10 research outputs found
Relativistic positioning: four-dimensional numerical approach in Minkowski space-time
We simulate the satellite constellations of two Global Navigation Satellite
Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the
Schwarzschild space-time produced by an idealized spherically symmetric non
rotating Earth. The trajectories are then circumferences centered at the same
point as Earth. Photon motions are described in Minkowski space-time, where
there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010),
between the emission and inertial coordinates of any event. Here, this relation
is implemented in a numerical code, which is tested and applied. The first
application is a detailed numerical four-dimensional analysis of the so-called
emission coordinate region and co-region. In a second application, a GPS
(Galileo) satellite is considered as the receiver and its emission coordinates
are given by four Galileo (GPS) satellites. The bifurcation problem (double
localization) in the positioning of the receiver satellite is then pointed out
and discussed in detail.Comment: 16 pages, 9 figures, published (online) in Astrophys. Space Sc
GPS observables in general relativity
I present a complete set of gauge invariant observables, in the context of
general relativity coupled with a minimal amount of realistic matter (four
particles). These observables have a straightforward and realistic physical
interpretation. In fact, the technology to measure them is realized by the
Global Positioning System: they are defined by the physical reference system
determined by GPS readings. The components of the metric tensor in this
physical reference system are gauge invariant quantities and, remarkably, their
evolution equations are local.Comment: 6 pages, 1 figure, references adde
Evaluation of the BCS Approximation for the Attractive Hubbard Model in One Dimension
The ground state energy and energy gap to the first excited state are
calculated for the attractive Hubbard model in one dimension using both the
Bethe Ansatz equations and the variational BCS wavefunction. Comparisons are
provided as a function of coupling strength and electron density. While the
ground state energies are always in very good agreement, the BCS energy gap is
sometimes incorrect by an order of magnitude, particularly at half-filling.
Finite size effects are also briefly discussed for cases where an exact
solution in the thermodynamic limit is not possible. In general, the BCS result
for the energy gap is poor compared to the exact result.Comment: 25 pages, 5 Postscript figure
Apodization effects in Fourier transform infrared difference spectra
Artifacts may occur in Fourier transform infrared (FTIR) spectra due to the apodization of the interferograms of intense bands. Selected examples of boxcar and triangular apodization effects on difference spectra have been previously reported. This paper reports the first such calculation performed for the Happ-Genzel apodization function, which is often used on modern spectrometers. In order to compare boxcar, triangular, and Happ-Genzel apodization functions we calculate (i) difference-spectrum artifacts, (ii) apparent versus true peak absorbances, and (iii) a measure of integrated artifact area for several true peak intensities of Lorentzian-band shapes. Values of p (ratio of full bandwidth at half height to nominal resolution) are emphasized which commonly occur in the transmission-mode spectroscopy of transparent or translucent solid samples