The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes.Comment: 18 pages Latex, 13 eps-figure

The 2+1 Kepler Problem and Its Quantization

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.Comment: 59 pages, LaTeX2e, 9 eps figure

Winding Solutions for the two Particle System in 2+1 Gravity

Using a PASCAL program to follow the evolution of two gravitating particles in 2+1 dimensions we find solutions in which the particles wind around one another indefinitely. As their center of mass moves `tachyonic' they form a Gott-pair. To avoid unphysical boundary conditions we consider a large but closed universe. After the particles have evolved for some time their momenta have grown very large. In this limit we quantize the model and find that both the relevant configuration variable and its conjugate momentum become discrete.Comment: 15 pages Latex, 4 eps figure

Panel Discussion - Management of Eurasian watermilfoil in the United States using native insects: State regulatory and management issues

While researchers have evaluated the potential of native insect herbivores to manage nonindigenous aquatic plant species such as Eurasian watermilfoil ( Myriophyllum spicatum L.), the practical matters of regulatory compliance and implementation have been neglected. A panel of aquatic nuisance species program managers from three state natural resource management agencies (Minnesota, Vermont and Washington) discussed their regulatory and policy concerns. In addition, one ecological consultant attempting to market one of the native insects to manage Eurasian watermilfoil added his perspective on the special challenges of distributing a native biological control agent for management of Eurasian watermilfoil

Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2+1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein Gordon equation.Comment: 58 pages, 3 eps figures, presentation of the classical theory improve

Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates

We find that the momentum conjugate to the relative distance between two gravitating particles in their center of mass frame is a hyperbolic angle. This fact strongly suggests that momentum space should be taken to be a hyperboloid. We investigate the effect of quantization on this curved momentum space. The coordinates are represented by non commuting, Hermitian operators on this hyperboloid. We also find that there is a smallest distance between the two particles of one half times the Planck length.Comment: 18 pages Latex, 2 eps figure

Broad Absorption Line Variability in Radio-Loud Quasars

We investigate C IV broad absorption line (BAL) variability within a sample of 46 radio-loud quasars (RLQs), selected from SDSS/FIRST data to include both core-dominated (39) and lobe-dominated (7) objects. The sample consists primarily of high-ionization BAL quasars, and a substantial fraction have large BAL velocities or equivalent widths; their radio luminosities and radio-loudness values span ~2.5 orders of magnitude. We have obtained 34 new Hobby-Eberly Telescope (HET) spectra of 28 BAL RLQs to compare to earlier SDSS data, and we also incorporate archival coverage (primarily dual-epoch SDSS) for a total set of 78 pairs of equivalent width measurements for 46 BAL RLQs, probing rest-frame timescales of ~80-6000 d (median 500 d). In general, only modest changes in the depths of segments of absorption troughs are observed, akin to those seen in prior studies of BAL RQQs. Also similar to previous findings for RQQs, the RLQs studied here are more likely to display BAL variability on longer rest-frame timescales. However, typical values of |Delta_EW| and |Delta_EW|/ are about 40+/-20% lower for BAL RLQs when compared with those of a timescale-matched sample of BAL RQQs. Optical continuum variability is of similar amplitude in BAL RLQs and BAL RQQs; for both RLQs and RQQs, continuum variability tends to be stronger on longer timescales. BAL variability in RLQs does not obviously depend upon their radio luminosities or radio-loudness values, but we do find tentative evidence for greater fractional BAL variability within lobe-dominated RLQs. Enhanced BAL variability within more edge-on (lobe-dominated) RLQs supports some geometrical dependence to the outflow structure.Comment: 27 pages, 16 figures, 6 tables, accepted to MNRAS, full Appendix A at http://www.macalester.edu/~bmille13/balrlqs.htm