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Vascular and non-vascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear…
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…
We present computer simulations run with a stochastic cellular automaton which describes $d=1$ particle systems connected to reservoirs which keep two different densities at the endpoints. We fix the parameters so that there is a phase…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
The 3D network originated by the faces of irregular Poissonian Voronoi Polyhedrons may represent the backbone on which the galaxies are originated. As a consequence the spatial appearance of the catalogs of galaxies can be reproduced. The…
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired…
Polariton condensates have proved to be model systems to investigate topological defects, as they allow for direct and non-destructive imaging of the condensate complex order parameter. The fundamental topological excitations of such…
Continuous cellular automata are rocketing in popularity, yet developing a theoretical understanding of their behaviour remains a challenge. In the case of Lenia, a few fundamental open problems include determining what exactly constitutes…
Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive…
Inspired by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytical treatment a simple domino cellular automaton with…
We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…
Biological cells are able to generate intricate structures and respond to external stimuli, sculpting their membrane from within. Simplified biomimetic systems can aid in understanding the principles which govern these shape changes and…
We show that the Voronoi cells of the lattice of integer flows of a finite connected graph $G$ in the quadratic vector space of real valued flows have the following very precise combinatorics: the face poset of a Voronoi cell is isomorphic…
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…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Surprisingly, the order-$k$ Voronoi diagram of line segments had received no attention in the computational-geometry literature. It illustrates properties surprisingly different from its counterpart for points; for example, a single…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
Patchy colloidal model with three and four equivalent patches, confined in the attractive random porous media, undergo re-entrant gas-liquid phase separation with the possibility for the liquid phase density to approach zero. This unusual…
Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. A…