Related papers: Geometric Frustration and Interparticle Gap Size D…
We report calculations of the density of maximally random jamming (aka random close packing) of one-component and binary hard disc fluids. The theoretical structure used provides a common framework for description of the hard disc liquid to…
The Milky Way's satellite galaxies and Globular Clusters (GCs) are known to exhibit an anisotropic spatial distribution. We examine in detail this anisotropy by the means of the inertia tensor. We estimate the statistical significance of…
We study a variant of intersection representations with unit balls, that is, unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far sets, the goal is to…
Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the…
We study the problem of assortative and disassortative partitions on random $d$-regular graphs. Nodes in the graph are partitioned into two non-empty groups. In the assortative partition every node requires at least $H$ of their neighbors…
Discs form a compact packing of the plane if they are interior disjoint and the graph which connects the center of mutually tangent discs is triangulated. There is only one compact packing by discs all of the same size, called hexagonal…
We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
We provide a new analysis of the system of partial differential equations describing the radial and vertical equilibria of the plasma in accretion disks. In particular, we show that the partial differential system can be separated once a…
Dust grains with sizes around (sub)mm are expected to couple only weakly to the gas motion in regions beyond 10 au of circumstellar disks. In this work, we investigate the influence of the spatial distribution of such grains on the (sub)mm…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices $n$ points distributed independently and uniformly in the $d$-dimensional unit ball, with two vertices adjacent if and only if their $l_p$-distance is at most…
Aims: We derive the 3-D HI volume density distribution for the Galactic disk out to R = 60 kpc. Methods: Our analysis is based on parameters for the warp and rotation curve derived previously. The data are taken from the…
The densest amorphous packing of rigid particles is known as random close packing. It has long been appreciated that higher densities are achieved by using collections of particles with a variety of sizes. The variety of sizes is often…
Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density phi, among other packing…
Volume of metric balls relates to rate-distortion theory and packing bounds on codes. In this paper, the volume of balls in complex Grassmann manifolds is evaluated for an arbitrary radius. The ball is defined as a set of hyperplanes of a…
Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales.…
Conical surfaces pose an interesting challenge to crystal growth: a crystal growing on a cone can wrap around and meet itself at different radii. We use a disk-packing algorithm to investigate how this closure constraint can geometrically…
It is presented a numerical study on the unjamming packing fraction of bi- and polydisperse disk packings, which are generated through compression of a monodisperse crystal. In bidisperse systems, a fraction f_+ = 40% up to 80% of the total…
We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of…