Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Competition is the underlying mechanism controlling viscous fingering
  and wormhole growth   Viscous fingering and wormhole growth are complex nonlinear unstable
phenomena. We view both as the result of competition for water in which the
capacity of an instability to grow depends on its ability to carry water. We
derive empirical solutions to quantify the finger/wormhole flow rate in
single-, two-, and multiple-finger systems. We use these solutions to show that
fingering and wormhole patterns are a deterministic result of competition. For
wormhole growth, controlled by dissolution, we solve re-active transport
analytically within each wormhole to compute dissolution at the wormhole walls
and tip. The generated patterns (both for viscous fingering and wormhole growth
under moderate Damk ohler values) follow a power law decay of the number of
fingers/wormholes with depth with an exponent of -1 consistent with field
observations

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The categories of this paper are: hep-lat
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph