Accurate singular values and differential qd algorithms

Summary. We have discovered a new implementation of the qd algorithm that has a far wider domain of stability than Rutishauser's version. Our algorithm was developed from an examination of the {Cholesky~LR} transformation and can be adapted to parallel computation in stark contrast to traditional qd. Our algorithm also yields useful a posteriori upper and lower bounds on the smallest singular value of a bidiagonal matrix. The zero-shift bidiagonal QR of Demmel and Kahan computes the smallest singular values to maximal relative accuracy and the others to maximal absolute accuracy with little or no degradation in efficiency when compared with the LINPACK code. Our algorithm obtains maximal relative accuracy for all the singular values and runs at least four times faster than the LINPACK code. Received August 8, 1993/Revised version received May 26, 1993     

Oscillator strength of a two-dimensional D ion in magnetic fields

In the present paper we determine the oscillator strength of two-dimensional (2D) D⁻ ions under the influence of a static magnetic field. The results are important for the analysis of the optical transitions observed in semiconductor quantum wells. We have applied the ab initio procedure Hyperspherical Adiabatic Approach, based on the use of hyperspherical coordinates. This approach uses an adiabatic separation of the total wave function that allows accurate energies determination from molecular-like potential curves. The convergence is obtained in a systematic way by the inclusion of non-adiabatic couplings without the need of adjustable parameters.     

Production of a bose einstein condensate of metastable helium atoms

We recently observed a Bose-Einstein condensate in a dilute gas of ⁴He in the 2³S₁ metastable state. In this article, we describe the successive experimental steps which led to the Bose-Einstein transition at 4.7 μK: loading of a large number of atoms in a MOT, efficient transfer into a magnetic Ioffé-Pritchard trap, and optimization of the evaporative cooling ramp. Quantitative measurements are also given for the rates of elastic and inelastic collisions, both above and below the transition. Received 15 October 2001     

Letter: Bounds on the Deficit Solid Angle Parameter from Solar System Tests

We analyze the Mercury perihelion precession, the bending of starlight, and the radar echo delay in the Schwarzschild field modified by the presence of a solid angle deficit. By using the experimental data we obtain that the parameter characterizing the solid angle deficit is less than 10^–9, 10^–8 and 10^–9, respectively, on the length scales associated with such phenomena. In particular, if the solid angle deficit is generated by a global monopole, it is shown that within the length scales associated with such phenomena, the observational data available constrain the monopole energy scale to lower bounds which are in considerable agreement with the limits derived from grand unified theory and cosmology.     

Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA^1/2/k)^1/2. The structure of the T-shaped cavity has four degrees of freedom: L₀/L₁ (ratio between the lengths of the stem and bifurcated branches), H₁/L₁ (ratio between the thickness and length of the bifurcated branches), H₀/L₀ (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L₁/L₀) _○○ and (H₀/L₀)_○, the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.