Orientadores: Eduardo Granado Monteiro da Silva, Juan Carlos Paredes Campoy / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-15T13:45:19Z (GMT). No. of bitstreams: 1 Ardito_FabioMachado1984-_M.pdf: 6352423 bytes, checksum: edd5885909fe50631ed33ee3dcd760ec (MD5) Previous issue date: 2010 / Resumo: Espectroscopia Raman é uma ferramenta muito versátil e poderosa na investigação de mudanças de fase estruturais ou eletrônicas, principalmente quando aliada à possibilidade de se atingir altos campos magnéticos e baixas temperaturas. Neste projeto, introduzimos uma montagem capaz de caracterizar as propriedades de transporte eletrônico simultaneamente à obtenção de espectros Raman nestas condições de temperatura e campo, visando possibilitar a verificação in-situ do comportamento macroscópico do material a ser estudado. Descrevemos aqui o procedimento de montagem experimental, configuração, automação otimização deste sistema. Níveis de ruído muito baixos foram obtidos,consistentes como esperado pelas especificações dos instrumentos utilizados. A montagem foi aplicada a dois casos de interesse à Física do Estado Sólido. Primeiramente, níveis de Landau em grafite pirolítico altamente orientado (HOPG), oriundos da quantização dos níveis de energia dos portadores de carga sob ação de um campo magnético, foram diretamente observados por espectroscopia Raman. Simultaneamente, foram realizadas medidas de magnetorresistência feito Hall no HOPG, que comprovaram a reprodutibilidade de efeitos quânticos já reportados na literatura. Também foram investigadas as origens do acoplamento spin-fônon gigante na perovskita dupla Ba2FeReO6, obtendo-se a frequência de um modo de estiramento do oxigênio, em baixas temperaturas sob um campo magnético de 1,5 tesla, simultaneamente a medidas de magnetorresistência. Estas últimas serviram como uma sonda indireta da orientação relativa dos domínios magnéticos neste material, comprovaram que as medidas de Raman com campo foram tomadas com os domínios orientados. A ausência de qualquer mudança na frequência do modo de vibração com o campo aplicado indica que o grau de liberdade orbital dos elétrons 5d do Re não é important no mecanismo de acoplamento spin- fônon neste material / Abstract: The Raman Spectroscopy is a powerful and versatile tool in the investigation of structural and electronic phases transitions, specially when allied with the possibility of reaching high magnetic fields and low temperatures. In this project, we introduce an assembly capable of characterizing electronic transport properties simultaneously to the Raman spectra acquisition, in such conditions, allowing in situ verification of the macroscopic behavior of the material under study. We describe in this dissertation the procedures of assembly, configuration, automation and optimization of such system. Very low noise levels were obtained, in agreement with the specifications of the instruments used in this system. The assembly was employed in two cases of interest for solid stat physics. First, Landau Levels in highly ordered pyrolytic graphite (HOPG), due to energy quantization of charge carriers by a magnetic field, were directly observed by Raman spectroscopy. Simultaneously, magnetor sistanc and Hall effect measurements were carried out for HOPG, attesting the reproducibility of quantum effects already reported in the literature . Also, the origin of giant spin-phonon coupling into the double perovskit Ba2FeReO6 was investigated by obtaining the frequency of the oxygen stretching mode at low temperatures and under a magnetic field of 1.5 tesla, simultaneously to magnetoresistance measurements. The latter were taken as an indirect probe of the relative orientation of the magnetic domains in the material, proving that the Raman experiments with field were obtained with oriented domains. The absence of any change in the frequency of this mode with field indicat that the orbital degree of freedom of the Re 5d electrons is not important for the mechanism of spin-phonon coupling in this material / Mestrado / Física da Matéria Condensada / Mestre em Física

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-22T12:37:32Z No. of bitstreams: 1 josielcarlosdesouzagomes.pdf: 11267373 bytes, checksum: 393a01f57f4f5afaaf46890b84f4a7ac (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-12-22T12:42:22Z (GMT) No. of bitstreams: 1 josielcarlosdesouzagomes.pdf: 11267373 bytes, checksum: 393a01f57f4f5afaaf46890b84f4a7ac (MD5) / Made available in DSpace on 2016-12-22T12:42:22Z (GMT). No. of bitstreams: 1 josielcarlosdesouzagomes.pdf: 11267373 bytes, checksum: 393a01f57f4f5afaaf46890b84f4a7ac (MD5) Previous issue date: 2015-02-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A nanotecnologia é uma área de estudo promissora e que nos mostra resultados bastante surpreendentes. Amostras magnéticas (Cobalto e liga de Permalloy (Ni81Fe19), por exemplo) em escala nanométrica, têm como aplicabilidade importante a gravação magnética devido à crescente demanda por meios de gravação cada vez mais rápidos e de alta capacidade de armazenamento. Para determinados tamanhos de nanofios, observa-se a presença de domínios magnéticos e paredes de domínios do tipo vórtice ou transversal que podem ser transportadas para diferentes regiões sem deformação. Pode-se usar tais paredes como bit de informação mas, para isso, precisa-se conhecer com detalhes o comportamento dessas paredes em diversas situações. Neste presente trabalho utilizamos simulações numéricas para estudar o comportamento da magnetização em nanofios retangulares (nanofitas) de Permalloy-79, que apresentam parede de domínio transversal entre domínios “head-to-head”. Utilizamos nestas simulações um modelo no qual os momentos magnéticos interagem através da interação de troca e a interação dipolar. Embora a maioria dos trabalhos encontrados utilizem campo magnético para mover a parede, optamos por aplicar corrente de spin-polarizado na direção do nanofio devido ao fato de ser mais prático de ser produzido. A dinâmica do sistema é regida pelas equações de Landau-Lifshitz-Gilbert e a atuação da corrente é introduzida nessas equações. Fizemos uma abordagem teórica na qual pode-se mostrar como esta equação de Landau-Lifshitz-Gilbert para aplicação de corrente foi obtida. A integração da equação de Landau-Lifshitz-Gilbert é feita utilizando o método de Runge-Kutta e de Predição-Correção. Baseado nessas teorias, escrevemos um programa na linguagem Fortran-90 para realizar as simulações. Em nossos resultados observamos o comportamento da velocidade da parede de domínio em função do tempo e da densidade de corrente. Comparamos estes resultados com a bibliografia. / Nanotechnology is a promising field of study and show us pretty amazing results. Magnetic samples (Cobalt and alloy Permalloy (81NiFe19), for example) at the nanometer scale, have as important applicability the magnetic recording due to the growing demand for recording media ever faster and high storage capacity. For certain sizes of nanowires, it is observed the presence of magnetic domains and vortex domain walls or transverse domain wall which can be transported to different regions without deformation. It can use such walls as bit of information, but for that it is necessary to know in detail the behavior of these walls in various situations. In this work we used numerical simulations to study the behavior of the magnetization in rectangular nanowires (nanostrip) of Permalloy-79, which have transverse domain wall between domains "head-to-head."We used in these simulations a model in which the magnetic moments interact through the exchange interaction and the dipolar interaction. Although most studies found use magnetic field to move the wall, we decided to apply spin-polarized current toward the nanowire due the fact that it is more practical to be produced. The dynamics of the system is governed by the equations of Landau-Lifshitz-Gilbert and the current performance is introduced in these equations. We made a theoretical approach in which you can show how this equation of Landau-Lifshitz-Gilbert for applying current was obtained. The integration of the equation of Landau-Lifshitz-Gilbert is done using the Runge-Kutta and Prediction-Correction methods. Based on these theories, we wrote a program in Fortran-90 language to perform the simulations. In our results we observed the behavior of the domain wall velocity as a function of time and current density. We compare these results with the literature.

Este trabalho aborda o escoamento incompressível ao redor de um cilindro circular. A tese que se quer defender, com base em experimentos numéricos, é: A equação de Landau pode ser obtida a partir das equações de Navier-Stokes por uma análise de estabilidade não-linear global. A teoria produz um procedimento bem-definido para determinação dos coeficientes da equação de Landau, permitindo assim a sua interpretação como um modelo simplificado (equações reduzidas de Navier-Stokes) para a predição das forças aplicadas pelo fluido ao cilindro, que podem ser comparados com resultados experimentais. O modelo não-linear se baseia em uma teoria assintótica que, como se sabe, tem sua faixa de validade no espaço de parâmetros determinada a posteriori, por meio da própria comparação com dados de laboratório. Resultados na faixa 46 <= Re <= 80 são apresentados. Descobriu-se, que a faixa de aplicabilidade da teoria como aqui exposta é restrita, não excedendo em muito o valor crítico do número de Reynolds. Argumentos são expostos para justificar esta afirmação e possíveis maneiras de modificar a teoria para estender esta faixa são apresentadas. São reportados, ainda, teoria e resultados sobre um novo tipo de condição de contorno,denominado impedância fluida, que permite reduzir o tamanho do domínio de cálculo necessário para simulação de escoamentos externos, comparativamente à comumente utilizada condição de outflow. Neste caso, abordou-se a faixa 20 <= Re <= 600. / This work adresses the incompressible flow around a circular cylinder. What we want to prove, based on numerical experiments, reads: The Landau equation can be derived from the Navier-Stokes equations by means of a global nonlinear stability analysis. The theory leads to a procedure for calculating numerically the coefficients of these equation, thus permitting their interpretation as a simplified model - reduced Navier-Stokes equation - for the prediction of the forces applied by the fluid on the cylindrical structure, which can be compared against experimental data. The nonlinear model is based on an asymptotic theory which, as is known, has its validity range in the parameter space determined a posteriori. The focus lies in the range 46 <= Re <= 80. It was found that the theorys applicability range as presented here is restricted to a small neighborhood of Rec. This affirmation in justified and possible means of modifying the theory in order to enlarge this range are proposed. Theory and results concerning a new type of boundary condition called fluid impedance are also reported, permitting the reduction of the domain size necessary for simulating external flows, comparatively to the commonly used outflow condition. In this case, the range 20 <= Re <= 600 was considered.

En physique des plasmas, le transport des électrons peut être décrit d'un point de vue cinétique ou d'un point de vue hydrodynamique.En théorie cinétique, une équation de Fokker-Planck couplée aux équations de Maxwell est utilisée habituellement pour décrire l'évolution des électrons dans un plasma collisionnel. Plus précisément la solution de l'équation cinétique est une fonction de distribution non négative f spécifiant la densité des particules en fonction de la vitesse des particules, le temps et la position dans l'espace. Afin d'approcher la solution de ce problème cinétique, de nombreuses méthodes de calcul ont été développées. Ici, une méthode déterministe est proposée dans une géométrie plane. Cette méthode est basée sur différents schémas numériques d'ordre élevé . Chaque schéma déterministe utilisé présente de nombreuses propriétés fondamentales telles que la conservation du flux de particules, la préservation de la positivité de la fonction de distribution et la conservation de l'énergie. Cependant, le coût de calcul cinétique pour cette méthode précise est trop élevé pour être utilisé dans la pratique, en particulier dans un espace multidimensionnel.Afin de réduire ce temps de calcul, le plasma peut être décrit par un modèle hydrodynamique. Toutefois, pour les nouvelles cibles à haute énergie, les effets cinétiques sont trop importants pour les négliger et remplacer le calcul cinétique par des modèles habituels d'Euler macroscopiques. C'est pourquoi une approche alternative est proposée en considérant une description intermédiaire entre le modèle fluide et le modèle cinétique. Pour décrire le transport des électrons, le nouveau modèle réduit cinétique M1 est basé sur une approche aux moments pour le système Maxwell-Fokker-Planck. Ce modèle aux moments utilise des intégrations de la fonction de distribution des électrons sur la direction de propagation et ne retient que l'énergie des particules comme variable cinétique. La variable de vitesse est écrite en coordonnées sphériques et le modèle est défini en considérant le système de moments par rapport à la variable angulaire. La fermeture du système de moments est obtenue sous l'hypothèse que la fonction de distribution est une fonction d'entropie minimale. Ce modèle satisfait les propriétés fondamentales telles que la conservation de la positivité de la fonction de distribution, les lois de conservation pour les opérateurs de collision et la dissipation d'entropie. En outre une discrétisation entropique avec la variable de vitesse est proposée sur le modèle semi-discret. De plus, le modèle M1 peut être généralisé au modèle MN en considérant N moments donnés. Le modèle aux N-moments obtenu préserve également les propriétés fondamentales telles que les lois de conservation et la dissipation de l'entropie. Le schéma semi-discret associé préserve les propriétés de conservation et de décroissance de l'entropie. / In plasma physics, the transport of electrons can be described from a kinetic point of view or from an hydrodynamical point of view.Classically in kinetic theory, a Fokker-Planck equation coupled with Maxwell equations is used to describe the evolution of electrons in a collisional plasma. More precisely the solution of the kinetic equations is a non-negative distribution function f specifying the density of particles as a function of velocity of particles, the time and the position in space. In order to approximate the solution of such problems, many computational methods have been developed. Here, a deterministic method is proposed in a planar geometry. This method is based on different high order numerical schemes. Each deterministic scheme used presents many fundamental properties such as conservation of flux particles, preservation of positivity of the distribution function and conservation of energy. However the kinetic computation of this accurate method is too expensive to be used in practical computation especially in multi-dimensional space.To reduce the computational time, the plasma can be described by an hydrodynamic model. However for the new high energy target drivers, the kinetic effects are too important to neglect them and replace kinetic calculus by usual macroscopic Euler models.That is why an alternative approach is proposed by considering an intermediate description between the fluid and the kinetic level. To describe the transport of electrons, the new reduced kinetic model M1 proposed is based on a moment approach for Maxwell-Fokker-Planck equations. This moment model uses integration of the electron distribution function on the propagating direction and retains only the energy of particles as kinetic variable. The velocity variable is written in spherical coordinates and the model is written by considering the system of moments with respect to the angular variable. The closure of the moments system is obtained under the assumption that the distribution function is a minimum entropy function. This model is proved to satisfy fundamental properties such as the non-negativity of the distribution function, conservation laws for collision operators and entropy dissipation. Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model. Moreover the M1 model can be generalized to the MN model by considering N given moments. The N-moments model obtained also preserves fundamental properties such as conservation laws and entropy dissipation. The associated semi-discrete scheme is shown to preserve the conservation properties and entropy decay.

L’objectif de cette thèse est d’explorer analytiquement et numériquement la dynamique d’aimantation de nanoparticules magnétiques. Nous montrons qu’il est possible de contrôler efficacement le retournement d’aimantation d’une nanoparticule à l’aide d’une excitation autorésonante. Cette étude révèle que l’amortissement de Gilbert et la température altèrent l’efficacité de ce procédé, tandis que les interactions dipolaires peuvent le faciliter. Les propriétés stationnaires d’une monocouche de nanoparticules sont également étudiées en reproduisant numériquement des courbes ZFC. Nous observons ainsi qu’un désordre structurel ne modifie pas la température de blocage. Enfin, nous étudions le comportement d’un ensemble de nanoparticules en interaction dans un fluide à l’aide de simulations de dynamique moléculaire. Nous retrouvons les configurations à l’équilibre en forme de chaînes et d’anneaux, puis nous examinons les aspects dynamiques en mettant en évidence l’existence d’ondes de spins. / The goal of this thesis is to explore analytically and numerically the magnetization dynamics in magnetic nanoparticles. Firstly, we study the Néel dynamics of fixed. We show that one can efficiently control the magnetization reversal of a nanoparticle by using a chirped excitation (autoresonance). This study reveals that the Gilbert damping and the temperature alter the efficiency of the reversal, while dipolar interactions can improve it. The stationary properties of a monolayer of nanoparticles are then examined by computing ZFC curves with a Monte Carlo method. We observe that structural disorder has no effect on the blocking temperature. Finally, we investigate the behavior of an ensemble of interacting nanoparticles moving in a fluid with a molecular dynamics approach. Our numerical simulations reproduce the usual chain and ring-like equilibrium configurations. We then study the dynamics of these structures and show the existence of super-spin waves.

Ce mémoire de thèse présente une approche semi-analytique des différentes solutions solitons spatio-temporelles de l'équation cubique quintique de Ginzburg-Landau complexe étendue à (3+1)D (GL3D).La méthode semi-analytique choisie est celle des coordonnées collectives qui permet d'approcher le champ exact, dont l'expression analytique est inconnue, par une fonction d'essai, qui comporte un nombre limité de paramètres physiques.En appliquant cette procédure à l'équation GL3D, nous obtenons un système d'équations variationnelles qui gouverne l'évolution des paramètres de la balle de lumière. Nous montrons que cette approche des coordonnées collectives est incomparablement plus rapide que la procédure de résolution directe de l'équation GL3D. cette rapidité permet d'obtenir, en un temps record, une cartographie générale des comportements dynamiques des balles de lumière. Cette cartographie révèle une riche variété d'états dynamiques faite de balles de lumière stationnaires, oscillantes et rotatives.Finalement, les résultats de cette thèse prédisent l'existence de plusieurs familles de balles de lumière, et précisent les domaines respectifs de leurs paramètres physiques. Cette prédiction constitue un pas en avant dans les efforts entrepris ces dernières années en vue d'une démonstration expérimentale de ce type d'impulsions. / This thesis presents a semi-analytical approach for the search of (3+1)D spatio-temporal soliton solutions of the complex cubic-quintic Ginzburg-Landau equation (GL3D).We use a semi-analytical method called collective coordinate approach, to obtain an approximate profile of the unknown pulse field. This ansatz function is chosen to be a function of a finite number of parameters describing the light pulse.By applying this collective corrdinate procedure to the GL3D equation, we obtain a system of variational equations which give the evolution of the light bullet parameters as a function of the propagation distance. We show that the collective coordinate approach is uncomparably faster than the direct numerical simulation of the propagation equation. This permits us to obtain, efficiently, a global mapping of the dynamical behavior of light bullets, which unveils a rich variety of dynamical states comprising stationary, pulsating and rotating light bullets.Finally the existence of several types of light bullets is predicted in specific domains of the equation parameters. Altogether, this theoretical and numerical work may be a useful tool next to the efforts undertaken these last years observing light bullets experimentally.

Orientadores: Ana Luiza Cardoso Pereira, Luiz Eduardo Moreira Carvalho de Oliveira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-28T09:45:49Z (GMT). No. of bitstreams: 1 SolisLerma_DanielAlejandro_M.pdf: 11339360 bytes, checksum: 0efee568f2b70411f8fcb14075392b26 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho foram estudados os efeitos de bordas com terminações perfeitamente definidas de uma rede de grafeno no regime Hall quântico sobre as propriedades eletrônicas deste sistema. O problema foi abordado com uso da aproximação tight-binding incluindo os efeitos do campo magnético e desordem no modelo. Estudou-se primeiramente o efeito das bordas nos níveis de energia do sistema, em espectros tipo borboleta de Hofstadter. Então o foco foi analisar as propriedades de localização eletrônica dos estados de borda, e as particularidades da distribuição das funções de onda nestes casos. Para investigar os estados de borda e determinar, para cada um dos estados eletrônicos, o quanto da função de onda encontra-se localizada nas bordas, foi criada uma quantidade nomeada Edge Fraction, denida como a somatória das amplitudes da função de onda na região das bordas, que numa aproximação semiclássica foi aqui considerada como a região delimitada por uma distância 2'B das bordas, onde 'B é o comprimento magnético. Com o uso do Edge Fraction, analisando-se as contribuições armchair e zigzag separadamente, em redes de grafeno quadradas, encontrou-se que há regiões de energia onde as funções de onda claramente cam mais localizadas num determinado tipo de borda. Este comportamento presume-se que é produto da competição que existe entre os potenciais devidos à presença de bordas e desordem no sistema, que evidenciam-se também no espectro de energia tipo borboleta de Hofstadter. Os resultados obtidos contribuem para o entendimento das propriedades de localização em redes de grafeno com bordas / Abstract: In this work the effects of sharp edges in the electronic properties of graphene lattices in the quantum Hall regime were studied. The problem was addressed using the tight-binding approximation including the effects of the magnetic eld and disorder in the model. It was studied at rst the effect of the edges in the energy levels of the system, through Hofstadter's buttery-like spectrum. Then we focused on analysing the localization properties of edge states and the particularities of the wave function distributions for these cases. To investigate the edge states and to determine, for each electronic state, how much of the wave function is localized at the edges, it was created a quantity called Edge Fraction. This quantity was dened as the probability density sum in the edge region, which in a semi-classical approximation, was considered here as the region limited by a distance 2'B from the edges, where 'B is the magnetic length. Using the Edge Fraction and analysing the contributions of armchair and zigzag edges separately, in squared lattices, it was found that there are energy regions where the wave functions are clearly more localized in a specic edge type. This behaviour is believed to be a result of the competition between the potential due to the presence of the edge and the potential due to the disorder in the system, which are also present in the Hofstadter energy spectrum. The results obtained contribute to the understanding of the localization properties of graphene lattices with edges / Mestrado / Física / Mestre em Física / 1247644 / CAPES

Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-01T08:41:01Z (GMT). No. of bitstreams: 1 Almeida_DalsonEloy_D.pdf: 2470369 bytes, checksum: 93d3b945f62f374cfd686217575dda95 (MD5) Previous issue date: 2017 / Resumo: Nesta tese estudamos a relação entre antiferromagnetismo e supercondutividade em pnictídeos à base de ferro. Este estudo será feito através da análise de uma energia livre de Ginzburg-Landau de parâmetros de ordem acoplados que será derivada de um modelo microscópico. Em particular, estamos interessados em saber se a transição entre os estados ordenados é de primeira ordem ou se as duas ordens podem coexistir. Para o caso de supercondutividade convencional as duas fases puras nunca coexistem. Entretanto, quando a supercondutividade é não-convencional e a condição de nesting perfeito não é satisfeita, pode haver um regime intermediário de coexistência microscópica das duas ordens. Nesta nova fase termodinâmica, as simetrias de rotação no espaço de spins, de reversão temporal e U(1) são quebradas simultânea e localmente. Logo, os canais de supercondutividade singleto e tripleto se misturam quanticamente. Em outras palavras, uma componente tripleto secundária do estado supercondutor é gerada. Os diagramas de fases do sistema são apresentados e analisamos também como flutuações magnéticas, acima da temperatura de Néel pura, afetam a temperatura de transição tripleto. Investigamos também o efeito da magnetização alternada no efeito Josephson, i.e., na supercorrente que flui através de uma junção entre dois supercondutores na fase de coexistência. Por fim, mas não menos importante, estudamos o efeito de proximidade em uma interface entre um supercondutor e um antiferromagneto. Veremos que os pares de Cooper podem penetrar a região magnética e em consequência, uma componente tripleto é induzida próximo da interface / Abstract: In this thesis, we study the interplay between antiferromagnetism and superconductivity in iron pnictides. This study will be done analyzing a free energy of coupled order parameters which will be derived from a microscopic model. In particular, we are interested if the phase transition between the ordered states is first order or if the two orders can coexist. For the case of conventional superconductivity, the two phases cannot coexist. However, when superconductivity is unconventional and the perfect nesting condition is not satisfied, there can exist an intermediary state of microscopic coexistence of the two orders. In this new thermodynamic phase, spin rotation, time reversal and U(1) symmetries are simultaneously and locally broken. Therefore, the singlet and triplet superconductivity channels are quantum mechanically mixed. In other words, a secondary triplet component is generated. The phase diagrams of the system are presented and we also analyze the effect of magnetic fluctuations above the pure Néel temperature on the triplet temperature transition. We also investigate the effects of the staggered magnetization on the Josephson effect, i.e., on the supercurrent that flows through a junction of two superconductors in the coexistence phase. Last, but not least, we study the proximity effect at an interface between a superconductor and an antiferromagnet. We will see that the Cooper pairs can penetrate the magnetic region and consequently a triplet component is induced near the interface / Doutorado / Física / Doutor em Ciências / 140834/2013-3 / 2342/15-4 / CNPQ / CAPES / BEX

Cette thèse est consacrée à l'analyse des singularités apparaissant dans des équations différentielles partielles elliptiques non linéaires découlant de la physique mathématique, de la biologie mathématique, et de la géométrie conforme. Les thèmes abordés sont le modèle de supraconductivité de Ginzburg-Landau, le problème de Lin-Ni-Takagi, le modèle de Keller-Segel de la chimiotaxie, et le problème de courbure scalaire prescrite. Le modèle de Ginzburg-Landau est une description phénoménologique de la supraconductivité. Une caractéristique essentielle des supraconducteurs de type II est la présence de vortex, qui apparaissent au-dessus d'une certaine valeur de la force du champ magnétique appliqué, appelée premier champ critique. Nous nous intéressons au régime de epsilon petit, où epsilon est l'inverse du paramètre de Ginzburg-Landau (une constante du matériau). Dans ce régime, les vortex sont au premier ordre des singularités topologiques de co-dimension 2. Nous fournissons une construction quantitative par approximation de vortex en dimension trois pour l'énergie de Ginzburg-Landau, ce qui donne une approximation des lignes de vortex ainsi qu'une borne inférieure pour l'énergie, qui est optimale au premier ordre et vérifiée au niveau epsilon. En utilisant ces outils, nous analysons ensuite le comportement des minimiseurs globaux en dessous et proche du premier champ critique. Nous montrons que, en dessous de cette valeur critique, les minimiseurs de l'énergie de Ginzburg-Landau sont des configurations sans vortex et que les minimiseurs, proche de cette valeur, ont une vorticité bornée. Le problème de Lin-Ni-Takagi apparait comme l'ombre (dans la littérature anglaise ``shadow'') du système de Gierer-Meinhardt d'équations de réaction-diffusion qui modélise la formation de motifs biologiques. Ce problème est celui de trouver des solutions positives d'une équation critique dans un domaine régulier et borné de dimension trois, avec une condition de Neumann homogène au bord. Dans cette thèse, nous construisons des solutions à ce problème présentant un comportement explosif en un point du domaine, lorsqu'un certain paramètre converge vers une valeur critique. La chimiotaxie est l'influence de substances chimiques dans un environnement sur le mouvement des organismes. Le modèle de Keller-Segel pour la chimiotaxie est un système de diffusion-advection composé de deux équations paraboliques couplées. Ici, nous nous intéressons aux états stationnaires radiaux de ce système. Nous sommes alors amenés à étudier une équation critique dans la boule unité de dimension 2, avec une condition de Neumann homogène au bord. Dans cette thèse, nous construisons plusieurs familles de solutions radiales qui explosent à l'origine de la boule, et se concentrent sur le bord et/ou sur une sphère intérieure, lorsqu' un certain paramètre converge vers zéro. Enfin, nous étudions le problème de la courbure scalaire prescrite. Étant donnée une variété Riemannienne compacte de dimension n, nous voulons trouver des métriques conformes dont la courbure scalaire soit une fonction prescrite, qui dépend d'un petit paramètre. Nous supposons que cette fonction a un point critique qui satisfait une hypothèse de platitude appropriée. Nous construisons plusieurs métriques, qui explosent lorsque le paramètre converge vers zéro, avec courbure scalaire prescrite. / This thesis is devoted to the analysis of singularities in nonlinear elliptic partial differential equations arising in mathematical physics, mathematical biology, and conformal geometry. The topics treated are the Ginzburg-Landau model of superconductivity, the Lin-Ni-Takagi problem, the Keller-Segel model of chemotaxis, and the prescribed scalar curvature problem. The Ginzburg-Landau model is a phenomenological description of superconductivity. An essential feature of type-II superconductors is the presence of vortices, which appear above a certain value of the strength of the applied magnetic field called the first critical field. We are interested in the regime of small epsilon, where epsilon is the inverse of the Ginzburg-Landau parameter (a material constant). In this regime, the vortices are at main order co-dimension 2 topological singularities. We provide a quantitative three-dimensional vortex approximation construction for the Ginzburg-Landau energy, which gives an approximation of vortex lines coupled to a lower bound for the energy, which is optimal to leading order and valid at the epsilon-level. By using these tools we then analyze the behavior of global minimizers below and near the first critical field. We show that below this critical value, minimizers of the Ginzburg-Landau energy are vortex-free configurations and that near this value, minimizers have bounded vorticity. The Lin-Ni-Takagi problem arises as the shadow of the Gierer-Meinhardt system of reaction-diffusion equations that models biological pattern formation. This problem is that of finding positive solutions of a critical equation in a bounded smooth three-dimensional domain, under zero Neumann boundary conditions. In this thesis, we construct solutions to this problem exhibiting single bubbling behavior at one point of the domain, as a certain parameter converges to a critical value. Chemotaxis is the influence of chemical substances in an environment on the movement of organisms. The Keller-Segel model for chemotaxis is an advection-diffusion system consisting of two coupled parabolic equations. Here, we are interested in radial steady states of this system. We are then led to study a critical equation in the two-dimensional unit ball, under zero Neumann boundary conditions. In this thesis, we construct several families of radial solutions which blow up at the origin of the ball and concentrate on the boundary and/or an interior sphere, as a certain parameter converges to zero. Finally, we study the prescribed scalar curvature problem. Given an n-dimensional compact Riemannian manifold, we are interested in finding bubbling metrics whose scalar curvature is a prescribed function, depending on a small parameter. We assume that this function has a critical point which satisfies a suitable flatness assumption. We construct several metrics, which blow-up as the parameter goes to zero, with prescribed scalar curvature.

Cette thèse est consacrée à l’étude de certains problèmes variationnels de type transition de phase vectorielle ou "phase-field" qui font intervenir une contrainte de divergence. Ces modèles sont généralement basés sur une énergie dépendant d’un paramètre qui peut représenter une grandeur physique négligeable ou qui est liée à une méthode d’approximation numérique par exemple. Une question centrale concerne alors le comportement asymptotique de ces énergies et des minimiseurs globaux ou locaux lorsque ce paramètre tend vers 0. Cette thèse présente différentes stratégies prenant en compte la contrainte de divergence. Elles seront illustrées à travers l’étude de deux modèles. Le premier est une approximation du modèle Eulérien pour le transport branché par un modèle de type phase-field avec divergence prescrite. Nous montrons comment une estimation uniforme de l’énergie, en fonction de la contrainte sur la divergence, permet d’établir un résultat de Gamma-convergence. Le second modèle, en lien avec la théorie du micromagnétisme, concerne des énergies de type Aviles-Giga dans un cadre vectoriel avec contrainte de divergence. Nous illustrerons dans quelle mesure la méthode d’entropie permet de caractériser les minimiseurs globaux. Dans certaines situations nous montrerons une conjecture de type De Giorgi concernant la symétrie 1D des minimiseurs globaux de l’énergie sous une contrainte au bord. / This thesis is devoted to the study of phase-field type variational models with divergence constraint. These models typically involve an energy depending on a parameter which represents a negligible physical quantity or is linked to some numerical approximation method for instance. A central question concerns the asymptotic behavior of these energies and of their global or local minimizers when this parameter goes to 0. We present different strategies which allow to take the divergence constraint into account. They will be illustrated in two models. The first one is a phase-field type approximation, involving a divergence constraint, of the Eulerian model for branched transportation. We illustrate how uniform estimates on the energy, depending on the constraint on the divergence, allow to establish a Gamma-convergence result. The second model, related to micromagnetics, concerns Aviles-Giga type energies for divergence-free vector fields. We use the entropy method in order to characterize global minimizers. In some situations, we will prove a De Giorgi type conjecture concerning the one-dimensional symmetry of global minimizers under boundary conditions.