Edge Currents and Vertex Operators for Chern-Simons Gravity

We apply elementary canonical methods for the quantization of 2+1 dimensional gravity, where the dynamics is given by E. Witten's $ISO(2,1)$ Chern-Simons action. As in a previous work, our approach does not involve choice of gauge or clever manipulations of functional integrals. Instead, we just require the Gauss law constraint for gravity to be first class and also to be everywhere differentiable. When the spatial slice is a disc, the gravitational fields can either be unconstrained or constrained at the boundary of the disc. The unconstrained fields correspond to edge currents which carry a representation of the $ISO(2,1)$ Kac-Moody algebra. Unitary representations for such an algebra have been found using the method of induced representations. In the case of constrained fields, we can classify all possible boundary conditions. For several different boundary conditions, the field content of the theory reduces precisely to that of 1+1 dimensional gravity theories. We extend the above formalism to include sources. The sources take into account self- interactions. This is done by punching holes in the disc, and erecting an $ISO(2,1)$ Kac-Moody algebra on the boundary of each hole. If the hole is originally sourceless, a source can be created via the action of a vertex operator $V$. We give an explicit expression for $V$. We shall show that when actingComment: 42 pages, UAHEP 925, SU-4240-508, INFN-NA-IV-92/1

Dynamics of fingering convection II: The formation of thermohaline staircases

Regions of the ocean's thermocline unstable to salt fingering are often observed to host thermohaline staircases, stacks of deep well-mixed convective layers separated by thin stably-stratified interfaces. Decades after their discovery, however, their origin remains controversial. In this paper we use 3D direct numerical simulations to shed light on the problem. We study the evolution of an analogous double-diffusive system, starting from an initial statistically homogeneous fingering state and find that it spontaneously transforms into a layered state. By analysing our results in the light of the mean-field theory developed in Paper I, a clear picture of the sequence of events resulting in the staircase formation emerges. A collective instability of homogeneous fingering convection first excites a field of gravity waves, with a well-defined vertical wavelength. However, the waves saturate early through regular but localized breaking events, and are not directly responsible for the formation of the staircase. Meanwhile, slower-growing, horizontally invariant but vertically quasi-periodic gamma-modes are also excited and grow according to the gamma-instability mechanism. Our results suggest that the nonlinear interaction between these various mean-field modes of instability leads to the selection of one particular gamma-mode as the staircase progenitor. Upon reaching a critical amplitude, this progenitor overturns into a fully-formed staircase. We conclude by extending the results of our simulations to real oceanic parameter values, and find that the progenitor gamma-mode is expected to grow on a timescale of a few hours, and leads to the formation of a thermohaline staircase in about one day with an initial spacing of the order of one to two metres.Comment: 18 pages, 9 figures, associated mpeg file at http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF

Variable Cycle Engine Technology Program Planning and Definition Study

The variable stream control engine, VSCE-502B, was selected as the base engine, with the inverted flow engine concept selected as a backup. Critical component technologies were identified, and technology programs were formulated. Several engine configurations were defined on a preliminary basis to serve as demonstration vehicles for the various technologies. The different configurations present compromises in cost, technical risk, and technology return. Plans for possible variably cycle engine technology programs were formulated by synthesizing the technology requirements with the different demonstrator configurations

A Study of the Dynamics of Dust from the Kuiper Belt: Spatial Distribution and Spectral Energy Distribution

The dust produced in the Kuiper Belt (KB) spreads throughout the Solar System forming a dust disk. We numerically model the orbital evolution of KB dust and estimate its equilibrium spatial distribution and its brightness and spectral energy distributions (SED), assuming greybody absorption and emission by the dust grains. We show that the planets modify the KB disk SED, so potentially we can infer the presence of planets in spatially unresolved debris disks by studying the shape of their SEDs. We point out that there are inherent uncertainties in the prediction of structure in the dust disk, owing to the chaotic dynamics of dust orbital evolution imposed by resonant gravitational perturbations of the planets.Comment: 19 pages, 14 figures in jpg, accepted to A

Noncommutative BTZ Black Hole and Discrete Time

We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to $R\times S^1$ symplectic leaves, where $R$ is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.Comment: 10 page

Regarding the Accretion of 2003 VB12 (Sedna) and Like Bodies in Distant Heliocentric Orbits

Recently, Brown et al. (2004) reported the exciting discovery of an ~800 km radius object, (90377) Sedna, on a distant, eccentric orbit centered at ~490 AU from the Sun. Here we undertake a first look exploring the feasibility of accreting this object and its possible cohorts between 75 AU (Sedna's perihelion distance) and 500 AU (Sedna's semi-major axis distance) from the Sun. We find such accretion possible in a small fraction of the age of the solar system, if such objects were initially on nearly circular orbits in this region, and if the solar nebula extended outward to distances far beyond the Kuiper Belt. If Sedna did form in situ, it is likely to be accompanied by a cohort of other large bodies in this region of the solar system.Comment: 06 pages, plus 2 tables and 2 figure

The Chern-Simons Source as a Conformal Family and Its Vertex Operators

In a previous work, a straightforward canonical approach to the source-free quantum Chern-Simons dynamics was developed. It makes use of neither gauge conditions nor functional integrals and needs only ideas known from QCD and quantum gravity. It gives Witten's conformal edge states in a simple way when the spatial slice is a disc. Here we extend the formalism by including sources as well. The quantum states of a source with a fixed spatial location are shown to be those of a conformal family, a result also discovered first by Witten. The internal states of a source are not thus associated with just a single ray of a Hilbert space. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. We also argue in favor of a similar nonabelian result. The spin-statistics theorem is established for Chern-Simons dynamics even though the sources are not described by relativistic quantum fields. The proof employs geometrical methods which we find are strikingly transparent and pleasing. It is based on the research of European physicists about ``fields localized on cones.'