / In the first part of thesis we deal with two-phase multicomponent, partially miscible, compressible flow in porous media. Displacement of one phase by another is analyzed. We examine non ideal solutions, pressure is variable, and phase compositions, densities and viscosities are variable functions of pressure.The process is described by Riemann problem which admits discontinuous solutions.We developed a numerical-analytical method of solution to explicitly determine all shock parameters before solving the flow equations. This method is based on splitting thermodynamics and hydrodynamics, suggested in [Oladyshkin, Panfilov 2006]. Earlier this method was inapplicable to Riemann problem, due to the lack of Hugoniot conditions. In this thesis we have constructed additional Hugoniot conditions.In the second part we examine two-phase flow when the single-phase zones appear, in this zone the fluid is over/under-saturated and two-phase flow equations degenerate and they cannot be used. We proposed to describe two-phase and over/under-saturated single-phase zones by uniform system of classic two-phase equations while extending the concept of phase saturation to be negative and higher than one. Physically it means that the oversaturated single-phase states are considered as pseudo two-phase states consisting an imaginary phase with negative saturation. Such an extension of saturation requires developing some consistence conditions which have developed in this thesis.The last part then is devoted to extend the HT-split model to the case of three-phase compositional flow. We have obtained the general asymptotic model, in which the thermodynamics and hydrodynamics are split

Ce travail porte sur l’étude des transformations induites par les procédés industriels (TIPI) dans le domaine de l’industrie pharmaceutique. Il se focalise sur le procédé de compression directe et sur deux principes actifs modèles qui sont la caféine et la carbamazépine. Des méthodes de caractérisations expérimentales des transitions de phases dans les comprimés ont été développées. La densité des comprimés a été mesurée par tomographie à rayons X et évaluée en surface par micro-indentation. Des méthodes thermiques telles que l’ACD et l’ATG ont été utilisées pour estimer les transformations dans tout le volume des comprimés. La spectroscopie Raman à basses fréquences a été appliquée pour la première fois pour cartographier la surface des comprimés. La spectroscopie Raman à hautes fréquences a été développée dans le but d’augmenter le nombre de données et d’automatiser le traitement des spectres. La transformation de la caféine forme I (métastable) en forme II (stable) nécessite plusieurs années dans les conditions ambiantes. Les investigations menées sur la caféine I ont révélé que la transition est induite par la compression directe car une transformation partielle en forme II est mesurée dans tout le volume du comprimé. La transformation continue au sein du comprimé lors de son stockage et le taux de transformation reste supérieur à celui de la poudre de caféine forme I non comprimée. Les quantifications misent en place par ACD et spectroscopie Raman à basses fréquences ont montré des transformations de la forme I dans tout le volume des comprimés et leur valeur est indépendante de l’intensité de la pression de compression. De plus, les deux formes de la caféine coexistent à l’échelle micrométrique, ce qui tend à prouver que des cristallites de forme II apparaissent dans tous les grains de caféine. La caféine formulée avec de la cellulose microcristalline présente un comportement plastique lors de la compression. La tomographie à rayons X révèle l’existence d’une zone locale de densité plus élevée au niveau des parois latérales, sans que ceci influe localement sur le taux de transition de la caféine. L’emploi d’une caféine calibrée entraine un comportement plus fragmentaire, qui semble réduire le taux de transformation mesuré. Aucune transformation de phase solide de la carbamazépine dihydrate n’a été décelée par ATG et spectroscopie Raman dans les comprimés fabriqués. Il semble que ce principe actif soit stable en compression directe / The purpose of this study was to improve the understanding of process induced transformations (PITs) in the field of the pharmaceutical industry. This present study is focused on the direct compression process applied to two model active molecules named caffeine and carbamazepine. Experimental characterization methods of phase transitions in the tablets were developed. Densities inside the tablets were measured by X-ray computed micro-tomography and by micro-indentation at the surface. Thermal methods for DSC and TGA were applied in order to estimate transformation degrees of tablet parts. Low frequencies micro-Raman Spectroscopy (MRS) was used for the first time as a way for polymorphs mapping. Raman spectroscopy was also developed in the high frequencies range to increase the analyzed part area and to computerize the spectra treatment. Caffeine form I is transformed naturally toward caffeine form II but this transition can take many years at room temperature. Our investigations have shown that the direct compression process induced a partial transition of caffeine I toward caffeine II. Phase transition degree stayed higher in the tablet than in the non-compressed powder during two years. Quantification process was set up for DSC and low frequencies MRS. It was found that the pressure level did not influenced the transition degree. Moreover, both polymorphs coexist at the micrometer scale in all caffeine particles. Caffeine formulated with micro-crystalline cellulose exhibits a plastic behavior under compaction. X-ray tomography revealed higher densities zones next to the tablet slides but any impact on the transition degree was detected. The use of calibrated caffeine particles led to a more brittle behavior and seemed to decrease the transition degree. The investigations on carbamazepine dihydrate did not show any phase transformation of this active molecule induced by direct compression

Estudamos o diagrama de fases para uma classe de modelos de Ising ferromagnéticos em $ \\mathbb^2 $, com campo magnético externo periódico. O campo externo assume dois valores: $ h $ e $ -h $, onde $ h> 0 $. Os sítios associados a valores positivos e negativos do campo externo, formam uma configuração em forma de tabuleiro de xadrez (nós chamamos de {\\it cell-board configuration}), com células retangulares de tamanho $ L_1 \\times L_2 $ sítios, de tal forma que o valor total do campo externo é zero. Como principal resultado, mostramos a presença de uma transição de fase de primeira ordem. A transição de fase existe para $ h <\\frac + \\frac $, onde $ J $ é uma constante de interação. A prova é construida usando o método de {\\it reflection positivity (RP)}. Aplicamos uma desigualdade que é normalmente referida como a estimativa de {\\it chessboard}. Além disso, incluímos uma região de unicidade da medida de Gibbs em $h>4J$, isto usando um critério baseado nas ideias de percolação em desacordo. / We study the low-temperature phase diagram for a ferromagnetic Ising model on $\\mathbb^2$, with a periodical external magnetic field. The external field takes two values: $h$ and $-h$, where $h>0$. The sites associated with positive and negative values of external field form a cell-board configuration with rectangular cells of sides $L_1\\times L_2$ sites, such that the total value of the external field is zero. As a main result, we show the presence of a first-order phase transition. The phase transition holds if $h<\\frac+ \\frac$, where $J$ is an interaction constant. We use the reflection positivity (RP) method. We apply a key inequality which is usually referred to as the chessboard estimate. Furthermore, we prove uniqueness for Gibbs measure in $h>4J$, using a uniqueness condition obtained in terms of disagreement percolation.

The study of conformal symmetry is motivated through an example in statistical mechanics and then rigorously developed in quantum field theories in general spatial dimensions. In particular, primary fields are introduced as the fundamental objects of such theories and then studied in the formalism of radial quantization. The implications of conformal invariance on the functional form of correlation functions are studied in detail. Conformal blocks are defined and various approaches to their analytical and numerical calculation are presented with a special emphasis on the one-dimensional case. Building on these preliminaries, a modern formulation of the conformal bootstrap program and its various extensions are discussed. Examples are given in which bounds on the scaling dimensions in a one-dimensional theory are derived numerically. Using these results I motivate the technique of using the extremal functional bootstrap which I then develop in more detail. Many technical details are discussed and examples shown. After a brief discussion of conformal field theories with a boundary I apply numerical methods to find constraints on the spectrum of the 3D Ising model. Another application is presented in which I study the 4-point function on the boundary of a particular theory in Anti-de-Sitter space in order to approximate the mass spectrum of the theory. / O estudo da simetria conforme é motivado através de um exemplo em mecânica estatística e em seguida rigorosamente desenvolvido em teorias de campos quânticos em dimensões espaciais gerais. Em particular, os campos primários são introduzidos como os objetos fundamentais de tais teorias e então estudados através do formalismo de quantização radial. As implicações da invariância conforme na forma funcional das funções de correlação são estudadas em detalhe. Blocos conformes são definidos e várias abordagens para seu cálculo analítico e numérico são apresentadas com uma ênfase especial no caso unidimensional. Com base nessas preliminares, uma formulação moderna do programa de bootstrap conforme e suas várias extensões são discutidas. Exemplos são dados em que limites nas dimensões de escala em uma teoria unidimensional são derivados numericamente. Usando esses resultados, motivei a técnica de usar o bootstrap funcional extremo, que depois desenvolvo em mais detalhes. Diversos detalhes técnicos são discutidos e exemplos são apresentados. Após uma breve discussão das teorias de campo conformes com fronteiras, eu aplico métodos numéricos para encontrar restrições no espectro do modelo de Ising em 3D. Outra aplicação é apresentada em que eu estudo a função de 4 pontos na fronteira de uma teoria particular no espaço Anti-de-Sitter, a fim de aproximar o espectro de massa da teoria.

O estudo da dinâmica de populações vem adquirindo grande importância atualmente, por suas aplicações nas mais diversas áreas do conhecimento, como a biologia evolutiva, ecologia, economia e computação, entre outras. O uso de redes, ou autômatos celulares, para modelar dinâmicas populacionais é um recurso frequentemente utilizado por sua simplicidade no tratamento de problemas com alto grau de complexidade. Neste trabalho utilizamos autômatos celulares para simular dinâmicas populacionais onde analisamos transições de fases longe do equilíbrio em modelos de replicação em uma e duas dimensões, classificando-as de acordo com suas classes de universalidade. Também utilizamos redes para estudar as possíveis origens dos ciclos primos presentes nas cigarras do gênero Magicicada que habitam a América do Norte, mostrando que a predação não é necessária para o surgimento deste comportamento. / The study of population dynamics becomes even more important nowadays because of its applications in a wide range of subjects, such as evolutive biology, ecology, economics and computational sciences, among many others. The use of networks, as well as cellular automata, to simulate populational dynamics is an ordinary tool because of its simplicity in the treatement of very complicated problems. In this work we use cellular automata to simulate populational dynamics where non equilibrium phase transitions in replicator models in one and two dimensions are analyzed and characterized by their universality classes. We also use cellular automata to study the possible origins of prime number cycling present in northern american Magicicada, showing that it is possible to generate prime number year life cycles whithout any predation effects.

Em nossas simulações, efetuamos uma cuidadosa análise numérica dos algoritmos de Monte Carlos empregados na termalização de teorias de gauge e sistemas de spins contínuos. Dentre eles, apresentamos uma nova proposta que permite reduzir em cerca de 25% os tempos computacionais. Aplicamos este novo algoritmo ao estudo numérico da transição de desconfinamento da teoria de Yang-Mills (YM) SU(2) tridimensional, a temperatura finita, em redes com volumes de 502 X 4 sítios. Por fim, também utilizamos técnicas de Escala de tamanho finito (FSS), Dinâmica de Tempos Curtos e Métodos Variacionais para extrair os expoentes críticos e espectro de massas de blindagem desta teoria. / In our numerical simulations, we have done a careful analysis of Monte-Carlo algorithms usually applied in the thermalization of gauge theories and continuous-spin systems. Among them we present a new proposal that enables a reduction of roughly 25% in the computational time. We apply this new algorithm to a numerical study of the at finite temperature, using lattices with 502 x 4 sites. We also use Finite-Size-Scaling techniques, Short-Time Dynamics and Variational Methods to extract critical exponents and the spectrum of screening masses of the theory.

Cette thèse est consacrée à l'étude du comportement asymptotique de grands graphes et arbres aléatoires. Le premier modèle étudié est un modèle de graphe aléatoire inhomogène introduit par Bo Söderberg. Un chapitre de ce manuscrit est consacré à l'étude asymptotique de la taille des composantes connexes à proximité de la fenêtre critique, en le reliant à la longueur des excursions d'un mouvement brownien avec dérive parabolique, étendant les résultats obtenus par Aldous. Le chapitre suivant est consacré à un processus de graphes aléatoires proposé par Itai Benjamini, défini ainsi : les arêtes sont ajoutées indépendamment, à taux fixe. Lorsqu'un sommet atteint le degré k, toutes les arêtes adjacentes à ce sommet sont immédiatement supprimées. Ce processus n'est pas croissant, ce qui empêche d'utiliser directement certaines approches usuelles. L'utilisation de limites locales permet de montrer la présence (resp. l'absence) d'une composante géante à certaines étapes dans le cas k>=5 (resp. k<=3). Dans le cas k=4, ces résultats permettent de caractériser la présence d'une composante géante en fonction du caractère surcritique ou non d'un processus de branchement associé. Dans le dernier chapitre est étudiée la hauteur d'un arbre de Lyndon associé à un mot de Lyndon choisi uniformément parmi les mots de Lyndon de longueur n, prouvant que cette hauteur est approximativement c ln n, avec c=5,092... la solution d'un problème d'optimisation. Afin d'obtenir ce résultat, nous couplons d'abord l'arbre de Lyndon à un arbre de Yule, que nous étudions ensuite à l'aide de techniques provenant des théories des marches branchantes et des grandes déviations. / This thesis is dedicated to the study of the asymptotic behavior of some large random graphs and trees. First is studied a random graph model introduced by Bo Söderberg in 2002. One chapter of this manuscript is devoted to the study of the asymptotic behavior of the size of the connected components near the critical window, linking it to the lengths of excursion of a Brownian motion with parabolic drift. The next chapter talks about a random graph process suggested by Itai Benjamini, defined as follows: edges are independently added at a fixe rate. Whenever a vertex reaches degree k, all adjacent edges are removed. This process is non-increasing, preventing the use of some commonly used methods. By using local limits, in the spirit of the PWIT, we were able to prove the presence (resp. absence) of a giant component at some stages of the process when k>=5 (resp. k<=3). In the case k=4, these results allows to link the presence (resp. absence) of a giant component to the supercriticality (resp. criticality or subcriticality) of an associated branching process. In the last chapter, the height of random Lyndon tree is studied, and is proven to be approximately c ln n, in which c=5.092... the solution of an optimization problem. To obtain this result, we couple the Lyndon tree with a Yule tree, then studied with the help of branching walks and large deviations

In dieser Arbeit wird mit Hilfe der Gitter-Methode der Phasenübergang/Crossover bei nicht verschwindender Temperatur der Quantenchromodynamik mit zwei Quark Flavour untersucht sowie die thermodynamische Zustandsgleichung berechnet. Es wird dabei die Wilson twisted-mass Formulierung der Quark-Wirkung verwendet, welche hinsichtlich des Kontinuum-Limes eine automatische Verbesserung birgt. Erste belastbare Resultate mit dieser Wirkung bei endlicher Temperatur werden in dieser Arbeit gezeigt. Mehrere kleine Werte der Pion-Masse werden betrachtet mit dem Ziel, Aufschluss über die Ordnung des Phasenüberganges im chiralen Limes zu erhalten. Im Bereich der von uns simulierten Pion-Massen zwischen 300 und 700 MeV wird hierbei lediglich ein Crossover-Übergang beobachtet. Die Abhängigkeit der gemessenen Crossover-Temperatur von der Masse wird für eine Extrapolation zu verschwindender Masse hin verwendet unter der Annahme verschiedener Szenarien für den chiralen Limes. Dazu komplementär wird das chirale Kondensat, der Ordnungsparameter der spontanen Brechung der chiralen Symmetrie, vor dem Hintergrund der so genannten magnetischen Zustandsgleichung untersucht, welche das universelle Verhalten in der Nähe des Phasenüberganges für die Universalitätsklasse des O(4) Modells angibt. Hinsichtlich der Thermodynamik wird ausgehend von der Spur-Anomalie und unter Benutzung der Temperatur-Integral Methode der Druck und die Energiedichte im Crossover-Gebiet berechnet. Der Kontinuum-Limes der Spur-Anomalie wird mit mehreren Gitterdiskretisierungen der Temperatur Nt sowie unter Zuhilfenahme einer tree-level Korrektur untersucht. / In this thesis we report about an investigation of the finite temperature crossover/phase transition of quantum chromodynamics and the evaluation of the thermodynamic equation of state. To this end the lattice method and the Wilson twisted mass discretisation of the quark action are used. This formulation is known to have an automatic improvement of lattice artifacts and thus an improved continuum limit behaviour. This work presents first robust results using this action for the non-vanishing temperature case. We investigate the chiral limit of the two flavour phase transition with several small values of the pion mass in order to address the open question of the order of the transition in the limit of vanishing quark mass. For the currently simulated pion masses in the range of 300 to 700 MeV we present evidence that the finite temperature transition is a crossover transition rather than a genuine phase transition. The chiral limit is investigated by comparing the scaling of the observed crossover temperature with the mass including several possible scenarios. Complementary to this approach the chiral condensate as the order parameter for the spontaneous breaking of chiral symmetry is analysed in comparison with the O(4) universal scaling function which characterises a second order transition. With respect to thermodynamics the equation of state is obtained from the trace anomaly employing the temperature integral method which provides the pressure and energy density in the crossover region. The continuum limit of the trace anomaly is studied by considering several values of Nt and the tree-level correction technique.

Ce travail concerne l’altération du comportement de phase de membranes lipidiques lors de leur interaction avec des molécules hydrophiles ou hydrophobes. L’utilisation de sondes moléculaires de fluorescence sensibles à leur micro-environnement constitue un aspect majeur de ce travail. Les techniques de spectroscopie de fluorescence et de microscopie confocale ont été mises à profit pour l’étude du comportement de ces sondes, donnant accès au degré de compacité et d’ordre dans les membranes.Nos résultats montrent que le polystyrène, un plastique rencontré de façon commune dans les régions polluées des océans, présente la capacité de modifier le comportement de phase des membranes lipidiques, entrant notamment en compétition avec le cholestérol.Nous avons montré que la présence élevée de sucres, tel que l’on peut le rencontrer dans certaines situations relevant de la bio-préservation, a pour effet de rompre la qualité de compaction des lipides, et nous avons proposé un nouveau modèle thermodynamique pour interpréter nos résultats.Enfin, les effets sur la membrane de l’incorporation d’un polymère amphiphile comportant un cholestérol greffé ont été étudiés, dans le cadre de l’élaboration de nouvelles stratégies thérapeutiques à base de lipides. / This work focuses on the alterations of lipid membrane phase behavior upon interaction with hydrophobic and hydophilic molecules. One major aspect of this thesis is the employement of environment sensitive probes to obtain information on the lipid bilayer packing by means of confocal spectral imaging and fluorescence spectroscopy. Our results show that polystyrene, a commonly found plastic in ocean wastes, has the ability to disrupt the lipid bilayer phase behavior and has a competitive interaction with cholesterol. The presence of high concentration of sugars, relevant in the field of biopreservation, has been found to alter the lipid bilayer packing and a new thermodynamics model has been proposed to complement the experimental results. Finally, the effects of an amphiphilic cholesterol-grafted polymer on model membrane was investigated, providing insight into potential new lipid therapeutic strategies.