531 research outputs found
Generic metrics and the mass endomorphism on spin three-manifolds
Let be a closed Riemannian spin manifold. The constant term in the
expansion of the Green function for the Dirac operator at a fixed point is called the mass endomorphism in associated to the metric due to
an analogy to the mass in the Yamabe problem. We show that the mass
endomorphism of a generic metric on a three-dimensional spin manifold is
nonzero. This implies a strict inequality which can be used to avoid
bubbling-off phenomena in conformal spin geometry.Comment: 8 page
Bunburra Rockhole: Exploring the geology of a new differentiated asteroid
Bunburra Rockhole is the first recovered meteorite of the Desert Fireball Network. We expanded a bulk chemical study of the Bunburra Rockhole meteorite to include major, minor and trace element analyses, as well as oxygen and chromium isotopes, in several different pieces of the meteorite. This was to determine the extent of chemical heterogeneity and constrain the origin of the meteorite. Minor and trace element analyses in all pieces are exactly on the basaltic eucrite trend. Major element analyses show a slight deviation from basaltic eucrite compositions, but not in any systematic pattern. New oxygen isotope analyses on 23 pieces of Bunburra Rockhole shows large variation in both δ17O and δ18O, and both are well outside the HED parent body fractionation line. We present the first Cr isotope results of this rock, which are also distinct from HEDs. Detailed computed tomographic scanning and back-scattered electron mapping do not indicate the presence of any other meteoritic contaminant (contamination is also unlikely based on trace element chemistry). We therefore conclude that Bunburra Rockhole represents a sample of a new differentiated asteroid, one that may have more variable oxygen isotopic compositions than 4 Vesta. The fact that Bunburra Rockhole chemistry falls on the eucrite trend perhaps suggests that multiple objects with basaltic crusts accreted in a similar region of the Solar System
Geometrization of metric boundary data for Einstein's equations
The principle part of Einstein equations in the harmonic gauge consists of a
constrained system of 10 curved space wave equations for the components of the
space-time metric. A well-posed initial boundary value problem based upon a new
formulation of constraint-preserving boundary conditions of the Sommerfeld type
has recently been established for such systems. In this paper these boundary
conditions are recast in a geometric form. This serves as a first step toward
their application to other metric formulations of Einstein's equations.Comment: Article to appear in Gen. Rel. Grav. volume in memory of Juergen
Ehler
Initial data for a head on collision of two Kerr-like black holes with close limit
We prove the existence of a family of initial data for the Einstein vacuum
equation which can be interpreted as the data for two Kerr-like black holes in
arbitrary location and with spin in arbitrary direction. This family of initial
data has the following properties: (i) When the mass parameter of one of them
is zero or when the distance between them goes to infinity, it reduces exactly
to the Kerr initial data. (ii) When the distance between them is zero, we
obtain exactly a Kerr initial data with mass and angular momentum equal to the
sum of the mass and angular momentum parameters of each of them. The initial
data depends smoothly on the distance, the mass and the angular momentum
parameters.Comment: 15 pages, no figures, Latex2
Conformal structures of static vacuum data
In the Cauchy problem for asymptotically flat vacuum data the solution-jets
along the cylinder at space-like infinity develop in general logarithmic
singularities at the critical sets at which the cylinder touches future/past
null infinity. The tendency of these singularities to spread along the null
generators of null infinity obstructs the development of a smooth conformal
structure at null infinity. For the solution-jets arising from time reflection
symmetric data to extend smoothly to the critical sets it is necessary that the
Cotton tensor of the initial three-metric h satisfies a certain conformally
invariant condition (*) at space-like infinity, it is sufficient that h be
asymptotically static at space-like infinity. The purpose of this article is to
characterize the gap between these conditions. We show that with the class of
metrics which satisfy condition (*) on the Cotton tensor and a certain
non-degeneracy requirement is associated a one-form with conformally
invariant differential . We provide two criteria: If is real
analytic, is closed, and one of it integrals satisfies a certain
equation then h is conformal to static data near space-like infinity. If h is
smooth, is asymptotically closed, and one of it integrals satisfies a
certain equation asymptotically then h is asymptotically conformal to static
data at space-like infinity.Comment: 68 pages, typos corrected, references and details adde
Observation of diffractive orbits in the spectrum of excited NO in a magnetic field
We investigate the experimental spectra of excited NO molecules in the
diamagnetic regime and develop a quantitative semiclassical framework to
account for the results. We show the dynamics can be interpreted in terms of
classical orbits provided that in addition to the geometric orbits, diffractive
effects are appropriately taken into account. We also show how individual
orbits can be extracted from the experimental signal and use this procedure to
reveal the first experimental manifestation of inelastic diffractive orbits.Comment: 4 fig
Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations
We present new many-parameter families of strongly and symmetric hyperbolic
formulations of Einstein's equations that include quite general algebraic and
live gauge conditions for the lapse. The first system that we present has 30
variables and incorporates an algebraic relationship between the lapse and the
determinant of the three metric that generalizes the densitized lapse
prescription. The second system has 34 variables and uses a family of live
gauges that generalizes the Bona-Masso slicing conditions. These systems have
free parameters even after imposing hyperbolicity and are expected to be useful
in 3D numerical evolutions. We discuss under what conditions there are no
superluminal characteristic speeds
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Fish passage hydrodynamics New Zealand context
New Zealand is home to 57 native freshwater fish species, of which a considerable number are diadromous, having to move between freshwater and saltwater at least once during their lifecycle. The economic utilisation of New Zealand rivers has largely been carried out without fish migration behaviour in mind, resulting in thousands of structures that prevent fish migration up- and downriver. Remediation of existing structures, especially culverts, and construction of new, more fish friendly, structures requires in-depth knowledge of the needs of the target fish species. In April 2018, the New Zealand Fish Passage Guidelines were released, providing a design framework to enable fish passage in new and existing structures. In support of the new guidance, our project aims to gain insight into the swimming behaviour and performance of inanga (Galaxias maculatus) under various hydraulic conditions, in particular when swimming upstream, which is not well understood. For this purpose, we are designing a new experimental setup in a 600 mm wide flume at the Water Engineering Laboratory at the University of Auckland. We will study hydrodynamics of fish passes with roughened surfaces, baffles and energy dissipators. We will evaluate sensor equipment used to enable flow and fish tracking, with the intention of tracking individual inanga at critical cross sections. This will allow us to study fish response to turbulence, boundary layers, resting zones and wetted margins. We aim to gain valuable insight into design methods and materials that best help inanga, and potentially other members of the family Galaxiidae, with their migration. Eventually, the project aims to provide guidelines suitable for retrofitting existing and building new structures
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