Vortex Penetration Research Articles

Simulation of laboratory experiments for vortex dynamics at shallow tidal inlets using the fine resolution environmental hydrodynamics (Frehd) model

In this paper, we present the results of numerical simulations matched to laboratory experiments of tidal, starting-jet vortices forming at idealized, barotropic inlets. The laboratory experiments are for sinusoidally varying inflow/outflow along a wide, flat basin. Inlet configurations include simple inlets with negligible channel length as well as a longer inlet channels through a long barrier island and jettied inlet. Laboratory observations are made using particle image velocimetry, and we analyze the laboratory and numerical model velocity fields to compare starting-jet trajectory, diameter, and total circulation. The numerical simulations use the Fine Resolution Environmental Hydrodynamic model, solving the three-dimensional, hydrostatic, barotropic equations of motion. Our goal is to identify the minimum model attributes necessary to match the vortex properties. This is accomplished using a third-order upwind scheme for advection, a constant bottom friction drag coefficient, and a one-equation turbulence model for transport of turbulent kinetic energy. The optimal value of the bottom drag coefficient matches the time-average value at the basin inflow/outflow boundaries, and the optimal dissipation coefficient, $$C_{me}$$, was an order of magnitude smaller than literature values for a steady open-channel flow. We show that the drag coefficient mainly affects the advection speeds of the outer coastal waters, which control the penetration of the tidal vortices away from the inlet, and the lower turbulence dissipation rate results from the low turbulent dissipation in the large, shallow starting-jet vortices.

Inhomogeneous Ginzburg–Landau Parameter in a 2D Mesoscopic Superconductor

We study the behavior that the inclusion of zones with different Ginzburg–Landau parameters $$\kappa $$ has on the magnetization, Cooper pair density, and $$H_{1}$$ , the magnetic field in which the first vortex penetration occurs, in a superconducting 2D square in the presence of an external applied magnetic field H. We report anomalous vortex configurations and an appreciable variation (no monotonic) of $$H_{1}$$ due to the inhomogeneity of $$\kappa (x,y)$$ . The behavior of the superconducting state for different values of the $$\kappa $$ , along with its respective variations, has been studied by including different convergence ratios in the time-dependent equations of the Ginzburg–Landau model. In addition, the variation of the magnetic susceptibility $$\chi $$ according to the applied magnetic field is shown, and how an understanding of the magnetic moment density $$\mu $$ present in the sample can be established.

Edge effect pinning in mesoscopic superconducting strips with non-uniform distribution of defects

Transport characteristics of nano-sized superconducting strips and bridges are determined by an intricate interplay of surface and bulk pinning. In the limiting case of a very narrow bridge, the critical current is mostly defined by its surface barrier, while in the opposite case of very wide strips it is dominated by its bulk pinning properties. Here we present a detailed study of the intermediate regime, where the critical current is determined, both, by randomly placed pinning centres and by the Bean-Livingston barrier at the edge of the superconducting strip in an external magnetic field. We use the time-dependent Ginzburg-Landau equations to describe the vortex dynamics and current distribution in the critical regime. Our studies reveal that while the bulk defects arrest vortex motion away from the edges, defects in their close vicinity promote vortex penetration, thus suppressing the critical current. We determine the spatial distribution of the defects optimizing the critical current and find that it is in general non-uniform and asymmetric: the barrier at the vortex-exit edge influence the critical current much stronger than the vortex-entrance edge. Furthermore, this optimized defect distribution has a more than 30% higher critical current density than a homogeneously disorder superconducting film.

Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array

The superconductor-insulator transition in two dimensions has been widely investigated as a paradigmatic quantum phase transition. The topic remains controversial, however, because many experiments exhibit a metallic regime with saturating low-temperature resistance, at odds with conventional theory. Here, we explore this transition in a novel, highly controllable system, a semiconductor heterostructure with epitaxial Al, patterned to form a regular array of superconducting islands connected by a gateable quantum well. Spanning nine orders of magnitude in resistance, the system exhibits regimes of superconducting, metallic, and insulating behavior, along with signatures of flux commensurability and vortex penetration. An in-plane magnetic field eliminates the metallic regime, restoring the direct superconductor-insulator transition, and improves scaling, while strongly altering the scaling exponent.

Magnetic field dependent microwave losses in superconducting niobium microstrip resonators

We describe an experimental protocol to characterize magnetic field dependent microwave losses in superconducting niobium microstrip resonators. Our approach provides a unified view that covers two well-known magnetic field dependent loss mechanisms: quasiparticle generation and vortex motion. We find that quasiparticle generation is the dominant loss mechanism for parallel magnetic fields. For perpendicular fields, the dominant loss mechanism is vortex motion or switches from quasiparticle generation to vortex motion, depending on the cooling procedures. In particular, we introduce a plot of the quality factor versus the resonance frequency as a general method for identifying the dominant loss mechanism. We calculate the expected resonance frequency and the quality factor as a function of the magnetic field by modeling the complex resistivity. Key parameters characterizing microwave loss are estimated from comparisons of the observed and expected resonator properties. Based on these key parameters, we find a niobium resonator whose thickness is similar to its penetration depth is the best choice for X-band electron spin resonance applications. Finally, we detect partial release of the Meissner current at the vortex penetration field, suggesting that the interaction between vortices and the Meissner current near the edges is essential to understand the magnetic field dependence of the resonator properties.

Unsteady aerodynamic model of flexible flapping wing

Bio-inspired flapping wing has potential application to micro air vehicles (MAV). Due to the nature of lightweight and flexibility of micro flapping wing structures, elastic deformation as a result of aeroelastic coupling is inevitable in flapping motion. This effect can be significant and beneficial to the aerodynamic performance as revealed in the present investigation for a flexible flapping wing of variable camber versus a rigid one. Firstly a two dimensional (2D) unsteady aerodynamic model (UAM) based on potential flow theory has been extended from previous study. Both leading and trailing edge discrete vortices are included in the model with unsteady Kutta condition satisfied to fully characterize the unsteady flow around a flapping wing. A wall function is created to modify the induced velocity of the vortices in the UAM to solve the vortices penetration problem. The modified UAM is then validated by comparing with CFD results of a typical insect-like flapping motion from previous research. Secondly the UAM is further extended for a flexible flapping wing of camber variation. Comparing with a rigid wing in a prescribed plunging and pitching motion, the results show lift increase with positive camber in upstroke by mitigating negative lift. The results also agree well with CFD simulation. Thirdly the 2D UAM is extended to calculate the aerodynamic forces of a 3D wing with camber variation, and validated by CFD results. Finally the model is applied to aerodynamic analysis of a 3D flexible flapping wing with aeroelastic coupling effect. Significant increase of lift coefficient can be achieved for a flexible flapping wing of positive camber and twist in upstroke produced by the structure elastic deformation.

Critical states in a superconducting plate: Effects of heat generation from flux motion

We have studied vortex penetration into a superconducting plate under a perpendicular magnetic field. Solving the heat transport equation and the Maxwell equations with the current-voltage relation for the superconductor simultaneously, current density and temperature distribution due to vortices motion are obtained. Taking the effect of heat generation into account, there is a size dependence of temperature rise.

Time-Dependent Ginzburg–Landau Simulations of the Critical Current in Superconducting Films and Junctions in Magnetic Fields

Understanding the magnetic field dependence of the critical current density (Jc) of superconductors is of considerable interest for optimizing their use in high field applications. Using time-dependent Ginzburg-Landau theory, we have completed simulations of the average electric field generated in thin film systems subject to transport currents in applied magnetic fields, and compared them to thin film systems containing narrow junctions of reduced critical temperature (Tc). For thin films in contact with insulating surfaces, Jc approaches the depairing current density at applied magnetic fields below the initial vortex penetration field and remains nonzero until close to Tinkham's parallel critical field. For thin films in contact with highly metallic surfaces, Jc was found to decrease to zero with decreasing film width. Adding a junction region to the film was found to broaden the transition to the normal state at all applied magnetic fields and reduce Jc of the film at zero field.

Thermal coupling effect on the vortex dynamics of superconducting thin films: time-dependent Ginzburg–Landau simulations

In this paper, vortex dynamics of superconducting thin films are numerically investigated by the generalized time-dependent Ginzburg–Landau (TDGL) theory. Interactions between vortex motion and the motion induced energy dissipation is considered by solving the coupled TDGL equation and the heat diffusion equation. It is found that thermal coupling has significant effects on the vortex dynamics of superconducting thin films. Branching in the vortex penetration path originates from the coupling between vortex motion and the motion induced energy dissipation. In addition, the environment temperature, the magnetic field ramp rate and the geometry of the superconducting film also greatly influence the vortex dynamic behaviors. Our results provide new insights into the dynamics of superconducting vortices, and give a mesoscopic understanding on the channeling and branching of vortex penetration paths during flux avalanches.

Three-Dimensional Simulation of Turbulent Hot-Jet Ignition for Air-CH4-H2 Deflagration in a Confined Volume

This work describes essential aspects of the ignition and deflagration process initiated by the injection of a hot transient gas jet into a narrowly confined volume containing air-CH4-H2 mixture. Driven by the pressure difference between a prechamber and a long narrow constant-volume-combustion (CVC) chamber, the developing jet or puff involves complex processes of turbulent jet penetration and evolution of multi-scale vortices in the shear layer, jet tip, and adjacent confined spaces. The CVC chamber contains stoichiometric mixtures of air with gaseous fuel initially at atmospheric conditions. Fuel reactivity is varied using two different CH4/H2 blends. Jet momentum is varied using different pre-chamber pressures at jet initiation. The jet initiation and the subsequent ignition events generate pressure waves that interact with the mixing region and the propagating flame, depositing baroclinic vorticity. Transient three-dimensional flow simulations with detailed chemical kinetics are used to model CVC mixture ignition. Pre-ignition gas properties are then examined to develop and verify criteria to predict ignition delay time using lower-cost non-reacting flow simulations for this particular case of study.

Optimized Time-Resolved Echo Particle Image Velocimetry- Particle Tracking Velocimetry Measurements Elucidate Blood Flow in Patients With Left Ventricular Thrombus.

Contrast ultrasound is a widely used clinical tool to obtain real-time qualitative blood flow assessments in the heart, liver, etc. Echocardiographic particle image velocimetry (echo-PIV) is a technique for obtaining quantitative velocity maps from contrast ultrasound images. However, unlike optical particle image velocimetry (PIV), routine echo images are prone to nonuniform spatiotemporal variations in tracer distribution, making analysis difficult for standard PIV algorithms. This study introduces optimized procedures that integrate image enhancement, PIV, and particle tracking velocimetry (PTV) to obtain reliable time-resolved two-dimensional (2D) velocity distributions. During initial PIV analysis, multiple results are obtained by varying processing parameters. Optimization involving outlier removal and smoothing is used to select the correct vector. These results are used in a multiparameter PTV procedure. To demonstrate their clinical value, the procedures are implemented to obtain velocity and vorticity distributions over multiple cardiac cycles using images acquired from four left ventricular thrombus (LVT) patients. Phase-averaged data elucidate flow structure evolution over the cycle and are used to calculate penetration depth and strength of left ventricular (LV) vortices, as well as apical velocity induced by them. The present data are consistent with previous time-averaged results for the minimum vortex penetration depth associated with LVT occurrence. However, due to decay and fragmentation of LV vortices, as they migrate away from the mitral annulus, in two cases with high penetration, there is still poor washing near the resolved clot throughout the cycle. Hence, direct examination of entire flow evolution may be useful for assessing risk of LVT relapse before prescribing anticoagulants.

Surface Effects on the Dynamic Behavior of Vortices in Type II Superconducting Strips with Periodic and Conformal Pinning Arrays

Using molecular dynamics techniques, we simulate the vortex behavior in a type II superconducting strip in the presence of triangular and two types of conformal pinning arrays, one with a pinning gradient perpendicular to the driving force (C1) and the other parallel (C2), at zero temperature. A transport force is applied in the infinite direction of the strip, and the magnetic field is increased until the rate between the density of vortices (n v ) and pinning (n p ) reaches n v /n p = 1.5. Our results show a monotonic increase, by steps, of the vortex density with the applied magnetic field. Besides, each pinning lattice presents a different vortex penetration delay. For the triangular pinning array, different than the case of infinite films, here the system exhibits only one pronounced depinning force peak at n v /n p = 1. However, the depinning force peak is present for only one value of field, in the range of fields where n v /n p = 1 is stable. For the case of conformal pinning arrays, in analogy to what is observed in infinite films, no commensurability depinning force peaks were found. In the present case, the C1 array is more efficient at low fields, all arrays are equivalent in the intermediate fields, and the C2 array is more efficient for high fields. We also show that for the C1 array at high fields, vortices depin following the conformal arches, from the edge to the center. For the C2 array, the depinning force is higher when compared to that of C1, because this particular conformal structure prevents the formation of easy vortex flow channels.

Signature of multigap nodeless superconductivity in fluorine-doped NdFeAsO

We investigate the temperature dependence of the lower critical field $H_{c1}(T)$, the field at which vortices penetrate into the sample, of a high-quality fluorine-doped NdFeAsO single crystal under static magnetic fields $H$ parallel to the $c$-axis. The temperature dependence of the first vortex penetration field has been experimentally obtained and pronounced changes of the $H_{c1}$(T) curvature are observed, which is attributed to the multiband superconductivity. Using a two-band model with $s$-wave-like gaps, the temperature-dependence of the lower critical field $H_{c1}(T)$ can be well described. These observations clearly show that the superconducting energy gap in fluorine-doped NdFeAsO is nodeless. The values of the penetration depth at $T$ = 0\,K have been determined and confirm that the pnictide superconductors obey an Uemura-style relationship between $T_{c}$ and $\lambda_{ab}(0)^{-2}$

The Influence of Pinning Centers in the Magnetization of the Mesoscopic Superconductors

In this work, we study the mesoscopic superconducting samples with pinning centers using the time-dependent Ginzburg-Landau theory (TDGL). The pinning centers are introduced via the phenomenological function f(r) Sorensen et al. (Physica C 533, 40–43 2017). We calculated the magnetization curves M(H) for some distances d from the boundary of the sample to the position of the pinning center. From this investigation arises the relation between the first magnetic field H p and the distance d. It shows that the pinning centers located close to the boundary of the sample decrease H p , and also the existence of two regimes of the penetration of the vortices. The magnetization curves revel the existence of ruddle of jumps for low magnetic fields for small distances d, indicating a complex vortex penetration.

Anisotropic thermomagnetic avalanche activity in field-cooled superconducting films

The electrodynamic behavior of isotropic superconducting Nb films cooled below their critical temperature in the presence of in-plane applied magnetic fields is investigated using magneto-optical imaging. A specially designed local flux injector is used to show that the frozen-in in-plane vortices strongly guide and enhance the penetration of perpendicular vortices, whereas their penetration across the array of in-plane vortices is essentially unchanged. This result provides the key to understanding why field-cooled square superconducting films show anisotropic nucleation of flux avalanches (jumps) along the four edges. The explanation is based on an analytical model for thermomagnetic avalanche nucleation in type-II superconducting films, and allows one to understand the entire scenario of different flux dynamics observed experimentally.

Two-phase sink vortex suction mechanism and penetration dynamic characteristics in ladle teeming process

At the late stage of continuous casting (CC) ladle teeming, sink vortex can suck the liquid slag into tundish, and cause negative influences on the cleanliness of molten steel. To address this issue, a two-phase fluid mechanical modeling method for ladle teeming was proposed. Firstly, a dynamic model for vortex suction process was built, and the profiles of vortex flow field were acquired. Then, based on the level set method (LSM), a two-phase 3D interface coupling model for slag entrapment was built. Finally, in combination with high-order essentially non-oscillatory (ENO) and total variation diminishing (TVD) methods, a LSM-based numerical solution method was proposed to obtain the 3D coupling evolution regularities in vortex suction process. Numerical results show that the vortex with higher kinetic energy can form an expanded sandglass-shape region with larger slag fraction and lower rotating velocity; there is a pressure oscillation phenomenon at the vortex penetration state, which is caused by the energy shock of two-phase vortex penetration coupling.

Magnetic and thermodynamic properties of CuxTiSe2 single crystals

We present a detailed study of the phase diagram of copper intercalated TiSe$_2$ single crystals, combining local Hall-probe magnetometry, tunnel diode oscillator technique (TDO), specific-heat, and angle-resolved photoemission spectroscopy measurements. A series of the Cu$_x$TiSe$_2$ samples from three different sources with various copper content $x$ and superconducting critical temperatures $T_c$ have been investigated. We first show that the vortex penetration mechanism is dominated by geometrical barriers enabling a precise determination of the lower critical field, $H_{c1}$. We then show that the temperature dependence of the superfluid density deduced from magnetic measurements (both $H_{c1}$ and TDO techniques) clearly suggests the existence of a small energy gap in the system, with a coupling strength $2\Delta_s \sim [2.4-2.8]k_BT_c$, regardless of the copper content, in puzzling contradiction with specific heat measurements which can be well described by one single large gap $2\Delta_l \sim [3.7-3.9]k_BT_c$. Finally, our measurements reveal a non-trivial doping dependence of the condensation energy, which remains to be understood.

The threshold temperature where type-I and type-II interchange in mesoscopic superconductors at the Bogomolnyi limit

In this work we discuss the H−T phase diagram for mesoscopic squared superconducting samples at the Bogomolnyi limit, where the Ginzburg–Landau constant κ=1/2. We calculate Hp(T), the vortex penetration field, and Hu(T) the upper critical field. Through the study of the temperature dependence on the Hp, it is possible to distinguish the region where the magnetic field penetrates into the sample, like a type-I or a type-II superconductor. It permits to determine the threshold temperature T⋆(L,H) where the phase transition from type-I to type-II occurs for some different sizes L of the mesoscopic superconducting samples. The calculation of the upper critical field Hu(T), for these samples, shows that, these two curves, Hp(T) and Hu(T), overlap at the threshold temperature mentioned above. The magnetization of the system was calculated for all sizes studied in this work, and for temperatures above and below T⋆(L,H). This study confirms the existence of the threshold temperature, T⋆(L,H), where type-I and type-II interchange in mesoscopic superconductors at the Bogomolnyi limit.

Magnetic-field-induced vortex-lattice transition in HgBa2CuO4+δ

Measurements of the $^{17}$O nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in HgBa$_{2}$CuO$_{4+\delta}$ were performed over a range of magnetic fields from 6.4 to 30\,T in the superconducting state. Oxygen isotope exchanged single crystals were investigated with doping corresponding to superconducting transition temperatures from 74\,K underdoped, to 78\,K overdoped. The apical oxygen site was chosen since its NMR spectrum has narrow quadrupolar satellites that are well separated from any other resonance. Non-vortex contributions to the spectra can be deconvolved in the time domain to determine the local magnetic field distribution from the vortices. Numerical analysis using Brandt's Ginzburg-Landau theory was used to find structural parameters of the vortex lattice, penetration depth, and coherence length as a function of magnetic field in the vortex solid phase. From this analysis we report a vortex structural transition near 15\,T from an oblique lattice with an opening angle of $73^{\circ}$ at low magnetic fields to a triangular lattice with $60^{\circ}$ stabilized at high field. The temperature for onset of vortex dynamics has been identified with vortex lattice melting. This is independent of the magnetic field at sufficiently high magnetic field similar to that reported for YBa$_2$Cu$_3$O$_7$ and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and is correlated with mass anisotropy of the material. This behavior is accounted for theoretically only in the limit of very high anisotropy.

Observation of two distinct pairs fluctuation lifetimes and supercurrents in the pseudogap regime of cuprate junctions

Pairs fluctuation supercurrents and inverse lifetimes were measured on epitaxial c-axis junctions of the cuprates in the pseudogap regime, with a $PrBa_2Cu_3O_{7-\delta}$ barrier sandwiched in between two $YBa_2Cu_3O_{7-\delta}$ or doped $YBa_2Cu_3O_y$ electrodes, with or without magnetic fields parallel to the a-b planes. All junctions had a $\rm T_c(high)\approx 85-90$ K and a $\rm T_c(low)\approx 50-55$ K electrodes, allowing us to study pairs fluctuation supercurrents and inverse life times in between these two temperatures. In junctions with a pseudogap electrode under zero field, an excesss current due to pair fluctuations was observed which persisted at temperatures above $\rm T_c(low)$, in the pseudogap regime, and up to about $\rm T_c(high)$. No such excess current was observed in junctions without a pseudo-gap in the electrode. The measured conductance spectra at temperatures above $\rm T_c(low)$ were fitted using a modified fluctuations model by Scalapino [Phys. Rev. Lett. \textbf{24}, 1052(1970)] of a junction with a serial resistance. We found that in the pseudo-gap regime, the conductance vs voltage consists of a narrow peak sitting on top of a very broad peak. This yielded two distinct pairs fluctuation lifetimes in the pseudogap electrode which differ by an order of magnitude up to about $\rm T_c(high)$. Under in-plane fields, these two lifetime values remain separated in two distinct groups, which varied with increasing field moderately. We also found that detection of Amperian pairing [Phys. Rev. X \textbf{4}, 031017 (2014)] in our cuprate junctions is not feasible, due to Josephson vortices penetration into the superconducting electrodes which drove the necessary field above the depairing field.