Lock-in State Research Articles

Vortex Flow Around an In-Line Forced Oscillating Circular Cylinder

In this study, the flow features of vortex shedding from a circular cylinder oscillating along the direction of the flow were observed by visualizing water flow experiment at the ranges of the frequency ratio f/fK=0-6.2, amplitude ratio 2a/d=0.0625-1.0, and Reynolds number Re=570-1700. The variations of mean vortex shedding frequency were investigated and the existence range of the lock-in was shown. It was obtained that although the cylinder oscillation frequency is lower than the natural Karman vortex's frequency; the lock-in phenomenon arises. It was found that the distribution of the lock-in form in the lock-in region was shown and that it became the tendency where the range with the frequency which becomes the lock-in form of fVK/f=1/1 with the increase of amplitude ratio expands. The flow patterns were classified into five kinds by the configuration of vortex shedding and the direction of vortex shedding. The structure of the vortex flow which depends on the frequency ratio was clarified by observing flow from both to the axial direction and the direction of span. In the case of lock-in state fVK/f=1/1, two kinds of vortex structure were obtained. One of which was three-dimensional characteristic on the side of low oscillation frequency, and the other was two-dimensional characteristic on the side of high oscillation frequency. In the case of lock-in state fVKf=1/2, even if the lock-in had occurred, it was shown that the phase difference sometimes occurred to the direction of the span in vortex shedding.

Vortex Shedding from a Pair of In-Line Forced Oscillating Parallel Arranged Circular Cylinders (In the Case of Equal Diameter)

In this study, the flow features of vortex shedding from a pair of parallel arranged circular cylinders oscillating along the direction of the flow were observed by visualizing water flow experiment at the ranges of the frequency ratio f/fk=0-7, amplitude ratio 2a/d=0.125, 0.25, 0.5 and 0.75, gap ratio G/d=0.25, 0.75 and 1.75, and Reynolds numbers Re=470-670 (towing water tank test) and 700-750 (closed circuit water channel test). The variations of mean vortex shedding frequency from each oscillating cylinder were investigated. As a result of the experiments, typical flow patterns of lock-in state or un-lock-in state were shown every gap ratio G/d. Although the cylinder oscillation frequency f is lower than the natural Karman vortex's frequency fk, the lock-in phenomenon can be seen. It was found that the measurement result depended on the observation point because the rearrangement of vortex formation had changed the characteristics of the flow. When the cylinders were oscillated to the direction of flow, the flow pattern of bias gap flow became not seen. The map of lock-in state in the lock-in range was obtained. It was found that the lock-in range and the lock-in form were more different from the case of single oscillating cylinder.

X-ray scattering study of temperature dependence of a structural incommensurability of theωphase in Ti-V alloys

The incommensurate $\ensuremath{\omega}$ phase in titanium alloys has been revisited. A mechanism of the formation relevant to electron-lattice coupling has been re-investigated in terms of an x-ray-scattering technique on three kinds of single crystals, each containing 20, 24, and 27 mass % of vanadium respectively. The superlattice reflections of all systems observed for reduced wave vector $\mathbit{q}=(2∕3+\ensuremath{\Delta},2∕3+\ensuremath{\Delta},2∕3+\ensuremath{\Delta})$ at temperature $\ensuremath{\cong}30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ reveal the following three effects for their intensity distribution with increasing temperature, where $\ensuremath{\Delta}$ has a nonzero value giving the incommensurability: (1) decrease of the intensities, (2) increase of the distribution widths, and (3) reduction of the $\ensuremath{\Delta}$ values. The results suggest unstabilization of the lock-in state. A temperature region which indicates a notion of the transition is lowered with increasing concentration, implying excess of the valence electrons which prohibits lock-in nesting of the charge density wave. This idea was supported by molecular-orbital population analysis using cluster models of the two phases.

Interference between stationary and vibrating cylinder wakes

The flow behind two side-by-side tubes of identical diameter, d, one stationary and the other forced to oscillate in the lateral direction at an amplitude of A=0.1∼0.5d was examined. Two values of T/d, i.e., 2.2 and 3.5 were investigated, where T is the cylinder center-to-center spacing. The Reynolds number Re ranges from 150 to about 1000. The effect of A/d, T/d, and fe/fs, where fe is the cylinder oscillating frequency and fs is the vortex shedding frequency of an isolated stationary cylinder, on the vortex shedding and the wake structure was examined. Specific attention was given to the occurrence of lock-in, where vortex shedding from the oscillating cylinder synchronizes with fe. Significant influence of these parameters has been observed on the flow behind the cylinders in terms of the predominant vortex patterns and interactions between vortices. It has been found that the shedding frequency associated with the oscillating and the stationary cylinder can be modified as fe/fs approaches unity. Furthermore, the flow regime may change under the conditions of T/d=2.2 and A/d=0.5 from two distinct coupled streets to the combination of one narrow and one wide street. Subsequently, the lock-in state is considerably extended probably because multiple dominant frequencies in the asymmetrical flow regime can all be locked in with the structural oscillation.

Crossing vortex-lattices state probed by c-axis resistance in Bi2Sr2CaCu2O8+y

To investigate the properties of crossing lattices of pancake and Josephson vortices, we have measured the c-axis resistance Rc(H) as a function of field in Bi2Sr2CaCu2O8+y intrinsic Josephson junctions. When the sample is rotated in an applied field, Josephson-vortex flow resistance appears in the so-called lock-in state. Additionally, many equal steps of the resistance are observed in the range of fields where the crossing lattices are expected. The relationship between this phenomenon and crossing lattices is discussed.

Studies of the R-phase transformation in a Ti–51at.%Ni alloy by transmission electron microscopy

The R-phase transformation in a Ti–51at.%Ni shape memory alloy was studied by transmission electron microscopy including high resolution microscopy and in situ observations on cooling. It was found that prior to this transformation there is a wide temperature range at which an incommensurate phase exists in the alloy. The incommensurability decreases with the temperature decrease reaching finally the lock-in R-phase state.

Finite element analysis of bubbly flow around an oscillating square-section cylinder

The bubbly flow around a square-section cylinder, which is forced to oscillate normal to a uniform flow, is simulated by an incompressible two-fluid model. The model is solved by the Arbitrary Lagrangian–Eulerian (ALE) finite element method. The width of the cylinder is 30 mm . A bubbly flow is assumed, and the bubble diameter is set as 1 mm . The volumetric fraction of the gas-phase upstream of the cylinder is 0.05, where the Reynolds number defined by the volumetric velocity of the liquid-phase is 200. With an increment in the cylinder oscillation frequency Sc, the vortex shedding frequency St approaches the Sc value. When the Sc is increased beyond a critical value, the lock-in occurs, in which the vortex shedding is synchronized with the cylinder oscillation. The time-averaged drag coefficient and the root-mean-square of the lift coefficient for the cylinder take their maximum values at the lock-in state. The volumetric fraction of the gas-phase α g is higher in the wake of the cylinder, irrespective of the Sc value. The α g value is lower below the lock-in state and higher in the lock-in state than the value for the stationary cylinder.

Suppression of vortex pinning by field component parallel to the superconducting plane inBi2Sr2CaCu2O8

The response of magnetic fluxoids nearly parallel to the superconducting plane of the layered superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ has been investigated through the ac susceptibility measurement. The fluxoids respond diamagnetically due to pinning when they pierce the superconducting plane to form pancake vortices, but they are released due to melting and become mobile in the high field. The liberation is enhanced by approaching the parallel field direction by the effect of decoupling between planes and finally the vortex pinning is suppressed. The pinning of fluxoids with pancakes and releasing in relation to their lock-in state are presented.

Josephson plasma resonance and anomalous hysteresis in the vortex lock-in state in Bi 2Sr 2CaCuO 8+δ

We present data on the Josephson plasma resonance in Bi 2Sr 2CaCuO 8+δ in a field nominally aligned with the CuO 2 planes (the tilt angle θ<0.25°). At temperatures between 15 and 40 K, were find that the resonance field observed in sweep-up field scans is always smaller than that in sweep-down scans. The hysteresis has a sign opposite to that usually encountered in isotropic superconductors. A second unusual aspect of the hysteresis is that the turning field (maximum or minimum field in a particular scan cycle) influences the value of one of the resonance fields. We propose an explanation in which the critical field for vortex pancake nucleation and the existence of the vortex lock-in state generate a hysteresis loop in the B y −B z plane. The model accounts for the anomalous sign as well as other features observed. The experiment clarifies plasma resonance experiments performed close to alignment at low temperatures. We discuss the importance of zero-field cooling the sample in resonance measurements in this geometry.

Vortices in a La1.9Sr0.1CuO4 crystal: influence of the layered structure on magnetisation

Using a transverse vibrating sample magnetometer, we have made vector magnetisation measurements on a disk-shaped single crystal La1.9Sr0.1CuO4. Reversible behaviour of the c-axis component of magnetisation, and the angular dependences of the remanent moment are evidence of the vortex lock-in state. The lock-in angle dependence on temperature and applied magnetic field are in agreement with theory.

Anomalous hysteresis in the Josephson plasma resonance ofBi2Sr2CaCuO8+δfor fields close to alignment with theabplane

We present data on the Josephson plasma resonance in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCuO}}_{8+\mathrm{\ensuremath{\delta}}}$ in a field nominally aligned with the ${\mathrm{CuO}}_{2}$ planes (the tilt angle $\ensuremath{\theta}l0.25\ifmmode^\circ\else\textdegree\fi{}$). At temperatures between 15 and 40 K, we find that the resonance field observed in sweep-up field scans is always smaller than that in sweep-down scans. The hysteresis has a sign opposite to that usually encountered in isotropic superconductors. A second unusual aspect of the hysteresis is that the turning field (maximum or minimum field in a particular scan cycle) influences the value of one of the resonance fields. We propose an explanation in which the critical field for vortex pancake nucleation and the existence of the vortex lock-in state generate a hysteresis loop in the ${B}_{y}$-${B}_{z}$ plane. The model accounts for the anomalous sign as well as other features observed. The experiment clarifies plasma resonance experiments performed close to alignment at low temperatures. We discuss the importance of zero-field cooling the sample in resonance measurements in this geometry.

NMR in the (BEDT) 2X organic superconductors

We review recent NMR studies of a layered organic superconductor of the (BEDT) 2X family. First the normal state prop erties are discussed. The central issue is the importance of the interplay between antiferromagnetism and superconductivity in these materials demonstrated by the observation of a pseudogap developing prior to the superconducting transition. The use of high pressure to tune the amplitude of AF fluctuations enables us to draw a general phase diagram of the family. In the second part the NMR experiments in the superconducting state are presented. One of the fundamental questions addressed by these experiments is the symmetry of the order parameter related to the pairing mechanism. The most spectacular NMR measurements are those performed in the lock-in state, which give access to the density of superconducting excitations at low energy. These experiments suggest that the pairing state may be unconventional featuring an anisotropic superconducting gap, possibly with nodes.

NMR in the 2D Organic Superconductors

We review recent NMR studies of the layered organic superconductors of the (BEDT) 2 X family. First the normal state properties are discussed. The central issue is the importance of the interplay between antiferromagnetism and superconductivity in these materials demonstrated by the observation of a pseudogap developing prior to the superconducting transition. An extended analysis of the Knight shift and the nuclear relaxation rate gives an evidence for strong antiferromagnetic fluctuations enhanced by Coulomb repulsion and the nesting of the Fermi surface. The NMR data show some analogy with High T c superconductors however the comparison is not straightforward as there is no clear evidence for spin-charge decoupling. The use of high pressure to tune the amplitude of AF fluctuations enables us to draw a general phase diagram of the family. In the second part the NMR experiments in the superconducting state are presented. One of the fundamental questions addressed by these experiments is the symmetry of the order parameter related to the pairing mechanism. The most spectacular NMR measurements are those performed in the lock-in state, which give access to the density of superconducting excitations at low energy. These experiments suggest that the pairing state may be unconventional featuring an anisotropic superconducting gap, possibly with nodes. Finally, the NMR contribution to the understanding of the nature of the vortex state is discussed in the context of recent results on k-(ET) 2 Cu[N(CN) 2 ]Br where the 1 H relaxation was used as a probe of the vortex density fluctuations.

Superconducting state of kappa -(ET)2CUBr studied by 13C NMR: Evidence for vortex-core-induced nuclear relaxation and unconventional pairing.

We present the first $^{13}\mathrm{C}$ NMR measurements carried out in the superconducting state of a two-dimensional organic superconducting single crystal. Spin lattice relaxation rate and Knight shift are reported for magnetic fields parallel and perpendicular to the conducting layers. For perpendicular fields, the relaxation is dominated by the electronic excitations in the vortex cores. From the field dependence of ${({T}_{1})}^{\ensuremath{-}1}$ we obtain the upper critical field [${H}_{c2}(0)=10$ T]. In parallel orientation, the absence of field dependence reveals the existence of a lock-in state, where only relaxation by superconducting excitations is expected. The ${({T}_{1})}^{\ensuremath{-}1}$ then exhibits a ${T}^{3}$ law suggesting an unconventional pairing with a very anisotropic gap.

Computation of Vortex Lock-In in the Laminar Wake of a Circular Cylinder Using Unsteady Monopole Sources

The vortex lock-in in the laminar wake behind a circular cylinder induced by the unsteady monopole source is numerically simulated in this paper. The artificial compressibility method is employed to solve the incompressible Navier-Stokes equations. A high-order accurate upwind flux-difference finite-volume scheme is used to discretize the flow field. The unsteady monopole source is simulated by a pulsating volume flux through the cylinder surface at a prescribed forcing frequency and amplitude. The forcing amplitude is set to a fixed value while the frequency is varied to search for the lock-in region. The flow field of the periodic lock-in state is examined in detail. Finally, the effects of a higher amplitude and a different source location are briefly investigated.

Unsteady Fluid Force Acting on Two Tandem Circular Cylinders Subjected to Two-Phase Cross-Flow

To understand the excitation and suppression effects of air bubbles on the vibration of two tandem cylinders, we experimentally investigate the characteristics of unsteady fluid force in the lift direction acting on the downstream cylinder having a pitch-to-diameter ratio of 3.0 and subjected to two-phase bubble cross-flow. The average diameter of bubbles is about 3 to 4 mm. Experiments to measure the unsteady fluid force are performed, changing the void fraction at three different reduced velocities (2.15, 4.88, and 7.05) for oscillation amplitudes ranging from 5.0 to 15.0 mm. The downstream cylinder is forced to oscillate sinusoidally at the natural frequency of the upstream cylinder in water. Experiments reveal the following major characteristics of fluid force. (1) At low reduced velocity, almost no difference is observed in the characteristics with respect to void fraction and oscillation amplitude ; (2) air bubbles reduce the fluid force in the range of the void fraction a≤5% and at a smalloscillation amplitude for the lock-in state reduced velocity ; and (3) at high reduced velocity, unsteady fluid force increases with void fraction.

Evidence for Josephson vortices in (BEDT-TTF)2Cu(NCS)2.

We present evidence for and study the properties of coreless Josephson vortices (parallel to the superconducting layers) in the organic superconductor (BEDT-TTF${)}_{2}$Cu(NCS${)}_{2}$, using ac susceptibility measurements in the mixed state. We observe (1) extremely weak-pinning restoring forces for flux motion parallel to the layers, due to the absence of the vortex normal core; (2) single vortex (noncollective) pinning, due to weak interactions between Josephson vortices; (3) the ``lock-in'' of the vortices parallel to the layers when the dc field is applied at an arbitrary angle; and (4) highly nonlinear response to the ac field h in the lock-in state, above a threshold of h\ensuremath{\sim}0.5 G. The behavior of tilted flux lines is dominated by the much stronger pinning and collective interactions of two-dimensional Abrikosov ``pancake'' vortices, and linear response is largely restored when the flux lines unlock from the layers. We measure the Josephson penetration depth to be ${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\perp}}}$(T=5 K)\ensuremath{\sim}200 \ensuremath{\mu}m, yielding a penetration depth anisotropy of \ensuremath{\gamma}=${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\perp}}}$/${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\parallel}}}$\ensuremath{\sim}160-350.

Vortex shedding from an oscillating circular cylinder in a uniform flow

In this study, the vortex shedding from a circular cylinder in forced oscillation in the direction of a uniform flow was investigated by visualizing water flows around it at Reynolds numbers of 260–2460. It was observed that the frequency of vortex shedding from the oscillating cylinder tends to be equal to n times the cylinder's oscillation frequency ( n = 0.5, 1, 2, 3,…), even if the oscillation frequency is smaller than the natural Karman vortex frequency. This tendency can be considered a sort of “lock-in” phenomenon, and its features vary with both oscillation amplitude and Reynolds number. It was also known that flows of vortex shedding wakes in the lock-in states can be classified into three typical patterns depending on the lock-in frequency ratio n ( n = 0.5, 1, 2, 3,…). At the lock-in states of n = 2, 3,…, a set of vortices are shed with shorter and longer periods during one cycle of cylinder oscillation. At the lock-in state of n = 1, a twin vortex street is formed; twin vortices are also formed at n = 0.5, but a Karman vortex street appears instead of the twin vortex street. When the vortex shedding is out of a lock-in state, the flow pattern of the wake becomes very complex. Although the instantaneous vortex shedding frequency varies with the change of relative velocity in one cycle of the cylinder oscillation, the rate of variation of the vortex shedding frequency is greater than that of the relative flow velocity. Even if the oscillation frequency is as small as about 10% of the Karman vortex frequency, the vortex shedding shows a tendency to deviate from the state of so-called quasi-steady vortex shedding.

Columnar-defect-induced resistivity minima and Bose glass scaling of linear dissipation inTl2Ba2CaCu2O8epitaxial films

The angular dependence of the flux flow resistivity [rho]([Theta],[ital T],[ital H]) in Tl[sub 2]Ba[sub 2]CaCu[sub 2]O[sub 8] is measured as the external field is brought into alignment with heavy-ion-irradiation-induced columnar defects. A flux lock-in state, manifested as a minimum in the [rho]([Theta],[ital T],[ital H]) data, evolves as the system is cooled deeper into the mixed state. This observation provides compelling evidence for non-zero line tension of vortices in this highly anisotropic superconductor. The temperature dependence of the flux flow resistivity at perfect alignment is consistent with Bose glass theory of vortex localization at columnar defects.

Vortex lock-in state in a layered superconductor.

We report clear evidence for a vortex ``lock-in'' state in the organic superconductor (BEDTTTF${)}_{2}$Cu(SCN${)}_{2}$, from ac susceptibility measurements with crossed ac and dc fields. A dc field applied parallel to the conducting planes causes a rapid decrease in the screening of the ac field. Identical behavior is initially observed for dc fields applied at an angle, but the screening recovers to nearly the zero-field value when the perpendicular field component exceeds a threshold. This indicates that vortices are locked between the layers below the threshold, and move freely along the planes. Above threshold, the vortices pierce the planes, and their motion is drastically inhibited.