A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves

The geodesic as well as the geodesic deviation equation for impulsive gravitational waves involve highly singular products of distributions (\theta\de, \theta^2\de, \de^2). A solution concept for these equations based on embedding the distributional metric into the Colombeau algebra of generalized functions is presented. Using a universal regularization procedure we prove existence and uniqueness results and calculate the distributional limits of these solutions explicitly. The obtained limits are regularization independent and display the physically expected behavior.Comment: RevTeX, 9 pages, final version (minor corrections, references added

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

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

Knowledge support of simulation model reuse

This describes the knowledge support for engineering design based on virtual modelling and simulation. These are the results of the EC Clockwork project. A typical and important step in the development of a simulation model is the phase of reusing. Virtual modelling and simulation often use the components of previous models. The usual problem is that the only remaining part of the previous simulation models is the model itself. However, a large amount of knowledge and intermediate models have been used, developed and then lost. A special methodology and special tools have therefore been developed on support of storing, retrieving and reusing the knowledge from previous simulation models. The knowledge support includes informal knowledge, formal knowledge and intermediate engineering models. This paper describes the overall methodology and tools, using the example of developing a simulation model of Trijoint, a new machine tool

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

Anthropogenic extinctions conceal widespread evolution of flightlessness in birds

Human-driven extinctions can affect our understanding of evolution, through the nonrandom loss of certain types of species. Here, we explore how knowledge of a major evolutionary transition—the evolution of flightlessness in birds—is biased by anthropogenic extinctions. Adding data on 581 known anthropogenic extinctions to the extant global avifauna increases the number of species by 5%, but quadruples the number of flightless species. The evolution of flightlessness in birds is a widespread phenomenon, occurring in more than half of bird orders and evolving independently at least 150 times. Thus, we estimate that this evolutionary transition occurred at a rate four times higher than it would appear based solely on extant species. Our analysis of preanthropogenic avian diversity shows how anthropogenic effects can conceal the frequency of major evolutionary transitions in life forms and highlights the fact that macroevolutionary studies with only small amounts of missing data can still be highly biased

Overexpression of melanoma inhibitory activity (MIA) enhances extravasation and metastasis of A-mel 3 melanoma cells in vivo

The secreted MIA protein is strongly expressed by advanced primary and metastatic melanomas but not in normal melanocytes. Previous studies have shown that MIA serum levels correlate with clinical tumour progression in melanoma patients. To provide direct evidence that MIA plays a role in metastasis of malignant melanomas, A-mel 3 hamster melanoma cells were transfected with sense- and antisense rhMIA cDNA and analysed subsequently for changes in their tumorigenic and metastatic potential. Enforced expression of MIA in A-mel 3 cells significantly increased their metastatic potential without affecting primary tumour growth, cell proliferation or apoptosis rate in hamsters, compared with control or antisense transfected cells. Additionally, MIA overexpressing transfectants showed a higher rate of both tumour cell invasion and extravasation. Cells transfected with MIA antisense generally exerted an opposite response. The above changes in function attributed to the expression of MIA may underlie the contribution of MIA to the malignant phenotype. © 2000 Cancer Research Campaig

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