Generation of orthogonal boundary-fitted coordinate systems

A method is presented for computing orthogonal boundary fitted coordinate systems for geometries with coordinate distributions specified on all boundaries. The system which has found most extensive use in generating boundary fitted grids is made up of Poisson equations, of which the functions P and Q provide a means for controlling the spacing and density of grid lines in the coordinate system. While questions remain concerning the existence and uniqueness of orthogonal systems, the generating method presented adds to the available, useful techniques for constructing these systems

Gravitational Lensing and the Hubble Deep Field

We calculate the expected number of multiply-imaged galaxies in the Hubble Deep Field (HDF), using photometric redshift information for galaxies with m_I < 27 that were detected in all four HDF passbands. A comparison of these expectations with the observed number of strongly lensed galaxies constrains the current value of Omega_m-Omega_Lambda, where Omega_m is the mean mass density of the universe and Omega_Lambda is the normalized cosmological constant. Based on current estimates of the HDF luminosity function and associated uncertainties in individual parameters, our 95% confidence lower limit on Omega_m-Omega_Lambda ranges between -0.44, if there are no strongly lensed galaxies in the HDF, and -0.73, if there are two strongly lensed galaxies in the HDF. If the only lensed galaxy in the HDF is the one presently viable candidate, then, in a flat universe (Omega_m+Omega_Lambda=1), Omega_Lambda < 0.79 (95% C.L.). These limits are compatible with estimates based on high-redshift supernovae and with previous limits based on gravitational lensing.Comment: 4 pages (aipproc.sty), 2 figures. To appear in "After the dark ages: when galaxies were young," proceedings of the 9th Annual October Astrophysics Conference, eds. S. S. Holt & E. P. Smit

Positivity and topology in lattice gauge theory

The admissibility condition usually used to define the topological charge in lattice gauge theory is incompatible with a positive transfer matrix.Comment: 6 pages, revtex; revision has some clarifications and additional references, representing the final version to appear in Physical Revie

Fate of the false monopoles: induced vacuum decay

We study a gauge theory model where there is an intermediate symmetry breaking to a meta- stable vacuum that breaks a simple gauge group to a U (1) factor. Such models admit the existence of meta-stable magnetic monopoles, which we dub false monopoles. We prove the existence of these monopoles in the thin wall approximation. We determine the instantons for the collective coordinate that corresponds to the radius of the monopole wall and we calculate the semi-classical tunneling rate for the decay of these monopoles. The monopole decay consequently triggers the decay of the false vacuum. As the monopole mass is increased, we find an enhanced rate of decay of the false vacuum relative to the celebrated homogeneous tunneling rate due to Coleman [1].Comment: 10 pages, 4 figure

Quantum Fermion Hair

It is shown that the Dirac operator in the background of a magnetic %Reissner-Nordstr\"om black hole and a Euclidean vortex possesses normalizable zero modes in theories containing superconducting cosmic strings. One consequence of these zero modes is the presence of a fermion condensate around magnetically charged black holes which violates global quantum numbers.Comment: 16pp (harvmac (l)) and 2 figs.(not included

Diagrammatic perturbation theory and the pseudogap

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical fields. The model describes quasiparticles coupled to spin or charge fluctuations and is solved by a Monte Carlo sampling of the molecular field distributions. The non-perturbative solution is compared to various approximations based on diagrammatic perturbation theory. When the molecular field correlations are sufficiently weak, the diagrammatic calculations capture the qualitative aspects of the quasiparticle spectrum. For a range of model parameters near the magnetic boundary, we find that the quasiparticle spectrum is qualitatively different from that of a Fermi liquid in that it shows a double peak structure, and that the diagrammatic approximations we consider fail to reproduce, even qualitatively, the results of the Monte Carlo calculations. This suggests that the pseudogap induced by a coupling to antiferromagnetic fluctuations and the spin-splitting of the quasiparticle peak induced by a coupling to ferromagnetic spin-fluctuations lie beyond diagrammatic perturbation theory

A Characterization of the Brightness Oscillations During Thermonuclear Bursts From 4U 1636-536

The discovery of nearly coherent brightness oscillations during thermonuclear X-ray bursts from six neutron-star low-mass X-ray binaries has opened up a new way to study the propagation of thermonuclear burning, and may ultimately lead to greater understanding of thermonuclear propagation in other astrophysical contexts, such as in Type Ia supernovae. Here we report detailed analyses of the ~580 Hz brightness oscillations during bursts from 4U 1636-536. We investigate the bursts as a whole and, in more detail, the initial portions of the bursts. We analyze the ~580 Hz oscillations in the initial 0.75 seconds of the five bursts that were used in a previous search for a brightness oscillation at the expected ~290 Hz spin frequency, and find that if the same frequency model describes all five bursts there is insufficient data to require more than a constant frequency or, possibly, a frequency plus a frequency derivative. Therefore, although it is appropriate to use an arbitrarily complicated model of the ~580 Hz oscillations to generate a candidate waveform for the ~290 Hz oscillations, models with more than two parameters are not required by the data. For the bursts as a whole we show that the characteristics of the brightness oscillations vary greatly from burst to burst. We find, however, that in at least one of the bursts, and possibly in three of the four that have strong brightness oscillations throughout the burst, the oscillation frequency reaches a maximum several seconds into the burst and then decreases. This behavior has not been reported previously for burst brightness oscillations, and it poses a challenge to the standard burning layer expansion explanation for the frequency changes.Comment: 18 pages including three figures, uses aaspp4.sty, submitted to The Astrophysical Journal on April