5,364 research outputs found
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 .
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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
Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory
Phase-contrast microscopy is used to monitor the shapes of micron-scale
fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed
temperature, each vesicle undergoes thermal shape fluctuations. We are able
experimentally to characterize the thermal shape ensemble by digitizing the
vesicle outline in real time and storing the time-sequence of images. Analysis
of this ensemble using the area-difference-elasticity (ADE) model of vesicle
shapes allows us to associate (map) each time-sequence to a point in the
zero-temperature (shape) phase diagram. Changing the laboratory temperature
modifies the control parameters (area, volume, etc.) of each vesicle, so it
sweeps out a trajectory across the theoretical phase diagram. It is a
nontrivial test of the ADE model to check that these trajectories remain
confined to regions of the phase diagram where the corresponding shapes are
locally stable. In particular, we study the thermal trajectories of three
prolate vesicles which, upon heating, experienced a mechanical instability
leading to budding. We verify that the position of the observed instability and
the geometry of the budded shape are in reasonable accord with the theoretical
predictions. The inability of previous experiments to detect the ``hidden''
control parameters (relaxed area difference and spontaneous curvature) make
this the first direct quantitative confrontation between vesicle-shape theory
and experiment.Comment: submitted to PRE, LaTeX, 26 pages, 11 ps-fi
Unbiased flux calibration methods for spectral-line radio observations
Position and frequency switching techniques used for the removal of the
bandpass dependence of radio astronomical spectra are presented and discussed
in detail. Both methods are widely used, although the frequency dependence of
the system temperature and/or noise diode is often neglected. This leads to
systematic errors in the calibration that potentially have a significant impact
on scientific results, especially when using large-bandwidth receivers or
performing statistical analyses. We present methods to derive an unbiased
calibration using a noise diode, which is part of many heterodyne receivers. We
compare the proposed methods and describe the advantages and bottlenecks of the
various approaches. Monte Carlo simulations are used to qualitatively
investigate both systematics and the error distribution of the reconstructed
flux estimates about the correct flux values for the new methods but also the
'classical' case. Finally, the determination of the frequency-dependent noise
temperature of the calibration diode using hot-cold measurements or
observations of well-known continuum sources is also briefly discussed.Comment: 25 pages, 30 figures. Accepted for publication in A&
Analyzing X-Ray Pulsar Profiles: Geometry and Beam Pattern of EXO 2030+375
The pulse profiles of the transient Be/X-ray binary EXO 2030+375 show strong
dependence on energy, as well as on its luminosity state, and are asymmetric in
shape. We want to identify the emission components of the two magnetic poles in
the pulsed emission to understand the geometry of the neutron star and its beam
pattern. We utilize a pulse-profile decomposition method that enables us to
find two symmetric pulse profiles from the magnetic poles of the neutron star.
The symmetry characteristics of these single-pole pulse profiles give
information about the position of the magnetic poles of the neutron star
relative to its rotation axis. We find a possible geometry for the neutron star
in EXO 2030+375 through the decomposition of the pulse profiles, which suggests
that one pole gets closer to the line of sight than the other and that, during
the revolution of the neutron star, both poles disappear behind the horizon for
a short period of time. A considerable fraction of the emission arises from a
halo while the pole is facing the observer and from the accretion stream of the
other pole while it is behind the neutron star, but the gravitational line
bending makes the emission visible to us.Comment: 8 pages, 9 figures, accepted for publication in A&
Gravity-Induced Shape Transformations of Vesicles
We theoretically study the behavior of vesicles filled with a liquid of
higher density than the surrounding medium, a technique frequently used in
experiments. In the presence of gravity, these vesicles sink to the bottom of
the container, and eventually adhere even on non - attractive substrates. The
strong size-dependence of the gravitational energy makes large parts of the
phase diagram accessible to experiments even for small density differences. For
relatively large volume, non-axisymmetric bound shapes are explicitly
calculated and shown to be stable. Osmotic deflation of such a vesicle leads
back to axisymmetric shapes, and, finally, to a collapsed state of the vesicle.Comment: 11 pages, RevTeX, 3 Postscript figures uuencode
Giant vesicles at the prolate-oblate transition: A macroscopic bistable system
Giant phospholipid vesicles are shown to exhibit thermally activated
transitions between a prolate and an oblate shape on a time scale of several
seconds. From the fluctuating contour of such a vesicle we extract ellipticity
as an effective reaction coordinate whose temporal probability distribution is
bimodal. We then reconstruct the effective potential from which we derive an
activation energy of the order of in agreement with theoretical
calculations. The dynamics of this transition is well described within a
Kramers model of overdamped diffusion in a bistable potential. Thus, this
system can serve as a model for macroscopic bistability.Comment: 10 pages, LaTeX, epsfig, 4 eps figures included, to appear in
Europhys. Let
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