628 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 ÎŽ17O and ÎŽ18O, 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
Structure sensitivity of silver-catalyzed ethylene epoxidation
The influence of particle size (20-200 nm) of Ag/α-Al 2O 3 catalysts for epoxidation of ethylene to ethylene oxide (EO) under industrial conditions was investigated. Small silver particles up to 40 nm are predominantly monocrystalline and show a decreasing weight-normalized reaction rate with increasing particle size. Particles larger than 50 nm consist of multiple silver crystallites with a much smaller domain size between 25 and 30 nm. For these polycrystalline silver particles, the weight-normalized reaction rate is independent of particle size. The ethylene conversion rate normalized to the external surface area increases when the silver particles become larger. We attribute this to a specific role of the grain boundaries between silver crystallites in supplying oxygen atoms to the external surface. Oxygen is likely activated at defects of an otherwise low-reactivity silver surface (for oxygen adsorption) followed by diffusion along grain boundaries, dissolution in the bulk, and diffusion to the external surface, where oxygen atoms react with ethylene. The reaction rate normalized to the surface area of the first outer shell of crystallites making up silver particles is independent of size for polycrystalline particles. A higher reaction pressure benefits ethylene oxidation rate and EO selectivity due to a higher oxygen coverage. Adding chlorine further improves the EO selectivity through modification of the active surface. The same particle size dependences are observed at 1 bar and at 20 bar without and with chlorine. The main finding of our work is that for large enough particles the ethylene oxidation rate normalized to the silver weight is independent of size. In addition to the size-independent weight-based activity, the preference for larger particles in industrial catalysts can be attributed to the high silver loadings used to obtain larger silver particles. The resulting high coverage of the α-Al 2O 3 support with silver decreases undesired consecutive reactions of EO on its hydroxyl groups. </p
Structure sensitivity of silver-catalyzed ethylene epoxidation
The influence of particle size (20-200 nm) of Ag/α-Al 2O 3 catalysts for epoxidation of ethylene to ethylene oxide (EO) under industrial conditions was investigated. Small silver particles up to 40 nm are predominantly monocrystalline and show a decreasing weight-normalized reaction rate with increasing particle size. Particles larger than 50 nm consist of multiple silver crystallites with a much smaller domain size between 25 and 30 nm. For these polycrystalline silver particles, the weight-normalized reaction rate is independent of particle size. The ethylene conversion rate normalized to the external surface area increases when the silver particles become larger. We attribute this to a specific role of the grain boundaries between silver crystallites in supplying oxygen atoms to the external surface. Oxygen is likely activated at defects of an otherwise low-reactivity silver surface (for oxygen adsorption) followed by diffusion along grain boundaries, dissolution in the bulk, and diffusion to the external surface, where oxygen atoms react with ethylene. The reaction rate normalized to the surface area of the first outer shell of crystallites making up silver particles is independent of size for polycrystalline particles. A higher reaction pressure benefits ethylene oxidation rate and EO selectivity due to a higher oxygen coverage. Adding chlorine further improves the EO selectivity through modification of the active surface. The same particle size dependences are observed at 1 bar and at 20 bar without and with chlorine. The main finding of our work is that for large enough particles the ethylene oxidation rate normalized to the silver weight is independent of size. In addition to the size-independent weight-based activity, the preference for larger particles in industrial catalysts can be attributed to the high silver loadings used to obtain larger silver particles. The resulting high coverage of the α-Al 2O 3 support with silver decreases undesired consecutive reactions of EO on its hydroxyl groups. </p
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
Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
Symmetric hyperbolic systems of equations are explicitly constructed for a
general class of tensor fields by considering their structure as r-fold forms.
The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance
of the so-called "superenergy" tensors, which provide the necessary symmetric
positive matrices, is emphasized and made explicit. Thereby, a unified
treatment of many physical systems is achieved, as well as of the sometimes
called "higher order" systems. The characteristics of these symmetric
hyperbolic systems are always physical, and directly related to the null
directions of the superenergy tensor, which are in particular principal null
directions of the tensor field solutions. Generic energy estimates and
inequalities are presented too.Comment: 24 pages, no figure
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
The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence
We calculate the volumes of a large class of Einstein manifolds, namely
Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones
described by polynomial embedding relations in C^n. These volumes are important
because they allow us to extend and test the AdS/CFT correspondence. We use
these volumes to extend the central charge calculation of Gubser (1998) to the
generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These
volumes also allow one to quantize precisely the D-brane flux of the AdS
supergravity solution. We end by demonstrating a relationship between the
volumes of these Einstein spaces and the number of holomorphic polynomials
(which correspond to chiral primary operators in the field theory dual) on the
corresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde
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