Related papers: Maximally Dense Disc Packings on the Plane
What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution.…
Let a planar residual set be a set obtained by removing countably many disjoint topological disks from an open set in the plane. We prove that the residual set of a planar packing by curves that satisfy a certain lower curvature bound has…
The level of dust vertical settling and radial dust concentration in disks is of critical importance for understanding the efficiency of planet formation. We present the first uniform analysis of the vertical extent of millimeter dust for a…
Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of…
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…
In this note we prove that for any compact subset $S$ of a Busemann surface $({\mathcal S},d)$ (in particular, for any simple polygon with geodesic metric) and any positive number $\delta$, the minimum number of closed balls of radius…
In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of infinite inversive distance circle packings in the plane.…
Given a covering of the plane by closed unit discs $\mathcal F$ and two points $A$ and $B$ in the region doubly covered by $\mathcal F$, what is the length of the shortest path connecting them that stays within the doubly covered region?…
An old conjecture of Zs. Tuza says that for any graph $G$, the ratio of the minimum size, $\tau_3(G)$, of a set of edges meeting all triangles to the maximum size, $\nu_3(G)$, of an edge-disjoint triangle packing is at most 2. Here,…
Based on numerical simulations that we have carried out, we provide evidence that for regular polygons with $\sigma= 6j$ sides (with $j=2,3,\dots$), $N(k)=3 k (k+1)+1$ (with $k=1,2,\dots$) congruent disks of appropriate size can be nicely…
We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities. Using simulations and experiments, we find that ordered as well as disordered structures emerge, depending on the amount of internal…
This paper encompasses the mathematical derivations of the analytic and generalized formula and recurrence relations to find out the radii of n umber of circles inscribed or packed in the plane region bounded by circular arcs (including…
We formulate the problem of generating dense packings of nonoverlapping, non-tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the Adaptive Shrinking Cell…
Motivated in part by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of jammed ellipse packings over a much wider range of particle aspect ratios ($\alpha$) than has been previously…
In this work we extend recent study of the properties of the dense packing of "superdisks," by Y. Jiao, F. H. Stillinger and S. Torquato, Phys. Rev. Lett. 100, 245504 (2008), to the jammed state formed by these objects in random sequential…
In this paper we study congruent and non-congruent hyperball (hypersphere) packings of the truncated regular octahedron and cube tilings. These are derived from the Coxeter simplex tilings $\{p,3,4\}$ $(7\le p \in \mathbb{N})$ and…
In this paper, we study the 3D strip packing problem in which we are given a list of 3-dimensional boxes and required to pack all of them into a 3-dimensional strip with length 1 and width 1 and unlimited height to minimize the height used.…
What is the largest constant $c\in [0,1]$ with the property that every finite collection $\mathcal{C}$ of axis-parallel squares in the plane admits a disjoint sub-collection $\mathcal{S}$ occupying at least a fraction $c$ of the area…
This work analyzes the distribution and size of interparticle gaps arising in an ensemble of hexagonal unit structures in the xy plane when packing disks with a Gaussian distribution of radii with mean (r) and standard deviation $\Delta r$.…
The vertical thickness of debris discs is often used as a measure of these systems' dynamical excitation and as clues to the presence of hidden massive perturbers such as planetary embryos. However, this argument could be flawed because the…