Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.Comment: 36 pages, 15 figures, REVTEX documen

Discriminating Codes in Geometric Setups

We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset $S^* \subseteq S$ of minimum cardinality such that for each point $p_i \in P$, the subset $S_i^* \subseteq S^*$ covering $p_i$ satisfies $S_i^*\neq \emptyset$, and each pair $p_i,p_j \in P$, $i \neq j$, we have $S_i^* \neq S_j^*$. In the \emph{continuous version} of the problem, the solution set $S^*$ can be chosen freely among a (potentially infinite) class of allowed geometric objects. In the 1-dimensional case ($d=1$), the points in $P$ are placed on a horizontal line $L$, and the objects in $S$ are finite-length line segments aligned with $L$ (called intervals). We show that the discrete version of this problem is NP-complete. This is somewhat surprising as the continuous version is known to be polynomial-time solvable. Still, for the 1-dimensional discrete version, we design a polynomial-time $2$-approximation algorithm. We also design a PTAS for both discrete and continuous versions in one dimension, for the restriction where the intervals are all required to have the same length. We then study the 2-dimensional case ($d=2$) for axis-parallel unit square objects. We show that both continuous and discrete versions are NP-complete, and design polynomial-time approximation algorithms that produce $(16\cdot OPT+1)$-approximate and $(64\cdot OPT+1)$-approximate solutions respectively, using rounding of suitably defined integer linear programming problems. We show that the identifying code problem for axis-parallel unit square intersection graphs (in $d=2$) can be solved in the same manner as for the discrete version of the discriminating code problem for unit square objects

Galactic conformity and central/satellite quenching, from the satellite profiles of M* galaxies at 0.4 < z < 1.9 in the UKIDSS UDS

We explore the redshift evolution of a curious correlation between the star formation properties of central galaxies and their satellites (‘galactic conformity') at intermediate to high redshift (0.4 9.7, around central galaxies at the characteristic Schechter function mass, M ∼ M*. We fit the radial profiles of satellite number densities with simple power laws, finding slopes in the range −1.1 to −1.4 for mass-selected satellites, and −1.3 to −1.6 for passive satellites. We confirm the tendency for passive satellites to be preferentially located around passive central galaxies at 3σ significance and show that it exists to at least z ∼ 2. Meanwhile, the quenched fraction of satellites around star-forming galaxies is consistent with field galaxies of equal stellar masses. We find no convincing evidence for a redshift-dependent evolution of these trends. One simple interpretation of these results is that only passive central galaxies occupy an environment that is capable of independently shutting off star formation in satellite galaxies. By examining the satellites of higher stellar mass star-forming galaxies (log(M*/M⊙) > 11), we conclude that the origin of galactic conformity is unlikely to be exclusively due to the host dark matter halo mass. A halo-mass-independent correlation could be established by either formation bias or a more physical connection between central and satellite star formation histories. For the latter, we argue that a star formation (or active galactic nucleus) related outburst event from the central galaxy could establish a hot halo environment which is then capable of quenching both central and satellite galaxie

The mineralogy of newly formed dust in active galactic nuclei

The tori around active galactic nuclei (AGN) are potential formation sites for large amounts of dust, and they may help resolve the so-called dust budget crisis at high redshift. We investigate the dust composition in 53 of the 87 Palomar Green (PG) quasars showing the 9.7 micron silicate feature in emission. By simultaneously fitting the mid-infrared spectroscopic features and the underlying continuum, we estimate the mass fraction in various amorphous and crystalline dust species. We find that the dust consists predominantly of alumina and amorphous silicates, with a small fraction in crystalline form. The mean crystallinity is 8 +/- 6%, with more than half of the crystallinities greater than 5%, well above the upper limit determined for the Galaxy. Higher values of crystallinity are found for higher oxide fractions and for more luminous sources.Comment: 24 pages, 9 figures, accepted for publication in Planetary and Space Scienc

Number counts and clustering properties of bright Distant Red Galaxies in the UKIDSS Ultra Deep Survey Early Data Release

We describe the number counts and spatial distribution of 239 Distant Red Galaxies (DRGs), selected from the Early Data Release of the UKIDSS Ultra Deep Survey. The DRGs are identified by their very red infrared colours with (J-K)AB>1.3, selected over 0.62 sq degree to a 90% completeness limit of KAB~20.7. This is the first time a large sample of bright DRGs has been studied within a contiguous area, and we provide the first measurements of their number counts and clustering. The population shows strong angular clustering, intermediate between those of K-selected field galaxies and optical/infrared-selected Extremely Red Galaxies. Adopting the redshift distributions determined from other recent studies, we infer a high correlation length of r0~11 h-1 Mpc. Such strong clustering could imply that our galaxies are hosted by very massive dark matter halos, consistent with the progenitors of present-day L>L* elliptical galaxies.Comment: 5 pages, 4 figures, revised version accepted to MNRAS. Higher-resolution figures available from the authors on reques