Density functional calculations for the structure of vortices in superfluid4He

The structure of a rectilinear vortex in superfluid ⁴ He at zero temperature is studied using a Density Functional method. The superfluid circulation is included via the Feynman-Onsager approximation. The energy and the density profile of a vortex are predicted for several values of the external pressure. The instability of the vortex line at negative pressure is discussed.     

The Vortex Lability In a Supersaturated Superfluid 3 He-4 He Mixture and the Quantum Phase-Separation Kinetics

The supersaturated superfluid ³ He-⁴ He mixture in the presence of quantized vortices is considered. A specific type of the lability against the vortex core expansion arises from concentrating ³ He atoms onto the vortex core. This affects significantly the region of the ³ He concentrations at which the rate of nucleating stable ³ He-concentrated phase can be noticeable. The most clear case of the vortex structure is a straight-line vortex with the uniformly distributed 3He atoms along the core. Such lability leads to some features in the thermal activation and quantum tunneling nucleation, resulting, in particular, in a relatively small supersaturation of about 1% which can be achieved. The critical value of the supersaturations corresponding to the vortex lability is dispersed because of the finite size of the ³ He-concentrated phase along the vortex core. We analyze this dispersion and its effect on the quantum separation in supersaturated ³ He-⁴ He mixtures. The value of the supersaturation conserves its order of the magnitude, changing only by a numerical factor. We also emphasize an important difference of the coefficient in the term responsible for the lability from the superfluid density s. The supersaturation observed in experiments lies within the range of the vortex lability and, probably, is connected with this lability.     

NMR Spectroscopy of the Double-Quantum Vortex in Superfluid 3He-A

The double-quantum vortex line with continuous (singularity-free) structure is the most common linear defect in rotating ³He-A. Its well-known experimental signature is a frequency-shifted satellite peak in the NMR spectrum. It arises from the absorption of spin wave excitations, which are localized bound states in the dipole-unlocked soft vortex core. In first approximation, the intensity of the satellite peak is proportional to the number of vortex lines. With increased measuring resolution we have found that the absorption contribution of individual vortex lines is not identical, but displays small variations, which depend on the non-uniform global orbital ^ l texture. We attribute the effect to small texture-dependent changes in the ^ l distribution in the soft core, which modify the attractive potential of the localized spin waves. This property can be used for studying the global order parameter texture in the rotating container.     

Dissipative Vortex Motion in Fermi Superfluids at Ultra Low Temperatures

We discuss in detail the recently proposed mechanism of dissipation and damping of the vortex motion in Fermi superfluids at temperatures much smaller than the critical one (Silaev, Phys. Rev. Lett., 108:045303, 2012). In the absence of the heat bath of normal component the kinetic energy of the superflow is transferred to the vortex core fermions due to the accelerated vortex motion. The resulting local heating of the vortex cores creates the heat flux carried by non-equilibrium quasiparticles emitted by moving vortices. Here we study this peculiar kinetics of localized quasiparticles beyond relaxation time approximation, calculate the decrement of Kelvin waves and the total power losses in Kelvin wave cascade realized by the turbulent motion of ³He-B.     

Intrinsic and extrinsic mechanisms of vortex formation in superfluid3He-B

We report on the first comprehensive measurements of critical superflow velocities in³He-B which allow different mechanisms of vortex formation to be identified. As a function of temperatureT and pressureP, we measure the critical angular velocity Ω_c(T, P) at which vortices start to form in slowly accelerating rotation in a cylindrical container filled with³He-B. Owing to the long coherence length ξ(T, P)∼10–100 nm, either trapped remanent vorticity or intrinsic nucleation may dominate vortex formation, depending on the roughness of the container wall and the presence of loaded traps. NMR measurement with a resolution of one single vortex line allows us to distinguish between different processes: (1) Three extrinsic mechanisms of vortex formation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit for intrinsic nucleation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a critical velocity v_c(T, P)=Ω_c(T, P), whereR is the radius of the container. We findv _c (T, P) to be related to the calculated intrinsic stability limitv _ch (T, P) of homogeneous superflow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.     

Vortices in Doped 4He Clusters

We investigate the properties of liquid ⁴ He_N clusters hosting a quantized vortex pinned to a dopant atom (Ne or Xe) or molecule (SF ₆ or HCN). A density functional theory is used to calculate the stationary configurations of pure and doped clusters, with and without vortex, up to N=1000. A liquid drop formula is then proposed that accurately describes the total energy of the complex and allows one to extrapolate the results to larger N values. We find that forming a dopant+vortex+ ⁴ He_N complex is energetically favored below a critical size N _cr , which strongly depends on the type of dopant.     

Quantum effects and the resistive transition in superconducting granular films

Static and dynamic properties of an array of Josephson junctions shunted by Ohmic resistors are discussed within a quantum Ginzburg-Landau theory. The phase diagram at zero temperature is calculated in mean field approximation. It shows that global superconductivity atT=0 is possible only if the normal-state film resistanceR _n is smaller than a critical valueR _n ^c which depends only logarithmically on the Josephson coupling and charging energies. The particular valueR _n ^c =6.5 k found in recent experiments on granular films is in reasonable agreement with estimates for these parameters. A phenomenological order parameter relaxation mechanism is introduced and the associated fluctuation-induced conductivity and diamagnetic susceptibility aboveT _c are determined. The resulting precursor conductivity does not explain the observed exponential decrease withR _n-R _n ^c of the residual resistance at low temperature. However, a very simple model for the resistance due to vortex flow, generalizing the classical Kosterlitz-Thousless picture, is in good agreement with the experimental data.     

Quantized Vortices Beside the Superfluid-Normal Interface

We consider a quantized vortex line parallel to the interface between the concentrated (c) and dilute (d) phases of a liquid ³ He- ⁴ He mixture. The vortex produces a groove-like distortion of the interface deflected into the d-phase. As a vortex approaches the interface, the bending flexure increases, reaching a maximum of 0.65m at a critical distance of 1.3m. Closer positions become absolutely unstable. Distortion of the interface leads to strong reduction of the threshold (6.3cm/s) for the Helmholtz-Kelvin tangential instability.     

The orientational phase transition at a vortex in3He-B

The orientational phase transition in the vicinity of a single vortex in³He-B is studied. It is the phase transition from a uniformn-texture withn parallel to the magnetic field and the vortex line to ann-texture that is nonuniform near the vortex. The problem of the instability of the the uniformn-texture is equivalent to the quantum mechanical two-dimensional problem of a bound state in a field with an attractive potential 1/r ². The orientational phase transition at a vortex array is also considered. In the limit of large vortex density the orientational phase transition transforms to the phase transition studied by Gongadze et al. The theoretical results are compared with the observed phase transition at a vortex in³He-B.     

Quantized vortex ring dynamics and the vortex core radius in He II

Using a newly developed time-of-flight technique, we have determined the temperature dependence of the vortex core radius in the range 0.35 K T 0.60 K by means of precise measurements of vortex ring dynamics. One of us (W.I.G.) has extended this work to a measurement of the pressure dependence of the vortex core radius. Our results are in agreement with the earlier work of Rayfield and Reif atT=0.28 K and zero pressure ¹ and with a model of the vortex core proposed by Glaberson, Strayer, and Donnelly. ^2,3 The precision of our measurements enabled us to observe differences in the dynamics of oppositely charged vortex rings in the same electric field configurations. We were able to quantitively account for these differences in a simple way by incorporating the frictional drag associated with the ion bound on the vortex core into the equations of motion. Our results suggest that the negative ion shape is not greatly distorted by its presence on the vortex core, nor is the negative ion strongly shielded by the vortex velocity field. Some of our results have been previously reported. ^4–6 Research supported in part by the National Science Foundation.During part of the period of this research, M. Steingart held an N.D.E.A. Title IV Fellowship.Alfred P. Sloan Foundation Fellow.     

Superfluid Phase Transition of 3He-4He Mixture Films Adsorbed on Alumina Powder

The superfluid phase transition of ³ He- ⁴ He mixture films adsorbed on 500 Å alumina powder has been studied for mixture films whose superfluid thickness is less than a monolayer. The transitions are found to be controlled by the Kosterlitz-Thouless critical line, but a strong broadening of the transition is observed as the ³ He concentration is increased. Analyzing the broadening in terms of a KT vortex-pair theory modified for the the finite powder size yields a vortex core parameter which increases nearly linearly with added ³ He. Also observed in these measurements is a temperature-dependent and ³ He-dependent depletion of the superfluid density at low temperatures, which is thought to arise from the high-frequency ripplon/third sound excitations of the film.     

Angular momentum of the fields of a few-mode fiber: I. A perturbed optical vortex

This paper presents the results of studies of the physical nature of the electrodynamic angular momentum of a stable CV ₊₁ ⁺ vortex in a few-mode fiber. It shows that the angular momentum of a CV ₊₁ ⁺ vortex can be conventionally divided into orbital and spin angular momenta. The longitudinal component of the fundamental HE ₁₁ ⁺ mode on the axis of the fiber has a pure screw dislocation with a topological charge of e=+1. The longitudinal component of a CV ₊₁ ⁺ vortex also has a pure screw dislocation on the axis of the fiber with a topological charge of e=+2. Therefore, perturbation of a CV ₊₁ ⁺ vortex by the field of the fundamental HE ₁₁ ⁺ mode removes the degeneracy of the pure screw dislocations of the longitudinal and transverse components of the field and breaks down the structural stability of the CV ₊₁ ⁺ vortex. As a result, an additional azimuthal flux of energy with an angular momentum opposite to that of the fundamental flux is induced. An analogy is drawn between the stream lines of a perturbed CV vortex and the stream lines of an inviscid liquid flowing around a rotating cylinder. Studies of the evolution of a CV vortex in a parabolic fiber show that they are structurally stable when acted on by the perturbing field of the HE ₁₁ ⁺ mode. However, perturbing a CV ₊₁ ⁺ 1 vortex of a stepped fiber with the field of the HE ₁₁ ⁺ mode destroys the structural stability of the vortex. It is found that the propagation of a circularly polarized CV vortex can be represented as a helical wavefront screwing into the medium of the fiber. The propagation of a linearly polarized vortex in free space is characterized by the translational displacement (without rotation) of a helical wavefront. Pis’ma Zh. Tekh. Fiz. 23, 74–81 (November 12, 1997)     

On unsteady airfoil-vortex interaction

Summary An experimental investigation on unsteady airfoil-vortex interaction has been done. The incident vortex, to interact with a downstream airfoil (NACA 0018, chord lengthc=20 mm), is generated by a square cylinder (side lengthD=20 mm). The square cylinder and airfoil are arranged in tandem and the spacing ratioL/D of the central distance to the side length is set a constant value of 4.625. The free stream Mach numbers are varied between 0.153 and 0.750, whereas the free stream Reynolds numbers (based on the side lengthD) are varied between 0.713×10⁵ and 3.44×10⁵.It is found that as the incident vortex approaches the airfoil, the circulation and scale are decreased until it arrives at a position near the leading edge of the airfoil. During this stage, some circulation of the incident vortex is transferred to the secondary vortex generated on the airfoil opposite to the surface that the incident vortex approaches. Thus, circulation and scale of the secondary vortex are increased. However, after the incident vortex goes further downstream, no circulation of the incident vortex is transferred to the secondary vortex effectively. As the result, both of the incident vortex and secondary vortex decay due to the viscous dissipation through the interaction with the boundary layer of the airfoil. The locus of the incident vortex is deviated in such a way that it goes away from the airfoil. The streamwise position of the secondary vortex is adjusted by the incident vortex, orvice versa, so as to meet each other just behind the trailing edge of the airfoil.With 8 Figures     

The mobility of ions trapped on vortex lines in pure4He and3He-4He solutions

We present measurements of the mobility of positive and negative ions trapped on vortex lines in pure⁴He and dilute³He-⁴He solutions over the temperature range 1.6>T>0.3 K. In pure⁴He below about 0.7 K, we observe several new effects not seen at higher temperatures and not easily explained with existing theories. Most notable are an enhanced broadening of the ion pulse and a rapid increase in the mobility with decreasing temperature. Measurements of the electric field dependence of the drift velocity in pure⁴He at low temperatures show a limiting velocity for sufficiently large fields. This behavior can be explained using a simple resonance theory. The inverse mobility data for solutions show sharp increases at certain critical temperatures, which are interpreted as being associated with the condensation of³He atoms onto the vortex cores. The dependence of the critical temperature on the bulk³He concentration is found to be in good agreement with a simple condensation theory. An extension of arguments used in this theory to lower temperatures leads to the picture of a³He-rich core growing with decreasing temperature, consistent with our lower temperature experimental data.Supported in part by a grant from the National Science Foundation.     

On “A note on the flow in a trailing vortex” by K. K. Tam

Summary In a recent paper in this Journal (7, 1973, 1–6) Tam suggested that early work by Batchelor on the decay of a laminar trailing vortex was in error. Tam's claim was that the decay of axial velocity defect at the center of the vortex went asx ⁻¹ instead ofx ⁻¹ logx. The purpose of this note is to refute Tam's claim. A further term in the asymptotic expansion for the circulation in the vortex is also obtained.     

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios ofU _m toU ₀ are ofO(10⁻¹),O(1) andO(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re=10², 10³ and 3×10³ are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Kármán vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method. This study was supported by the National Natural Science Foundation of China and the Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, as well as by the National Basic Research project “Nonlinear Science”.     

Recombination of two vortex filaments and jet noise

The recombination of two vortex filaments in a viscous incompressible fluid is analysed by the use of the vorticity equation. The analysis is confined to a local flow field, where the recombination process occurs, and is based on several assumptions, such as the conservation of the fluid impulse, spatial symmetry of the flow field etc. The flow field is expanded as polynomials of coordinates, and variations of their coefficients are obtained by the use of the vorticity equation. It is proved that the process is completed within a short time ofO (σ ²/Γ) and the viscous effect is essential;σ and Γ are the size and the circulation of the vortex filaments, respectively. This result is applied to predict the far-field noise of a circular jet by assuming that the main noise source is the recombination process in deformed vortex rings in the jet near field. The predicted noise intensity shows theU dependence and has an additional new factor (d/σ)⁶;U is the jet velocity andd is the average spacing between vortex rings.     

Investigation of quantized circulation in superfluid 3He-B

We have studied circulation in superfluid ³He-B with a vibrating wire. We find that the circulation quantum equals h/2m ₃ to within experimental error at several pressures. We have also measured circulation in rotating superfluid ³He-B, and have observed a precessional motion of a single vortex line. Finally, we have found the unexpected result that circulation around the wire does not affect the pair-breaking critical velocity.     

On continuum models of ductile fracture

Several fracture criteria are reviewed with respect to ductile fracture. It is suggested that both critical crack-tip displacement, 2V _c ^*, and critical fracture strain,∃ ^*, criteria may describe the fracture of a ductile second phase rod in a ductile matrix. As a first approximation, this is experimentally verified by observations of ductile stainless steel fibres fracturing in an age-hardened aluminium matrix. For 0.05, 0.10 and 0.20 volume fraction composites, the average fracture strains are calculated to be 1.15 as compared to a measured average of 0.93 while the average critical crack-tip displacement is calculated to be 0.50 mm as compared to an “observed” average of 0.40 mm. The statistical variation in the fracture strain was not sufficiently small to allow any choice between these proposed criteria. In fact, both the experimental and theoretical evidence point to the equivalency of these criteria as given by 2V _c ^*=π/^*∃^* where /^* is the microstructural unit in front of the crack over which the strain is greater than or equal to∃ ^*.     

Interplay Between Vorticity and Chirality Inside the Vortex Core in Chiral p-Wave Superconductors

The vortex core in chiral p-wave superconductors exhibits various properties owing to the interplay between the vorticity and chirality inside the vortex core. In the chiral p-wave superconductors, the site-selective nuclear spin-lattice relaxation rate T ^–1 ₁ is theoretically studied inside the vortex core within the framework of the quasiclassical theory of superconductivity. T ^–1 ₁ at the vortex center depends on the sense of the chirality relative to the sense of the magnetic field. The effect of a tilt of the magnetic field upon T ^–1 ₁ is investigated. The effect of the anisotropy in the superconducting gap and the Fermi surface is then investigated. The result is expected to be experimentally observed as a sign of the chiral pairing state in a superconducting material Sr₂RuO₄.