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 $1+1$ 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 $1+1$ 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 Li0.9_{0.9}Mo6_6O17_{17}

Temperature dependent high resolution photoemission spectra of quasi-1 dimensional Li$_{0.9}$Mo$_6$O$_{17}$ 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. Li$_{0.9}$Mo$_6$O$_{17}$ 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