Equilibrium Configurations of Homogeneous Fluids in General Relativity

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference, accepted by MNRA

Are Orthogonal Separable Coordinates Really Classified?

We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new, algebraic geometric approach to the classification of orthogonal separable coordinates by studying the structure of this variety. We give an example where this approach reveals unexpected structure in the well known classification and pose a number of problems arising naturally in this context

Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity

Using a multi domain spectral method, we investigate systematically the general-relativistic model for axisymmetric uniformly rotating, homogeneous fluid bodies generalizing the analytically known Maclaurin and Schwarzschild solutions. Apart from the curves associated with these solutions and a further curve of configurations that rotate at the mass shedding limit, two more curves are found to border the corresponding two parameter set of solutions. One of them is a Newtonian lens shaped sequence bifurcating from the Maclaurin spheroid sequence, while the other one corresponds to highly relativistic bodies with an infinite central pressure. The properties of the configuration for which both the gravitational and the baryonic masses, moreover angular velocity, angular momentum as well as polar red shift obtain their maximal values are discussed in detail. In particular, by comparison with the static Schwarzschild solution, we obtain an increase of 34.25% in the gravitational mass. Moreover, we provide exemplarily a discussion of angular velocity and gravitational mass on the entire solution class.Comment: 4 pages, 4 figures, 1 table, submitted to A&A, corrected eq. for W, W' in 3.

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.org

Coronavirus-Pandemie: Die Feiertage und den Jahreswechsel für einen harten Lockdown nutzen : 7. Ad-hoc-Stellungnahme zr Coronavirus-Pandemie - 08.Dezember 2020

Die gegenwärtige Situation ist nach wie vor ernst und droht sich weiter zu verschärfen. Trotz des seit Anfang November in Deutschland geltenden Teil-Lockdowns sind die Infektionszahlen auf einem sehr hohen Niveau. Jeden Tag sterben mehrere Hundert Menschen. Die Krankenhäuser und insbesondere das medizinische Personal sind bereits jetzt an ihren Grenzen und die Gesundheitsämter überlastet. Um die Kontrolle über das Infektionsgeschehen zurückzuerlangen, empfiehlt die Nationale Akademie der Wissenschaften Leopoldina in der Ad-hoc-Stellungnahme „Coronavirus-Pandemie: Die Feiertage und den Jahreswechsel für einen harten Lockdown nutzen“ ein zweistufiges Vorgehen. Die Rahmenbedingungen ‒ Weihnachtsferien in Bildungseinrichtungen und eingeschränkter Betrieb in vielen Unternehmen und Behörden – bieten die Chance, in der Eindämmung der Pandemie ein großes Stück voranzukommen

Incorporating Neighborhood Reduction for the Solution of the Planar p-Median Problem

Two efficient neighbourhood reduction schemes are proposed for the solution of the p-Median problem on the plane. Their integration into a local search significantly reduces the run time with an insignificant deterioration in the quality of the solution. For completeness this fast local search is also embedded into one of the most powerful meta-heuristic algorithms recently developed for this continuous location problem. Excellent results for instances with up to 1060 demand points with various values of p are reported. Eight new best known solutions for ten instances of a large problem with 3,038 demand points and up to 500 facilities are also found

Human redundancy as safety measure in automation monitoring

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The present study addresses effects of human redundancy on automation monitoring performance. Fourty-six participants performed a multi-task, consisting of three sub-tasks which simulate basic demands of operators in a chemical plant. One of the tasks involved the monitoring of an automated process. Participants were randomly assigned to three groups: (1) “Non-Redundant”: participants worked on all tasks alone. (2) “Redundant”: participants were informed that a second crewmate would work in parallel on the monitoring task. (3) “Redundant-Feedback”: like the “redundant” condition with the additional information that crewmembers’ individual monitoring performance would be tracked and fed back. Results provide evidence of social loafing effects in monitoring performance. Participants in the “redundant” condition cross-checked the automation significantly less than participants in the other groups. Moreover they were more prone to miss automation failures which occurred surprisingly. The anticipation that individual performance will be tracked and fed back after the task in the “redundant-feedback” group reduced this effect. The results suggest that human redundancy does not necessarily constitute an effective measure for enhancing reliability of automation monitoring and that expected positive effects can at least partially be off-set by a sort of social-loafing effect

Bi-objective robust optimization

It is important, in practice, to find robust solutions to optimisation problems. This issue has been the subject of extensive research focusing on single-objective problems. Recently, researchers also acknowledged the need to find robust solutions to multi-objective problems and presented some first results on this topic. In this paper, we deal with bi-objective optimisation problems in which only one objective function is uncertain. The contribution of our paper is three-fold. Firstly, we introduce and analyse four different robustness concepts for bi-objective optimisation problems with one uncertain objective function, and we propose an approach for defining a meaningful robust Pareto front for these types of problems. Secondly, we develop an algorithm for computing robust solutions with respect to these four concepts for the case of discrete optimisation problems. This algorithm works for finite and for polyhedral uncertainty sets using a transformation to a multi-objective (deterministic) optimisation problem and the recently published concept of Pareto robust optimal solutions (Iancu & Trichakis, 2014). Finally, we apply our algorithm to two real-world examples, namely aircraft route guidance and the shipping of hazardous materials, illustrating the four robustness concepts and their solutions in practical applications