Covariants of binary sextics and vector-valued Siegel modular forms of genus two

We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2

Status of center dominance in various center gauges

We review arguments for center dominance in center gauges where vortex locations are correctly identified. We introduce an appealing interpretation of the maximal center gauge, discuss problems with Gribov copies, and a cure to the problems through the direct Laplacian center gauge. We study correlations between direct and indirect Laplacian center gauges.Comment: Presented by S. Olejnik at the NATO Advanced Research Workshop "Confinement, Topology, and other Non-Perturbative Aspects of QCD", Jan. 21-27, 2002, Stara Lesna, Slovakia. 10 pages, 3 figures (8 EPS files), uses crckapb.st

Radius Dependent Luminosity Evolution of Blue Galaxies in GOODS-N

We examine the radius-luminosity (R-L) relation for blue galaxies in the Team Keck Redshift Survey (TKRS) of GOODS-N. We compare with a volume-limited, Sloan Digital Sky Survey sample and find that the R-L relation has evolved to lower surface brightness since z=1. Based on the detection limits of GOODS this can not be explained by incompleteness in low surface-brightness galaxies. Number density arguments rule out a pure radius evolution. It can be explained by a radius dependent decline in B-band luminosity with time. Assuming a linear shift in M_B with z, we use a maximum likelihood method to quantify the evolution. Under these assumptions, large (R_{1/2} > 5 kpc), and intermediate sized (3 < R_{1/2} < 5 kpc) galaxies, have experienced Delta M_B =1.53 (-0.10,+0.13) and 1.65 (-0.18, +0.08) magnitudes of dimming since z=1. A simple exponential decline in star formation with an e-folding time of 3 Gyr can result in this amount of dimming. Meanwhile, small galaxies, or some subset thereof, have experienced more evolution, 2.55 (+/- 0.38) magnitudes. This factor of ten decline in luminosity can be explained by sub-samples of starbursting dwarf systems that fade rapidly, coupled with a decline in burst strength or frequency. Samples of bursting, luminous, blue, compact galaxies at intermediate redshifts have been identified by various previous studies. If there has been some growth in galaxy size with time, these measurements are upper limits on luminosity fading.Comment: 34 Total pages, 15 Written pages, 19 pages of Data Table, 13 Figures, accepted for publication in Ap

Noise thermometry and electron thermometry of a sample-on-cantilever system below 1 Kelvin

We have used two types of thermometry to study thermal fluctuations in a microcantilever-based system below 1 K. We measured the temperature of a cantilever's macroscopic degree-of-freedom (via the Brownian motion of its lowest flexural mode) and its microscopic degrees-of-freedom (via the electron temperature of a metal sample mounted on the cantilever). We also measured both temperatures' response to a localized heat source. We find it possible to maintain thermal equilibrium between these two temperatures and a refrigerator down to at least 300 mK. These results are promising for ongoing experiments to probe quantum effects using micromechanical devices

Static SU(3) potentials for sources in various representations

The potentials and string tensions between static sources in a variety of representations (fundamental, 8, 6, 15-antisymmetric, 10, 27 and 15-symmetric) have been computed by measuring Wilson loops in pure gauge SU(3). The simulations have been done primarily on anisotropic lattices, using a tadpole improved action improved to O(a_{s}^4). A range of lattice spacings (0.43 fm, 0.25 fm and 0.11 fm) and volumes ($8^3\times 24$, $10^3 \times 24$, $16^3 \times 24$ and $18^3 \times 24$) has been used in an attempt to control discretization and finite volume effects. At intermediate distances, the results show approximate Casimir scaling. Finite lattice spacing effects dominate systematic error, and are particularly large for the representations with the largest string tensions.Comment: Version to appear in PR

The Merging History of Massive Black Holes

We investigate a hierarchical structure formation scenario describing the evolution of a Super Massive Black Holes (SMBHs) population. The seeds of the local SMBHs are assumed to be 'pregalactic' black holes, remnants of the first POPIII stars. As these pregalactic holes become incorporated through a series of mergers into larger and larger halos, they sink to the center owing to dynamical friction, accrete a fraction of the gas in the merger remnant to become supermassive, form a binary system, and eventually coalesce. A simple model in which the damage done to a stellar cusps by decaying BH pairs is cumulative is able to reproduce the observed scaling relation between galaxy luminosity and core size. An accretion model connecting quasar activity with major mergers and the observed BH mass-velocity dispersion correlation reproduces remarkably well the observed luminosity function of optically-selected quasars in the redshift range 1<z<5. We finally asses the potential observability of the gravitational wave background generated by the cosmic evolution of SMBH binaries by the planned space-born interferometer LISA.Comment: 4 pages, 2 figures, Contribute to "Multiwavelength Cosmology", Mykonos, Greece, June 17-20, 200