3,715 research outputs found
A variational principle for cyclic polygons with prescribed edge lengths
We provide a new proof of the elementary geometric theorem on the existence
and uniqueness of cyclic polygons with prescribed side lengths. The proof is
based on a variational principle involving the central angles of the polygon as
variables. The uniqueness follows from the concavity of the target function.
The existence proof relies on a fundamental inequality of information theory.
We also provide proofs for the corresponding theorems of spherical and
hyperbolic geometry (and, as a byproduct, in spacetime). The spherical
theorem is reduced to the euclidean one. The proof of the hyperbolic theorem
treats three cases separately: Only the case of polygons inscribed in compact
circles can be reduced to the euclidean theorem. For the other two cases,
polygons inscribed in horocycles and hypercycles, we provide separate
arguments. The hypercycle case also proves the theorem for "cyclic" polygons in
spacetime.Comment: 18 pages, 6 figures. v2: typos corrected, final versio
Minimal surfaces and particles in 3-manifolds
We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic,
anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these
manifolds admit ``nice'' foliations and explicit metrics, and whether the space
of these metrics has a simple description in terms of Teichm\"uller theory. In
the hyperbolic settings both questions have positive answers for a certain
subset of the quasi-Fuchsian manifolds: those containing a closed surface with
principal curvatures at most 1. We show that this subset is parameterized by an
open domain of the cotangent bundle of Teichm\"uller space. These results are
extended to ``quasi-Fuchsian'' manifolds with conical singularities along
infinite lines, known in the physics literature as ``massive, spin-less
particles''.
Things work better for globally hyperbolic anti-de Sitter manifolds: the
parameterization by the cotangent of Teichm\"uller space works for all
manifolds. There is another description of this moduli space as the product two
copies of Teichm\"uller space due to Mess. Using the maximal surface
description, we propose a new parameterization by two copies of Teichm\"uller
space, alternative to that of Mess, and extend all the results to manifolds
with conical singularities along time-like lines. Similar results are obtained
for de Sitter or Minkowski manifolds.
Finally, for all four settings, we show that the symplectic form on the
moduli space of 3-manifolds that comes from parameterization by the cotangent
bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde
Charge order, orbital order, and electron localization in the Magneli phase Ti4O7
The metal-insulator transition of the Magneli phase Ti4O7 is studied by means
of augmented spherical wave (ASW) electronic structure calculations as based on
density functional theory and the local density approximation. The results show
that the metal-insulator transition arises from a complex interplay of charge
order, orbital order, and singlet formation of those Ti 3d states which mediate
metal-metal bonding inside the four-atom chains characteristic of the material.
Ti4O7 thus combines important aspects of Fe3O4 and VO2. While the charge
ordering closely resembles that observed at the Verwey transition, the orbital
order and singlet formation appear to be identical to the mechanisms driving
the metal-insulator transition of vanadium dioxide.Comment: 11 pages, 4 figures, more information at
http://www.physik.uni-augsburg.de/~eyert
The Attributional Double Standard : Actor-Observer Differences in Predicting the Relationship Between Attitudes and Behaviors
It was hypothesized that subjects who took the role of interaction observers ration than actors would predict a closer relationship between attitudes and behaviors and would report greater confidence in behavioral predictions derivable from an actor\u27s attitude statements. One hundred sixty-eight subjects assumed the role of either actor or observer in scenarios of group interactions in which a central person made a statement about a particular attitude object. As predicted, subjects in the observer role reported that specific future behaviors (e.g., loaning money, helping to study for a test) had a greater likelihood of occurrence following an attitude statement (e.g., I like Pat ) than did subjects in the actor role, and observers were more confident than actors in these predictions. In addition, the favorability of the attitude statement was directly related to the strength of predictions, and the central person\u27s familiarity with the audience was directly related to confidence in predictions. Observers apparently view attitude statements as reliable indications of internal dispositions that serve as a potential cause of subsequent behaviors, while actors view attitude statements as tenuous orientations that can be modified in accord with future situational contingencies
New Luttinger liquid physics from photoemission on LiMoO
Temperature dependent high resolution photoemission spectra of quasi-1
dimensional LiMoO evince a strong renormalization of its
Luttinger liquid density-of-states anomalous exponent. We trace this new effect
to interacting charge neutral critical modes that emerge naturally from the
two-band nature of the material. LiMoO is shown thereby to
be a paradigm material that is capable of revealing new Luttinger physics.Comment: 4 pages, 3 figures. Accepted for publication by Phys. Rev. Let
Prospectus, November 4, 2004
https://spark.parkland.edu/prospectus_2004/1026/thumbnail.jp
The detector control system of the ATLAS experiment
The ATLAS experiment is one of the experiments at the Large Hadron Collider, constructed to study elementary particle interactions in collisions of high-energy proton beams. The individual detector components as well as the common experimental infrastructure are supervised by the Detector Control System (DCS). The DCS enables equipment supervision using operator commands, reads, processes and archives the operational parameters of the detector, allows for error recognition and handling, manages the communication with external control systems, and provides a synchronization mechanism with the physics data acquisition system. Given the enormous size and complexity of ATLAS, special emphasis was put on the use of standardized hardware and software components enabling efficient development and long-term maintainability of the DCS over the lifetime of the experiment. Currently, the DCS is being used successfully during the experiment commissioning phase
Prospectus, October 21, 2004
https://spark.parkland.edu/prospectus_2004/1024/thumbnail.jp
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