Vortex States and Magnetization Properties in Mesoscopic Superconducting Ring Structures: A Finite-Element Analysis

The time-dependent Ginzburg–Landau equations have been solved numerically by a finite-element analysis for mesoscopic superconducting ring structures with different inner radii. For given applied magnetic fields, we have studied the influences of the inner radius on the vortex states and the magnetization properties of these systems. Our results show that the multivortex states can be stabilized in the mesoscopic superconducting ring with proper inner radius. Magnetization curves show that the magnetic vortices penetrate easily into the superconductor, and the system is magnetized easily for the superconducting ring with smaller inner radius.     

Observation of the Curved and Entangled Vortex Tubes in 3D Mesoscopic Cubic Superconductors

The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for the superconducting samples with a cubic shape in a uniform external magnetic field. We obtain the different vortex patterns as a function of the magnetic field perpendicular to its surface. The vortex tubes must reach the surface perpendicularly in order to avoid a supercurrent component pointing outwards the surface. At the same time, we observed the arrangement of spiral vortices in the cubic superconductor. These results show that our approach is an effective and useful to interpret experimental data on vortex states in the mesoscopic superconductors.     

Vortex Configurations in a Mesoscopic Superconducting Ring Structure: A Finite-Element Analysis

The time-dependent Ginzburg–Landau equations have been solved numerically by a finite-element analysis for a mesoscopic superconducting ring structure. For given applied magnetic fields we have simulated the dynamical behavior of the penetrating magnetic vortices into the superconductor. Moreover, we investigated the vortex configurations and found a vortex state with two stable vortex shells in the mesoscopic superconducting ring due to the enhanced surface superconductivity.     

Magnetic Flux Penetration in a Mesoscopic Superconductor with a Slit

In this work, the vortex nucleation process in a mesoscopic squared superconductor with a slit is numerically investigated in terms of time dependent Ginzburg–Landau theory. We have calculated, simultaneously, the Gibbs free energy and the vortex configuration in function of time, it allows to identify the correspondence between special points in the Gibbs free energy and the configuration of the vortex system.     

闭孔泡沫金属三维细观模型建模方法

该文在深入分析闭孔泡沫金属CT扫描图像的基础上,根据其细观结构特点,提出了泡沫金属三维细观模型建模方法。首先,根据闭孔泡沫金属胞孔形状和尺寸分布特性,提出了采用随机椭球体模拟胞孔的建模方法,通过采用随机投放算法,建立了三维胞孔随机投放模型;其次,提出了有限元网格剖分算法,通过引入材料属性识别算法,建立了泡沫金属三维有限元细观模型。在此基础上,研究了冲击荷载下泡沫金属的力学性能,分析了细观损伤破坏机理和能量吸收特性。结果表明,该文建立的三维细观模型,能够较好地反映泡沫金属材料的力学性能和细观损伤破坏机理。     

Magnetic vortex state stability, reversal and dynamics in restricted geometries

Magnetic vortices are typically the ground states in geometrically confined ferromagnets with small magnetocrystalline anisotropy. In this article I review static and dynamic properties of the magnetic vortex state in small particles with nanoscale thickness and sub-micron and micron lateral sizes (magnetic dots). Magnetic dots made of soft magnetic material shaped as flat circular and elliptic cylinders are considered. Such mesoscopic dots undergo magnetization reversal through successive nucleation, displacement and annihilation of magnetic vortices. The reversal process depends on the stability of different possible zero-field magnetization configurations with respect to the dot geometrical parameters and application of an external magnetic field. The interdot magnetostatic interaction plays an important role in magnetization reversal for dot arrays with a small dot-to-dot distance, leading to decreases in the vortex nucleation and annihilation fields. Magnetic vortices reveal rich, non-trivial dynamical properties due to existance of the vortex core bearing topological charges. The vortex ground state magnetization distribution leads to a considerable modification of the nature of spin excitations in comparison to those in the uniformly magnetized state. A magnetic vortex confined in a magnetically soft ferromagnet with micron-sized lateral dimensions possesses a characteristic dynamic excitation known as a translational mode that corresponds to spiral-like precession of the vortex core around its equilibrium position. The translation motions of coupled vortices are considered. There are, above the vortex translation mode eigenfrequencies, several dynamic magnetization eigenmodes localized outside the vortex core whose frequencies are determined principally by dynamic demagnetizing fields appearing due to restricted dot geometry. The vortex excitation modes are classified as translation modes and radially or azimuthally symmetric spin waves over the vortex ground state. Studying the spin eigenmodes in such systems provides valuable information to relate the particle dynamical response to geometrical parameters. Unresolved problems are identified to attract attention of researchers working in the area of nanomagnetism.     

Flux confinement by artificial arrays and clusters in superconducting films

We have studied the superconducting properties of antidot arrays and mesoscopic antidot clusters near the superconducting-normal phase boundary. Characteristic minima and maxima have been observed in the magnetore-sistance, critical current and phase boundary caused by the formation of stable vortex configurations at the antidots. A comparison with a simple theoretical model has shown that the effects in the arrays as well as in the clusters originate from quantization of the fluxoid at the antidots. This model has enabled an identification of all vortex configurations.     

Three-dimensional spin configuration of ferromagnetic nanocubes

We have systematically investigated three-dimensional spin configurations in ferromagnetic nanocubes using micromagnetic simulation with variation of cube geometry. For thin cuboids, a spin configuration exhibits a four-domain Landau state with a magnetic vortex structure at the center as in the case of a thin film square. For a thick cube, a complex spin configuration with an S-type cylindrically asymmetric vortex having two cores on a pair of surfaces while a leaf-like and a C-type states are observed on the other two pairs of cube surfaces. Competition between the geometrical symmetry and magnetic energy minimization condition in ferromagnetic nanocubes leads to the complex spin structure with a spontaneously broken symmetry.     

Vortex States of Two-Component Bose-Einstein Condensates with and Without Internal Josephson Coupling

We study the equilibrium structure of vortex states in rotating two-component Bose–Einstein condensates. Each component forms respectively a vortex state and the intercomponent coupling makes a rich variety of structures combining these two vortex states. We show a phase diagram of stable vortex states in the intercomponent-coupling versus rotation-frequency. As the intercomponent coupling and the rotation frequency increase, the interlocked vortex lattices undergo structural transition from a triangular lattice to a square one. In a strongly phase-separated regime, vortex cores in each component overlap, forming double-core vortex lattices and serpentine vortex sheets. We also discuss the effect of Josephson coupling between two components on the vortex states.     

Effect of Columnar Defects on Magnetization of Mesoscopic Superconductors

In this work we investigated magnetization and vortex configurations in mesoscopic superconducting samples in the presence of square columnar defects (CDs). We solved numerically the nonlinear TDGL equations for different samples to study magnetization as a function of the applied magnetic field. In calculations, we focused mainly on four samples with different numbers of CDs which have the same total surface area. In this way, the total superconducting area remained the same with increasing the number of CDs for a fixed sample size. We found that the superconducting regions still exist inside the sample at high applied magnetic fields with increasing the number of CDs but irreversible effects became increasingly prominent, when the field is returned to zero. The results are discussed in frame of surface and pinning effects in mesoscopic systems.     

Three-dimensional vortex wake structure of flapping wings in hovering flight

Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.     

Vortex�CAntivortex Dynamics in a Mesoscopic Superconducting Prism with a Centered Antidot

In this work, we investigated theoretically the dynamics of the annihilation of a vortex?Cantivortex pair in a superconducting mesoscopic prism of square transversal section with a square antidot inserted at its center. The sample is immersed in a magnetic field applied perpendicular to the sample plane. It is assumed that the inner hole is made of a material whose properties are accounted on de Gennes boundary conditions via de Gennes extrapolation length (b parameter). We analyze the nucleation of vortices and antivortices by increasing the magnetic field from zero until the first vortex is created and then reversing the polarity of the applied magnetic field until an antivortex is also created. Depending on the b parameter, the vortex?Cantivortex encounter can take place at the hole or at the superconducting region around it. In the framework of the time dependent Ginzburg?CLandau theory, we calculate the magnetization, order parameter topology, the position and the velocity of the vortex and antivortex singularities as a function of time.     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

Effect of Anti-dots on the Magnetic Susceptibility in a Superconducting Long Prism

The magnetic susceptibility of a long mesoscopic superconducting square prism containing one/two (dot) anti-dots is calculated in the framework of the Ginzburg–Landau theoretical model. This magnetic susceptibility shows jumps at each of the vortex transition fields. We studied the influence of the number, size and geometry of the anti-dots on the magnetic susceptibility in a superconducting sample. We found interesting physical behavior when several kinds of materials filled into the anti-dot are considered.     

Reconstruction of the Charge Density Wave State Under the Applied Electric Field

Charge density wave (CDW) under an applied electric field in constraint geometry experience stresses, which can easily exceed a plastic threshold. The stress is resolved by the ground state reconstruction which proceed via creation of topological defects like solitons and dislocations??the CDW vortices. These states can be observed experimentally either in average at macroscopic scales of X-ray and multijunction space resolved studies, at mesoscopic scales of coherent X-ray micro-diffraction and nano-junctions or individually as by the STM. Here, we report numerical modeling taking into account multiple fields in their mutual nonlinear interactions: the phase and the amplitude of the CDW order parameter, distributions of the electric field, of the density and the current of normal carriers. Following events of creation and the subsequent evolution of dislocations, we find that vortices are formed in the junction when the voltage across, or the current through, exceed a threshold. The number of vortices remnant in the reconstructed ground state increases stepwise??in agreement with experiments. The vortex core concentrates the voltage drop across the junction giving rise to observed peaks of the interlayer tunneling. The studied reconstruction in junctions of CDWs may be relevant to modern efforts of the field-effect transformations in other correlated electronic systems.     

The structure and manipulation of vortex states in a superconducting square with 2×2 blind holes

We consider a mesoscopic square superconductor with 2×2 blind holes in the presence of a homogeneous magnetic field. Under suitable conditions a diagonal L=2 state is realized and the system reduces to double degenerate states with different flux configurations, which can be considered as logic states. We show the possibility of manipulation of these states by circulating currents in a loop near the superconductor.     

钢纤维增强超高性能混凝土抗压性能的细观数值模拟

利用LS-DYNA软件在细观层次上建立了三维钢纤维增强超高性能混凝土（Steel fiber reinforced ultra-high performance concrete,SF/UHPC）圆柱体试件有限元模型,对其轴心受压下的力学性能和裂缝发展进行了数值模拟。在验证细观数值模型的有效性和合理性的基础上进行参数分析,着重研究了钢纤维体积率、钢纤维长径比、形状效应和尺寸效应对超高性能钢纤维混凝土抗压强度、韧性和破坏形态的影响。最终,根据模拟结果拟合了超高性能钢纤维混凝土抗压强度计算公式。结果表明：三维超高性能钢纤维混凝土细观模型可以较好地模拟单轴受压应力条件下混凝土的静力性能和损伤破坏机制,所拟合的公式也能较好地预测超高性能钢纤维混凝土的抗压强度。     

Performing RVE calculations under constant stress triaxiality for monotonous and cyclic loading

In the present work the mesoscopic stress, strain rate and strain states of axisymmetric cells under two types of boundary loadings are formulated. Then, the stress triaxiality of axisymmetric cells is expressed in terms of the axial and radial mesoscopic stress components. Based on the formulations of the mesoscopic stress, three strategies for numerical realization of constant stress triaxiality are presented. The advantages and disadvantages of these strategies are discussed. These numerical strategies are implemented on the platform of the general‐purpose finite element programme ABAQUS. They can be applied for representative volume element (RVE) calculations under constant triaxiality, monotonous and cyclic loading controlled by displacement, force, traction and the mesoscopic equivalent strain of the RVE. Several numerical examples are shown to prove the effectivity of these strategies and programme. Copyright © 2005 John Wiley & Sons, Ltd.     

Vortex simulation for non-axisymmetric collision of a vortex ring with solid particles

This study is concerned with the numerical simulation for the non-axisymmetric collision between a vortex ring and solid particles. The vortex ring convects with its self-induced velocity in a quiescent air, and the half part collides with spherical glass particles. The vortex method for gas-particle two-phase flow proposed by the authors in a prior paper is used for the simulation. The Reynolds number of the vortex ring is 2600, and the particle diameter is 50 μm. The Stokes number, defined as the ratio of the particle response time to the characteristic time of the vortex ring, is 0.74. The simulation clarifies that the particles induce the vortices, having an axis parallel to the convection direction of the vortex ring, inside the vortex ring and that pairs of the positive and negative vortex tubes appear. It also highlights that highly organized three-dimensional vortical structures composed of the streamwise vortices yield the rapid deformation and collapse of the vortex ring.     

Connection of Vortices Between Spatially Different Phases in Two-Component Bose-Einstein Condensates

We study interfacial topological defects called boojums, a vortex ending or a connecting point of two kinds of vortex cores, in rotating two-component Bose-Einstein condensates. First, we show that the boojum exists at a vortex ending that connects to the interface of the strongly phase-separated condensates. Next, we study various boojums appearing between two phases characterized by different vortex structures, where the intercomponent s-wave scattering lengths are spatially varied. Using three-dimensional simulations of the Gross-Pitaevskii equations, we reveal the detailed structure of the boojums by visualizing its density distribution and effective superflow vorticity.