相关论文: Dense crystalline dimer packings of regular tetrah…

Recent numerical studies of the dark matter density profiles of massive galaxy clusters ($M_{\rm halo} > 10^{15}$M$_{\odot}$) show that their median radial mass density profile remains unchanged up to $z > 1$, displaying a highly…

Rigid particles pack into structures, such as sand dunes on the beach, whose overall stability is determined by the average number of contacts between particles. However, when packing spatially extended objects with flexible shapes,…

To explain the effect of electron density saturation at high phosphorus concentrations the model of negatively charged phosphorus clusters was compared with the experimental data. A number of negatively charged clusters incorporating a…

In 1993 Foisy et al. proved that the optimal Euclidean planar double bubble---the least-perimeter way to enclose and separate two given areas---is three circular arcs meeting at 120 degrees. We consider the plane with density $r^p$, joining…

Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…

Given an Apollonian Circle Packing $\mathcal{P}$ and a circle $C_0 = \partial B(z_0, r_0)$ in $\mathcal{P}$, color the set of disks in $\mathcal{P}$ tangent to $C_0$ red. What proportion of the concentric circle $C_{\epsilon} = \partial…

Piga, Sanhueza-Matamala, and Schacht recently established that the codegree Tur\'an density of 3-uniform tight cycles $C_\ell$ is $1/3$ for $\ell\in \{10, 13, 16\}$ and for all $\ell\geq 19$. In this note, we extend their proof to determine…

We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…

We determine the numbers of integral tetrahedra with diameter $d$ up to isomorphism for all $d\le 1000$ via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most $d$ in $O(d^5)$…

We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered…

In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $\mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We…

We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason - the problem of "super…

Most of the baryons in the Universe are thought to be contained within filaments of galaxies, but as yet, no single study has published the observed properties of a large sample of known filaments to determine typical physical…

In this paper we investigate the problem of finding the minimum edge density in families of convex, normal mosaics with unit volume cells in $n$-dimensional Euclidean space. In the first part of the paper we solve this problem for mosaics…

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…

We study jammed configurations of hard spheres as a function of compression speed using an event-driven molecular dynamics algorithm. We find that during the compression, the pressure follows closely the metastable liquid branch until the…

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…

A class of complete potential-density basis sets in cylindrical (R,phi,z) coordinates is presented. This class is suitable for stability studies of galactic disks in three dimensions and includes basis sets tailored for disks with vertical…

The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral…

We measured the system-integrated thermal emission of the binary Kuiper Belt Object 1999 TC36 at wavelengths near 24 and 70 microns using the Spitzer space telescope. We fit these data and the visual magnitude using both the Standard…