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 $M=N\times\mathbb{R}^2_1$, where $(N,h)$ is a Riemannian manifold of arbitrary dimension and $M$ carries the line element $ds^2=dh^2+ 2dudv+f(x)\delta(u)du^2$ with $dh^2$ the line element of $N$ and $\delta$ the Dirac measure. We prove a completeness result for such space-times $M$ with complete Riemannian part $N$.Comment: 13 pages, minor changes suggested by the referee

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

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

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

Isomorphisms of algebras of Colombeau generalized functions

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generalized functions on X to the ring of Colombeau generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page

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

Dispersal syndromes are poorly associated with climatic niche differences in the Azorean seed plants

Aim: Environmental niche tracking is linked to the species ability to disperse. While well investigated on large spatial scales, dispersal constraints also influence small-scale processes and may explain the difference between the potential and the realized niche of species at small scales. Here we test whether niche size and niche fill differ systematically according to dispersal syndrome within isolated oceanic islands. We expect that species with higher dispersal abilities (anemochorous or endozoochorous) will have a higher niche fill, despite their environmental niche size. Location: Azores archipelago. Taxon: Native seed plants. Methods: We combined a georeferenced database of the species distribution within the archipelago (Azorean Biodiversity Portal/GBIF) with an expert-based dispersal syndrome categorization and a high-resolution climatic grid (CIELO model). Using four climatic variables (Annual Mean Temperature, Mean Diurnal Range, Annual Precipitation, Precipitation Seasonality), we calculated a four-dimensional hypervolume to estimate the niche size of each species. Niche fill was quantified as the suitable climatic space of the island that was occupied by the focal species. Results: We found a significant relationship between dispersal syndromes and niche size, and also between dispersal syndromes and niche fill. Such relationships presented no phylogenetic signal. Endozoochorous species display higher niche fill compared to epizoochorous and hydrochorous species, and larger niches than anemochorous and epizoochorous. Differences among the remaining groups are not significant for either niche size or for niche fill. Main conclusions: The ability of a species to track its niche at small scales is not tightly related to its dispersal syndrome, although endozoochorous species track their niche more efficiently than the rest of groups. Despite being intuitively appealing, dispersal syndrome classifications might not be the most appropriate tools for understanding dispersal processes at small scales.info:eu-repo/semantics/acceptedVersio

Symmetries and geodesics in (anti-)de Sitter spacetimes with nonexpanding impulsive waves

We consider a class of exact solutions which represent nonexpanding impulsive waves in backgrounds with nonzero cosmological constant. Using a convenient 5-dimensional formalism it is shown that these spacetimes admit at least three global Killing vector fields. The same geometrical approach enables us to find all geodesics in a simple explicit form and describe the effect of impulsive waves on test particles. Timelike geodesics in the axially-symmetric Hotta-Tanaka spacetime are studied in detail. It is also demonstrated that for vanishing cosmological constant, the symmetries and geodesics reduce to those for well-known impulsive pp-waves.Comment: 16 pages, 3 figures, LaTeX 2e. To appear in Class. Quantum Gra

Remarks on the distributional Schwarzschild geometry

This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using generalized distributional geometry in the sense of Colombeau's (special) construction the nonlinearities are treated in a mathematically rigorous way. Moreover, generalized function techniques are used as a tool to give a unified discussion of various approaches taken in the literature so far; in particular we comment on geometrical issues