475 research outputs found
On the Geroch-Traschen class of metrics
We compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea
On the completeness of impulsive gravitational wave space-times
We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form ,
where is a Riemannian manifold of arbitrary dimension and carries
the line element with the line
element of and the Dirac measure. We prove a completeness result
for such space-times with complete Riemannian part .Comment: 13 pages, minor changes suggested by the referee
Geodesics in spacetimes with expanding impulsive gravitational waves
We study geodesic motion in expanding spherical impulsive gravitational waves
propagating in a Minkowski background. Employing the continuous form of the
metric we find and examine a large family of geometrically preferred geodesics.
For the special class of axially symmetric spacetimes with the spherical
impulse generated by a snapping cosmic string we give a detailed physical
interpretation of the motion of test particles.Comment: 12 pages, Revtex, final versio
Species–area relationships in continuous vegetation : evidence from Palaearctic grasslands
Aim: Species-area relationships (SARs) are fundamental scaling laws in ecology although their shape is still disputed. At larger areas power laws best represent SARs. Yet, it remains unclear whether SARs follow other shapes at finer spatial grains in continuous vegetation. We asked which function describes SARs best at small grains and explored how sampling methodology or the environment influence SAR shape.
Location: Palaearctic grasslands and other non-forested habitats.
Taxa: Vascular plants, bryophytes and lichens.
Methods: We used the GrassPlot database, containing standardised vegetation-plot data from vascular plants, bryophytes, and lichens spanning a wide range of grassland types throughout the Palaearctic and including 2057 nested-plot series with at least seven grain sizes ranging from 1 cm2 to 1024 m². Using non-linear regression, we assessed the appropriateness of different SAR functions (power, power quadratic, power breakpoint, logarithmic, Michaelis-Menten). Based on AICc, we tested whether the ranking of functions differed among taxa, methodological settings, biomes or vegetation types.
Results: The power function was the most suitable function across the studied taxonomic groups. The superiority of this function increased from lichens to bryophytes to vascular plants to all three taxonomic groups together. The sampling method was highly influential as rooted-presence sampling decreased the performance of the power function. By contrast, biome and vegetation type had practically no influence on the superiority of the power law.
Main conclusions: We conclude that SARs of sessile organisms at smaller spatial grains are best approximated by a power function. This coincides with several other comprehensive studies of SARs at different grain sizes and for different taxa, thus supporting the general appropriateness of the power function for modelling species diversity over a wide range of grain sizes. The poor performance of the Michaelis-Menten function demonstrates that richness within plant communities generally does not approach any saturation, thus calling into question the concept of minimal area
Concurrent Design of Railway Vehicles by Simulation Model Reuse
This paper describes a concurrent design approach to railway vehicle design. Current railway vehicles use many different concepts that are combined into the final design concept. The design support for such systems is based on reusing components from previous design cases. The key part of the railway vehicle design concept is its simulation model. Therefore the support is based on support for reuse of previous simulation models. The simulation models of different railway component concepts are stored using the methodology from the EU CLOCKWORK project. The new concept usually combines stored components
Deep-time climate legacies affect origination rates of marine genera
Biodiversity dynamics are shaped by a complex interplay between current conditions and historic legacy. The interaction of short- and long-term climate change may mask the true relationship of evolutionary responses to climate change if not specifically accounted for. These paleoclimate interactions have been demonstrated for extinction risk and biodiversity change, but their importance for origination dynamics remains untested. Here, we show that origination probability in marine fossil genera is strongly affected by paleoclimate interactions. Overall, origination probability increases by 27.8% [95% CI (27.4%, 28.3%)] when a short-term cooling adds to a long-term cooling trend. This large effect is consistent through time and all studied groups. The mechanisms of the detected effect might be manifold but are likely connected to increased allopatric speciation with eustatic sea level drop caused by sustained global cooling. We tested this potential mechanism through which paleoclimate interactions can act on origination rates by additionally examining a proxy for habitat fragmentation. This proxy, continental fragmentation, has a similar effect on origination rates as paleoclimate interactions, supporting the importance of allopatric speciation through habitat fragmentation in the deep-time fossil record. The identified complex nature of paleoclimate interactions might explain contradictory conclusions on the relationship between temperature and origination in the previous literature. Our results highlight the need to account for complex interactions in evolutionary studies both between and among biotic and abiotic factors
Benthic foraminifera as bioindicators for assessing reef condition in Kāne‘ohe Bay, O‘ahu, Hawai‘
The wave equation on singular space-times
We prove local unique solvability of the wave equation for a large class of
weakly singular, locally bounded space-time metrics in a suitable space of
generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by
our results and some examples added. Conclusion more detailed. Version to
appear in Communications in Mathematical Physic
Aichelburg-Sexl boost of an isolated source in general relativity
A study of the Aichelburg--Sexl boost of the Schwarzschild field is described
in which the emphasis is placed on the field (curvature tensor) with the metric
playing a secondary role. This is motivated by a description of the Coulomb
field of a charged particle viewed by an observer whose speed relative to the
charge approaches the speed of light. Our approach is exemplified by carrying
out an Aichelburg-- Sexl type boost on the Weyl vacuum gravitational field due
to an isolated axially symmetric source. Detailed calculations of the boosts
transverse and parallel to the symmetry axis are given and the results, which
differ significantly, are discussed.Comment: 25 pages, LateX2
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