Search results for "Mink"

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…

Positioning with stationary emitters in a two-dimensional space-time

2006

The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coord…

Positioning in a flat two-dimensional space-time: the delay master equation

2010

The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one …

Differential calculus on 'non-standard' (h-deformed) Minkowski spaces

1997

Maximal slicings in spherical symmetry: Local existence and construction

2011

We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.

On Chiral Quantum Superspaces

2011

We give a quantum deformation of the chiral Minkowski superspace in 4 dimensions embedded as the big cell into the chiral conformal superspace. Both deformations are realized as quantum homogeneous superspaces: we deform the ring of regular functions together with a coaction of the corresponding quantum supergroup.

Clustering statistics in cosmology

2002

The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the universe. Special topics discussed in this talk will be: description of the galaxy samples, selection effects and biases, correlation functions, Fourier analysis, nearest neighbor statistics, Minkowski functionals and structure statistics. Special attention will be devoted to scaling laws and the use of the lacunarity measures in the description of the cosmic texture.

Partition Function for the Harmonic Oscillator

2001

We start by making the following changes from Minkowski real time t = x0 to Euclidean “time” τ = tE:

Variable-Radius Offset Surface Approximation on the GPU

2020

Variable-radius offset surfaces find applications in various fields, such as variable brush strokes in 2D and 3D sketching and geometric modeling tools. In forensic facial reconstruction the skin surface can be inferred from a given skull by computing a variable-radius offset surface of the skull surface. Thereby, the skull is represented as a two-manifold triangle mesh and the facial soft tissue thickness is specified for each vertex of the mesh. We present a method to interactively visualize the wanted skin surface by rendering the variable-radius offset surfaces of all triangles of the skull mesh. We have also developed a special shader program which is able to generate a discretized vol…

Real and Complex Singularities

2016

In this paper a Minkowski analogue of the Euclidean medial axis of a closed and smooth plane curve is introduced. Its generic local configurations are studied and the types of shocks that occur on these are also determined.