Vortex rings and the superfluid λ-transition

A vortex-ring formulation of the₄He -transition provides a clear physical picture of the superfluid transition. The thermally excited rings are dipoles which orient in an applied flow field, and their net backflow cancels part of the applied flow, reducing the superfluid density. At the -point rings of infinite size drive the superfluid density to zero as a power law of the reduced temperature, with an exponent of 0.672. By fitting to the experimental superfluid amplitude the core energy of the smallest rings is found to be 6.1K at T and their diameter is 2.3 Å. It is proposed that these can be identified as the roton excitations of the Landau model. The vortex theory also yields new insights into topics such as boundary effects at a wall, finite-size effects, and the dynamics of the transition.     

Specific heat and superfluid density of bulk and confined4He near the λ-transition

The specific heat and superfluid density of liquid⁴He are calculated using a vortex-ring renormalization group theory, both for the bulk fluid and for confinement in a sphere of diameter L. In the finite geometry the superfluid density remains finite and universal at T, in agreement with Monte Carlo simulations and with finite-size scaling. The specific-heat peak is flattened in the finite geometry, and the onset temperature of the deviation from bulk behavior approaches T more closely as L is increased.     

Critical dynamics in the normal phase near the λ-transition in 3He-4He mixtures. I. Theoretical results

We study the asymmetric model of Siggia and Nelson for the critical dynamics of ³He-⁴He mixtures above T .The static effects resulting from the singular behavior of the susceptibilities are separated from genuine dynamic effects and treated in a consistent way. The calculated expressions for the thermal conductivity, thermal diffusion ratio and mass diffusion in the normal phase serve as a basis for a subsequent quantitative comparison with experiment. We use a field theoretical non-asymptotic renormalization procedure for our calculations. General relations resulting from the structure of the dynamical model for the mixtures are derived within this theoretical formulation.     

Critical dynamics in the normal phase near the λ-transition in 3He-4He mixtures. II. Comparison with experiment

We compare the experimental results for the temperature and concentration dependence of the thermal conductivity, the thermal diffusion ratio and the mass diffusion near the -transition with the results of a nonsymptotic renormalization group calculation of these transport coefficients. Satisfactory agreement is obtained for the first two coefficients, but discrepancies remain for the mass diffusion.     

Transition to Quantum Turbulence and the Propagation of Vortex Loops at Finite Temperatures

We performed numerical simulation of the transition to quantum turbulence and the propagation of vortex loops at finite temperatures in order to understand the experiments using vibrating wires in superfluid ⁴He by Yano et al. We injected vortex rings to a finite volume in order to simulate emission of vortices from the wire. When the injected vortices are dilute, they should decay by mutual friction. When they are dense, however, vortex tangle are generated through vortex reconnections and emit large vortex loops. The large vortex loops can travel a long distance before disappearing, which is much different from the dilute case. The numerical results are consistent with the experimental results.     

Mutual friction force in rotating helium II at low temperatures and near the λ-point

Mutual friction parameters in rotating He II are derived for the case of vortices kept at rest by external forces (surface pinning forces). They are different from those obtained in the theory of Hall and Vinen for the case of free vortices with the total momentum of the fluid being conserved. The difference increases if the temperature increases. In the critical region Hall and Vinen 's theory fails and the mutual friction problem is solved with the help of the phenomenological theory of superfluidity fitted to the critical behavior of known physical quantities. The theory is in satisfactory quantitative agreement with experimental data on the critical behavior of the mutual friction parameters B and B. The theory predicts a strong effect of the vortex pinning on the thermal counterflow in the critical region.     

Investigation of melting at the uranium γ phase by quantum and classical molecular dynamics methods

Melting at the high-temperature uranium γ phase at pressures up to 0.8 TPa and temperatures up to 2 × 10⁴ K is studied using quantum and classical molecular dynamics methods. The position of the equilibrium melting curve is estimated based on quantum calculations according to the Lindemann criterion. An interatomic-interaction potential is developed for classical molecular dynamics simulation of the properties of uranium in the γ phase and liquid state. The melting curve is calculated using the modified Z method. The curve is in agreement with the known experimental data at pressures below 0.1 TPa and the found estimate. The calculated melting curve is also compared with the Simon–Glatzel equation theoretical model.     

Vortex Formation and Annihilation in Rotating Superfluid 3He-B at Low Temperatures

In superfluid ³He-B the damping of vortex motion varies many orders of magnitude in the currently accessible temperature range from T _c to below 0.2?T _c. The large variation in the dynamics switches on sequentially different processes of vortex formation as a function of temperature. These can be examined in a smooth-walled rotating cylinder in the absence of surface pinning. We provide an overview of vortex formation in spin-up and of annihilation in spin-down measurements at temperatures below the hydrodynamic transition at 0.6?T _c where turbulence in the bulk volume becomes possible. Of central current interest are the very lowest temperatures at 0.2?T _c where the dynamic processes reflect on the properties of the T→0 limit.     

Attractive Vortex Interaction and the Intermediate-Mixed State of?Superconductors

The magnetic vortices in superconductors usually repel each other. Several cases are discussed when the vortex interaction has an attractive tail, and thus a minimum, leading to vortex clusters and chains. Decoration pictures then typically look like in the intermediate state of type-I superconductors, showing lamellae or islands of Meissner state or surrounded by Meissner state, but with the normal regions filled with Abrikosov vortices that are typical for type-II superconductors in the mixed state. Such intermediate-mixed state was observed and investigated in detail in pure Nb, TaN and other materials 40 years ago; last year it was possibly also observed in MgB₂, where it was called ??a totally new state?? and ascribed to the existence of two superconducting electron bands, one of type-I and one of type-II. The complicated electronic structure of MgB₂ and its consequences for superconductivity and vortices are discussed. It is shown that for the real superconductor MgB₂ which possesses a single transition temperature, the assumption of two independent order parameters with separate penetration depths and separate coherence lengths is unphysical.     

Mutual Friction in Superfluid 4He Near the λ-Line

We present experimental results for the thermal resistivity of superfluid ⁴He along several isobars between saturated vapor pressure and the melting pressure. The measurements are for the temperature range 1–T _c(q)/T <t<2×10^–5 and the heat-flux range 3<q<70 W/cm². Here t1–T/T , T is the transition temperature in the limit of zero q, and T _c is the transition temperature at finite q. The data suggest that the resistivity has an incipient singularity at T which can be described by the power law =(t/t ₀)^–(m+) where t ₀=(q/q ₀) ^x . However, the singularity is supplanted by the transition to a more highly dissipative phase at T _c(q)<T . The results suggest a mild dependence of m+ on the pressure P, but can be described quite well by m+=2.76, x=0.89, and q ₀=q _{0, 0}–q _{0, 1} P with q _{0, 0}=401Wcm^–2 and q _{0, 1}=–5.0Wcm^–2bars^–1. The results imply that the Gorter–Mellink mutual friction exponent m has a value close to 3.46 and is distinctly larger than the classical value m=3.     

Branching of the Falkner-Skan solutions for λ<0

Summary The Falkner-Skan equation f+ff+(1-f²)=0,f(0)=f(0), is discussed for <0. Two types of problems, one with f()=1 and another with f()=-1, are considered. For =0^- a close relation between these two types is found. For <-1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f-1. The numerical results indicate that the solution branches with f()=1 and those with f()=-1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for <-1, is presented.     

Paramagnetic Meissner Transitions in Pb Films and the?Vortex Compression Model

The magnetic flux exclusion known as Meissner effect resulting from a perfectly diamagnetic susceptibility ??=?1 is one of the defining features of type-I superconductivity. More recently some materials have been reported to undergo a transition to a paramagnetic state as they are cooled through their superconducting transition temperature (Svedlindh et?al. in Physica?C, pp.?162?C164, 1989; Li in Phys. Rep. 376:133?C223, 2003). This is known as the Paramagnetic Meissner Effect (PME). Here we report the observation of a transition from the Meissner state to a PME state in thin Pb films. We go on to show how simple modifications to the vortex compression model developed by Koshelev and Larkin (Phys. Rev.?B 52:13559?C13562, 1995) yield magnetization-vs-temperature curves in good qualitative agreement with the magnetization curves reported in the experiment.     

Critical properties of4He in aerogel near the λ-line

We measured the superfluid fraction _s/ and the isobaric thermal expansion coefficient _P of⁴He confined in an aerogel. Data were obtained near the -line along several isobars. Powerlaw fits to the results for _s/ as a function of tT/T_c–1 (T_c is the transition temperature) give a pressure—independent exponent =0.755 when a confluent singular term is included. Fits to the _P data of power laws yield the specific-heat exponents –0.6 and –1.0 above and below T_c respectively. When an analytic background term a×t is included in the fit, the pressure-independent value =–0.59 is permitted, but the amplitude ratio A/A is found to be near zero and the coefficient of the analytic term is large. The measured values for and or are inconsistent with hyperscaling in three dimensions.     

Studies of the critical velocity of superfluid4he in a 2 μm by 2 μm aperture in a thin foil at various frequencies

Measurements of the critical velocity behavior of oscillatory superfluid⁴He flow through a 2 m by 2 m square aperture in a 0.1 m thick titanium foil are being made at temperatures between 0.36 K and 2.1 K and at pressures of less than 0.4 bar at various frequencies between 50 Hz and 1000 Hz. The purpose of this work is to study a micron-size aperture for possible frequency-dependent deviations from the critical velocity behavior seen in submicron-size apertures. Preliminary results show a nearly linear decrease of critical velocity with increasing temperature that is similar to the temperature dependences seen in smaller apertures and that is approximately independent of frequency. However, at frequencies above 500 Hz, a region appears at the lowest temperatures in which supercritical behavior is dominated by large energy-loss events requiring a number of half-cycles for completion, a region that extends up to 1.1 K at 970 Hz.     

Transport properties in the superfluid phase of dilute3He-4He mixtures nearT λ

A cell for the simultaneous measurements of temperature and³He concentration gradients, induced by a heat currentQ across a fluid helium layer is described. This cell is operated over the temperature range 1.7T<2.5 K. Measurement of the anomalous boundary resistance R_b in superfluid⁴He(X(³He)2 ppb) near T for heat currents between 8 and 47 µW/cm² are described. The results for both the weakly divergent and the heat-dependent, more strongly divergent contributions to R _b are presented. The observed amplitude of the linear part is found to be larger than predictions by Onuki, by Ginzburg and Sobaynin and by Frank and Dohm, and also larger than recent data by Duncan and Ahlers (DA). These discrepancies are discussed in the light of the effective boundary area in the cell. The nonlinear part of R _b is consistent with the data by DA. It is found that the maximum observed R _b at the superfluid transition is independent ofQ. Analysis of the conductivity data of mixtures leads to the conjecture that R _b will decrease will the addition of³He. Our measurement of both the effective thermal diffusion ratiok _T ^* and of the thermal conductivity _eff over the range 10^–6<X<5×10^–2 show departures from the predictions by Khalatnikov. In particular forX<10^–3,k _T ^* is found to be a function of X, and _eff deviates from the predicted _effX ^–1. This last result confirms measurements with a previous cell. In the appendices, determinations and tabulations of auxiliary thermodynamic derivatives, such as (V/X)_T,P and (S/X)_T,P are presented.     

Measurements of the A ⇄ B transition in a magnetic field for superfluid3He near the polycritical point

Measurements of both AB and BA transitions have been made as a function of magnetic field up to 100 G at temperatures and pressures close to the polycritical point (PCP). Forms for the specific heat differenceC _A–C _B=C ₀ (P)–(P)(T _c –T)/T _c and for the magnetization differenceM _A–M _B=H(T _c –T)/T _c fit the data satisfactorily except very nearT _c , where some other mechanism, thought to be a free energy difference due to residual heat flows, tends to stabilize the A phase. The pressure of the PCP, taken to be that at whichC ₀ =0, is found to be 21.22±0.02 bar.Work supported by the U.S. Energy Research and Development Administration under contract number E(04-3)-34, P.A. 143.     

The Effect of the Pinning Center Size on the Vortex Pinning by?Embedded ZrO2 Nano-particles

The influence of pinning centers size on the superconducting properties was investigated. Through the addition of three batches of ZrO₂ nano-particles with mean size of D ₁=13 nm, D ₂=21 nm, and D ₃=85 nm, we have succeeded in incorporating effective artificial pinning centers within the YBCO matrix of the bulk superconductor. An enhancement in the flux pinning and an improvement in the critical current densities (transport critical current density J _ct and magnetic critical current density J _cm) were achieved. The results indicate that slight inclusions of ZrO₂ can greatly enhance the flux pinning capability of samples. Comparative analyses of the critical current densities and the resulting pinning force F _p for the three diameters have shown that pinning centers with finer size are much more efficient than those with a size larger than the coherence length ??.     

Numerical Analysis of the Jet‐Vortex Pattern of Flow in a Rectangular Trench

Numerical simulation of the vortex structure of threedimensional laminar flow in a rectangular trench of square cross section has been carried out on the basis of the finitevolume solution of steadystate Navier–Stokes equations.     

Refractive index measured by laser beam displacement at λ=1064 nm for solvents and deuterated solvents

The refractive index of a liquid is determined with 0.0003 accuracy from measurements of laser beam displacement by a liquid-filled standard 10 mm spectrophotometer cell. The apparatus and methods are described and the results of measurements at λ=1064 nm and T=25.0 °C for 30 solvents and deuterated solvents are presented. Several sources of potential systematic errors as large as 0.003 are identified, the most important being the curvature of the liquid cell windows. The measurements are analyzed accounting for the significant imperfections of the apparatus.