相关论文: Self-similar space-filling sphere packings in thre…

We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bi-cromatic packing known up to now.

Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we…

We present the first space-filling bearing in three dimensions. It is shown that a packing which contains only loops with even number of spheres can be constructed in a self-similar way and that it can act as a three dimensional bearing in…

How should you choose a good set of (say) 48 planes in four dimensions? More generally, how do you find packings in Grassmannian spaces? In this article I give a brief introduction to the work that I have been doing on this problem in…

In an earlier work, we proposed a generalization for the Apollonian packing in arbitrary dimensions and showed that the resulting object in four, five, and six dimensions have properties consistent with the Apollonian circle and sphere…

The three dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with X-ray Computed Tomography. We search for signatures of organization, we classify local…

We introduce the notion of a "crystallographic sphere packing," defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension. We exhibit for the first time an infinite family of…

We call a packing of hyperspheres in $n$ dimensions an Apollonian sphere packing if the spheres intersect tangentially or not at all; they fill the $n$-dimensional space; and every sphere in the packing is a member of a cluster of $n+2$…

We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled,…

A construction for sphere packings is introduced that is parallel to the ``anticode'' construction for codes. This provides a simple way to view Vardy's recent 20-dimensional sphere packing, and also produces packings in dimensions 22,…

Two dimensional space-filling bearings are dense packings of disks that can rotate without slip. We consider the entire first family of bearings for loops of size four and propose a hierarchical construction of their contact network. We…

We analyze Sz\"oll\H{o}si's recent construction of a conjecturally optimal five-dimensional kissing configuration and produce a new such configuration, the fourth to be discovered. We construct five-dimensional sphere packings from these…

If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…

Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We…

We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…

In discrete geometry, the contact number of a given finite number of non-overlapping spheres was introduced as a generalization of Newton's kissing number. This notion has not only led to interesting mathematics, but has also found…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…