منابع مشابه
Enumerating Rigid Sphere Packings
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 behavior at larger ones. In many systems there is no single, optimal packing that dominates, but rather one must understand the entire set of possible packings. As a step in thi...
متن کاملEnumerating Finite Sphere Packings
We consider packings of n identical spherical particles that bind to one another without deformation or overlap, and without any long range interactions. Combining graph theoretic enumeration with basic geometry, we analytically solve for packings of n ≤ 10 particles satisfying minimal rigidity constraints (≥ 3 contacts per particle and ≥ 3n− 6 total contacts). We find that the onset of packing...
متن کاملSphere Packings
This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section numbers with I, II, or F. Around each vertex is a modification of the Voronoi cell, called the V -cell ...
متن کاملSphere Packings Iii
Thus in the closest pack in three dimensions, the triangular pattern cannot exist without the square, and vice versa. Abstract: An earlier paper describes a program to prove the Kepler conjecture. This paper reduces the third step of that program to a system of inequalities and one exceptional connguration of spheres. Although these inequalities have not yet been rigorously established, they se...
متن کاملRegular Sphere Packings
A collection of non-overlapping spheres in the space is called a packing. Two spheres are said to be neighbours if they have a boundary point in common. A packing is called k-regular if each sphere has exactly k neighbours. We are concerned with the following question. What is the minimum number of not necessarily congruent spheres which may form a k-regular packing? In general, for which natur...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2016
ISSN: 0036-1445,1095-7200
DOI: 10.1137/140982337