Peshkov transducers of second sound

A system made up of a pair of Peshkov transducers situated at the opposite ends of a one-dimensional resonance cavity is investigated theoretically. Included are the dissipative effects of thermal diffusion and normal viscous slip through the superleak. Compared to the oscillating superleak transducer, there are two noteworthy differences: (1) The Peshkov transducer has more pronounced first-sound resonances at lower frequencies, complicating the interpretation. (2) Due to the separation of membrane and superleak, one can more easily reduce transducer dissipation, important in ³He and in ⁴He close to T.     

Dissipation in vibrating superleak second sound transducers

We have performed an experimental study of the generation and detection of second sound in⁴He using vibrating superleak second sound transducers. At temperatures well belowT and for low driving amplitudes, the magnitude of the generated second sound wave is proportional to the drive amplitude. However, nearT and for high drive amplitudes this is no longer the case—instead, the second sound amplitude saturates. In this regime we also find that overtones of the drive frequency are generated. Our results suggest that this behavior is due to critical velocity effects in the pores of the superleak in the generator transducer. This type of measurement may prove to be a useful way in which to study critical velocity effects in confined geometries.     

Photolithographic fabrication of high frequency second sound detectors

A photolithographic technique is described for the fabrication of superconducting thin films to detect high frequency second sound in liquid helium.     

Micro-tensile strength of sound primary second molar dentin

Although biomechanical properties of dentin are important factors to dentin bonding, as well as for understanding caries, cervical erosion/abfraction, and tooth fracture, limited information for primary teeth has been reported. This study evaluated the micro-tensile strength (MTS) of sound primary second molar dentin with an originally designed system that we have developed. Twenty-seven dumbbell-shaped specimens were prepared from eight teeth. The MTS of the dentin beneath the occlusal surface was measured and fractured dentin surfaces were observed using SEM. Data was analyzed using ANOVA subsequent to Fisher's PLSD at p < 0.05. The novel jig system used in this study allowed symmetric dumbbell-shaped and uniformly sized specimens. The mean (standard deviation) MTS of all the specimens was 38.2 (15.9) MPa. The mean MTS of the specimens sectioned from the central area (46.5 MPa) was significantly higher than those of the specimens that were sectioned from the most mesial (31.1 MPa) and distal (27.8 MPa) sides of the teeth. Sound primary second molar occlusal dentin showed regional variations in tensile strength. This might influence the prognosis of dental restorations.     

Oscillating superleak transducer of second sound: Amplitude and linewidth

Two oscillating superleak transducers, one serving as generator, the other as detector, of first and second sound, situated at opposite ends of a one-dimensional resonance cavity, are considered. Included in the analysis are the dissipative effects of normal viscous slip and thermal diffusion through the porous membrane. The calculated amplitude and linewidth of the receiver response, both close to and away from the membrane resonance, show good agreement with available experimental data.     

Instability of second sound under heat flow near the superfluid transition

In heat-carrying superfluids, second sounds become unstable when the difference between the superfluid velocity and the normal fluid velocity exceeds a critical value. We derive a nonlinear evolution equation of the phase of the complex order parameter in this unstable region near the superfluid transition. It indicates emergence of trains of soliton-like heat pulses, which will be nearly periodic in a weakly unstable regime and chaotic in a strongly unstable regime. Experimentally, this instability cannot be observed in usual one-dimensional geometries due to appearance of a normal fluid region at large heat currents. However, we predict that it can be realized in a cell with a constricted part.     

Proposal of holography with second sound in helium II

The possibility of holography with second sound waves in He II is investigated theoretically. The radiation pressure of the second sound deforms the liquid-gas interface and the resulting relief could serve as the hologram for the optical reconstruction. The necessary heat current densities are calculated. Inhomogeneities in He II that could be observed by second sound are: stationary heat currents, variations of concentration of the isotope He³, and possibly systems of vortex lines.     

Boundary conditions for second sound in superfluid 4He

Standing surface waves produced by second sound in superfluid ⁴He have been observed optically. A spectrum of 84 frequencies was obtained. The theoretical spectrum calculated by using the conventional boundary condition of zero heat transfer does not agree with the experimental spectrum. Good agreement is obtained by assuming nonzero heat transfer at the boundary. An empirical heat transfer coefficient is defined and calculated. The amplitudes of the surface waves are discussed and related to the heat transfer.Supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlischen Forschung.     

Shape analysis of pulsed second sound in He II

We have observed second sound in He II using a heat pulse method. At temperatures where well-developed second sound is observed, the entire pulse shape can be understood if heat sources and geometrical effects are properly taken into account.Work supported by the National Science Foundation under Grant DMR 72-02941 A04.     

Attenuation of second sound in bulk flowing He II

New measurements of second sound attenuation in bulk flowing He II are reported which extend to a region of higher Reynolds number. An expression for the attenuation explicitly containing the quantum vortex line density is developed which allows comparison with vortex line density data taken by other means. A bellows driven experimental apparatus is used to produce bulk flow velocities of 0 to 1 m/sec in a channel of 4.064 mm square internal cross section. Second sound pulses are produced by applying a square voltage pulse 200 s width and variable height to a strain gauge heater. The second sound pulses are detected with thin film sensors mounted 56 and 119 mm downstream. The velocity-dependent attenuation, measured as a function of bulk flow velocity at 1.5, 1.8, and 2.0 K, is compared with data from other researchers. The attenuation, and thus the vortex line density, appears to follow a gradual transition from laminar to turbulent behavior. Current theories do not account for the presence of quantized vortices in bulk flowing He II, where (v _n–v _s), and thus do not explain the observed second sound attentuation in this regime.     

Attenuation of second sound in He II under pressure

The propagation of second sound in He II has been studied as a function of temperature and pressure using a heat pulse technique. Considerable broadening of the pulses with decreasing temperature has been observed below 1.2 K over a range of pressures. Using an appropriate analysis, values of the velocity and coefficient of absorption of second sound have been obtained. The measurements extend to a lowest temperature of 0.75 K, below which severe attenuation precludes meaningful analysis. The results for the coefficient of absorption are compared with the theory of Khalatnikov and Chernikova.Work supported by the National Science Foundation under Grant DMR 72-02941 A04.Based in part on a thesis submitted by T. Worthington in partial fulfillment of the requirements for the Ph.D. degree at Wesleyan University.     

First and second sound in a weakly interacting dilute Bose gas

An explicit expression for the density response function in the hydrodynamic region has been given by Hohenberg and Martin, starting from the two-fluid equations of motion for a superfluid. We use their results to calculate the first and second sound resonances in a weakly interacting, dilute Bose-condensed gas. We only consider the intermediate temperature region, where the effect of the interactions may be treated as a small correction (nV ₀«k _B T). We use the transport coefficients obtained by Kirkpatrick and Dorfman. As expected for a gas, the second sound mode has appreciable weight in the density-fluctuation spectrum.     

Excitations and Their Temperature Dependence in Superfluid 4He Beyond the Roton

The temperature dependence of the dynamic structure factor S(Q,) for superfluid ⁴ He has been measured by inelastic neutron scattering for wave vectors between 2.3 and 2.6 Å ^–l. S(Q,) has two peaks: one sharp peak at low energies whose dispersion flattens out and whose strength decreases with increasing Q, and one broader peak at higher energies with a stronger dispersion. The first peak disappears gradually with increasing temperature, while only part of the second peak vanishes at T . This indicates the existence of a third broad contribution, related to atoms above the Bose condensate. The two-peak structure can be interpreted in terms of a Bose-condensate induced coupling of the two-particle spectrum to the one-particle spectrum. The overall temperature dependence is consistent with the density-quasiparticle picture.     

Virial theorem and the two molecule interaction potential

A method for determining the parameters of the two-molecule interaction potential is shown by the example of the Mie potential or the four-parameter Lennard-Jones potential (GLJ). The application of the virial theorem with respect to the Mie potential allows one to determine exponents at the intermolecular distance. The application of the theory of pair collisions for determination of the intermolecular repulsion potential is shown by the example of a number of substances. The statistic characteristic of gases that allows one to formulate the intermolecular attraction potential is found.     

Shape analysis of pulsed second sound in crystalline4He

We have observed that second-sound pulses in crystalline⁴He contain features corresponding to the input pulse power densityp(t) as well as to its time derivative, (t). By curve-fitting to an analytical expression for the entire response, values of the second-sound velocity and of the normal-process relaxation time _N have been obtained. The results for _N are in fair agreement with previous determinations. However, our values for the velocity lie systematically lower in a manner that can be qualitatively explained if the driving terms of the second-sound wave equation are properly taken into account. A new feature in our data is the emergence at low temperatures of a driving term with the time dependence ofp(t).Supported by the National Science Foundation.     

The Dynamic Structure Factor of 4He beyond the Roton Minimum

The dynamic structure factor S( , ) of ⁴ He is studied at zero temperature in the momentum region at and above the roton minimum by field-theoretical methods. The model is derived from the Gavoret-Nozières (GN) two particle propagator by introducing the concept of quasiparticles. In this way a connection between the field theory of GN and the phenomenological models of Zawadowski-Ruvalds-Solana (ZRS) type is obtained. An improved expression for the dynamic structure factor within ZRS-like models is found. Numerical results for S( , ) are presented for momentum and energy independent effective interactions between quasiparticles.     

Dynamics of the3He A-B interface in the velocity range of second sound

The movingA-B interface emits second sound which extracts the latent heat from the transition region. The amplitude is calculated for all interface velocities . A pronounced maximum is found if is close to the second sound velocity.     

Superleak transducers of second sound in3He-4He mixtures

In a recent second-sound experiment in a dilute³He-⁴He mixture, Church et al.¹¹ were able to understand most of their data with the theory by d'Humières, Launay, and Libchaber.⁸ However, significant discrepancies exist at lower frequencies. We show that diffusive currents across the superleak are responsible for this deviation. What is more, we are able to determine the diffusion coefficientD from the low-frequency data.The equations governing the performance of oscillating superleak transducers and Peshkov transducers are derived in a systematic manner. This pertains to pure He-II as well as to mixtures. Mistakes in earlier works on dissipative effects of superleak transducers are corrected. Explicit formulas are given for the amplitude and linewidth of second sound, and the experimentally relevant parameters are discussed.     

Excitations Beyond the Roton of Liquid 4He in Aerogel

The dynamic structure factor, S(Q, ), for wavevectors, 2.0Q3.6 Å ^–1 of liquid ⁴ He in 95% porous aerogel has been measured by inelastic neutron scattering methods. The aerogel was grown with deuterated materials and the multiple scattering involving the aerogel was negligible. S(Q, ) in the superfluid phase consists of a single peak plus broad intensity at higher energy , as in bulk superfluid ⁴ He. The single peak is identified with the phonon-roton excitation at higher Q. The weight in the peak, Z_Q , and the excitation energy dispersion curve, _Q , has the same basic wavevector dependence as in the bulk. The energy _Q is 2–3% below the bulk value at the end point and the peak is unobservable beyond Q=3 Å ^–1 within the present statistical precision. No peak is observed at T=2.3 K in normal ⁴ He suggesting, as in bulk ⁴ He, that the characteristic excitation at higher Q is associated with the superfluid phase.