Triangular arrangement of defects in a mesoscopic superconductor

By solving the time dependent Ginzburg-Landau equations, we investigated the influence of an internal triangular arrangement of point-like defects on the vortex configurations in a thin mesoscopic sample. The effect of the number of internal defects and their nature on the entrance position of the vortex is studied for a very thin circular sample. We found that the interplay between the vortex-vortex repulsion, the vortex-defect interaction and the interaction with the sample border leads to non-commensurate vortex configurations. © 2012 Elsevier B.V. All rights reserved.

Study of the threshold line between macroscopic and bulk behaviors for homogeneous type II superconductors

In this work we solved the time dependent Ginzburg-Landau equations to simulate homogeneous superconducting samples with square geometry for several lateral sizes. As a result of such simulations we notice that in the Meissner state, when the vortices do not penetrate the superconductor, the response of small samples are not coincident with that expected for the bulk ones, i.e., 4. πM=. -. H. Thus, we focused our analyzes on the way which the M(. H) curves approximate from the characteristic curve of bulk superconductors. With such study, we built a diagram of the size of the sample as a function of the temperature which indicates a threshold line between macroscopic and bulk behaviors. © 2013 Elsevier B.V.

Dinâmica de vórtices em filmes finos supercondutores de superfície variável

Pós-graduação em Ciência e Tecnologia de Materiais - FC

Multi-vortex State Induced by Proximity Effects in a Small Superconducting Square

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Vortex-antivortex annihilation in mesoscopic superconductors with a central pinning center

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Tower as magnetic antipinning core in a small superconducting sample

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influence of thermal gradient in vortex states of mesoscopic superconductors

In general, the studies of finite size effects in mesoscopic superconductors have been carried out in such a way that the temperature parameter is constant in the entire system. However, we could have situations where a real sample is near a heater source, as an example. In such situations, gradients of temperature are present. On the other hand, mesoscopic superconductors are interesting systems due to the fact that they present confinement effects which influence all the vortex dynamics. Thus, in this work we studied the influence of thermal gradients on the vortex dynamics in mesoscopic superconductors. For this purposes, we used the time dependent Ginzburg-Landau equations. The thermal gradients produce an asymmetric distribution of the currents around the system which, in turn, yield interesting vortex configurations and difficult the formation of giant vortices.

Magnetic flux quantum in a Superconducting concave/convex disk

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

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.

Fast and slowly evolving vector solitons in mode-locked fibre lasers

We report on a new vector model of an erbium-doped fibre laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. Unlike the previous models, it accounts for the vector nature of the interaction between an optical field and an erbium-doped active medium, slow relaxation dynamics of erbium ions, linear birefringence in a fibre, linear and circular birefringence of a laser cavity caused by in-cavity polarization controller and light-induced anisotropy caused by elliptically polarized pump field. Interplay of aforementioned factors changes coherent coupling of two polarization modes at a long time scale and so results in a new family of vector solitons (VSs) with fast and slowly evolving states of polarization. The observed VSs can be of interest in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetization in data storage devices and many other areas.

Dissipative vector solitons with fast evolving states of polarization

We report on a new vector model of an erbium doped fiber laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. It results in a new family of vector solitons with fast evolving states of polarization experimentally observed in our previous papers.

Comments on multiple oscillatory solutions in systems with time-delay feedback

A complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms is considered. In particular, multiple oscillatory solutions and their properties are studied. We present novel results regarding the disappearance of limit cycle solutions, derive analytical criteria for frequency degeneration, amplitude degeneration, frequency extrema. Furthermore, we discuss the influence of the phase shift parameter and show analytically that the stabilization of the steady state and the decay of all oscillations (amplitude death) cannot happen for global feedback only. Finally, we explain the onset of traveling wave patterns close to the regime of amplitude death.

Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters

Thesis (Ph.D.)--University of Washington, 2016-08