相关论文: Non-universal Voronoi cell shapes in amorphous ell…
We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in 2D that interact via repulsive contact forces. We measure the structural relaxation times obtained from the…
A collection of spherical particles can be packed tightly together into an amorphous packing known as "random close packing" (RCP). This structure is of interest as a model for the arrangement of molecules in simple liquids and glasses, as…
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…
The famous Kepler conjecture has a less spectacular, two-dimensional equivalent: The theorem of Thue states that the densest circle packing in the Euclidean plane has a hexagonal structure. A common proof uses Voronoi cells and analyzes…
We study the local structural changes along the jamming transitions in asymmetric bidisperse granu\-lar packings. The local structure of the packing is assessed by the contact orientational order, $\tilde{Q}_{\ell}$, that quantifies the…
The typical cell of a Voronoi tessellation generated by $n+1$ uniformly distributed random points on the $d$-dimensional unit sphere $\mathbb S^d$ is studied. Its $f$-vector is identified in distribution with the $f$-vector of a beta'…
The behavior of a system of two-dimensional elongated particles (discorectangles) packed into a slit between two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption…
The structure of random sphere packings in mechanical equilibrium in prescribed stress states, as studied by molecular dynamics simulations, strongly depends on the assembling procedure. Frictionless packings in the limit of low pressure…
Using sedimentation to obtain precisely controlled packings of noncohesive spheres, we find that the volume fraction $\phi_{\rm RLP}$ of the loosest mechanically stable packing is in an operational sense well defined by a limit process.…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
The weight space of the Ising perceptron in which a set of random patterns is stored is examined using the generating function of the partition function $\phi(n)=(1/N)\log [Z^n]$ as the dimension of the weight vector $N$ tends to infinity,…
We study the Voronoi volume function (VVF) -- the distribution of cell volumes (or inverse local number density) in the Voronoi tessellation of any set of cosmological tracers (galaxies/haloes). We show that the shape of the VVF of biased…
A voxelization based post-processing algorithm is proposed to analyze the packing of non-spherical particle assemblies simulated using the Discrete Element Method. Voxelization of the particle data allows for isolating the geometric…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
We study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation…
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…
Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to…
We investigate the statistical properties of two dimensional random cellular systems (froths) in term of their shell structure. The froth is analyzed as a system of concentric layers of cells around a given central cell. We derive exact…
We study the statistics of the Voronoi cell perimeter in large bi-pointed planar quadrangulations. Such maps have two marked vertices at a fixed given distance $2s$ and their Voronoi cell perimeter is simply the length of the frontier which…
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…