Related papers: Rotated sphere packing designs
In this paper we propose a heuristic technique for distributing points on the surface of a unit n-dimensional Euclidean sphere, generated as the orbit of a finite cyclic subgroup of orthogonal matrices, the so called cyclic group codes.…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling…
This study starts from the counter-intuitive question of how we can render a conventional stiff, non-stretchable and even brittle material conformable so that it can fully wrap around a curved surface, such as a sphere, without failure.…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
Although the concept of random close packing with an almost universal packing fraction of ~ 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric…
This paper deals with the problem of circle packing, in which the largest radii circle is to be fit in a confined space filled with arbitrary circles of different radii and centers. A circle packing problem is one of a variety of cutting…
This paper applies techniques from algebraic and differential geometry to determine how to best pack points in real projective spaces. We present a computer-assisted proof of the optimality of a particular 6-packing in…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions 8 and 24, where the…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper…
Compact packings are specific packings of spheres which can be seen as tilings and are good candidates to maximize the density. We show that the compact packings of the Euclidean space with two sizes of spheres are exactly those obtained by…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with…
Computer experiments are pivotal for modeling complex real-world systems. Maximizing information extraction and ensuring accurate surrogate modeling necessitates space-filling designs, where design points extensively cover the input domain.…