Related papers: Voronoi Cell Patterns: theoretical model and appli…

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…

The structure and dynamics of tissue cultures depend strongly on the physical and chemical properties of the underlying substrate. Inspired by previous advances in the context of inorganic materials, the use of patterned culture surfaces…

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…

The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges of these cells is ruled by a Markovian branching mechanism…

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…

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 describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to…

Although Poisson-Voronoi diagrams have interesting mathematical properties, there is still much to discover about the geometrical properties of its grains. Through simulations, many authors were able to obtain numerical approximations of…

Most current results on coverage control using mobile sensors require that one partitioned cell is the sole responsibility of one sensor. In this paper, we consider a class of generalized Voronoi coverage control problems by using higher…

In various types of many-particle systems, bidispersity is frequently used to avoid spontaneous ordering in particle configuration. In this study, the relation between bidispersity and disorder degree of particle configuration is…

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…

Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perform a sensitivity analysis for functions depending on sets…

We present a new particle-merging algorithm for the particle-in-cell method. Based on the concept of the Voronoi diagram, the algorithm partitions the phase space into smaller subsets, which consist of only particles that are in close…

Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…

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…

Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…

Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these…

Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We use this result…

The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial…

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting,…