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

A new Tolman test of a cosmic distance duality relation at 21 cm

Under certain general conditions in an expanding universe, the luminosity distance (d_L) and angular diameter distance (d_A) are connected by the Etherington relation as d_L = d_A (1 + z)^2. The Tolman test suggests the use of objects of known surface brightness, to test this relation. In this letter, we propose the use of redshifted 21 cm signal from disk galaxies, where neutral hydrogen (HI) masses are seen to be almost linearly correlated with surface area, to conduct a new Tolman test. We construct simulated catalogs of galaxies, with the observed size-luminosity relation and realistic redshift evolution of HI mass functions, likely to be detected with the planned Square Kilometer Array (SKA). We demonstrate that these observations may soon provide the best implementation of the Tolman test to detect any violation of the Etherington relation.Comment: 4 pages, 2 figures, 1 table, v2: published versio

Weak Lensing Detection of Cl 1604+4304 at z = 0.90

We present a weak lensing analysis of the high-redshift cluster Cl 1604+4304. At z=0.90, this is the highest-redshift cluster yet detected with weak lensing. It is also one of a sample of high-redshift, optically-selected clusters whose X-ray temperatures are lower than expected based on their velocity dispersions. Both the gas temperature and galaxy velocity dispersion are proxies for its mass, which can be determined more directly by a lensing analysis. Modeling the cluster as a singular isothermal sphere, we find that the mass contained within projected radius R is 3.69+-1.47 * (R/500 kpc) 10^14 M_odot. This corresponds to an inferred velocity dispersion of 1004+-199 km/s, which agrees well with the measured velocity dispersion of 989+98-76 km/s (Gal & Lubin 2004). These numbers are higher than the 575+110-85 km/s inferred from Cl 1604+4304 X-ray temperature, however all three velocity dispersion estimates are consistent within ~ 1.9 sigma.Comment: Revised version accepted for publication in AJ (January 2005). 2 added figures (6 figures total

Galois covers of the open p-adic disc

This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduction in the abelian case, and give an arithmetic reformulation of the local Oort Conjecture concerning the liftability of cyclic covers of germs of curves.Comment: 19 pages; substantial organizational and expository changes; this is the final version corresponding to the official publication in Manuscripta Mathematica; abstract update

Keck spectroscopy of CLASS gravitational lenses

We present the optical spectra of four newly discovered gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope as part of a program to study galaxy-scale gravitational lenses. From our spectra we found the redshift of the background source in CLASS B0128+437 (z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123 (z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we also discovered that CLASS B0631+519 may have two lensing galaxies (z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single unidentified emission line from the lensing galaxy in CLASS B0128+437 and the lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA

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

A Study of Nine High-Redshift Clusters of Galaxies: IV. Photometry and Sp ectra of Clusters 1324+3011 and 1604+4321

New photometric and spectroscopic observations of galaxies in the directions of three distant clusters are presented as part of our on-going high-redshift cluster survey. The clusters are CL1324+3011 at z = 0.76, CL1604+4304 at z = 0.90, and CL1604+4321 at z = 0.92. The observed x-ray luminosities in these clusters are at least a factor of 3 smaller than those observed in clusters with similar velocity dispersions at z <= 0.4. These clusters contain a significant population of elliptical-like galaxies, although these galaxies are not nearly as dominant as in massive clusters at z <= 0.5. We also find a large population of blue cluster members. Defining an active galaxy as one in which the rest equivalent width of [OII] is greater than 15 Angstroms, the fraction of active cluster galaxies, within the central 1.0 Mpc, is 45%. In the field population, we find that 65% of the galaxies with redshifts between z = 0.40 and z = 0.85 are active, while the fraction is 79% for field galaxies at z > 0.85. The star formation rate normalized by the rest AB B-band magnitude, SFRN, increases as the redshift increases at a given evolving luminosity. At a given redshift, however, SFRN decreases linearly with increasing luminosity indicating a remarkable insensitivity of the star formation rate to the intrinsic luminosity of the galaxy over the range -18 >= ABB >= -22. Cluster galaxies in the central 1 Mpc regions exhibit depressed star formation rates. We are able to measure significant evolution in the B-band luminosity function over the range 0.1 <= z <= 1. The characteristic luminosity increases by a factor of 3 with increasing redshift over this range.Comment: 64 pages, 18 figures, accepted for publication in the Astronomical Journal on May 25, 2001. Scheduled to appear in Sept 2001 issu

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

A versatile, automated and high-throughput drug screening platform for zebrafish embryos

Zebrafish provide a unique opportunity for drug screening in living animals, with the fast developing, transparent embryos allowing for relatively high-throughput, microscopy-based screens. However, the limited availability of rapid, flexible imaging and analysis platforms has limited the use of zebrafish in drug screens. We have developed an easy-to-use, customisable automated screening procedure suitable for high-throughput phenotype-based screens of live zebrafish. We utilised the WiScan® Hermes High Content Imaging System to rapidly acquire brightfield and fluorescent images of embryos, and the WiSoft® Athena Zebrafish Application for analysis, which harnesses an Artificial Intelligence-driven algorithm to automatically detect fish in brightfield images, identify anatomical structures, partition the animal into regions, and exclusively select the desired side-oriented fish. Our initial validation combined structural analysis with fluorescence images to enumerate GFP-tagged haematopoietic stem and progenitor cells in the tails of embryos, which correlated with manual counts. We further validated this system to assess the effects of genetic mutations and x-ray irradiation in high content using a wide range of assays. Further, we performed simultaneous analysis of multiple cell types using dual fluorophores in high throughput. In summary, we demonstrate a broadly applicable and rapidly customisable platform for high-content screening in zebrafish