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

Predicting the densest random disc packing fraction is an unsolved paradigm problem relevant to a number of disciplines and technologies. One difficulty is that it is ill-defined without setting a criterion for the disorder. Another is that…

Let $L \subset {\Bbb R}^3$ be the union of unit balls, whose centres lie on the $z$-axis, and are equidistant with distance $2d \in [2, 2\sqrt{2}]$. Then a packing of unit balls in ${\Bbb R}^3$ consisting of translates of $L$ has a density…

The ball (or sphere) packing problem with equal balls, without any symmetry assumption, in a $3$-dimensional space of constant curvature was settled by B\"or\"oczky and Florian for the hyperbolic space $\HYP$ in \cite{BF64} and by proving…

A sphere packing of the three-dimensional Euclidean space is compact if it has only tetrahedral holes, that is, any local maximum of the distance to the spheres is at equal distance to exactly four spheres. This papers describes all the…

Dense packings of nonoverlapping bodies in three-dimensional Euclidean space are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing…

A family of spherical caps of the 2-dimensional unit sphere $\mathbb{S}^2$ is called a totally separable packing in short, a TS-packing if any two spherical caps can be separated by a great circle which is disjoint from the interior of each…

Using experiments and simulations, we investigate the clusters that form when colloidal spheres stick irreversibly to -- or "park" on -- smaller spheres. We use either oppositely charged particles or particles labeled with complementary DNA…

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.…

We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have…

We construct the densest known two-dimensional packings of superdisks in the plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and…

We present a detailed investigation of static dipole polarizability of lithium clusters containing up to 22 atoms. We first build a database of lithium clusters by optimizing several candidate structures for the ground state geometry for…

We prove that the set $\{0, 1, 4, 6\}$ achieves the minimum packing density among all sets of integers with cardinality four, with a density of $\frac{1}{7}$.

Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…

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 paper we construct a new family of lattice packings for superballs in three dimensions (unit balls for the $l^p_3$ norm) with $p \in (1, 1.58]$. We conjecture that the family also exists for $p \in (1.58, \log_2 3 =…

We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…

The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than $\pi/\sqrt{18}$. A computer assisted verification confirmed this conjecture in 1998. This article gives a historical…

We identify the maximally dense lattice packings of tangent-disk trimers with fixed bond angles ($\theta = \theta_0$) and contrast them to both their nonmaximally-dense-but-strictly-jammed lattice packings as well as the disordered jammed…

Using a Lubachevsky-Stillinger-like growth algorithm combined with biased SWAP Monte Carlo and transient degrees of freedom, we generate ultradense disordered jammed ellipse packings. For all aspect ratios $\alpha$, these packings exhibit…

In this paper we study the regular prism tilings and construct ball packings by geodesic balls related to the above tilings in the projective model of $\mathbf{Nil}$ geometry. Packings are generated by action of the discrete prism groups…