Unequal sphere packing
When the second sphere is much smaller than the first, it is possible to arrange the large spheres in a close-packed arrangement, and then arrange the small spheres within the octahedral and tetrahedral gaps.
People also ask
What is the best way to pack spheres?
In 1611, the physicist Johannes Kepler thought about the best way to pack three-dimensional spheres. For the base layer, he packed the spheres in a hexagonal arrangement, like the circles. He then placed a second layer of spheres over the first, filling the gaps.
Apr 30, 2024
What is the random packing of equal spheres?
Experiments and computer simulations have shown that the most compact way to pack hard perfect same-size spheres randomly gives a maximum volume fraction of about 64%, i.e., approximately 64% of the volume of a container is occupied by the spheres.
How many spheres can you pack around a sphere?
Before Hales' proof, it was well known that the kissing number in 3D is 12, i.e., that the maximum number of nonoverlapping spheres that one could fit around one sphere, each touching the one sphere, is 12. The way cannon balls and oranges are normally packed, every sphere touches 12 other spheres.
Which structure has the highest packing possible of same sized spheres?
The FCC and HCP packings are the densest known packings of equal spheres with the highest symmetry (smallest repeat units).
Given a set of unequal spheres and a poly- tope, the double goal is to assemble the spheres in such a way that. (i) they do not overlap with each other and (ii) ...
We propose a new solution method based on a combination of a branch-and-bound approach and the known local optimization method.
Feb 9, 2021 · I want to change the packing density to something more like 0.55, maybe even lower. Could this be done by using different sized dissolvable beads?
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Jul 3, 2012 · Unequal sphere packing is fascinating and has been examined extensively. ... Another search term is "mixed sphere packing," also "multi-sized ...
Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm.
Apr 30, 2024 · Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.
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Sphere packing is the problem of arranging non-overlapping spheres within some space, with the goal of maximizing the combined volume of the spheres.
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May 27, 2016 · The paper considers an optimization problem of packing different solid spheres into containers of the following types: a cuboid, a sphere, ...
We employ the Monte Carlo method to study a constrained optimization problem — packing hard spheres with unequal radii (r2 > r1) into a 3D bounded region ...