Vortex Bundles Research Articles

Interference mechanism of trailing edge flap shedding vortices with rotor wake and aerodynamic characteristics

A robust Reynolds-Averaged Navier-Stokes (RANS) based solver is established to predict the complex unsteady aerodynamic characteristics of the Active Flap Control (AFC) rotor. The complex motion with multiple degrees of freedom of the Trailing Edge Flap (TEF) is analyzed by employing an inverse nested overset grid method. Simulation of non-rotational and rotational modes of blade motion are carried out to investigate the formation and development of TEF shedding vortex with high-frequency deflection of TEF. Moreover, the mechanism of TEF deflection interference with blade tip vortex and overall rotor aerodynamics is also explored. In non-rotational mode, two bundles of vortices form at the gap ends of TEF and the main blade and merge into a single TEF vortex. Dynamic deflection of the TEF significantly interferes with the blade tip vortex. The position of the blade tip vortex consistently changes, and its frequency is directly related to the frequency of TEF deflection. In rotational mode, the tip vortex forms a helical structure. The end vortices at the gap sides co-swirl and subsequently merge into the concentrated beam of tip vortices, causing fluctuations in the vorticity and axial position of the tip vortex under the rotor. This research concludes with the investigation on suppression of Blade Vortex Interaction (BVI), showing an increase in miss distance and reduction in the vorticity of tip vortex through TEF phase control at a particular control frequency. Through this mechanism, a designed TEF deflection law increases the miss distance by 34.7% and reduces vorticity by 11.9% at the target position, demonstrating the effectiveness of AFC in mitigating BVI.

Flux creep regimes and vortex phase diagram in β-FeSe single crystals

We analyze the relationship between critical current densities (JC) and flux creep rates (S) in β-FeSe single crystals. This analysis was based on magnetization measurements. Additionally, we establish correlations with the recently reported magnetic field-induced geometrical deformation of the vortex lattice, transitioning from hexagonal to square shape due to a rhombic distortion [A. V. Putilov et al. Phys. Rev 99 (2019) 144514]. The results show that the magnetic field dependence of Jc displays distinct regimes, which is reflected by changes in S. The vortex dynamics is analyzed within the framework of the collective creep theory. S is characterized by low pinning energies and glassy exponents according to the expectation for small-bundles at low temperatures and magnetic fields where a hexagonal vortex lattice was reported. Conversely, we observe a systematic increase in S, resembling a shift from small to large vortex bundles, at magnetic fields corresponding to the rhombic distortion. Last, the relaxation rates exhibit significant values for magnetic fields where a square vortex lattice is expected, suggesting a potential crossover from elastic to plastic creep. Our findings highlight a direct relationship between vortex lattice deformations and a decrease in vortex pinning related to vortex-defect interactions.

Vortex-type equations on compact Riemann surfaces

In this paper, we prove a priori estimates for some vortex-type equations on compact Riemann surfaces. As applications, we recover existing estimates for the vortex bundle Monge-Ampère equation, prove an existence and uniqueness theorem for the Calabi-Yang-Mills equations on vortex bundles and get estimates for J-vortex equation. We prove an existence and uniqueness result relating Gieseker stability and the existence of almost Hermitian Einstein metrics, i.e., a Kobayashi-Hitchin type correspondence. We also prove Kählerness of the negative of the symplectic form which arises in the moment map interpretation of the Calabi-Yang-Mills equations in [9].

Two-dimensional Brownian motion of active particle on superfluid helium surface

We report an experimental study of the 2D dynamics of active particles driven by quantum vortices on the free surface of superfluid helium at T = 1.45 К. The particle motion at short times (< 25 ms) relates to anomalous diffusion mode typical for active particles, while for longer times it corresponds to normal diffusion mode. The values of the rotational and translational kinetic energies of the particle allow to determine for the first time the intensity of the particle-vortex interaction and the dissipation rate of the vortex bundle energy. Strong bonding between a particle and a vortex is explained by coupling of normal and superfluid components.

J-equation on holomorphic vector bundles

We introduce the J-equation on holomorphic vector bundles over compact Kähler manifolds and investigate some fundamental properties as well as examples of solutions. In particular, we provide an algebraic condition called (asymptotic) J-stability in terms of subbundles on compact Kähler surfaces, and a numerical criterion on vortex bundles via dimensional reduction. Also, we discuss an application for the vector bundle version of the deformed Hermitian–Yang–Mills equation in the small volume regime.

The Demailly systems with the vortex ansatz

For an arbitrary-rank vector bundle over a projective manifold, J.-P. Demailly proposed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor to settle a conjecture of Griffiths on the equivalence of Hartshorne ampleness and Griffiths positivity. In this article, we have studied two proposed systems and proved that these equations have smooth solutions for the Vortex bundle using the continuity method.

Observation of intermediate mixed state in high-purity cavity-grade Nb by magneto-optical imaging

Suppression of the occurrence of remanent vortices is necessary to improve the quality factor of superconducting resonators. In particular, the flux-expulsion dynamics in Nb during cooling has become of major interest to researchers focusing on superconducting cavities. To study the vortex states and their behavior in high-purity cavity-grade Nb, we used a magneto-optical imaging technique to perform real-space observations of the magnetic field distributions during the field-cooling and field-scanning processes. In the field-cooling process, the distributions were observed to undergo phase separation into vortex and Meissner regions, as would be expected in an intermediate mixed state (IMS). The vortex regions in the IMS, such as vortex bundles, tend to be larger in higher fields, in contrast to the Meissner regions, which experience shrinkage. In the field-scanning process, domelike field profiles, which indicate a geometrical barrier with very weak bulk pinning, were observed. The existence of the IMS suggests that cavity-grade Nb is in a type-II/1 superconductor regime, in which attractive interaction between vortices at a length scale of the penetration depth is crucial for the behavior of vortices.

Bathtub vortex in superfluid He4

We have investigated the structure of macroscopic suction flows in superfluid $^4$He. In this study, we primarily analyze the structure of the quantized vortex bundle that appears to play an important role in such systems. Our study is motivated by a series of recent experiments conducted by a research group in Osaka City University [Yano $\textit{et. al.}$, J. Phys. Conf. Ser. $\textbf{969}$, 012002 (2018)]; they created a suction vortex using a rotor in superfluid $^4$He. They also reported that up to $10^4$ quantized vortices accumulated in the central region of the rotating flow. The quantized vortices in such macroscopic flows are assumed to form a bundle structure; however, the mechanism has not yet been fully investigated. Therefore, we prescribe a macroscopic suction flow to the normal fluid and discuss the evolution of a giant vortex ($\textit{i.e.}$, one with a circulation quantum number exceeding unity) and a bundle of singly quantized vortices from a small number of seed vortices. Then, using numerical simulations, we discuss several possible characteristic structures of the bundle in such a flow, and we suggest that the actual steady-state bundle structure in the experiment can be verified by measuring the diffusion constant of the vortex bundle after the macroscopic normal flow has been switched off. By applying extensive knowledge of the superfluid $^4$He system, we elucidate a new type of macroscopic superfluid flow and identify a novel structure of quantized vortices.

Vortex phases and glassy dynamics in the highly anisotropic superconductor HgBa2CuO4+\u03b4

We present an extensive study of vortex dynamics in a high-quality single crystal of HgBa2CuO4+δ, a highly anisotropic superconductor that is a model system for studying the effects of anisotropy. From magnetization M measurements over a wide range of temperatures T and fields H, we construct a detailed vortex phase diagram. We find that the temperature-dependent vortex penetration field Hp(T), second magnetization peak Hsmp(T), and irreversibility field Hirr(T) all decay exponentially at low temperatures and exhibit an abrupt change in behavior at high temperatures T/Tc >~ 0.5. By measuring the rates of thermally activated vortex motion (creep) S(T, H) = |dlnM(T, H)/dlnt|, we reveal glassy behavior involving collective creep of bundles of 2D pancake vortices as well as temperature- and time-tuned crossovers from elastic (collective) dynamics to plastic flow. Based on the creep results, we show that the second magnetization peak coincides with the elastic-to-plastic crossover at low T, yet the mechanism changes at higher temperatures.

On the Closure Problem of the Coarse-Grained Hydrodynamics of Turbulent Superfluids

The coarse-grained hydrodynamics of turbulent superfluid fluids describes the fluid flow in terms of two equations for the averaged normal and superfluid velocities. These two equations are coupled via the mutual friction term, which contains the quantity $${\mathcal {L}}(r,t)$$ –the vortex line density (VLD) of the vortex tangle. The question of how to treat the quantity $${\mathcal {L}}(r,t)$$ –the so-called closure procedure is crucial for the correct description of flow of turbulent superfluids. The article provides a critical analysis of several approaches to the closure procedure. The first one, which is usually referred to as HVBK method suggests to express the quantity $${\mathcal {L}}(r,t)$$ via coarse-grained vorticity $$\nabla \times {\mathbf {v}}_{s}$$ using the famous Feynman rule. This method and idea on the vortex bundle structure, which justifies the use of the HVBK approach, are analyzed and discussed in detail. Another approach that has been popular before, but is still used sometimes, is called the Gorter–Mellink relation. This method suggests that the VLD $${\mathcal {L}}(r,t)$$ is proportional to the squared relative velocity between normal and superfluid components $$\propto (v_{n}-v_{s})^{2}$$ . One more variant of the closure procedure, discussed in the paper, is based on the method in which the vortex line density $${\mathcal {L}}(r,t)$$ is not expressed directly via the velocity (and/or vorticity) field, but is an independent equipollent variable, controlled by a separate equation. The latter approach is called as hydrodynamics of superfluid turbulence (HST). The advantages and disadvantages of each method are discussed.

Coarse-grained pressure dynamics in superfluid turbulence

Coarse-grained superfluid dynamics are investigated through detailed numerical simulation at the level of individual quantized vortex lines. Simulations show a strong correlation between the formation of quantized vortex bundles and the production of extreme negative pressure regions in excess of 3 standard deviations. This motivates the use of experimental pressure measurements for probing superfluid turbulence at low temperatures.

Mathematical modeling of current-voltage characteristics of high-temperature superconductors with fractal boundaries of normal phase clusters

The fractality effect of the normal phase clusters' boundaries of a high-temperature superconductor YBa2Cu3O7−x (YBCO) on the magnetic flux creep is investigated. Experimental current-voltage and magnetoresistive characteristics of YBCO at the boiling point of nitrogen are obtained. Based on the model of intergranular clusters with fractal boundaries, an approximation of the experimental data is obtained after geometric-probability analysis of the photomicrographs of the samples. A model of the magnetoresistive state caused by flux creep is proposed for various transport currents, and experimental and empirical dependences of the fractal dimension of the normal YBCO phase cluster boundaries on the constant magnetic field are found. The magnetic field intensity is determined for a given fractal dimension, at which the vortex penetration into the granules begins. It is shown that the state of the samples corresponds to the metastable phase of the vortex glass. The connectivity index of the stall paths of the vortex bundles at the percolation threshold is calculated.

Effect of Ni doping on vortex pinning in CaK(Fe1−xNix)4As4 single crystals

We study the correlation between chemical composition and vortex dynamics in Ni-doped $\mathrm{CaK}{(\mathrm{F}{\mathrm{e}}_{1\ensuremath{-}x}\mathrm{N}{\mathrm{i}}_{x})}_{4}\mathrm{A}{\mathrm{s}}_{4}$ ($x=0$, 0.015, 0.025, 0.03, and 0.05) single crystals by performing measurements of the critical current densities ${J}_{c}$ and the flux creep rates $S$. The magnetic relaxation of all the crystals is well described by the collective creep theory. The samples display a glassy exponent \ensuremath{\mu} within the predictions for vortex bundles in a weak pinning scenario and relatively small characteristic pinning energy (${U}_{0}l100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$). The undoped crystals display modest ${J}_{c}$ values at low temperatures and high magnetic fields applied along the $c$ axis. ${J}_{c}(T)$ dependences at high fields display an unusual peak. The enhancement in ${J}_{c}(T)$ matches with an increase in ${U}_{0}$ and the appearance of a second peak in the magnetization. As Ni doping increases, whereas there is a monotonic decrease in ${T}_{c}$ there is a nonmonotonic change in ${J}_{c}$. Initially ${J}_{c}$ increases, reaching a maximum value for $x=0.015$, and then ${J}_{c}$ decreases for $x\ensuremath{\ge}0.025$. This change in ${J}_{c}$($x$) is coincident with the onset of antiferromagnetic order. The magnetic field dependence of ${J}_{c}(H)$ also manifests a change in behavior between these $x$ values. The analysis of the vortex dynamics for small and intermediate magnetic fields shows a gradual evolution in the glassy exponent \ensuremath{\mu} with Ni content, $x$. This implies that there is no appreciable change in the mechanism that determines the vortex relaxation.

Helicity in superfluids: Existence and the classical limit

The analog of hydrodynamic helicity in superfluids is zero for all flows. A semiclassical limit is found in the link and writhe of bundles of superfluid vortices. Numerical simulations show that the dynamics of semiclassical helicity closely resemble those seen in experiments in viscous fluids.

Numerical research of the swirling supersonic gas flows in the self-vacuuming vortex tube

This article presents the results of simulation for a special type of vortex tubes – self-vacuuming vortex tube (SVVT), for which extreme values of temperature separation and vacuum are realized. The main results of this study are the flow structure in the SVVT and energy loss estimations on oblique shock waves, gas friction, instant expansion and organization of vortex bundles in SVVT.

Effect of secondary swirl in supersonic gas and plasma flows in the self-vacuuming vortex tube

This article presents the results of simulation for a special type of vortex tubes – self-vacuuming vortex tube (SVT), for which extreme values of temperature separation and pressure drop are realized. The main results of this study are the flow structure in the SVT and energy loss estimations on oblique shock waves, gas friction, instant expansion and organization of vortex bundles in SVT.

Strong influence of the oxygen stoichiometry on the vortex bundle size and critical current densities Jc of GdBa2Cu3Ox-coated conductors grown by co-evaporation

We report on the influence of oxygen stoichiometry on the vortex creep mechanism of GdBa2Cu3Ox-coated conductors produced by co-evaporation. The oxygen stoichiometry of the films, x, was modified in a controlled way between 6.85 and 7, which resulted in systematic and reversible control of the superconducting critical temperature between about 78 and 93 K. The change in the oxygen stoichiometry produces a strong reduction in the self-field critical current densities Jc without significantly modifying the power-law dependence at intermediate magnetic fields, which indicates a negligible contribution of oxygen vacancies to the pinning. In addition, the characteristic glassy exponent μ shows a systematic diminution from about 1.63 at x = 7 to about 1.12 at x = 6.85. The results are compared with those obtained for proton- and oxygen-irradiated films, in which the vortex dynamics is determined by a balance between the improved pinning, originating from nanocluster inclusion, and the suppressed superconducting properties due to disorder in the nanoscale.

Experimental research of high field pinning centers in 2% C doped MgB2 wires at 20 K and 25 K

High field pinning centers in MgB2 doped with 2 at. % carbon under a low and a high hot isostatic pressures have been investigated by transport measurements. The field dependence of the transport critical current density was analyzed within the different pinning mechanisms: surface pinning, point pinning, and pinning due to spatial variation in the Ginzburg-Landau parameter (Δκ pinning). Research indicates that a pressure of 1 GPa allows similar pinning centers to Δκ pinning centers to be obtained. This pinning is very important, because it makes it possible to increase the critical current density in high magnetic fields at 20 K and 25 K. Our results indicate that the δTc and δl pinning mechanisms, which are due to a spatial variation in the critical temperature (Tc) and the mean free path, l, respectively, create dislocations. The high density of dislocations with inhomogeneous distribution in the structure of the superconducting material creates the δl pinning mechanism. The low density of dislocations with inhomogeneous distribution creates the δTc pinning mechanism. Research indicates that the hot isostatic pressure process makes it possible to obtain a high dislocation density with a homogeneous distribution. This allows us to obtain the δTc pinning mechanism in MgB2 wires. In addition, a high pressure increases the crossover field from the single vortex to the small vortex bundle regime (Bsb) and improves the δTc pinning mechanism. Our research has proved that a high pressure significantly increases the crossover field from the small bundle to the thermal regime (Bth), with only a modest decrease in Tc of 1.5 K, decreases the thermal fluctuations, increases the irreversibility magnetic field (Birr) and the upper critical field (Bc2) in the temperature range from 4.2 K to 25 K, and reduces Birr and Bc2 above 25 K.

AC susceptibility of the Hg0.3La0.7Ba2Ca3(Cu0.95Ag0.5)4O10+δ superconductor

In this work, the temperature, magnetic field and frequency dependence of the ac susceptibility of Hg0.3La0.7Ba2Ca3(Cu0.95Ag0.5)4O10+δ were studied. The superconductivity still survives even at this amount of Ag. The magnetic field dependence of the irreversibility line (IL) and the flux pinning of this compound are discussed and compared with those of low Ag content. The IL exhibits thermally activated behaviour. A collective creep of the vortex bundle also occurs for this level of doping. A crossover from a two- to a three-dimensional system is suggested at T/Tc=0.75 and a magnetic field, Hdc=0.04T. Based on vortex glass phase transition theory, the effective pinning energy, ueff, was calculated. The change in the characteristic temperature of the studied compound and that of low Ag content samples are summarised. Comparisons with similar materials are discussed.

Quantum Turbulence: Vortex Bundle Collapse and Kolmogorov Spectrum

The statement of problem is motivated by the idea of modeling the classical turbulence with a set of chaotic quantized vortex filaments in superfluids. Among various arguments supporting the idea of quasi-classic behavior of quantum turbulence, the strongest, probably, is the k dependence of the spectra of energy, \(E(k)\propto k^{-5/3}\) obtained in numerical simulations and experiments. At the same time, the mechanism of classical vs. quantum turbulence is not clarified and the source of the \(k^{-5/3}\) dependence is unclear. In this work, we concentrated on the nonuniform vortex bundles. This choice is related to the actively discussed question concerning a role of collapses in the vortex dynamics in formation of turbulent spectra. We demonstrate that the nonuniform vortex bundles, which appear in result of nonlinear vortex dynamics, generates an energy spectrum which is close to the Kolmogorov dependence \(\propto k^{-5/3}\).