相关论文: Generalized Voronoi Tessellation as a Model of Two…

Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…

Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…

High energy experimental data can be viewed as a sampling of the relevant phase space. We point out that one can apply Voronoi tessellations in order to understand the underlying probability distributions in this phase space. Interesting…

Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…

Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…

Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…

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…

Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this…

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…

Detachment and fracture are central to many tissue-level processes, but they are challenging to simulate with Voronoi-type models that typically assume a confluent tissue. Here we analyze the finite Voronoi model, a nonconfluent extension…

Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…

The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are…

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…

General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be…

We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is…

The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and…

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…

In this paper we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in…

Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…