Sector Models - A Toolkit for Teaching General Relativity. Part 1: Curved Spaces and Spacetimes

Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. For online teaching materials, see http://www.spacetimetravel.org . ----- F\"ur die Vermittlung der Allgemeinen Relativit\"atstheorie in der Schule, im Grund- oder im Nebenfachstudium besteht das Anliegen, eine fachlich befriedigende Darstellung zu geben, die nicht mehr als Schulmathematik voraussetzt. Wir stellen in diesem Beitrag einen solchen Zugang vor. Das zentrale Werkzeug unserer Einf\"uhrung sind sogenannte Sektormodelle, die gekr\"ummte R\"aume im Sinne des Regge-Kalk\"uls durch eine Zerlegung in kleine, ungekr\"ummte Sektoren beschreiben, \"ahnlich der Triangulierung einer gekr\"ummten Fl\"ache. Wir schildern einen Workshop f\"ur Sch\"uler/innen und Studierende, in dem gekr\"ummte R\"aume anhand von Sektormodellen Schwarzer L\"ocher eingef\"uhrt werden. Wir beschreiben ferner die Erweiterung auf Sektormodelle gekr\"ummter Raumzeiten. Raumzeitliche Sektormodelle setzen Grundkenntnisse der Speziellen Relativit\"atstheorie voraus. Online-Materialien unter http://www.tempolimit-lichtgeschwindigkeit.de .Comment: bilingual: English version 18 pages, 9 figures, for associated movies see http://www.spacetimetravel.org/sectormodels1/sectormodels1.html. German version 19 pages, 9 figures, for associated movies see http://www.tempolimit-lichtgeschwindigkeit.de/sectormodels1/sectormodels1.htm

Precision mass determinations with the electric mass filter

Mass determinations of medium weight elements with electric mass filter, and mass ratios of xenon isotope

Internal rotation of subdwarf B stars: limiting cases and asteroseismological consequences

Observations of the rotation rates of horizontal branch (HB) stars show puzzling systematics. In particular, cooler HB stars often show rapid rotation (with velocities in excess of 10 km/s), while hotter HB stars typically show much smaller rotation velocities. Simple models of angular momentum evolution of stars from the main sequence through the red giant branch fail to explain these effects. In general, evolutionary models in all cases preserve a rapidly rotating core. The observed angular velocities of HB stars require that some of the angular momentum stored in the core reaches the surface. To test the idea that HB stars contain such a core, one can appeal to detailed computations of trace element abundences and rotational mixing. However, a more direct probe is available to test these limiting cases of angular momentum evolution. Some of the hottest horizontal branch stars are members of the pulsating sdB class. They frequently show rich pulsation spectra characteristic of nonradially pulsating stars. Thus their pulsations probe the internal rotation of these stars, and should show the effects of rapid rotation in their cores. Using models of sdB stars that include angular momentum evolution, we explore this possibility and show that some of the sdB pulsators may indeed have rapidly rotating cores.Comment: accepted for publication in The Astrophysical Journa

Diurnal and annual variations of meteor rates at the arctic circle

Meteors are an important source for (a) the metal atoms of the upper atmosphere metal layers and (b) for condensation nuclei, the existence of which are a prerequisite for the formation of noctilucent cloud particles in the polar mesopause region. For a better understanding of these phenomena, it would be helpful to know accurately the annual and diurnal variations of meteor rates. So far, these rates have been little studied at polar latitudes. Therefore we have used the 33 MHz meteor radar of the ALOMAR observatory at 69&deg; N to measure the meteor rates at this location for two full annual cycles. This site, being within 3&deg; of the Arctic circle, offers in addition an interesting capability: The axis of its antenna field points (almost) towards the North ecliptic pole once each day of the year. In this particular viewing direction, the radar monitors the meteoroid influx from (almost) the entire ecliptic Northern hemisphere. <P style='line-height: 20px;'> We report on the observed diurnal variations (averaged over one month) of meteor rates and their significant alterations throughout the year. The ratio of maximum over minimum meteor rates throughout one diurnal cycle is in January and February about 5, from April through December 2.3&plusmn;0.3. If compared with similar measurements at mid-latitudes, our expectation, that the amplitude of the diurnal variation is to decrease towards the North pole, is not really borne out. <P style='line-height: 20px;'> Observations with the antenna axis pointing towards the North ecliptic pole showed that the rate of deposition of meteoric dust is substantially larger during the Arctic NLC season than the annual mean deposition rate. The daylight meteor showers of the Arietids, Zeta Perseids, and Beta Taurids supposedly contribute considerably to the June maximum of meteor rates. We note, though, that with the radar antenna pointing as described above, all three meteor radiants are close to the local horizon but all three radiants were detected

Noctilucent clouds and the mesospheric water vapour: The past decade

The topic of this paper is the sensitivity of the brightness of noctilucent clouds (NLC) on the ambient water vapour mixing ratio f(H2O). Firstly, we use state-of-the-art models of NLC layer formation to predict NLC brightness changes in response to changes in the 80km mixing ratio f(H2O) for the two cases of ground-based 532nm lidar observations at 69° N and for hemispheric satellite SBUV observations at 252nm wavelength. In this study, we include a re-evaluation of the sensitivity of NLC brightness to changes in solar Lyman α flux. Secondly, we review observations of episodic changes in f(H2O) and those in NLC brightness, the former being available since 1992, the latter since 1979. To this review, we add a new series of observations of f(H2O), performed in the Arctic summer at the ALOMAR observatory. The episodic change exhibited by the Arctic summer means of f(H2O) turns out to be quite different from all those derived from annual means of f(H2O). The latter indicate that since 1996 a significant reduction of annually averaged upper mesospheric water vapour has occurred at low, mid, and high latitudes. These decreases of f(H2O) have been observed over the same time period in which a slow increase of SBUV NLC albedo has occurred. From this scenario and additional arguments we conclude that the cause for the observed long-term increase in NLC albedo remains to be identified. We close with comments on the very different character of decadal variations in NLC brightness and occurrence rate

Systematic Two-band Model Calculations of the GMR Effect with Metallic and Nonmetallic Spacers and with Impurities

By an accurate Green's function method we calculate conductances and the corresponding Giant Magneto-Resistance effects (GMR) of two metallic ferromagnetic films separated by different spacers, metallic and non-metallic ones, in a simplified model on a sc lattice, in CPP and CIP geometries (i.e. current perpendicular or parallel to the planes), without impurities, or with interface- or bulk impurities. The electronic structure of the systems is approximated by two hybridized orbitals per atom, to mimic s-bands and d-bands and their hybridization. We show that such calculations usually give rough estimates only, but of the correct order of magnitude; in particular, the predictions on the impurity effects depend strongly on the model parameters. One of our main results is the prediction of huge CPP-GMR effects for {\it non-metallic} spacers in the ballistic limit.Comment: Revised version; discussions and references improved; accepted by JMM

Burgpfeifer. Mitteilungen aus Donaustauf und Sulzbach. Sonderbeilage

Darin u. a.: N. N.: Die Walhalla und ihre Landschaft; Klärschlammdeponie; Bräuberg, Fürstengarten und Altwasser in Donaustauf; Walhalla und Salvatorkirch

Ab-initio-calculations of the GMR-effect in Fe/V multilayers

In a self-consistent semi-empirical numerical approach based on ab-initio-calculations for small samples, we evaluate the GMR effect for disordered (001)-(3--Fe/3--V)$_\infty$ multilayers by means of a Kubo formalism. We consider four different types of disorder arrangements: In case (i) and (ii), the disorder consists in the random interchange of some Fe and V atoms, respectively, at interface layers; in case (iii) in the formation of small groups of three substitutional Fe atoms in a V interface layer and a similar V group in a Fe layer at a different interface; and for case (iv) in the substitution of some V atoms in the innermost V layers by Fe. For cases (i) and (ii), depending on the distribution of the impurities, the GMR effect is enhanced or reduced by increasing disorder, in case (iii) the GMR effect is highest, whereas finally, in case (iv), a negative GMR is obtained (''inverse GMR'').Comment: LaTex, 30 pages, including 16 drawings; to appear in JMM