Vortex Excitations Research Articles

Vortex excitation: Three design rules tested on 13 industrial chimneys

The design rules for cross-wind vibrations given by DIN 4133 and the CICIND model code can give results that differ a factor 6 or more. Still, both design rules are included in the Eurocode. In this paper we apply a model closely related to the Vickery–Basu model, of which the CICIND model code and several other Codes of Practice are simplified derivates, to 13 industrial steel chimneys of which the operational history is known in some detail. The results are much more reliable than either DIN 4133 or the CICIND model code. The dominant parameter is the influence of turbulence on the aerodynamic damping parameter. This site specific parameter is neglected or too strongly simplified in all current Codes of Practice.

Evolution from BCS to Berezinskii-Kosterlitz-Thouless Superfluidity in One-Dimensional Optical Lattices

We analyze the finite temperature phase diagram of fermion mixtures in one-dimensional optical lattices as a function of interaction strength. At low temperatures, the system evolves from an anisotropic three-dimensional Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength increases. We calculate the critical temperature as a function of interaction strength, and identify the region where the dimensional crossover occurs for a specified optical lattice potential. Finally, we show that the dominant vortex excitations near the critical temperature evolve from multiplane elliptical vortex loops in the three-dimensional regime to planar vortex-antivortex pairs in the two-dimensional regime, and we propose a detection scheme for these excitations.

Vortex oscillations induced by spin-polarized current in a magnetic nanopillar: Analytical versus micromagnetic calculations

We investigate the vortex excitations induced by a spin-polarized current in a magnetic nanopillar by means of micromagnetic simulations and analytical calculations. Damped motion, stationary vortex rotation and the switching of the vortex core are successively observed for increasing values of the current. We demonstrate that even for small amplitude of the vortex motion, the analytical description based the classical Thiele approach can yield quantitatively and qualitatively unsound results. We suggest and validate a new analytical technique based on the calculation of the energy dissipation.

Detection of vortex excitations in a Bi2Sr2Ca2Cu3O10 crystal at temperatures above the critical temperature by EPR of the surface layer

Vortex excitations have been detected at temperatures both below and above the critical temperature when investigating local magnetic fields on the surface of a Bi2Sr2Ca2Cu3O10 single crystal by means of an electron paramagnetic resonance (EPR) probe. A thin layer of a diphenyl picrylhydrazyl organic radical deposited on the crystal surface is used as the EPR probe. A narrow EPR signal makes it possible to detect weak distortions of the magnetic field appearing at T ≿ Tc. The analysis of the temperature dependences of the resonance field and the EPR linewidth is thebasis of the assumption of the vortex nature of magnetic excitations in this temperature range.

Topological insulator on the kagome lattice

Itinerant electrons in a two-dimensional Kagome lattice form a Dirac semi-metal, similar to graphene. When lattice and spin symmetries are broken by various periodic perturbations this semi-metal is shown to spawn interesting non-magnetic insulating phases. These include a two-dimensional topological insulator with a non-trivial Z_2 invariant and robust gapless edge states, as well as dimerized and trimerized `Kekule' insulators. The latter two are topologically trivial but the Kekule phase possesses a complex order parameter with fractionally charged vortex excitations. A charge density wave is shown to couple to the Dirac fermions as an effective axial gauge field.

Biot-Savart correlations in layered superconductors

We discuss the superconductor-to-normal phase transition in an infinite-layered, type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices and assume that the dominant interlayer coupling is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group (RG) flow, is that the phase transition in this model is a Kosterlitz-Thouless transition despite being a three-dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence is that the jump in the measured in-plane superfluid stiffness, a universal quantity in $2d$ Kosterlitz-Thouless theory, receives a small nonuniversal correction (of order 1% in ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and resolves some conflicting views.

Some aspects of the dynamic cross-wind response of tall industrial chimney

The paper is concerned with the numerical study of the cross-wind response of the 295 m-tall six-flue industrial chimney, located in the power station of Belchatow, Poland. The response of the chimney due to turbulent wind flow is caused by the lateral turbulence component and vortex excitation with taking into account motion-induced wind forces. The cross-wind response has been estimated by means of the random vibration approach. Three power spectral density functions suggested by Kaimal, Tieleman and Solari for the evaluation of the lateral turbulence component response are taken into account. The vortex excitation response has been calculated by means of the Vickery and Basu's model including some complements. Motion-induced wind forces acting on a vibrating chimney have been modeled as a nonlinear aerodynamic damping force. The influence of three components mentioned above on the total cross-wind response of the chimney has been investigated. Moreover, the influence of damping ratios, evaluated by Multi-mode Random Decrement Technique, and number of mode shapes of the chimney have been examined. Computer programmes have been developed to obtain responses of the chimney. The numerical results and their comparison are presented.

On the critical point of an interacting two-dimensional trapped Bose gas

We consider a quantized vortex excitation in a two-dimensional, harmonically trapped Bose gas and derive an equation for the Berezinskii-Kosterlitz-Thouless transition temperature based on a simple free-energy argument. We relate the critical phase-space density at the transition to the ratio between the entropy gain and the corresponding cost in energy of creating a free vortex excitation in the system.

Vortex 'puddles' and magic vortex numbers in mesoscopic superconducting disks

The magnetic properties of a superconducting disk change dramatically when its dimensions become mesoscopic. Unlike large disks, where the screening currents induced by an applied magnetic field are strong enough to force vortices to accumulate in a 'puddle' at the centre, in a mesoscopic disk the interaction between one of these vortices and the edge currents can be comparable to the intervortex repulsion, resulting in a destruction of the ordered triangular vortex lattice structure at the centre. Vortices instead form clusters which adopt polygonal and shell-like structures which exhibit magic number states similar to those of charged particles in a confining potential, and electrons in artificial atoms. We have fabricated mesoscopic high temperature superconducting Bi2Sr2CaCu2O8+δ disks and investigated their magnetic properties using magneto-optical imaging (MOI) and high resolution scanning Hall probe microscopy (SHPM). The temperature dependence of the vortex penetration field measured using MOI is in excellent agreement with models of the thermal excitation of pancake vortices over edge barriers. The growth of the central vortex puddle has been directly imaged using SHPM and magic vortex numbers showing higher stability have been correlated with abrupt jumps in the measured local magnetisation curves.

Low frequency magnetization excitations in magnetic nanopillars induced by a dc spin-polarized current

We present observations of low frequency, (fundamentals ≤1 GHz) current-driven magnetization dynamics at 293 K in partially patterned Py (24 nm)/Cu(10)/Py(6), elliptical, nanopillars, with the top Py(6) magnetic layer and part of the Cu layer shaped into an ∼70×140 nm2 nanopillar and the rest left extended. The magnetoresistance curves for applied current I≈2 mA, and the spin-transfer-torque curves for applied magnetic field H≈0, both behave as expected for simple, uncoupled magnetic layers. We describe several behaviors similar to those previously seen and associated with excitation and dynamics of vortices: sharp, low frequency (f) peaks at H=0, with df/dI∼40 MHz/mA; hysteretic behavior with the direction of sweep of current I; disappearance of the peaks for parallel field larger than 10 mT and for perpendicular field larger than 400 mT; nonmonotonic power production as a function of I. Two new behaviors are the “simultaneous” presence of such peaks for both I>0 and I<0, and strong asymmetry of the I<0 peaks when H is reversed.

Critical Slowing Down of Triangular Lattice Spin-3/2 Heisenberg Antiferromagnet Li7RuO6 via 7Li NMR

We report on 7 Li NMR studies of single crystals of the triangular-lattice Heisenberg antiferromagnet Li 7 RuO 6 . A slow critical divergence with a wide critical region of | T / T N -1|≤7 was observed in 7 Li nuclear spin–lattice relaxation rate. The slowing down of staggered spin fluctuations was analyzed in a renormalized classical region of a two-dimensional triangular-lattice nonlinear sigma model. Spin stiffness constant was found to decrease to about 20% of its value in spin-wave approximation. The effect of spin frustration, e.g., Z 2 vortex excitations on critical phenomena, is suggested.

Exotic vortex effect on the alternating order around impurities in two-dimensional antiferromagnets

It is well known that a magnetic field applied onto a Heisenberg antiferromagnet acts as an effective easy-plane anisotropy leading, in the case of two dimensions, to a Berezinskii–Kosterlitz–Thouless transition at a field-dependent temperature. If a nonmagnetic impurity is introduced in the lattice, an island of finite staggered magnetization develops, for which a recently proposed effective model predicts a universal shape that is almost independent of temperature and whose amplitude decays exponentially with the distance from the impurity. This picture was confirmed for the two-dimensional spin-12 case by quantum Monte Carlo simulations, whose outcomes, however, display also a counterintuitive effect: as the temperature approaches the critical value, the field-induced staggered magnetization surprisingly increases its range, which reaches a maximum before definitely dropping to zero in the disordered phase. In this paper an explanation of such a strange behavior is given as the result of vortex excitation.

Finite-frequency dynamics of vortex loops at the 4He superfluid phase transition

The finite-frequency dynamics of the 4He superfluid phase transition can be formulated in terms of the response of thermally excited vortex loops to an oscillating flow field. The key parameter is the Hausdorff fractal dimension dH of the loops, which affects the dynamics because the frictional force on a loop is proportional to the total perimeter P of the loop, which varies as P ∼ adH where a is the loop diameter. Solving the 3D Fokker-Planck equation for the loop response at frequency ω yields a superfluid density which varies at Tλ as ω1/(dH-1). This power-law variation with ω agrees with the scaling form found by Fisher, Fisher, and Huse, since the dynamic exponent z is identified as z = dH -1. Flory scaling for the self-avoiding loops gives a fractal dimension in terms of the space dimension d as dH = (d + 2)/2, yielding z = d/2 = 3/2 for d = 3, in complete agreement with dynamic scaling.

円柱の下流に十字交差配置された帯状の平板による振動制御 : 第2報,帯状平板による渦励振の励起と抑制(流体工学,流体機械)

The specific aim of this work is to develop a new technique to control vortex excitations of a circular cylinder by utilizing interference of a downstream strip-plate in cruciform arrangement. In the previous paper, it is shown that the two longitudinal vortices, trailing vortex and necklace vortex, shed in the vicinity of the crossing of a fixed circular cylinder/strip-plate system. In this paper, the circular cylinder was supported elastically so as to allow cross-flow motion and influence of the strip-plate on vortex excitation was investigated with the same wind tunnel apparatus. The strip-plate suppresses Karman vortex excitation more effectively compared with a downstream circular cylinder. A wider strip-plate has a larger suppression effect. The trailing vortex induces vortex excitation when gap-to-diameter ratio s/d less than 0.3. When the strip-plate width w is equal to the upstream circular cylinder diameter d, the velocity range for longitudinal vortex excitation is 5 times wider than the case of the downstream circular cylinder. The necklace vortex excitations dose not occur for strip-plates with w/d≥0.75, as expected from the fixed-cylinder experiment. Longitudinal vortex excitation by downstream strip-plate occurs over a wide velocity range, and it can be easily controlled by s/d adjusting.

Microfluidic mixing under low frequency vibration

In the laminar flow regime which characterizes the operation of most microfluidic systems, mixing is governed primarily by molecular diffusion. An increase in the interfacial surface between the fluids contained in the system facilitates the mixing process. This can be obtained by active external perturbation, requiring complex systems and complex operation, or passively by clever design over the geometrical constraints. Here, we describe an active micromixer technique based on the excitation of vortices in proximity to sharp corners of junctions, as a result of simple low frequency vibration of the device. Results showing the working principle in both static and fluid through conditions are presented.

Modelling of aero-acoustic wave propagation in low Mach number corrugated pipe flow

This paper sets out to investigate parameters that determine flow-induced vibrations in flexible, corrugated pipes. A central element in this paper is a mathematical model that describes the phenomenon. The presented model is designed to capture the aero-acoustic wave behaviour of gas that flows in a corrugated pipe, exploring the feedback analysis. This model involves the coupling between the large-scale acoustic behaviour in a pipe and a line of self-excited oscillators representing vortex excitation caused by flow over corrugations.

角柱のギャロッピングに対する下流平板の影響(流体工学,流体機械)

Galloping of a square cylinder can be suppressed by the downstream strip-plate set in cruciform arrangement with a gap s. In addition, another strong vibration is generated at certain conditions of the flow velocity and gap s. The specific aim of this work is to confirm generality of these phenomena for various dimension systems and nondimensional parameters by the wind tunnel experiment. When the width of the downstream strip-plate w is equal to the side length of the square cylinder d, the suppression of galloping and the strong vibration are observed for all the square cylinders. The effective region of suppression is affected by w. The strong vibration is confirmed to be the longitudinal vortex excitation from measurement of the dominant frequency of the velocity fluctuation near the cross and flow visualization.

Vortex condensation in the dual Chern–Simons–Higgs model

The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern–Simons–Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual Chern–Simons–Higgs model, we determine the location of the critical value for the Chern–Simons parameter below which vortex condensation can happen in the system. The effects of self-energy quantum corrections to the vortex field are also considered.

Quantum vortices within the complex quantum Hamilton–Jacobi formalism

Quantum vortices are investigated in the framework of the quantum Hamilton-Jacobi formalism. A quantum vortex forms around a node in the wave function in the complex space, and the quantized circulation integral originates from the discontinuity in the real part of the complex action. Although the quantum momentum field displays hyperbolic flow around a node, the corresponding Polya vector field displays circular flow. It is shown that the Polya vector field of the quantum momentum function is parallel to contours of the probability density. A nonstationary state constructed from eigenstates of the harmonic oscillator is used to illustrate the formation of a transient excited state quantum vortex, and the coupled harmonic oscillator is used to illustrate quantization of the circulation integral in the multidimensional complex space. This study not only analyzes the formation of quantum vortices but also demonstrates the local structures for the quantum momentum field and for the Polya vector field near a node of the wave function.

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.