Densest Packings of More than Three d -Spheres Are Nonplanar
نویسندگان
چکیده
We prove that for a densest packing of more than three d–balls, d ≥ 3, where the density is measured by parametric density, the convex hull of their centers is either linear (a sausage) or at least 3–dimensional. This is also true for restrictions to lattice packings. The proofs require a Lagrange–type theorem from number theory and Minkowski’s theory of mixed volumes.
منابع مشابه
Densest local sphere-packing diversity. II. Application to three dimensions.
The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius R(min)(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 [A. B. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E 81, 041305 (2010)], we described our method for finding the putative densest packings of N spher...
متن کاملDensest binary sphere packings.
The densest binary sphere packings in the α-x plane of small to large sphere radius ratio α and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known "alloy" phases including, for example, the AlB(2) (hexagonal ω), HgBr(2), and AuTe(2) structures, and to XY(n) structu...
متن کاملDensest columnar structures of hard spheres from sequential deposition.
The rich variety of densest columnar structures of identical hard spheres inside a cylinder can surprisingly be constructed from a simple and computationally fast sequential deposition of cylinder-touching spheres, if the cylinder-to-sphere diameter ratio is D is an element of [1,2.7013]. This provides a direction for theoretically deriving all these densest structures and for constructing such...
متن کاملHard convex lens-shaped particles: Densest-known packings and phase behavior.
By using theoretical methods and Monte Carlo simulations, this work investigates dense ordered packings and equilibrium phase behavior (from the low-density isotropic fluid regime to the high-density crystalline solid regime) of monodisperse systems of hard convex lens-shaped particles as defined by the volume common to two intersecting congruent spheres. We show that, while the overall similar...
متن کاملMaximally dense packings of two-dimensional convex and concave noncircular particles.
Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London) 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space R(d). W...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 24 شماره
صفحات -
تاریخ انتشار 2000