A teoria de campo médio para o modelo de Ashkin-Teller com interações ferromagnéticas de longo alcance na presença de campos magnéticos aleatórios foi desenvolvida. Isso foi conseguido através do uso do truque de réplicas para a obtenção da energia livre e do estudo analítico das equações integrais acopladas dos parâmetros de ordem, da estabilidade de suas soluções e das suas expansões para T &#8804 Tc. Inicialmente, foram determinadas as expressões gerais das funções termodinâmicas do modelo no caso em que existiam três campos magnéticos aleatórios com distribuições gaussianas. Em seguida, foi examinado o caso particular do modelo com um só campo magnético aleatório na direção de Z = &#8249 &#948 S &#8250. A estratégia adotada se mostrou poderosa pois possibilitou a caracterização detalhada do diagrama de fases com várias superfícies de coexistência e das linhas de pontos críticos. As equações integrais das funções termodinâmicas desse caso particular foram discutidas e resolvidas numericamente para valores especiais das constantes de interação e da variância. Para o caso particular do modelo na presença de campos magnéticos aleatórios nas direções &#8249 S &#8250 e &#8249 &#948 &#8250, foram determinadas e discutidas as expressões das funções termodinâmicas. Foram também obtidas as equações das superfícies de instabilidade da solução paramagnética. Foi provado que a transição entre as fases paramagnética e de Baxter é sempre de primeira ordem. Outro resultado original da tese foi a verificação da existência da simetria de dilatação e contração do modelo de Potts na presença de campos magnéticos aleatórios. Essa simetria permite que o estudo da energia livre no intervalo q&#8712 (1,2) forneça o comportamento termodinâmico do sistema para todo q>2. / The meanfield theory of the long range Ashkin-Teller model in random fields was developed. This was obtained by using the replica trick and the study of the coupled integral equations for the order parameters, the stability of their solutions, and their expansions for T &#8804 Tc. Inicially, the expressions of the thermodynamic functions for the model in three random fields with Gaussian distributiuons were determined. After this, it was examined the particular case of the model with only one random field in the Z = &#8249 &#948 S &#8250 direction. The strategy revealed itself powerful by the detailed characterization of the phase diagram with several coexistence surfaces and lines of critical points. The integral equations of the thermodynamic functions for this particular case were discussed and numerically solved for special values of the interaction constants and field distribution variance. For the particular case of the model with random fields in the &#8249 S &#8250 and &#8249 &#948 &#8250, directions, the expressions were also determined and discussed. The equations of the instability surfaces for the paramagnetic solution were obtained, and it was proved that the para-Baxter transition line is always of first order. Another original result of the thesis was the verification of the the existence of the dilatation and contration symmetry in the Potts model with random fields. This symmetry permits that the study of the free energy in the q&#8712(1,2) interval supplies the thermodynamics behavior of the system for q>2.

Dans le cadre de la fusion par confinement inertiel, nous présentons une analyse des effets du champ magnétique sur le développement linéaire des instabilités de Richtmyer-Meshkov, en magnétohydrodynamique idéale d’une part, et de Rayleigh-Taylor au front d’ablation, dans les phases d’accélération et de décélération d’autre part.A l’aide d’un code linéaire de perturbation, nos simulations mono mode nous permettent de confirmer, pour l’instabilité de Richtmyer-Meshkov, la stabilisation apportée par la composante du champ magnétique parallèle au vecteur d’onde des perturbations de l’interface, dont l’amplitude oscille au cours du temps. Nous montrons que la prise en compte de la compressibilité n’apporte pas de changements significatifs par rapport au modèle impulsionnel incompressible existant dans la littérature. Dans nos simulations numériques bidimensionnelles, en géométrie plane, de l’instabilité de Rayleigh-Taylor dans la phase d’accélération, nous prenons en compte le phénomène d’auto-génération de champ magnétique induite par cette instabilité. Nous montrons qu’il est possible d’atteindre des valeurs de champ de l’ordre de quelques teslas et que la croissance de l’amplitude des perturbations transite plus rapidement vers un régime de croissance non-linéaire avec, notamment, un développement accru de la troisième harmonique. Nous proposons également une adaptation d’un modèle existant, étudiant l’effet d’anisotropie de conductivité thermique sur le taux de croissance de l’instabilité de Rayleigh-Taylor au front d’ablation, pour tenter de prendre en compte les effets des champs magnétiques auto-générés sur le taux de croissance de l’instabilité de Rayleigh-Taylor. Enfin, dans une étude numérique à deux dimensions, en géométrie cylindrique, nous analysons les effets des champs magnétiques auto-générés par l’instabilité de Rayleigh-Taylor dans la phase de décélération. Cette dernière étude révèle l’apparition de champs magnétiques pouvant atteindre plusieurs milliers de teslas sans pour autant affecter le comportement de l’instabilité de Rayleigh-Taylor. / In the context of inertial confinement fusion we investigate effects of magnetic fields on the development in the linear regime of two hydrodynamic instabilities: Richtmyer-Meshkov instability using ideal magnetohydrodynamics and ablative Rayleigh-Taylor instability in both acceleration and deceleration stages.Direct numerical simulations with a linear perturbation code enable us to confirm the stabilizing effect of the component of the magnetic field along the perturbations wave vector. The amplitude doesn’t grow linearly in time but experiences oscillations instead. The compressibility taken into account in the code does not affect predictions given by an already existing impulsive and incompressible model.As far as Rayleigh-Taylor instability is concerned we study the effects of self-generated magnetic fields that arise from the development of the instability itself. In the acceleration stage we perform two dimensional simulations in planar geometry. We show that magnetic fields of about 1T can be generated and that the instability growth transits more rapidly into nonlinear growth with the enhancement of the development of the third harmonic. We also propose an adaptation of an existing model that aims at studying thermal conductivity anisotropy effects, to take into account the effects of the self-generated magnetic fields on the Rayleigh-Taylor instability growth rate.Finally, in the deceleration stage, we perform two dimensional simulations in cylindrical geometry that take into account self-generation of magnetic fields due to the instability development. It reveals magnetic fields of about several thousands of teslas that are not strong enough though to affect the instability behavior.

Le but de cette étude est de concevoir, fabriquer et caractériser une puce microfluidique afin de mettre en oeuve la capture de nanoparticules magnétiques fonctionnalisées en vue de la reconnaissance d’anticorps spécifiques (couplage d’une très grande spécificité et sensibilité). Après avoir modélisé et simulé les performances de la microbobine intégrée dans le canal de la puce microfluidique en prenant soin de limiter la température du fluide à 37°C, la capture devant être effective, le microsystème est fabriqué en salle blanche en utilisant des procédés de fabrication collective. La fabrication du microdispositif en PDMS a aussi donné lieu à l’optimisation de procédés de modification de surface afin d’assurer la ré-utilisation du microdispositif (packaging réversible) et la limitation de l’adsorption non spécifique. L’immobilisation des anticorps su les billes (300 nm) a été menée à l’intérieur du canal en utilisant un protocole de type ELISA éprouvé. Le procédé a montré qu’il était également efficient pour cet environnement puisque nous avons pu mettre ne évidence la capture de nanoparticules / In this study, a concept of microfluidic chip with embedded planar coils is designed and fabricated for the aim of trapping effectively functionalized magnetic nanobeads and immobilizing antibody (IgG type). The planar coils as a heart of microfluidic chip is designed with criterion parameters which are optimized from simulation parameters of the maximum magnetic field, low power consumption and high power efficiency by FE method. The characterization of microcoils such as effectively nanobeads (300 nm) at low temperature (<37oC) is performed and confirmed. The channel network in PDMS material is designed for matching with entire process (including mixing and trapping beads) in microfluidic chip. A process of PDMS’s surface modification is also carried out in the assemble step of chip in order to limit the non-specific adsorption of many bio substances on PDMS surface. The microfluidic chip assemble is performed by using some developed techniques of reversible packaging PDMS microfluidic chip (such as stamping technique, using non-adhesive layer, oxygen plasma combining with solvent treatment). These packaging methods are important to reused microchip (specially the bottom substrate) in many times. The immobilization of antibody IgG-type is performed inside microfluidic chip following the standard protocol of bead-based ELISA in micro test tube. The result showed that IgG antibodies are well grafted on the surface of carboxyl-beads (comparing to result of standard protocol); these grafted antibodies are confirmed by coupling them with labeled second antibody (Fab-FITC conjugation).

Optical long baseline interferometry was recently established as a technique capable of resolving stars and their circumstellar environments at the milliarcsecond (mas) resolution level. This high-resolution opens an entire new window to the study of astrophysical systems, providing information inaccessible by other techniques. Astrophysical disks are observed in a wide variety of systems, from galaxies up to planetary rings, commonly sharing similar physical processes. Two particular disk like systems are studied in the thesis: (i) B He-rich stars that exhibits magnetic fields in order of kG and that trap their winds in structures called magnetospheres; and (ii) Be stars, fast rotating stars that create circumstellar viscous disks. This study uses the interferometric technique to investigate both the photosphere proper and the circumstellar environment of these stars. The objective is to combine interferometry with other observational techniques (such as spectroscopy and polarimetry) to perform a complete and well-constrained physical description of these systems. This description is accompanied by radiative transfer models performed by the HDUST code. / Interferometria óptica de longa linha de base recentemente estabeleceu-se como uma técnica capaz de resolver estrelas e seus ambientes circunstelares no nível de mili segundos de arcos (\\textit). Esta alta resolução abre uma janela inteiramente nova para o estudo de sistemas astrofísicos, fornecendo informações inacessíveis por outras técnicas. Discos astrofísicos são observados numa ampla variedade de sistemas, de galáxias à discos planetários, em geral compartilhando de processos físicos similares. Dois sistemas de discos foram estudados nesta tese: (i) o estrelas B ricas em He e que possuem campos magnéticos da ordem de kG e que confinam seus ventos em estruturas chamadas magnetosferas; e (ii) estrelas Be, estrelas de rotação rápida que criam um disco circumstelar viscoso. Este estudo usa a técnica interferométrica para investigar ambas a própria fotosfera e o ambiente circunstelar destas estrelas. O objetivo é combinar a interferometria com outras técnicas observacionais (tal como espectroscopia e polarimetria) para realizar uma descrição física completa e precisa destes sistemas. Esta descrição é acompanhada por modelos de transferência radiativa executados pelo código HDUST.

Ma thèse est consacrée aux nouveaux phénomènes nano-optiques et aux dispositifs basés sur l'interaction spin-orbite de la lumière (SOI). Tout d'abord, il a été démontré un SOI uniquement piloté par le champ magnétique de la lumière permettant de diriger avec précision les ondes de surface de Bloch, offrant ainsi une nouvelle manifestation du champ magnétique optique. Ensuite, nous avons proposé et démontré le concept de nano-antenne plasmonique hélicoïdale à ondes progressives (TW-HPA), c’est-à-dire un fil hélicoïdal en or étroit alimenté optiquement par une nano-antenne dipolaire dans une configuration « end-firing ». Une telle nano-antenne a été démontrée comme la première optique de polarisation sublongueur d’onde. L’agencement de TW-HPAs à l’échelle de quelques microns a permis de convertir « à la carte » un faisceau polarisé linéairement en une distribution de faisceaux directifs présentant des polarisations différentes définies de façon déterministe par la géométrie et les dimensions des nano-antennes. Par le biais d’un couplage en champ proche de quatre nano-antennes à hélicités opposées, nous avons obtenus une optique sublongueur d’onde permettant un degré de liberté dans le contrôle de la polarisation qui est interdit avec les composants et méthodes classiques basées sur l’exploitation de matériaux biréfringents ou dichroïques, ou de métamatériaux imitant ces propriétés. / My thesis is devoted to novel nano-optical phenomena and devices based on spin-orbit interaction (SOI) of light. First, magnetic spin-locking, i.e., an SOI solely driven by the magnetic field of light, is demonstrated with Bloch surface waves. It provides a new manifestation of the magnetic light field. Then, we propose and demonstrate the concept of traveling-wave plasmonic helical antenna (TW-HPA), consisting of a narrow helical gold-coated wire non-radiatively fed with a dipolar nano-antenna. By swirling surface plasmons, the TW-HPA combines subwavelength illumination and polarization transformation. The TW-HPA is demonstrated to radiate on the subwavelength scale almost perfectly circularly polarized optical waves upon illumination with linearly polarized light. With this subwavelength plasmonic antenna, we developed strongly integrated arrays of point-light emissions of opposite handedness and tunable intensities. Finally, by coupling two couples of TW-HPAs of opposite handedness, we obtained new polarization properties so far unattainable.

La micro fusion laser d'un lit de poudre (SLM) permet la réalisation de pièces complexes avec des microstructuresfines. Cette technologie présente de nombreux avantages mais se heurte encore à une faible disponibilité des poudres d'alliages. En SLM, la pièce est d'abord conçue par CAO (conception assistée par ordinateur), puis construite couche par couche avec un faisceau laser commandé par un ordinateur. Dans ce cadre, le travail effectué dans cette thèse a consisté à étudier et à développer une nouvelle méthode pour réaliser des pièces en alliages et en composites à partir de mélanges de poudres élémentaires, ouvrant ainsi la voie à une grande variété de compositions.Au niveau expérimental le choix s'est porté sur le système aluminium-silicium avec différentes teneurs en silicium (12, 18 et 50% en poids). L'effet de l'ajout d'un champ magnétique statique a aussi été proposé comme un outil supplémentaire de contrôle de la microstructure.Dans le processus de fabrication de pièces par SLM la puissance du laser et la vitesse de balayage déterminent au premier chef la densité, la microstructure, la composition des phases et les propriétés mécaniques du produit. Une analyse systématique de l'effet de ces paramètres sur l'alliage Al - Si fabriqué par SLM à partir de mélanges de poudres est présentée. Des alliages ont été ainsi obtenus pour plusieurs domaines de composition visés correspondant à des applications pratiques (structures légères, système tribologique, emballage électronique, ...).Les microstructures fines obtenues grâce à la solidification rapide des matériaux fondus conduit à des propriétés quise comparent de façon favorable à celles obtenues avec les techniques classiques d'élaboration et de mise en oeuvre. / As a new manufacturing technology, Selective laser melting (SLM) has a large potential in the manufacturing of complex parts with ultrafine microstructure.Selective laser melting has many significant advantages over traditional manufacturing methods but still faces a low availability of powder materials. With SLM, the part is firstly designed via 3D computer-aided design (CAD)), then built layer-by-layer with a high energy computer-controlled laser beam The work done in this study was therefore aiming at developing a new way to obtain alloys and composites directly from elemental powder mixtures with a large composition flexibility.Experimentally the choice was made of the aluminum-silicon system with several silicon contents (12, 18, 50 wt. %).Adding a static magnetic field was also considered as an additional way to control the microstructure. When parts are manufactured by SLM, laser power and scanning speed are the main parameters determining the density, microstructure, phase composition and mechanical properties. A systematic analysis of the role of these parameter on the manufacturing of Al - Si alloys by SLM from mixtures of powders was therefore conducted. Al - Si alloys with a very fine microstructure were thus obtained for several composition ranges corresponding to practical applications (lightweight structures, high wear resistance alloys, electronic packaging material, ...). The properties of the materials obtained in this way, according to the performed characterizations, compares favorably with those obtained via the conventional production technologies.

This thesis describes new methods of evaluating the efficiency of three-phase induction machines using synthetic loading. Synthetic loading causes the induction machine to draw full-load current without the need to connect a mechanical load to the machine's drive shaft. The synthetic loading methods cause the machine to periodically accelerate and decelerate, producing an alternating motor-generator action. This action causes the machine, on average over each synthetic loading cycle, to operate at rated rms current, rated rms voltage and full-load speed, thereby producing rated copper losses, iron loss and friction and windage loss. The excitation voltages are supplied from a PWM inverter with a large capacity DC bus capable of supplying rated rms voltage. The synthetic loading methods of efficiency evaluation are verified in terms of the individual losses in the machine by using a new dynamic model that accounts for iron loss and all parameter variations. The losses are compared with the steady-state loss distribution determined using very accurate induction machine parameters. The parameters were identified using a run-up-to-speed test at rated voltage and the locked rotor and synchronous speed tests conducted with a variable voltage supply. The latter tests were used to synthesise the variations in stator leakage reactance, magnetising reactance and the equivalent iron loss resistance over the induction machine's speed range. The run-up-to-speed test was used to determine the rotor resistance and leakage reactance variations over the same speed range. The test method results showed for the first time that the rotor leakage reactance varied in the same manner as the stator leakage and magnetising reactances with respect to current. When all parameter variations are taken into account there is good agreement between theoretical and measured results for the synthetic loading methods. The synthetic loading methods are applied to three-phase induction machines with both single- and double-cage rotors to assess the effect of rotor parameter variations in the method. Various excitation waveforms for each method were used and the measured and modelled efficiencies compared to conventional efficiency test results. The results verify that it is possible to accurately evaluate the efficiency of three-phase induction machines using synthetic loading.

Dans le cadre d'une approche Higher Tamm Dancoff Approximation notée HTDA, nous avons étudié les corrélations vibrationnelles de type quadrupole, avec et sans appariement. Le champ moyen a été déterminé dans le cadre d'une approche microscopique utilisant l'interaction effective de Skyrme. Une interaction résiduelle schématique de type delta plus quadrupole-quadrupole, tenant compte en particulier de l'appariement neutron-proton T=0 et T=1 a été utilisé. Les résultats obtenus pour la résonance géante quadrupolaire isoscalaire du noyau Ca40 ont été comparés aux données expérimentales et à d'autres résultats théoriques. Nous avons également étudié un gaz de fermions piégés dans un potentiel d'oscillateur harmonique à 2D, et à température nulle, en présence d'un champ magnétique uniforme. Les expressions exactes des quelques grandeurs thermodynamiques ont été dérivées à partir de la matrice densité de Bloch.

Ideal magnetohydrodynamics (MHD) simulations are known to have problems in satisfying the solenoidal constraint (i.e. the divergence of magnetic field should be equal to zero, $ ablacdotvec{B} = 0$). The simulations become unstable unless specific measures have been taken. In this thesis, a solenoidal constraint satisfying technique that allows discrete satisfaction of the solenoidal constraint up to the machine accuracy is presented and validated with a variety of test cases. Due to its inspiration from Chorin's artificial compressibility method developed for incompressible CFD applications, the technique was named as extit{artificial compressibility analogy (ACA)} approach. It is demonstrated that ACA is a purely hyperbolic, stable and consistent technique, which is moreover easy to implement. Unlike some other techniques, it does not pose any problems of the sort that $ ablacdotvec{B}$ errors accumulate in the vicinity of the stagnant regions of flow. With these crucial properties, ACA is thought to be a remedy to the drawbacks of the most commonly used solenoidal constraint satisfying techniques in the literature namely: Incorrect shock capturing and poor performance of the convective stabilization mechanism in regions of stagnant flow for Powell's source term method; exceedingly complex implementation for constrained transport technique due to the staggered grid representation; computationally expensive nature due to the necessity of a Poisson solver combined with hyperbolic/elliptic numerical methods for classical projection schemes. In the first chapter of the thesis, general background knowledge is given about plasmas, MHD and its history, a certain class of upwind finite volume methods, namely Riemann solvers, and their applications in MHD, the definition, constituents, formation mechanisms and effects of space weather and some of the space missions that are and will be performed in its prediction. Secondly, detailed analysis of the compressible ideal MHD equations is given in the form of the derivation of the equations, their dimensionless numbers which will be of use to specify the flows in the following chapters, and finally, the presentation of the MHD waves and discontinuities, which indicates the complexity of the system of ideal MHD equations and therefore their further numerical analysis. The next discussion is about the main subject of the thesis, namely the solenoidal constraint satisfying techniques. First of all, the definition and significance of the solenoidal constraint is given. Afterwards, the most common solenoidal constraint satisfying techniques in the literature are reviewed along with their abovementioned drawbacks. Moreover, particular emphasis is given to the Powell's source term approach which was also implemented in the upwind finite volume MHD solver developed. In addition, the hyperbolic divergence cleaning technique is presented in detail together with the resemblance and differences between it and ACA. Some other solenoidal constraint satisfying techniques are briefly mentioned at this stage. After these, ACA is presented in the following way: The point of inspiration, which is the analogy made with Chorin's artificial compressibility method developed for incompressible CFD, the introduction of the modified system of ideal MHD equations due to ACA, the derivation of the wave equation governing the propagation of $ ablacdotvec{B}$ errors and the analytical consistency proof. Having finished the core discussion of the thesis, the solver developed and its constituents are given in the fourth chapter. Furthermore, a brief overview of the platform into which this solver was implemented, namely COOLFluiD, is also given at this point. Afterwards, a thorough numerical verification of the ACA approach has been made on an increasingly complex suite of test cases. The results obtained with ACA and Powell's source term implementations are given in order to numerically analyse and verify ACA and compare the two methods and validate them with the results from literature. The sixth chapter is devoted to further validation of ACA performed with a variety of more advanced space weather-related simulations. In this chapter, also the $vec{B}_{ extrm{0}} + vec{B}_{ extrm{1}}$ splitting technique used to treat planetary magnetosphere is presented along with its application to ACA and Powell's source term approaches. This technique is utilized in obtaining the solar wind/Earth's magnetosphere interaction results and is based on suppressing the direct inclusion of the Earth's magnetic field, which is a dipole field, in the solution variables. In this way, problems are avoided with the energy equation that could arise from the drastic change of the ratio of the dipole field and the variable field computed by the solver (i.e. $frac{lvertvec{B}_{ extrm{0}}lvert}{lvertvec{B}_{ extrm{1}}lvert}$) in the computational domain. Finally, conclusions and future perspectives related to the material presented in the thesis are put forward.

I denna avhandling, som omfattar fyra forskningsartiklar, betraktas två operatorer inom den matematiska fysiken. De båda tidigare artiklarna innehåller resultat för Schrödingeroperatorn med Aharonov-Bohm-magnetfält. I artikel I beräknas spektrum och egenfunktioner till denna operator i R2 explicit i ett antal fall då en radialsymmetrisk skalärvärd potential eller ett konstant magnetfält läggs till. I flera av de studerade fallen kan den skarpa konstanten i Lieb-Thirrings olikhet beräknas för γ = 0 och γ ≥ 1. I artikel II bevisas semiklassiska uppskattningar för moment av egenvärdena i begränsade tvådimensionella områden. Vidare presenteras ett exempel då den generaliserade diamagnetiska olikheten, framlagd som en förmodan av Erdős, Loss och Vougalter, är falsk. Numeriska studier kompletterar dessa resultat. De båda senare artiklarna innehåller ett flertal spektrumuppskattningar för Heisenberg-Laplace-operatorn. I artikel III bevisas skarpa olikheter för spektret till Dirichletproblemet i (2n + 1)-dimensionella områden med ändligt mått. Låt λk och μk beteckna egenvärdena till Dirichlet- respektive Neumannproblemet i ett område med ändligt mått. N. D. Filonov har bevisat olikheten μk+1 &lt; λk för den euklidiska Laplaceoperatorn. I artikel IV visas detta resultat för Heisenberg-Laplaceoperatorn i tredimensionella områden som uppfyller vissa geometriska villkor. / In this thesis, which comprises four research papers, two operators in mathe- matical physics are considered. The former two papers contain results for the Schrödinger operator with an Aharonov-Bohm magnetic field. In Paper I we explicitly compute the spectrum and eigenfunctions of this operator in R2 in a number of cases where a radial scalar potential and/or a constant magnetic field are superimposed. In some of the studied cases we calculate the sharp constants in the Lieb-Thirring inequality for γ = 0 and γ ≥ 1. In Paper II we prove semi-classical estimates on moments of the eigenvalues in bounded two-dimensional domains. We moreover present an example where the generalised diamagnetic inequality, conjectured by Erdős, Loss and Vougalter, fails. Numerical studies complement these results. The latter two papers contain several spectral estimates for the Heisenberg Laplacian. In Paper III we obtain sharp inequalities for the spectrum of the Dirichlet problem in (2n + 1)-dimensional domains of finite measure. Let λk and μk denote the eigenvalues of the Dirichlet and Neumann problems, respectively, in a domain of finite measure. N. D. Filonov has proved that the inequality μk+1 &lt; λk holds for the Euclidean Laplacian. In Paper IV we extend his result to the Heisenberg Laplacian in three-dimensional domains which fulfil certain geometric conditions. / QC 20100712