24,712 research outputs found
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 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 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
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 . We give an explicit expression for . 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
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
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 symplectic leaves,
where is associated with the Schwarzschild time. Quantization may then lead
to a discrete spectrum for the time operator.Comment: 10 page
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.'
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