The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow

We study an experimentally realizable system containing stable black hole-white hole acoustic horizons in toroidally trapped Bose-Einstein condensates - the quantum de Laval nozzle. We numerically obtain stationary flow configurations and assess their stability using Bogoliubov theory, finding both in hydrodynamic and non-hydrodynamic regimes there exist dynamically unstable regions associated with the creation of positive and negative energy quasiparticle pairs in analogy with the gravitational Hawking effect. The dynamical instability takes the form of a two mode squeezing interaction between resonant pairs of Bogoliubov modes. We study the evolution of dynamically unstable flows using the truncated Wigner method, which confirms the two mode squeezed state picture of the analogue Hawking effect for low winding number.Comment: 12 pages, 10 figure

An experimental investigation of leading-edge vortex augmentation by blowing

A wind tunnel test was conducted to determine the effects of over-the-wing blowing as a means of augmenting the leading-edge vortex flow of several pointed-tip, sharp-edged planforms. Arrow, delta, and diamond wings with leading-edge sweeps of 30 and 45 degrees were mounted on a body-of-revolution fuselage and tested in a low-speed wind tunnel at a Mach number of 0.2. Nozzle location data, pitch data, and flow-visualization pictures were obtained for a range of blowing rates. Results show pronounced increases in vortex lift due to the blowing

Thermal Analysis of As-received and Clinically Retrieved Copper-Nickel-Titanium Orthodontic Archwires

Objective: To compare as-received copper-nickel-titanium (CuNiTi) archwires to those used in patients by means of differential scanning calorimetry (DSC). Also, the thermal or phase properties of 27°C, 35°C, and 40°C CuNiTi archwires were studied to ascertain if their properties match those indicated by the manufacturer. Materials and Methods: Six wires of 27°C, 35°C, and 40°C CuNiTi were tested as-received, and six each of the 27°C and 35°C wires were examined after use in patients for an average of approximately 9 and 7 weeks, respectively. Segments of archwire were investigated by DSC over the temperature range from −100°C to 150°C at 10°C per minute. Results: There were no significant differences between as-received and clinically used 27°C and 35°C wires for all parameters (heating onset, endset, and enthalpy and cooling onset, endset, and enthalpy), except the 27°C wires exhibited a significant decrease in the heating enthalpy associated with the martensite-to-austenite transition after clinical use. The heating endsets (austenite finish temperatures) of the 27°C and 35°C wires were within 2°C of those claimed by the manufacturer, but the 40°C wires were found to be nearer to 36°C than 40°C. Conclusions: Clinical use of CuNiTi wires resulted in few differences when compared with as-received wires analyzed by DSC. Two temperature varieties of CuNiTi are reasonably within the parameters of those identified by the manufacturer

Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis

We investigate the properties of the stochastic Gross-Pitaevskii equation describing a condensate interacting with a stationary thermal cloud derived by Gardiner and coworkers. We find the appropriate Ehrenfest relations for the SGPE, including the effect of growth noise and projector terms arising from the energy cutoff. This is carried out in the high temperature regime appropriate for the SGPE, which simplifies the action of the projectors. The validity condition for neglecting the projector terms in the Ehrenfest relations is found to be more stringent than the usual condition of validity of the truncated Wigner method or classical field method -- which is that all modes are highly occupied. In addition it is required that the overlap of the nonlinear term with the lowest energy eigenstate of the non-condensate band is small. We show how to use the Ehrenfest relations along with the corrections generated by the projector to monitor dynamical artifacts arising from the cutoff. We also investigate the effect of using different bases to describe a harmonically trapped BEC at finite temperature by comparing the condensate fraction found using the plane wave and single particle bases. We show that the equilibrium properties are strongly dependent on the choice of basis. There is thus an optimal choice of plane wave basis for a given cut-off energy and we show that this basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.Comment: 23 pages, 5 figure

The Luminosity Functions of Old and Intermediate-Age Globular Clusters in NGC 3610

The WFPC2 Camera on board HST has been used to obtain high-resolution images of NGC 3610, a dynamically young elliptical galaxy. These observations supersede shorter, undithered HST observations where an intermediate-age population of globular clusters was first discovered. The new observations show the bimodal color distribution of globular clusters more clearly, with peaks at (V-I)o = 0.95 and 1.17. The luminosity function (LF) of the blue, metal-poor population of clusters in NGC 3610 turns over, consistent with a Gaussian distribution with a peak Mv ~= -7.0, similar to old globular-cluster populations in ellipticals. The red, metal-rich population of clusters has a LF that is more extended toward both the bright and faint ends, as expected for a cluster population of inter-mediate age. It is well fit by a power law with an exponent of alpha = -1.78 +-0.05, or -1.90+-0.07 when corrected for observational scatter. A Kolmogorov-Smirnov test confirms the significant difference between the LFs of the red and blue clusters, with a probability of less than 0.1% that they come from the same population. A comparison with the Fall & Zhang cluster disruption models shows marginal agreement with the observed LF, although there are differences in detail. In particular, there is no clear evidence of the predicted turnover at the faint end. A by-product of the analysis is the demonstration that, at any given metallicity, the peak of the LF should remain nearly constant from 1.5 Gyr to 12 Gyr, since the effect of the disruption of faint clusters is almost perfectly balanced by the fading of the clusters. This may help explain the apparent universality of the peak of the globular cluster luminosity function. (Abridged)Comment: 32 pages, LaTeX, 13 PS figures, 1 table; to appear in AJ (July 2002

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.

Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation

The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behaviour when quantisation of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.Comment: 24 pages, 15 figure