Related papers: Coordinate Conditions and Their Implementation in …

The analysis of the dynamics of radial movement in different reference frames used in cosmology is made. Use of different frames leads to the difference in inertial forces resulting in different observable effects. The important effect is…

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric…

Computing an ensemble of random fields using conditional simulation is an ideal method for retrieving accurate estimates of a field conditioned on available data and for quantifying the uncertainty of these realizations. Methods for…

In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…

Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a…

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for…

If there is a null gradient field in 1+3 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is much helpful for simplifying and…

A technique for object localization based on pose estimation and camera calibration is presented. The 3-dimensional (3D) coordinates are estimated by collecting multiple 2-dimensional (2D) images of the object and are utilized for the…

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in…

A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi…

The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by…

Conducting levitated mechanical experiments in extreme conditions has long been the aim of researchers, as it allows for the investigation of new fundamental physics phenomena. One of the great frontiers has been sending these experiments…

In order to do relativistic gravimetry one needs to define a system of null coordinates for a given constellation of satellites. We present here three methods in order to find the null coordinates of an event in a Schwarzschild geometry. We…

Models for the observational appearance of astrophysical black holes rely critically on accurate general-relativistic ray tracing and radiation transport to compute the intensity measured by a distant observer. In this paper, we illustrate…

In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…

This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…

Humans have the remarkable ability to use held objects as tools to interact with their environment. For this to occur, humans internally estimate how hand movements affect the object's movement. We wish to endow robots with this capability.…

Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…

Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…

To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…