Vortex structure in superconductors with a many-component order parameter

Abstract

The phenomenological theory of superconductors with a many-component order parameter (OP) is developed. On the basis of a generalized Ginzburg-Landau functional, equations for a two-component-OP superconductor are derived. It is shown that such a superconductor is specified by three length dimensionality parameters—penetration depth λ, correlation length ζ, and width d of the boundary between two superconducting-phase domains. With λ ? d ? ζ, the equations for the OP of a superconductor in a magnetic field can be explored analytically. The transition from the superconducting to the mixed phase may occur not only by the formation of ordinary Abrikosov vortices, but also owing to vortices that have two cores, each transferring a half-integral flux quantum. The total flux transferred by a vortex certainly constitutes an integral quantum. The cores of such a dimer are interconnected by two domain walls, which exercise confinement within the dimer. The distance between the cores in the dimer is of the order of d. Within a domain wall that separates two superconducting-phase domains, a dimer may fall apart into two vortices with a half-integral flux quantum.

For many-component-OP superconductors in a magnetic field, vortex structures of a more complicated nature than a dimer may occur. An individual core may transfer a fractional flux quantum, but the structure as a whole transfers an integral flux quantum. Confinement of individual cores occurs owing to a complicated system of domain walls determined by the topological charges of these vortices.

Under certain conditions, on attaining field H _c1, vortices may arise first in the domain walls, carrying a fractional flux quantum, and then within the superconducting domains.     

Slowly moving matter-wave gap soliton propagation in weak random optical lattices

We systematically investigate slowly moving matter-wave gap soliton propagation in weak random optical lattices. With the weak randomness, an effective-particle theory is constructed to show that the motion of a gap soliton is similar to a particle moving in random potentials. Based on the effective-particle theory, the effects of the randomness on gap solitons are obtained and the trajectories of gap solitons are well predicted. Moreover, the general laws that describe the movement depending on the weak randomness are obtained. We find that with an increase of the random strength, the ensemble-average velocity reduces slowly and the reflection probability becomes larger. The theoretical results based on the effective-particle theory are confirmed by the numerical simulations based on the Gross-Pitaevskii equation.     

涡场中黏附性颗粒团聚体粒径分布的预测

黏附性颗粒团聚现象在自然界和工业界普遍存在,扰动流场中黏附性颗粒间的碰撞、摩擦和吸附等动力学行为,导致团聚体形态不断演化,准确预测黏附性颗粒团聚体的粒径分布是调控颗粒团聚过程的重要前提。本文通过二维泰勒格林涡场中黏附性颗粒团聚的数值模拟研究,明确了利用Monte Carlo模型预测团聚体粒径分布的可行性及其适用范围,发现当黏附性颗粒间内聚数小于3.5×10^?4时,Monte Carlo模型可较好的预测团聚体粒径分布,且相对误差小于±30%;而当内聚数大于3.5×10^?4后,Monte Carlo模型不再适用。     

Kinetic theory of Onsager’s vortices in two-dimensional hydrodynamics

Starting from the Liouville equation and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body correlations and collective effects into account. This equation is valid at the order 1/N$1/N$ where N?1$N?1$ is the number of point vortices in the system (we assume that their individual circulation scales like γ∼1/N$\gamma \sim 1/N$). It gives the first correction, due to graininess and correlation effects, to the 2D Euler equation that is obtained for N→+∞$N\to +\infty$. For axisymmetric distributions, this kinetic equation does not   relax towards the Boltzmann distribution of statistical equilibrium. This implies either that (i) the “collisional” (correlational) relaxation time is larger than N_tD$N{t}_D$, where _tD$t_D$ is the dynamical time, so that three-body, four-body… correlations must be taken into account in the kinetic theory, or (ii) that the point vortex gas is non-ergodic (or does not mix well) and will never attain statistical equilibrium. Non-axisymmetric distributions may relax towards the Boltzmann distribution on a timescale of the order N_tD$N{t}_D$ due to the existence of additional resonances, but this is hard to prove from the kinetic theory. On the other hand, 2D Euler unstable vortex distributions can experience a process of “collisionless” (correlationless) violent relaxation towards a non-Boltzmannian quasistationary state (QSS) on a very short timescale of the order of a few dynamical times. This QSS is possibly described by the Miller–Robert–Sommeria (MRS) statistical theory which is the counterpart, in the context of two-dimensional hydrodynamics, of the Lynden-Bell statistical theory of violent relaxation in stellar dynamics.     

Spatio-temporal analysis of the turbulent flow in a ribbed channel

The turbulent flow in a channel with transverse ribs over one wall is studied experimentally. The height of the obstacles is about one tenth of the channel height, and the spacing is 10 times their height. The Reynolds number based on the channel hydraulic diameter and bulk flow velocity is 15,000. Velocity fields are obtained with high spatial and temporal resolution along the streamwise/wall-normal plane by means of time-resolved particle image velocimetry. Beside mean velocity and Reynolds stresses, the flow is investigated through two-point correlations, distributions of spanwise-swirling events, space–time velocity diagrams and power spectral density. Although the separated flow reattaches before the following obstacle is approached, a strong rib-to-rib interaction occurs. Spanwise vortices, 0.2 rib heights in size, are generated in the free shear layer, travel across the whole pitch, and may impact on the next rib. The large scale motions triggered by the separation grow in size until they reach the following obstacle. Flapping of the separated shear layer is observed at frequencies consistent with previous studies, causing the instantaneous reattachment point to fluctuate. The flapping initiates at the downstream edge of the obstacle tip, rather than at the upstream edge where the instantaneous separation occurs.     

Interaction between longitudinal vortices and flat plate boundary layer

The interaction between longitudinal vortices and flat plate boundary layer has been studied numerically for both laminar and turbulent flow situations. The vortices are assumed to be placed in an otherwise two-dimensional boundary layer flow. The flow is assumed to be incompressible and steady. Considering the fact that the velocity, vorticity and temperature gradients in the transverse directions are much larger than the longitudinal (streamwise) gradients for these flows, the original Navier Stokes equations are parabolized in the streamwise direction. A simple model, based on Boussinesq hypothesis, is used for turbulent flow. The discretized equations are then solved step by step in the streamwise direction, using an iterative procedure at each station. Numerical solutions have been obtained for different parameters, such as the Reynolds number, the circulation and the initial position of the vortices. The computed flow patterns and the skin friction coefficient and Stanton number are found to be qualitatively consistent with available experimental results. It is shown that the interaction between the vortices and the boundary layer may severely disturb the boundary layer flow field and thus considerably increase the local skin friction and heat transfer rate on surface of an aircraft.     

Corner flow of a suspension of rigid rods

Stress singularities in the neighbourhood of sharp corners can be a source of severe problems in the numerical simulation of non-Newtonian flows leading to loss of convergence with grid refinement (G.G. Lipscombe, R. Kennings and M.M. Denn, J. Non-Newtonian Fluid Mech., 24 (1987) 85 [1]). For Newtonian flows the nature of this singularity is given by the analysis of Dean and Montagnon (W.R. Dean and P.E. Montagnon, Phil. Trans. R. Soc. London, Ser. A., 308 (1949) 199 [2]) in terms of similarity solutions. In this paper we extend this similarity analysis to a suspension of rigid rods. In the limit of nearly full extension the FENE constitutive model has the same behaviour as such a suspension. Our analysis predicts the possibility of lip vortices but their behaviour is somewhat inconsistent with those observed experimentally.     

无叶扩压器离心式压气机内旋涡运动的数值研究

本文的目的是用数值计算方法来研究离心式压气机叶轮内的旋涡运动。所用的数值方法是在工程热物理所发展的时间相关有限体积法．在流场计算的基础上,应用速度矢量、微团的面积和体积示踪、旋度和熵增等后处理程序与方法来研究与显示旋涡运动的存在与发展．文中用这些手段研究了离心式叶轮中的各类旋涡并给出了拓扑图,对于二次流动还给出了它的模型．     

Accumulation and Release of Self-Field Generated Vortices in Percolative YBa2Cu3O7-δ-Films

Pulsed laser heating of current biased percolative YBa₂Cu₃O_7--films can be used to generate and release self-field induced vortices. A laser pulse yields a voltage signal due to penetration of bias current induced magnetic flux in absence of an external magnetic field. Upon retooling, strongly pinned vortices remain in the film. These remanent vortices have been detected after disconnecting the bias source in the currentless film. Applying a subsequent second laser pulse, again yields a signal voltage but of inverse sign due to magnetic flux redistribution.     

Drag reduction by flow separation control on a car after body

New development constraints prompted by new pollutant emissions and fuel consumption standards (Corporate Average Economy Fuel) require that automobile manufacturers develop new flow control devices capable of reducing the aerodynamic drag of motor vehicles. The solutions envisaged must have a negligible impact on the vehicle geometry. In this context, flow control by continuous suction is seen as a promising alternative. The control configurations identified during a previous 2D numerical analysis are adapted for this purpose and are tested on a 3D geometry. A local suction system located on the upper part of the rear window is capable of eliminating the rear window separation on simplified fastback car geometry. Aerodynamic drag reductions close to 17% have been obtained. Copyright © 2008 John Wiley & Sons, Ltd.