Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How dense can one pack spheres of arbitrary size distribution?   We present the first systematic algorithm to estimate the maximum packing
density of spheres when the grain sizes are drawn from an arbitrary size
distribution. With an Apollonian filling rule, we implement our technique for
disks in 2d and spheres in 3d. As expected, the densest packing is achieved
with power-law size distributions. We also test the method on homogeneous and
on empirical real distributions, and we propose a scheme to obtain
experimentally accessible distributions of grain sizes with low porosity. Our
method should be helpful in the development of ultra-strong ceramics and high
performance concrete.

7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: eess