相关论文: Dense crystalline dimer packings of regular tetrah…
We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\lceil p^{3}/2\rceil$ spheres. For this family of packings, the previous…
We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic groups can have. The problem for non-cubic groups was studied in previous papers by D. Bochis and the second author…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
In this article we consider an open conjecture about coherently labelling a polyhedron in three dimensions. We exhibit all the forty eight possible coherent labellings of a tetrahedron. We also exhibit that some simplicial polyhedra like…
Let $\mathcal{P}$ be a packing of circular disks of radius $\rho>0$ in the Euclidean, spherical, or hyperbolic plane. Let $0\leq\lambda\leq\rho$. We say that $\mathcal{P}$ is a $\lambda$-separable packing of circular disks of radius $\rho$…
We compile observations of the surface mass density profiles of dense stellar systems, including globular clusters in the Milky Way and nearby galaxies, massive star clusters in nearby starbursts, nuclear star clusters in dwarf spheroidals…
Based on Minkowski's work on critical lattices of 3-dimensional convex bodies we present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As an application we calculate densest…
We describe a new numerical procedure for generating dense packings of disks and spheres inside various geometric shapes. We believe that in some of the smaller cases, these packings are in fact optimal. When applied to the previously…
In this paper, a result of Albert, Atkinson, Handley, Holton, and Stromquist [Electron. J. Combin. 9 (2002), #R5] which characterizes the optimal packing behavior of the pattern 1243 is generalized in two directions. The packing densities…
It is well known that the lattice packing density and the lattice covering density of a triangle are $\frac{2}{3}$ and $\frac{3}{2}$ respectively. We also know that the lattices that attain these densities both are unique. Let…
We resolve the inner region of a massive cluster forming in a cosmological LCDM simulation with a mass resolution of 2*10^6 Msun and before z=4.4 even 3*10^5 Msun. This is a billion times less than the clusters final virial mass and a…
From the kinematics of 137 spirals we find that the DM halo density profiles are self-similar at least out to R_opt and show core radii much larger that the corresponding disk scale-lenghts. The luminous regions of spirals consist of…
The Hales program to prove the Kepler conjecture on sphere packings consists of five steps, which if completed, will jointly comprise a proof of the conjecture. We carry out step five of the program [outlined in math.MG/9811073], a proof…
We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead,…
Koszul type Coxeter simplex tilings exist in hyperbolic $n$-space $\mathbb{H}^n$ up to $ n = 9$, and their horoball packings achieve the highest known regular ball packing densities for $n = 3, 4, 5$. In this paper we determine the optimal…
The structural properties of dense random packings of identical hard spheres (HS) are investigated. The bond order parameter method is used to obtain detailed information on the local structural properties of the system for different…
Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra,…
We exhaustively search quaternary metal hydrides based on the (13-2-1) and (13-3-1) structures that are the two of the putative densest ternary sphere packings in cubic systems [R. Koshoji \textit{et al.}, Phys. Rev. E \textbf{104}, 024101…
In \cite{Sz13-1} we defined and described the {\it regular infinite or bounded} $p$-gonal prism tilings in $\SLR$ space. We proved that there exist infinitely many regular infinite $p$-gonal face-to-face prism tilings $\cT^i_p(q)$ and…