Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Ginzburg-Landau turbulence in quasi-CW Raman fiber lasers

Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers. Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers.

Teoria de Landau-Ginzburg para o estado supercondutor nemático

O objetivo geral deste projeto é propor um modelo bidimensional que descreva o novo estado supercondutor, que apresenta simetria de cristal líquido, chamado de supercondutor nemático. O estudo começa com uma introdução sobre a teoria de Landau-Ginzburg das transições de fase, onde são discutidos conceitos como parâmetro de ordem e as ordens das transições de fase, que são essenciais para o desenvolvimento deste projeto. Em seguida, é feita uma discussão sobre as principais características dos supercondutores como a resistência zero, o efeito Meissner-Ochsenfeld, os tipos de supercondutores, o surgimento de vórtices e uma análise sobre a teoria de Landau-Ginzburg para transição de fase metal-supercondutor. Após isto, é feita uma abordagem sobre os principais tipos de cristais líquidos, com destaque ao cristal líquido nemático, onde é desenvolvida a teoria de Landau-Ginzburg para transição de fase isotrópica-nemática e um estudo sobre o surgimento de disclinações no cristal líquido nemático em duas dimensões. Por fim, é apresentado o modelo proposto para descrever o estado supercondutor nemático, com a construção da teoria de Landau-Ginzburg, o estudo do acoplamento entre as fases e os defeitos topológicos presentes nesse estado.

Dualidade na teoria de Landau-Ginzburg da supercondutividade

Neste trabalho abordamos a teoria de Ginzburg-Landau da supercondutividade (teoria GL). Apresentamos suas origens, características e resultados mais importantes. A idéia fundamental desta teoria e descrever a transição de fase que sofrem alguns metais de uma fase normal para uma fase supercondutora. Durante uma transição de fase em supercondutores do tipo II é característico o surgimento de linhas de fluxo magnético em determinadas regiões de tamanho finito chamadas comumente de vórtices. A dinâmica destas estruturas topológicas é de grande interesse na comunidade científica atual e impulsiona incontáveis núcleos de pesquisa na área da supercondutividade. Baseado nisto estudamos como essas estruturas topológicas influenciam em uma transição de fase em um modelo bidimensional conhecido como modelo XY. No modelo XY vemos que os principais responsáveis pela transição de fase são os vórtices (na verdade pares de vórtice-antivórtice). Villain, observando este fato, percebeu que poderia tornar explícita a contribuição desses defeitos topológicos na função de partição do modelo XY realizando uma transformação de dualidade. Este modelo serve como inspiração para a proposta deste trabalho. Apresentamos aqui um modelo baseado em considerações físicas sobre sistemas de matéria condensada e ao mesmo tempo utilizamos um formalismo desenvolvido recentemente na referência [29] que possibilita tornar explícita a contribuição dos defeitos topológicos na ação original proposta em nossa teoria. Após isso analisamos alguns limites clássicos e finalmente realizamos as flutuações quânticas visando obter a expressão completa da função correlação dos vórtices o que pode ser muito útil em teorias de vórtices interagentes (dinâmica de vórtices).

Dinâmica das transições quiral e de desconfinamento da cromodinâmica quântica com o modelo Polyakov-Nambu-Jona-Lasinio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Satisfação do cliente na área da restauração

Dissertação de Mestrado , Ciências Económicas e Empresariais, Faculdade de Economia, Universidade do Algarve, 2008

Quantum Aspects of Solitons and Deformations on Ad'S IND. 4'x C'P POT.3' ('S POT. 7')

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica de campos escalares fora do equilíbrio

Pós-graduação em Física - IFT

Accelerating CFD via local POD plus Galerkin projections

Se desarrollan varias técnicas basadas en descomposición ortogonal propia (DOP) local y proyección de tipo Galerkin para acelerar la integración numérica de problemas de evolución, de tipo parabólico, no lineales. Las ideas y métodos que se presentan conllevan un nuevo enfoque para la modelización de tipo DOP, que combina intervalos temporales cortos en que se usa un esquema numérico estándard con otros intervalos temporales en que se utilizan los sistemas de tipo Galerkin que resultan de proyectar las ecuaciones de evolución sobre la variedad lineal generada por los modos DOP, obtenidos a partir de instantáneas calculadas en los intervalos donde actúa el código numérico. La variedad DOP se construye completamente en el primer intervalo, pero solamente se actualiza en los demás intervalos según las dinámicas de la solución, aumentando de este modo la eficiencia del modelo de orden reducido resultante. Además, se aprovechan algunas propiedades asociadas a la dependencia débil de los modos DOP tanto en la variable temporal como en los posibles parámetros de que pueda depender el problema. De esta forma, se aumentan la flexibilidad y la eficiencia computacional del proceso. La aplicación de los métodos resultantes es muy prometedora, tanto en la simulación de transitorios en flujos laminares como en la construcción de diagramas de bifurcación en sistemas dependientes de parámetros. Las ideas y los algoritmos desarrollados en la tesis se ilustran en dos problemas test, la ecuación unidimensional compleja de Ginzburg-Landau y el problema bidimensional no estacionario de la cavidad. Abstract Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems. The proposed methods come from a new approach to the POD-based model reduction procedures, which combines short runs with a given numerical solver and a reduced order model constructed by expanding the solution of the problem into appropriate POD modes, which span a POD manifold, and Galerkin projecting some evolution equations onto that linear manifold. The POD manifold is completely constructed from the outset, but only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure. In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional model computation. Application of the developed techniques to the approximation of transients in laminar fluid flows and the simulation of attractors in bifurcation problems shows very promising results. The test problems considered to illustrate the various ideas and check the performance of the algorithms are the onedimensional complex Ginzburg-Landau equation and the two-dimensional unsteady liddriven cavity problem.

Inertial mass of a vortex in cuprate superconductors

We present here a calculation of the inertial mass of a moving vortex in cuprate superconductors. This is a poorly known basic quantity of obvious interest in vortex dynamics. The motion of a vortex causes a dipolar density distortion and an associated electric field which is screened. The energy cost of the density distortion as well as the related screened electric field contributes to the vortex mass, which is small because of efficient screening. As a preliminary, we present a discussion and calculation of the vortex mass using a microscopically derivable phase-only action functional for the far region which shows that the contribution from the far region is negligible and that most of it arises from the (small) core region of the vortex. A calculation based on a phenomenological Ginzburg-Landau functional is performed in the core region. Unfortunately such a calculation is unreliable; the reasons for it are discussed. A credible calculation of the vortex mass thus requires a fully microscopic non-coarse-grained theory. This is developed, and results are presented for an s-wave BCS-like gap, with parameters appropriate to the cuprates. The mass, about 0.5m(e) per layer, for a magnetic field along the c axis arises from deformation of quasiparticle states bound in the core and screening effects mentioned above. We discuss earlier results, possible extensions to d-wave symmetry, and observability of effects dependent on the inertial mass. [S0163-1829(97)05534-3].

Theoretical studies on magnetic superconductors

The discovery of magnetic superconductors has posed the problem of the coexistence of two kinds of orders (magnetic and superconducting) in some temperature intervals in these systems. New microscopic mechanisms developed by us to explain the coexistence and reentrant behaviour are reported. The mechanism for antiferromagnetic superconductors which shows enhancement of superconductivity below the magnetic transition is found relevant for rare-earth systems having less than half-filled f-atomic shells. The theory will be compared with the experimental results of SmRh4B4 system. A phenomenological treatment based on a generalized Ginzburg-Landau approach will also be presented to explain the anomalous behaviour of the second critical field in some antiferromagnetic superconductors. These magnetic superconductors provide two kinds of Bose fields, namely, phonons and magnons which interact with each other and also with the conduction electrons. Theoretical studies of the effects of the excitations of these modes on superconducting pairing and magnetic ordering in these systems will be discussed.

Magnetic superconductors: Model theories and experimental properties of rare-earth compounds

Superconducting and magnetically long-range ordered states were believed to be mutually exclusive phenomena. The discovery of rare-earth compounds in recent years, which exhibit both superconductivity and magnetic ordering (ferromagnetic, antiferromagnetic or sinusoidal), has led to considerable theoretical and experimental work on such systems. In the present article, we give a review of various theoretical models and important experimental results. In the theoretical sections, we start with the Abrikosov-Gorkov pair breaking theory for dilute alloys and discuss its improvement in the work of Müller-Hartmann and Zittartz. Then, in the context of magnetic superconductors, various microscopic theories that have been advanced are presented. These predict re-entrant behaviour in some systems (ferromagnetic superconductors) and coexistence regions in others (particularly antiferromagnetic superconductors). Following this, phenomenological generalized Ginzburg-Landau theories for two kinds of orders (superconducting and magnetic) are presented. A section dealing with renormalization group analysis of phase diagrams in magnetic superconductors is given. In experimental sections, the properties of each rare-earth compounds (ternary as well as some tetranery) are reviewed. These involve susceptibility, heat capacity, resistivity, upper critical field, neutron scattering and magnetic resonance measurements. The anomalous behaviour of the upper critical field of antiferromagnetic superconductors near the Néel temperature is discussed both in theory sections and experimental section for various systems.

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H c 2(T) in antiferromagnetic superconductors RE(Mo)6S8; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M Q (T) and superconducting order parameter psgr cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.

Study of magnetic field effect on the specific heat and entropy in DyBa2Cu3O7-x

The change in the specific heat by the application of magnetic field up to 161 for high temperature superconductor system for DyBa2Cu3O7-x by Revaz et al. [23] is examined through the phenomenological Ginzburg-Landau(G-L) theory of anisotropic Type-II superconductors. The observed specific heat anomaly near T-c with magnetic field is explained qualitatively through the expression <Delta C > = (B-a/T-c) t/(1 - t)(alpha Theta(gamma)lambda(2)(m)(0)), which is the anisotropic formulation of the G-L theory in the London limit developed by Kogan and coworkers; relating to the change in specific heat Delta C for the variation of applied magnetic field for different orientations with c-axis. The analysis of this equation explains satisfactorily the specific heat anomaly near T-c and determines the anisotropic ratio gamma as 5.608, which is close to the experimental value 5.3 +/- 0.5given in the paper of Revaz et al. for this system. (C) 2010 Elsevier B.V. All rights reserved.

Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].