相关论文: On non-Poissonian Voronoi tessellations

In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

$n$ independent random points drawn from a density $f$ in $R^d$ define a random Voronoi partition. We study the measure of a typical cell of the partition. We prove that the asymptotic distribution of the probability measure of the cell…

votess is a library for computing parallel 3D Voronoi tessellations on heterogeneous platforms, from CPUs and GPUs, to future accelerator architectures. To do so, it leverages the SYCL abstraction layer to achieve portability and…

This paper presents a range of results in partial differential equations (PDEs) in which Voronoi patterns arise. We investigate the connection between the solution to an elliptic equation and its probabilistic interpretation as a stochastic…

Currently, grid and glass methods are the two most popular choices to generate uniform particle distributions (i.e., pre-initial conditions) for cosmological $N$-body simulations. In this article, we introduce an alternative method called…

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from…

In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the…

We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input…

We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a…

Stereology allows shifting from the 3D distribution of the volumes of Poissonian Voronoi Diagrams to their 2D cross-sections. The basic assumption is that the 3D statistics of the volumes of the voids in the local Universe has a…

We introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation…

Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…

We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the…

We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…

We introduce an algorithm to estimate the redshift distribution of a sample of galaxies selected photometrically given a subsample with measured spectroscopic redshifts. The approach uses a non-parametric Voronoi tessellation density…

Consider a planar random point process made of the union of a point (the origin) and of a Poisson point process with a uniform intensity outside a deterministic set surrounding the origin. When the intensity goes to infinity, we show that…

Using 3D Vorono\text{\"i} analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using Direct Numerical Simulations (DNS). We independently vary the Taylor Reynolds number $R_\lambda…

Let $\Xi$ be a discrete set in ${\mathbb{R}}^d$. Call the elements of $\Xi$ centers. The well-known Voronoi tessellation partitions ${\mathbb{R}}^d$ into polyhedral regions (of varying sizes) by allocating each site of ${\mathbb{R}}^d$ to…

The zero cell of a parametric class of random hyperplane tessellations depending on a distance exponent and an intensity parameter is investigated, as the space dimension tends to infinity. The model includes the zero cell of stationary and…