Related papers: Sphere paths in outer space
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
We perform numerical simulations of the approach to spacetime singularities. The simulations are done with sufficient resolution to resolve the small scale features (known as spikes) that form in this process. We find an analytical formula…
In this article, two methods of addressing path planning for a Dubins vehicle moving on a sphere are considered, wherein either spherical coordinates or a moving frame are considered to describe the vehicle's motion. The primary…
We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology…
We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse…
We study critical trajectories in the sphere for the $1/2$-Bernoulli's bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of…
In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done…
The dark matter distribution of the Milky Way remains among the major unsolved problems about our home galaxy. The masses of other spiral galaxies can be determined from their rotation curves through long-slit spectroscopy. But for the…
We prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curves in the manifold. The result is an extension of Nash $C^1$ Embedding Theorem. For more general metric spaces the same…
The location of objects on the celestial sphere is a fundamental measurement in astronomy, and the distribution of these objects within the Milky Way is important for understanding their evolution as well as the large scale structure of the…
This paper examines options for orbit configurations for a space interferometer. In contrast to previously presented concepts for space very long baseline interferometry, we propose a combination of regular and retrograde near-Earth…
The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size.…
In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…
Space debris is a major threat to the satellite infrastructure. A collision with even small particle, e.g. 1 cm of size, can cause a catastrophic event when the parent body, spacecraft or upper stage, will break up into hundreds of…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
We suggest how versions of Schramm's SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain.
Research in extrasolar-planet science is data-driven. With the advent of radial-velocity instruments like HARPS and HARPS-N, and transit space missions like Kepler, our ability to discover and characterise extrasolar planets is no longer…
Interferometry is a powerful technique for making sensitive, high-fidelity images of the sky, but is limited in its ability to measure extended or diffuse emission. Better images of extended astronomical objects can be obtained by…
Walk on Spheres algorithms leverage properties of Brownian Motion to create Monte Carlo estimates of solutions to a class of elliptic partial differential equations. We propose a new caching strategy which leverages the continuity of paths…