Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Apollonian structure in the Abelian sandpile   The Abelian sandpile process evolves configurations of chips on the integer
lattice by toppling any vertex with at least 4 chips, distributing one of its
chips to each of its 4 neighbors. When begun from a large stack of chips, the
terminal state of the sandpile has a curious fractal structure which has
remained unexplained. Using a characterization of the quadratic growths
attainable by integer-superharmonic functions, we prove that the sandpile PDE
recently shown to characterize the scaling limit of the sandpile admits certain
fractal solutions, giving a precise mathematical perspective on the fractal
nature of the sandpile.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat