Related papers: How to measure spatial distances?
In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced…
Intuitively, one would expect a more skillful forecast if predicting weather averaged over one week instead of the weather averaged over one day, and similarly for different spatial averaging areas. However, there are few systematic studies…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
We formulate geodesics on a manifold in terms of a parallel transfer of a particle state vector transformed by local Lorentz and Yang-Mills symmetry groups. This formulation leads to an introduction of a canonical one-form the eigenvalues…
Clock-comparison experiments conducted in space can provide access to many unmeasured coefficients for Lorentz and CPT violation. The orbital configuration of a satellite platform and the relatively large velocities attainable in a…
Spatial association and heterogeneity are two critical areas in the research about spatial analysis, geography, statistics and so on. Though large amounts of outstanding methods has been proposed and studied, there are few of them tend to…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
If a clock, mathematically modeled by a parametrized timelike curve in a general-relativistic spacetime, is given, the radar method assigns a time and a distance to every event which is sufficiently close to the clock. Several geometric…
The notion of spacetime symmetry is essential to describe gravitating physical systems like planets, stars, black holes, or the universe as a whole, since they possess, at least to good approximation, spherical, axial, or spatially…
Transportation distance information is a powerful resource, but location records are often censored due to privacy concerns or regulatory mandates. We outline methods to approximate, sample from, and compare distributions of distances…
Clocks in different heights or with different velocities run with different speeds. For global positioning systems these effects are much too large to be ignored. Nevertheless, in classical and quantum mechanics we get high accuracy using a…
What is the distance between two points in spacetime? This is a basic geometric question, which so far has no single, definitive answer. Unlike their Riemannian cousins, Lorentzian manifolds are not known to carry a canonical distance…
The $\mathcal{G}_I^0$ distribution is able to characterize different regions in monopolarized SAR imagery. It is indexed by three parameters: the number of looks (which can be estimated in the whole image), a scale parameter and a texture…
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling…
In this note we reduce the problem of geodesic connectedness in a wide class of G\"odel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by…
Even the best scientific equipment can only partially observe reality. Recorded data is often lower-dimensional, e.g., two-dimensional pictures of the three-dimensional world. Combining data from multiple experiments then results in a…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
Herein we shall argue for the utility of "spacetime geodesy", a point of view where one delays as long as possible worrying about dynamical equations, in favour of the maximal utilization of both symmetries and geometrical features. This…