Related papers: Enumerating rigid sphere packings
We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to…
An arrangement of pseudocircles is a collection of simple closed curves on the sphere or in the plane such that any two of the curves are either disjoint or intersect in exactly two crossing points. We call an arrangement intersecting if…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…
Rotating clusters or vortices are formations of agents that rotate around a common center. These patterns may be found in very different contexts: from swirling fish to surveillance drones. Here, we propose a minimal model for…
Clusters of galaxies are the largest gravitationally-bound objects in the Universe, having diameters on order of Mpc. Our work asked whether their shapes (morphologies) change over time as the Universe ages. We observed a sample of 165…
We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of…
In this paper we formulate the problem of packing unequal rectangles/squares into a fixed size circular container as a mixed-integer nonlinear program. Here we pack rectangles so as to maximise some objective (e.g. maximise the number of…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from…
Assemblies of purely repulsive and frictionless particles, such as emulsions or hard spheres, display very curious properties near their jamming transition, which occurs at the random close packing for mono-disperse spheres. Although such…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in $\mathbb{R}^d$ and show that in $\mathbb{R}^3$ this problem is equivalent to determining the maximal coordination of a…
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…
Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packings are known. The packing of 2D crosses does…
Non-spherical emulsion droplets can be stabilized by densely packed colloidal particles adsorbed at their surface. In order to understand the microstructure of these surface packings, the ordering of hard spheres on ellipsoidal surfaces is…
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…
The core structure of galaxy clusters is fundamentally important. Even though self-gravitating systems have no stable equilibrium state due to their negative heat capacity, numerical simulations find density profiles which are universal in…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
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…