Related papers: Discovering New Physics with Voronoi Tessellations
Characterizing the spacing of primary dendrite arms in directionally-solidified microstructures is an important step for developing process-structure-property relationships by enabling the quantification of (i) the influence of processing…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…
This paper introduces the Heteroscedastic AddiVortes model, a Bayesian non-parametric regression framework that simultaneously models the conditional mean and variance of a response variable using adaptive Voronoi tessellations. By…
The lecture notes describe the Delaunay Tessellation Field Estimator for Cosmic Web analysis. The high sensitivity of Voronoi/Delaunay tessellations to the local point distribution is used to obtain estimates of density and related…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analyzed using Voronoi tessellation of the particle positions, considering different…
Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…
We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random…
We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological properties with high probability. This strengthens a theorem of…
Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
We propose finite-time measures to compute the divergence, the curl and the velocity gradient tensor of the point particle velocity for two- and three-dimensional moving particle clouds. For this purpose, a tessellation of the particle…
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
Vortex states of photons, electrons, and other particles are freely propagating wave packets with helicoidal wave fronts winding around the axis of a phase vortex. A particle prepared in a vortex state carries a non-zero orbital angular…
Perturbed lattices provide simple models for studying many physical systems. In this paper we study the distribution of Voronoi chains, blocks, and clusters with prescribed combinatorial features in the perturbed square lattice,…
We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests…
In this work, we study a new model for continuum line-of-sight percolation in a random environment driven by the Poisson-Voronoi tessellation in the $d$-dimensional Euclidean space. The edges (one-dimensional facets, or simply 1-facets) of…
The intersections between a spherical shell and the faces of Voronoi's polyhedrons are numerically evaluated. The nodes of these intersections are the points that share the same distances from three nuclei. The nodes are assumed to be the…