Search results for "Log-polar coordinates"
showing 4 items of 4 documents
Coordinates for quasi-Fuchsian punctured torus space
1998
We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely the classical Fuchsian space with Fenchel-Nielsen coordinates and the Maskit embedding. We also show how they relate to the pleating coordinates of Keen and Series.
Positioning systems in Minkowski space-time: Bifurcation problem and observational data
2012
In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus…
Emission and null coordinates: geometrical properties and physical construction
2011
A Relativistic Positioning System is defined by four clocks (emitters) broadcasting their proper time. Then, every event reached by the signals is naturally labeled by these four times which are the emission coordinates of this event. The coordinate hypersurfaces of the emission coordinates are the future light cones based on the emitter trajectories. For this reason the emission coordinates have been also named null coordinates or light coordinates. Nevertheless, other coordinate systems used in different relativistic contexts have the own right to be named null or light coordinates. Here we analyze when one can say that a coordinate is a null coordinate and when one can say that a coordin…
Comparison between the fCCZ4 and BSSN formulations of Einstein equations in spherical polar coordinates
2015
Recently, we generalized a covariant and conformal version of the Z4 system of the Einstein equations using a reference metric approach, that we denote as fCCZ4. We successfully implemented and tested this approach in a 1D code that uses spherical coordinates and assumes spherical symmetry, obtaining from one to three orders of magnitude reduction of the Hamiltonian constraint violations with respect to the BSSN formulation in tests involving neutron star spacetimes. In this work, we show preliminary results obtained with the 3D implementation of the fCCZ4 formulation in a fully 3D code using spherical polar coordinates.