1,670 research outputs found
Minimal data at a given point of space for solutions to certain geometric systems
We consider a geometrical system of equations for a three dimensional
Riemannian manifold. This system of equations has been constructed as to
include several physically interesting systems of equations, such as the
stationary Einstein vacuum field equations or harmonic maps coupled to gravity
in three dimensions. We give a characterization of its solutions in a
neighbourhood of a given point through sequences of symmetric trace free
tensors (referred to as `null data'). We show that the null data determine a
formal expansion of the solution and we obtain necessary and sufficient growth
estimates on the null data for the formal expansion to be absolutely convergent
in a neighbourhood of the given point. This provides a complete
characterization of all the solutions to the given system of equations around
that point.Comment: 26 pages, no figure
Degradation of Toluene and Trichloroethylene by Burkholderia cepacia G4 in Growth-Limited Fed-Batch Culture
Burkholderia (Pseudomonas) cepacia G4 was cultivated in a fed-batch bioreactor on either toluene or toluene plus trichloroethylene (TCE). The culture was allowed to reach a constant cell density under conditions in which the amount of toluene supplied equals the maintenance energy demand of the culture. Compared with toluene only, the presence of TCE at a toluene/TCE ratio of 2.3 caused a fourfold increase in the specific maintenance requirement for toluene from 22 to 94 nmol mg of cells (dry weight)-1 h-1. During a period of 3 weeks, approximately 65% of the incoming TCE was stably converted to unidentified products from which all three chlorine atoms were liberated. When toluene was subsequently omitted from the culture feed while TCE addition continued, mutants which were no longer able to grow on toluene or to degrade TCE appeared. These mutants were also unable to grow on phenol or m- or o-cresol but were still able to grow on catechol and benzoate. Plasmid analysis showed that the mutants had lost the plasmid involved in toluene monooxygenase formation (pTOM). Thus, although strain G4 is much less sensitive to TCE toxicity than methanotrophs, deleterious effects may still occur, namely, an increased maintenance energy demand in the presence of toluene and plasmid loss when no toluene is added.
The wave equation on axisymmetric stationary black hole backgrounds
Understanding the behaviour of linear waves on black hole backgrounds is a
central problem in general relativity, intimately connected with the nonlinear
stability of the black hole spacetimes themselves as solutions to the Einstein
equations--a major open question in the subject. Nonetheless, it is only very
recently that even the most basic boundedness and quantitative decay properties
of linear waves have been proven in a suitably general class of black hole
exterior spacetimes. This talk will review our current mathematical
understanding of waves on black hole backgrounds, beginning with the classical
boundedness theorem of Kay and Wald on exactly Schwarzschild exteriors and
ending with very recent boundedness and decay theorems (proven in collaboration
with Igor Rodnianski) on a wider class of spacetimes. This class of spacetimes
includes in particular slowly rotating Kerr spacetimes, but in the case of the
boundedness theorem is in fact much larger, encompassing general axisymmetric
stationary spacetimes whose geometry is sufficiently close to Schwarzschild and
whose Killing fields span the null generator of the horizon.Comment: 20 pages, 6 pages, to appear in the proceedings of the Spanish
Relativity Meeting, Salamanca 200
Apparent horizons in D-dimensional Robinson-Trautman spacetime
We derive the higher dimensional generalization of Penrose-Tod equation
describing apparent horizons in Robinson-Trautman spacetimes. New results
concerning the existence and uniqueness of its solutions in four dimensions are
proven. Namely, previous results of Tod are generalized to nonvanishing
cosmological constant.Comment: 4 pages, 1 figure, to appear in ERE 2008 conference proceedings, to
be published by AI
Accelerated expansion through interaction
Interactions between dark matter and dark energy with a given equation of
state are known to modify the cosmic dynamics. On the other hand, the strength
of these interactions is subject to strong observational constraints. Here we
discuss a model in which the transition from decelerated to accelerated
expansion of the Universe arises as a pure interaction phenomenon. Various
cosmological scenarios that describe a present stage of accelerated expansion,
like the LCDM model or a (generalized) Chaplygin gas, follow as special cases
for different interaction rates. This unifying view on the homogeneous and
isotropic background level is accompanied by a non-adiabatic perturbation
dynamics which can be seen as a consequence of a fluctuating interaction rate.Comment: 4 pages, to appear in the Proceedings of the Spanish Relativity
Meeting ERE2008 in Salamanca, September 200
Information geometry of asymptotically AdS black holes
We investigate thermodynamic geometries of two families of asymptotically
Anti-de Sitter black holes, i.e. the Reissner-Nordstr\"om Anti-de Sitter in
four dimensions and the BTZ black hole. It is found that the Anti-de Sitter
space renders the geometry nontrivial (c.f. the Reissner-Nordstr\"om black hole
in asymptotically flat background). The BTZ black hole's thermodynamic geometry
is trivial despite the fact that it is characterized by the (negative)
cosmological constant. As a matter of curiosity we compute thermodynamic
geometry of these black holes regarding the cosmological constant as a true
parameter but no physically significant results can be derived.Comment: Contribution to proceedings of ERE2008, 4 page
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