Related papers: The "Yin-Yang Grid": An Overset Grid in Spherical …
We construct one Yang-Mills measure on a compact surface for each isomorphism class of principal bundles over this surface. For this, we define a new discrete gauge theory which is essentially a covering of the usual one. We prove that the…
The affine Yangian of $\mathfrak{gl}_1$ is isomorphic to the universal enveloping algebra of $\mathcal{W}_{1+\infty}$ and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family…
Nowadays, various stakeholders involved in the analysis of electric power distribution grids face difficulties in the data acquisition related to the grid topology and parameters of grid assets. To mitigate the problem and possibly…
In scientific computing, more computational power generally implies faster and possibly more detailed results. The goal of this study was to develop a framework to submit computational jobs to powerful workstations underused by nonintensive…
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries…
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…
We study a family of lattice-gas systems defined on semiregular grids, obtained by projecting the vertices of three different geodesic icosahedra onto a spherical surface. By using couplings up to third neighbors we explore various…
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
It will be described how to uniquely fix the gauge using Coulomb gauge fixing, avoiding the problem of Gribov copies. The fundamental modular domain, which represents a one-to-one representation of the set of gauge invariant degrees of…
We discuss how multi-grid computing schemes can be used to design hierarchical coordination architectures for energy systems. These hierarchical architectures can be used to manage multiple temporal and spatial scales and mitigate…
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…
A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
A common approach for modeling the environment of an autonomous vehicle are dynamic occupancy grid maps, in which the surrounding is divided into cells, each containing the occupancy and velocity state of its location. Despite the advantage…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
The representation of subgrid-scale orography is a challenge in the physical parameterization of orographic gravity-wave sources in weather forecasting. A significant hurdle is encoding as much physical information with as simple a…
We present SymPix, a special-purpose spherical grid optimized for efficient sampling of rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude…
We construct a variety of supersymmetric gauge theories on a spatial lattice, including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at…