Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local growth of icosahedral quasicrystalline tilings   Icosahedral quasicrystals (IQCs) with extremely high degrees of translational
order have been produced in the laboratory and found in naturally occurring
minerals, yet questions remain about how IQCs form. In particular, the
fundamental question of how locally determined additions to a growing cluster
can lead to the intricate long-range correlations in IQCs remains open. In
answer to this question, we have developed an algorithm that is capable of
producing a perfectly ordered IQC, yet relies exclusively on local rules for
sequential, face-to-face addition of tiles to a cluster. When the algorithm is
seeded with a special type of cluster containing a defect, we find that growth
is forced to infinity with high probability and that the resultant IQC has a
vanishing density of defects. The geometric features underlying this algorithm
can inform analyses of experimental systems and numerical models that generate
highly ordered quasicrystals.

28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol