Vortex dynamics in mesoscopic superconducting square of variable surface

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

Surface effects on vortex dynamics in thin type-II superconducting stripes with random pinning

We analyze the dynamics of a driven vortex lattice moving in a thin Superconducting stripe. The two dimensional stripe is assumed to be finite in the longitudinal direction, where we take into account the Surface effects, and infinite in the transversal direction. The numerical simulations are performed using the Langevin dynamics, including the vortex-vortex interaction, interaction of vortices with the surface current, vortex images, transport current and randomly distributed pinning centers. We show results for the differential resistivity and the vortex trajectories as a function of the external force. (C) 2004 Elsevier B.V. All rights reserved.

Vortex dynamics in the high-temperature superconductors YBa 2 Cu 3 O 7 and Bi 2 Sr 2 CaCu 2 O 8 + delta in low- and high-dissipative transport measurements

This thesis investigates phenomena of vortex dynamics in type II superconductors depending on the dimensionality of the flux-line system and the strength of the driving force. In the low dissipative regime of Bi_2Sr_2CaCu_2O_{8+delta} (BSCCO) the influence of oxygen stoichiometry on flux-line tension was examined. An entanglement crossover of the vortex system at low magnetic fields was identified and a comprehensive B-T phase diagram of solid and fluid phases derived.In YBa_2Cu_3O_7 (YBCO) extremely long (>100 mm) high-quality measurement bridges allowed to extend the electric-field window in transport measurements by up to three orders of magnitude. Complementing analyses of the data conclusively produced dynamic exponents of the glass transition z~9 considerably higher than theoretically predicted and previously reported. In high-dissipative measurements a voltage instability appearing in the current-voltage characteristics of type II superconductors was observed for the first time in BSCCO and shown to result from a Larkin-Ovchinnikov flux-flow vortex instability under the influence of quasi-particle heating. However, in an analogous investigation of YBCO the instability was found to appear only in the temperature and magnetic-field regime of the vortex-glass state. Rapid-pulse measurements fully confirmed this correlation of vortex glass and instability in YBCO and revealed a constant rise time (~µs).

Vortex dynamics in superconductors in the presence of anisotropic pinning

Vortex dynamics in two different classes of superconductors with anisotropic unidirected pinning sites was experimentally investigated by magnetoresistivity measurements: YBCO−films with unidirected twins and Nb-films deposited on faceted $mathrm Al_2O_3$ substrate surfaces. For the interpretation of the experimental results a theoretical model based on the Fokker-Planck equation was used. It was proved by X-ray measurements that YBCO films prepared on (001) $mathrm NdGaO_3$ substrates exhibit only one twin orientation in contrast to YBCO films grown on (100) $mathrm SrTiO_$3 substrates. The magnetoresistivity measurements of the YBCO films with unidirected twin boundaries revealed the existence of two new magnetoresistivity components, which is a characteristic feature of a guided vortex motion: an odd longitudinal component with respect to the magnetic field sign reversal and an even transversal component. However, due to the small coherence length in YBCO and the higher density of point-like defects comparing to high-quality YBCO single crystals, the strength of the isotropic point pinning was comparable with the strength of the pinning produced by twins. This smeared out all effects caused by the pinning anisotropy. The behaviour of the odd longitudinal component was found to be independent of the transport current direction with respect to the twin planes. The magnetoresistivity measurements of faceted Nb films demonstrated the appearance of an odd longitudinal and even transversal component of the magnetoresistivity. The temperature and magnetic field dependences of all relevant magnetoresistivity components were measured. The angles between the average vortex velocity vector and the transport current direction calculated from the experimental data for the different transport current orientations with respect to the facet ridges showed that the vortices moved indeed along the facet ridges. An anomalous Hall effect, i.e. a sign change of the odd transversal magnetoresistivity, has been found in the temperature and magnetic field dependences of the Hall resisitivity of the samples. The theory developed by V.~A.~Shklovskij was used for the explanation of the experimental data. It shows very good agreement with the experiment. The temperature dependence of the even longitudinal magnetoresistivity component of the samples could be very well fitted within the theoretical approach, using for the isotropic and anisotropic pinning potential simple potential with a symmetric triangular potential wells whose depths were estimated from the experimental data.

Vortex Shedding Dynamics in Long Aspect-Ratio Aerodynamics Bodies

The focus of the current dissertation is to study qualitatively the underlying physics of vortex-shedding and wake dynamics in long aspect-ratio aerodynamics in incompressible viscous flow through the use of the KLE method. We carried out a long series of numerical experiments in the cases of flow around the cylinder at low Reynolds numbers. The study of flow at low Reynolds numbers provides an insight in the fluid physics and also plays a critical role when applying to stalled turbine rotors. Many of the conclusions about the qualitative nature of the physical mechanisms characterizing vortex formation, shedding and further interaction analyzed here at low Re could be extended to other Re regimes and help to understand the separation of the boundary layers in airfoils and other aerodynamic surfaces. In the long run, it aims to provide a better understanding of the complex multi-physics problems involving fluid-structure-control interaction through improved mathematical computational models of the multi-physics process. Besides the scientific conclusions produced, the research work on streamlined and bluff-body condition will also serve as a valuable guide for the future design of blade aerodynamics and the placement of wind turbines and hydrakinetic turbines, increasing the efficiency in the use of expensive workforce, supplies, and infrastructure. After the introductory section describing the main fields of application of wind power and hydrokinetic turbines, we describe the main features and theoretical background of the numerical method used here. Then, we present the analysis of the numerical experimentation results for the oscillatory regime right before the onset of vortex shedding for circular cylinders. We verified the wake length of the closed near-wake behind the cylinder and analysed the decay of the wake at the wake formation region, and then studied the St-Re relationship at the Reynolds numbers before the wake sheds compared to the experimental data. We found a theoretical model that describes the time evolution of the amplitude of fluctuations in the vorticity field on the twin vortex wake, which accurately matches the numerical results in terms of the frequency of the oscillation and rate of decay. We also proposed a model based on an analog circuit that is able to interpret the concerning flow by reducing the number of degrees of freedom. It follows the idea of the non-linear oscillator and resembles the dynamics mechanism of the closed near-wake with a common configured sine wave oscillator. This low-dimensional circuital model may also help to understand the underlying physical mechanisms, related to vorticity transport, that give origin to those oscillations.

Generating vortex rings in Bose-Einstein condensates in the line-source approximation

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the curl of the superfluid velocity field is different from zero only on a circumference of a given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure, and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

Dynamics of the corotating vortices in dipolar Bose-Einstein condensates in the presence of dissipation

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.

The impacts of volcanic aerosol on stratospheric ozone and the Northern Hemisphere polar vortex: separating radiative-dynamical changes from direct effects due to enhanced aerosol heterogeneous chemistry

After major volcanic eruptions the enhanced aerosol causes ozone changes due to greater heterogeneous chemistry on the particle surfaces (HET-AER) and from dynamical effects related to the radiative heating of the lower stratosphere (RAD-DYN). We carry out a series of experiments with an atmosphere–ocean–chemistry–climate model to assess how these two processes change stratospheric ozone and Northern Hemispheric (NH) polar vortex dynamics. Ensemble simulations are performed under present day and preindustrial conditions, and with aerosol forcings representative of different eruption strength, to investigate changes in the response behaviour. We show that the halogen component of the HET-AER effect dominates under present-day conditions with a global reduction of ozone (−21 DU for the strongest eruption) particularly at high latitudes, whereas the HET-AER effect increases stratospheric ozone due to N2O5 hydrolysis in a preindustrial atmosphere (maximum anomalies +4 DU). The halogen-induced ozone changes in the present-day atmosphere offset part of the strengthening of the NH polar vortex during mid-winter (reduction of up to −16 m s-1 in January) and slightly amplify the dynamical changes in the polar stratosphere in late winter (+11 m s-1 in March). The RAD-DYN mechanism leads to positive column ozone anomalies which are reduced in a present-day atmosphere by amplified polar ozone depletion (maximum anomalies +12 and +18 DU for present day and preindustrial, respectively). For preindustrial conditions, the ozone response is consequently dominated by RAD-DYN processes, while under present-day conditions, HET-AER effects dominate. The dynamical response of the stratosphere is dominated by the RAD-DYN mechanism showing an intensification of the NH polar vortex in winter (up to +10 m s-1 in January). Ozone changes due to the RAD-DYN mechanism slightly reduce the response of the polar vortex after the eruption under present-day conditions.

Nonlinear evolution of harmonically forced perturbations on a wingtip vortex

Wingtip vortices are created by flying airplanes due to lift generation. The vortex interaction with the trailing aircraft has sparked researchers’ interest to develop an efficient technique to destroy these vortices. Different models have been used to describe the vortex dynamics and they all show that, under real flight conditions, the most unstable modes produce a very weak amplification. Another linear instability mechanism that can produce high energy gains in short times is due to the non-normality of the system. Recently, it has been shown that these non-normal perturbations also produce this energy growth when they are excited with harmonic forcing functions. In this study, we analyze numerically the nonlinear evolution of a spatially, pointwise and temporally forced perturbation, generated by a synthetic jet at a given radial distance from the vortex core. This type of perturbation is able to produce high energy gains in the perturbed base flow (10^3), and is also a suitable candidate for use in engineering applications. The flow field is solved for using fully nonlinear three-dimensional direct numerical simulation with a spectral multidomain penalty method model. Our novel results show that the nonlinear effects are able to produce locally small bursts of instability that reduce the intensity of the primary vortex.

Vortex evolution in the wake of accelerating low-aspect-ratio plates and three-dimensional bodies of revolution

To find examples of effecient locomotion and manoeuvrability, one need only turn to the elegant solutions natural flyers and swimmers have converged upon. This dissertation is specifically motivated by processes of evolutionary convergence, which have led to the propulsors and body shapes in nature that exhibit strong geometric collapse over diverse scales. These body features are abstracted in the studies presented herein using low-aspect-ratio at plates and a three-dimensional body of revolution (a sphere). The highly-separated vortical wakes that develop during accelerations are systematically characterized as a function of planform shape, aspect ratio, Reynolds number, and initial boundary conditions. To this end, force measurements and time-resolved (planar) particle image velocimetry have been used throughout to quantify the instantaneous forces and vortex evolution in the wake of the bluff bodies. During rectilinear motions, the wake development for the flat plates is primarily dependent on plate aspect ratio, with edge discontinuities and curvature playing only a secondary role. Furthermore, the axisymmetric case, i.e. the circular plate, shows strong sensitivity to Reynolds number, while this sensitivity quickly diminishes with increasing aspect ratio. For rotational motions, global insensitivity to plate aspect ratio has been observed. For the sphere, it has been shown that accelerations play an important role in the mitigation of flow separation. These results - expounded upon in this dissertation - have begun to shed light on the specific vortex dynamics that may be coopted by flying and swimming species of all shapes and sizes towards efficient locomotion.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Magnetic response of superconducting mesoscopic-size YBCO powder

In this work it is reported the magnetic behavior of submicron and mesoscopic-size superconducting YBCO powders, prepared by a modified polymeric precursors method. The grain size and microstructure were analyzed using scanning electron microscopy ( SEM). Measurements of magnetization and AC-susceptibility as a function of temperature were performed with a quantum design SQUID magnetometer. Our results indicated significant differences on the magnetic propreties, in connection with the calcination temperature and the pressure used to pelletize the samples. This contribution is part of an effort to study vortex dynamics and magnetic properties of submicron and mesoscopic-size superconducting samples. (C) 2008 Elsevier B. V. All rights reserved.