No description available.

Thesis--Munich. / Vita. Includes bibliographical references (p. x-xxv).

Recently, a number of spherical packing phases belonging to the class of Frank-Kasper (F-K) phases have been observed in a wide range of soft matter systems, including block copolymers, ionic surfactants, liquid crystalline dendrimers, and giant surfactants. Although their emergence in such systems has been conjectured to be due to a competition between mesodomain sphericity and incompressibility, we lack a description of a precise and general mechanism underlying the formation of F-K phases in soft matter systems. In this work, we consider the two most common F-K phases found in soft matter systems, the σ and A15 phases, and study their stability in the context of a well-known Landau model known as the Landau-Brazovskii model. This model has been applied to systems ranging from block copolymers to liquid crystals. We find that the phase behavior of the Landau-Brazovskii model is controlled only by two parameters, rather than by three parameters, as was suggested by previous works. We also find that the Landau-Brazovksii phase diagram contains regions in which the σ or A15 phase is the most stable among a set of candidate phases. The fact that such a simple model can predict these complex phases provides some insight into the question of why the occurrence of the Frank-Kasper phases in soft matter is so widespread. / Thesis / Master of Science (MSc) / Soft condensed matter physics studies the properties of materials that easily deform, such as soap, gel and plastic. Many of these materials can self-assemble into various fascinating ordered structures. One particularly complex class of structures, found in a wide range of soft materials, is the class of Frank-Kasper phases. Frank-Kasper phases in soft materials have potential applications in fields such as photonics, so their formation in these materials is particularly interesting. However, it is not well understood why the Frank-Kasper structures occur in so many soft materials. We investigate this problem, and show that the occurrence of these structures might be described by a very simple mathematical model known as the Landau-Brazovskii model. The fact that such a simple model can predict the complex Frank-Kasper phases provides insight into the origin of the widespread nature of the occurrence of Frank-Kasper phases in soft materials.

Ce travail porte sur des équations aux dérivées partielles issues de la physique mathématique, plus particulièrement sur celles régissant la supraconductivité. Ainsi, la majorité du travail concerne le modèle de Ginzburg-Landau, qui est un modèle macroscopique de supraconducteurs de type-II. Ce travail est divisé en deux parties principales: La première partie se focalise sur l'analyse des vortex du modèle de Ginzburg-Landau en deux dimensions pour les supraconducteurs de type-II, modèle conduisant à une estimation de la variation du nombre de vortex et à l'optimalité du réseau d'Abrikosov parmi les réseaux de Bravais. Nous avons également étudié certains modèles de stuctures des matériaux comme ceux de Lennard-Jones et de Thomas-Fermi. La seconde partie est consacrée à la fonctionnelle de Ginzburg-Landau en dimension $n$. Deux résultats principaux sont obtenus. L'un porte sur l'énergie renormalisée pour les minimiseurs de la fonctionnelle de Ginzburg-Landau. L'autre concerne les limites des solutions de l'équation de Ginzburg-Landau. Ces deux résultats sont fortement reliés aux applications $n$-harmoniques / Our work focus on the elliptic partial differential Equations arising from the mathematical physics, especially from the superconductivity. Therefore most of our work is on the Ginzburg-Landau model, which is a macroscopic model for the type-II superconductors. The work is divided into two big parts : this first part is on the vortices analysis of the Ginzburg-Landau model of Type-II superconductors in 2 dimensions, including the variations of the number of vortices and optimality of Abrikosov lattices among Bravais Lattices. We also have done some work related to the material structure, for example, the Lennard-Jones model and the Thomas-Fermi model. This second part is on the Ginzburg-Landau functional in $n$-dimensional case. Two main results are contained in this part: One is on the renormalized energy for minimizer of $n$-dimensional Ginzburg-Landau functional; The other one is on the limits of solutions to Ginzburg-Landau equations in $n$ dimension. Both of these two results are closely related to the p-harmonic maps

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-08-18T13:26:02Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao_FILLIPE_CESAR_07884743400.pdf: 6203092 bytes, checksum: 87063a6e43a5b0451757c513e7255e3e (MD5) / Made available in DSpace on 2016-08-18T13:26:02Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao_FILLIPE_CESAR_07884743400.pdf: 6203092 bytes, checksum: 87063a6e43a5b0451757c513e7255e3e (MD5) Previous issue date: 2015-07-31 / CNPq / O avan¸co tecnol´ogico tem permitido a constru¸c˜ao de sistemas supercondutores de baixas dimensionalidades, da ordem do comprimento de coerˆencia, ξ, e/ou comprimento de penetra¸c˜ao, λ. Esses sistemas s˜ao chamados de supercondutores mesosc ´opicos, onde se ´e capaz de alcan¸car correntes e campos cr´ıticos mais elevados. Dependendo do tamanho do supercondutor mesosc´opico, configura¸c˜oes de mol´eculas de v´ortices s˜ao obtidas tanto experimentalmente, como teoricamente usando a teoria de GL e a teoria de London. Nesse trabalho, utilizaremos o m´etodo variacional aplicado `a teoria de Ginzburg-Landau e a teoria de London para estudar v´ortices em discos supercondutores finos em campo magn´etico externo homogˆeneo e confinados em um potencial produzido por um dipolo magn´etico, respectivamente. Estudamos, inicialmente, discos supercondutores mesosc´opicos imersos em um meio isolante na presen¸ca de um campo magn´etico uniforme perpendicular ao plano do disco. Desprezamos os efeitos de desmagnetiza¸c˜ao e expandimos o parˆametro de ordem em fun¸c˜oes ortonormais do operador energia cin´etica. Para a obten¸c˜ao de v´ortices gigantes, representamos o parˆametro de ordem por apenas uma autofun¸c˜ao. Para estados de multiv´ortices, o parˆametro de ordem ´e representado como uma expans ˜A £o de duas autofun¸c˜oes, com vorticidades distintas. Observamos o comportamento da varia¸c˜ao da energia livre em fun¸c˜ao do campo magn´etico aplicado, para diversos tamanhos de discos supercondutores, acompanhando seus estados mais favor ´aveis. Na segunda parte da disserta¸c˜ao, estudamos a disposi¸c˜ao dos v´ortices e antiv´ortices confinados em um disco supercondutor atrav´es de campo magn´etico n˜ao homogˆeneo gerado por um dipolo magn´etico na dire¸c˜ao do eixo de simetria do disco, que possibilita a coexistˆencia de v´ortices e antiv´ortices, com diferentes configura¸c˜oes poss´ıveis. Para obtermos os estados com menor energia dentre as possibildades testadas, utilizamos como parˆametro de controle trˆes vari´aveis: a distˆancia radial ao eixo de simetria do dipolo, r0, a altura do dipolo em rela¸c˜ao ao disco, z0, e a magnitude do dipolo magn´etico, m0. Buscamos o valor da magnitude do dipolo no qual o estado sem v´ortices deixa de ser o metaest´avel, permitindo a existˆencia de estados com v´ortices. Os resultados mostram uma competi¸c˜ao entre o potencial de confinamento, efeitos produzidos pela borda do supercondutor e a intera¸c˜ao entre v´ortices, para manter os v´ortices e antiv´ortices no interior do disco. / Technological breakthroughs have allowed the construction of superconducting systems in low dimensionalities, which are of the order of the coherence length, ξ, and/or of the penetration depht, λ. These systems are called mesoscopic superconductors, which are capable of achieving high critical current and fields. Depending on the size of the mesoscopic superconducting, configurations of vortices molecules are obtained either experimentally or theoretically using the GL theory and the theory of London. In the present work, we apply the variational method to the Ginzburg- Landau theory and also the London theory to study vortices in thin superconductors disks submitted to an inhomogeneous magnetic field and confined to a potential produced by a magnetic dipole, respectively. We studied initially mesoscopic superconducting disks immersed in a insulation mean in the presence of a uniform magnetic field which is perpendicular to the plane of the disk. We neglect the demagnetization effects and expand the order parameter in orthonormal functions of the kinetic energy operator. To obtain giant vortices, the order parameter has only one eigenfunction. For multivortex states, the order parameter consists of two eigenfunctions, with different vorticities. We study the behaviour of free energy variation due to the applied magnetic field for different sizes of superconductor disks, and for different vortex states. In the second part of the dissertation, we study the arrangement of vortices and antivortices in a superconducting disk submitted to a non-homogeneous magnetic field generated by an out-plane magnetic dipole, which allows the coexistence of vortices and antivortices on different configurations. To get the states with lowest energy among the tested possibilities, we used three variables as control parameters: the radial distance from the disk symmetry axis to the dipole axis of symmetry, r0, the height of the dipole relative to the disc, z0, and the magnitude of the magnetic dipole, m0. We seek the value of the magnitude of the dipole in which the state with no vortices ceases to be the most stable one, allowing the existence of states with vortices. The results show a competition among the confinement potential, effects produced by the edge of the superconductor, and the interaction between vortices to keep the vortices and antivortices within the disc.

No description available.

No description available.

No description available.

Zugl.: Würzburg, Univ., Diss., 2007

Tese (doutorado)—Universidade de Brasília, Instituto de Física, 2016. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2017-02-13T14:20:53Z No. of bitstreams: 1 2016_DanielDouradodeAragãoSantos.pdf: 11726662 bytes, checksum: 466b96f2b7d83ab56c89e06f864925ea (MD5) / Approved for entry into archive by Raquel Viana(raquelviana@bce.unb.br) on 2017-03-22T16:49:32Z (GMT) No. of bitstreams: 1 2016_DanielDouradodeAragãoSantos.pdf: 11726662 bytes, checksum: 466b96f2b7d83ab56c89e06f864925ea (MD5) / Made available in DSpace on 2017-03-22T16:49:32Z (GMT). No. of bitstreams: 1 2016_DanielDouradodeAragãoSantos.pdf: 11726662 bytes, checksum: 466b96f2b7d83ab56c89e06f864925ea (MD5) / Nesse trabalho investigamos os efeitos da interação feixe-plasma por meio de um modelo hamiltoniano para um sistema composto de N partículas eletrostaticamente acopladas a uma onda. A discretização do sistema em feixes monocinéticos permite fazer uma abordagem perturbativa do problema e destacar importantes conexões entre as formulações hamiltoniana e vlasoviana. Por meio de resultados numéricos, mostramos que tanto o amortecimento como a amplificação de Landau surgem como consequência de um processo de phasemixing dos vários modos normais do sistema linearizado. Observamos que esse mecanismo possui características distintas dependendo se o sistema é estável ou instável. Os resultados obtidos para sistemas de muitos graus de liberdade foram possíveis graças ao desenvolvimento de uma nova técnica para obtenção de raízes complexas. Implementamos simulações de Vlasov via método semi-lagrangiano e descrevemos o processo de relaxação não colisional da distribuição de velocidades das partículas ressonantes e a evolução da intensidade da onda. Analisamos o espectro dos modos não amortecidos em plasmas livres quando se assume uma distribuição de velocidades estacionária com um pequeno (e suave) plateau nas vizinhanças da velocidade de fase da onda. Verificamos que essas oscilações são bastante sensíveis à forma do plateau principalmente quando possuem velocidades de fase próximas à velocidade térmica das partículas. Investigamos também, por meio do cálculo da função dielétrica, as modificações na relação de dispersão dos modos eletrostáticos em plasmas livres e plasmas magnetizados sujeitos a campo externo de radiação. Os cálculos são feitos com base em um modelo semiclássico, em que elétrons são descritos quanticamente e os campos classicamente. / In this work we discuss the effects of the beam-plasma interaction by means of a hamiltonian model for a system composed of N particles electrostatically coupled to a single wave. The discretization of the system in monokinetic beams allows us to use a perturbative approach of the problem and highlight important connections between the hamiltonian and vlasovian formulations. By means of numerical calculations, we show that both Landau damping and growth emerge due to a phase mixing mechanism that involves many normal modes of the linearized system. We observe that this mechanism exhibits a distinct behavior depending on whether the system is stable or unstable. For systems with many degrees of freedom, the results obtained were possible due to the development of a new root-finding technique in the complex plane. Using vlasovian simulations via semi-Lagrangian scheme we describe the process of collisionless relaxation of the velocity distribution for the resonant particles and the evolution of the wave intensity. We analyse the spectrum of undamped modes in free plasmas when one assumes a stationary velocity distribution with a small (and smooth) plateau centred on the wave phase speed.We find that these oscillations are quite sensitive to the shape of the plateau, mainly for those that have velocities close to the thermal particle velocity. We also investigate, using a semiclassical approach, the modifications in the dispersion relation of the electrostatic modes in free and magnetized plasmas subjected to external radiation field.