On Limits of Dense Packing of Equal Spheres in a Cube
نویسندگان
چکیده
منابع مشابه
On Limits of Dense Packing of Equal Spheres in a Cube
We examine packing of n congruent spheres in a cube when n is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of dp3/2e spheres. For this family of packings, the previous best-known arrangements were usually derived from a ccp by omission of a certain number of spheres without changing the initial structure. In this paper, we show that better arrangem...
متن کاملDense Packings of Equal Spheres in a Cube
We describe an adaptation of the billiard algorithm for finding dense packings of equal spheres inside a domain of the euclidean space. In order to improve the convergence of this stochastic algorithm, we introduce systematic perturbations in it. We apply this perturbed billiard algorithm in the case of n spheres in a cube and display all the optimal and best known packings up to n = 32. We imp...
متن کاملDensest Packing of Equal Spheres in Hyperbolic Space
We propose a method to analyze the density of packings of spheres of fixed radius in the hyperbolic space of any dimension m ≥ 2, and prove that for all but countably many radii, optimally dense packings must have low symmetry.
متن کاملPacking non-equal spheres into containers of different shapes
The article reviews a mathematical model of the optimization problem of packing different spheres into a container which can be a cuboid, a sphere, a right circular cylinder, an annular cylinder and a spherical layer. The assumption that sphere radii are variable is exploited. Based on the hypothesis a new way to derive starting point belonging to the feasible region of the problem is offered. ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/3784