Ensemble Density Functional Theory for Inhomogeneous Fractional Quantum Hall Systems

The fractional quantum Hall effect (FQHE) occurs at certain magnetic field strengths B*(n) in a two-dimensional electron gas of density n at strong magnetic fields perpendicular to the plane of the electron gas. At these magnetic fields strengths, the system is incompressible, i.e., there is a finite cost in energy for creating charge density fluctuations in the bulk, while the boundary of the electron gas has gapless modes of density waves. The bulk energy gap arises because of the strong electron-electron interactions. While there are very good models for infinite homogeneous systems and for the gapless excitations of the boundary of the electron gas, computational methods to accurately model finite, inhomogeneous systems with more then about ten electrons have not been available until very recently. We will here review an ensemble density functional approach to studying the ground state of large inhomogeneous spin polarized FQHE systems.Comment: 23 pages (revtex), 6 Postscript figures. To be published in Int. J. Quant. Chem. (invited talk at the 1996 Sanibel Symposium

Cosmic Mach Number as a Function of Overdensity and Galaxy Age

We carry out an extensive study of the cosmic Mach number (\mach) on scales of R=5, 10 and 20h^-1Mpc using an LCDM hydrodynamical simulation. We particularly put emphasis on the environmental dependence of \mach on overdensity, galaxy mass, and galaxy age. We start by discussing the difference in the resulting \mach according to different definitions of \mach and different methods of calculation. The simulated Mach numbers are slightly lower than the linear theory predictions even when a non-linear power spectrum was used in the calculation, reflecting the non-linear evolution in the simulation. We find that the observed \mach is higher than the simulated mean by more than 2-standard deviations, which suggests either that the Local Group is in a relatively low-density region or that the true value of \Omega_m is ~ 0.2, significantly lower than the simulated value of 0.37. We show from our simulation that the Mach number is a weakly decreasing function of overdensity. We also investigate the correlations between galaxy age, overdensity and \mach for two different samples of galaxies --- DWARFs and GIANTs. Older systems cluster in higher density regions with lower \mach, while younger ones tend to reside in lower density regions with larger \mach, as expected from the hierarchical structure formation scenario. However, for DWARFs, the correlation is weakened by the fact that some of the oldest DWARFs are left over in low-density regions during the structure formation history. For giant systems, one expects blue-selected samples to have higher \mach than red-selected ones. We briefly comment on the effect of the warm dark matter on the expected Mach number.Comment: 43 pages, including 15 figures. Accepted version in ApJ. Included correlation function of different samples of galaxies, and the cumulative number fraction distribution as a fcn. of overdensity. Reorganized figures and added some reference

Construction and Test of a Flux Modulation Superconducting Machine for Aircraft

International audienceThe increasing of drives towards More Electric Aircraft (MEA) or the development of electric propulsion aircraft calls for MW-class electrical machines with more compact and power dense designs. One way is to explore the use of superconducting materials to create a high magnetic field in order to reduce the mass of ferromagnetic components. This paper presents the construction and the test of a brushless axial flux superconducting machine. The brushless topology satisfies the aeronautics industry requirements in terms of maintenance, while the axial configuration ensures an optimal use of the anisotropic HTS tapes. The machine is classed as partially superconducting, only the inductor is made with superconducting materials. A special design concerning the use of a stationary cryostat is presented. This improvement reduces significantly the electromagnetic air-gap length. A 50kW prototype is manufactured with a minimal mass objective. The prototype constitutes a first step to a scale-up MW-class machine design

Spin-ensemble density-functional theory for inhomogeneous quantum Hall systems

We have developed an ensemble density-functional theory that includes spin degrees of freedom for non-uniform quantum Hall systems. We have applied this theory using a local-spin-density approximation to study the edge reconstruction of parabolically confined quantum dots. For a Zeeman splitting below a certain critical value, the edge of a completely polarized maximum density droplet reconstructs into a spin-unpolarized structure. For larger Zeeman splittings, the edge remains polarized and develops an exchange hole

The Age of the Oldest Stars in the Local Galactic Disk From Hipparcos Parallaxes of G and K Subgiants

We review the history of the discovery of field subgiant stars and their importance in the age dating of the Galactic disk. We use the cataloged data from the Hipparcos satellite in this latter capacity. Based on Hipparcos parallaxes accurate to 10% or better, the absolute magnitude of the lower envelope of the nearly horizontal subgiant sequence for field stars in the H-R diagram for B-V colors between 0.85 and 1.05 is measured to be M_V = 4.03 +/- 0.06. The age of the field stars in the solar neighborhood is found to be 7.9 +/- 0.7 Gyr by fitting the theoretical isochrones for [Fe/H] = +0.37 to the lower envelope of the Hipparcos subgiants. The same grid of isochrones yields ages, in turn, of 4.0 +/- 0.2 Gyr, 6.2 +/- 0.5 Gyr, and 7.5 to 10 Gyr for the old Galactic clusters M67, NGC188, and NGC6791. The ages of both the Galactic disk in the solar neighborhood and of NGC6791 are, nevertheless, likely between 3 and 5 Gyr younger than the oldest halo globular clusters, which have ages of 13.5 Gyr. The most significant results are (1) the supermetallicity of the oldest local disk stars, and (2) the large age difference between the most metal-poor component of the halo and the thick and thin disk in the solar neighborhood. These facts are undoubtedly related and pose again the problem of the proper scenario for the timing of events in the formation of the halo and the Galactic disk in the solar neighborhood. [Abstract Abridged]Comment: 44 pages, 12 Figures; accepted for publication in PASP; high resolution versions of Figures 1, 2, 6 and 9 available at http://bubba.ucdavis.edu/~lubin/Sandage

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Measurements of Anisotropy in the Cosmic Microwave Background Radiation at 0.5 Degree Angular Scales Near the Star Gamma Ursae Minoris

We present results from a four frequency observation of a 6 x 0.6 degree strip of the sky centered near the star Gamma Ursae Minoris during the fourth flight of the Millimeter-wave Anisotropy eXperiment (MAX). The observation was made with a 1.4 degree peak-to-peak sinusoidal chop in all bands. The FWHM beam sizes were 0.55 +/- 0.05 degrees at 3.5 cm-1 and 0.75 +/-0.05 degrees at 6, 9, and 14 cm-1. During this observation significant correlated structure was observed at 3.5, 6 and 9 cm-1 with amplitudes similar to those observed in the GUM region during the second and third flights of MAX. The frequency spectrum is consistent with CMB and inconsistent with thermal emission from interstellar dust. The extrapolated amplitudes of synchrotron and free-free emission are too small to account for the amplitude of the observed structure. If all of the structure is attributed to CMB anisotropy with a Gaussian autocorrelation function and a coherence angle of 25', then the most probable values of DeltaT/TCMB in the 3.5, 6, and 9 cm-1 bands are 4.3 (+2.7, -1.6) x 10-5, 2.8 (+4.3, -1.1) x 10-5, and 3.5 (+3.0, -1.6) x 10-5 (95% confidence upper and lower limits), respectively.Comment: 16 pages, postscrip

Measurements of Anisotropy in the Cosmic Microwave Background Radiation at Degree Angular Scales Near the Stars Sigma Hercules and Iota Draconis

We present results from two four-frequency observations centered near the stars Sigma Hercules and Iota Draconis during the fourth flight of the Millimeter-wave Anisotropy eXperiment (MAX). The observations were made of 6 x 0.6-degree strips of the sky with 1.4-degree peak to peak sinusoidal chop in all bands. The FWHM beam sizes were 0.55+/-0.05 degrees at 3.5 cm-1 and a 0.75+/-0.05 degrees at 6, 9, and 14 cm-1. Significant correlated structures were observed at 3.5, 6 and 9 cm-1. The spectra of these signals are inconsistent with thermal emission from known interstellar dust populations. The extrapolated amplitudes of synchrotron and free-free emission are too small to account for the amplitude of the observed structures. If the observed structures are attributed to CMB anisotropy with a Gaussian autocorrelation function and a coherence angle of 25', then the most probable values are DT/TCMB = (3.1 +1.7-1.3) x 10^-5 for the Sigma Hercules scan, and DT/TCMB = (3.3 +/- 1.1) x 10^-5 for the Iota Draconis scan (95% confidence upper and lower limits). Finally a comparison of all six MAX scans is presented.Comment: 13 pages, postscript file, 2 figure