Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similar and disordered front propagation in a radial Hele-Shaw
  channel with time-varying cell depth   The displacement of a viscous fluid by an air bubble in the narrow gap
between two parallel plates can readily drive complex interfacial pattern
formation known as viscous fingering. We focus on a modified system suggested
recently by [1], in which the onset of the fingering instability is delayed by
introducing a time-dependent (power-law) plate separation. We perform a
complete linear stability analysis of a depth-averaged theoretical model to
show that the plate separation delays the onset of non-axisymmetric
instabilities, in qualitative agreement with the predictions obtained from a
simplified analysis by [1]. We then employ direct numerical simulations to show
that in the parameter regime where the axisymmetrically expanding air bubble is
unstable to nonaxisymmetric perturbations, the interface can evolve in a
self-similar fashion such that the interface shape at a given time is simply a
rescaled version of the shape at an earlier time. These novel, self-similar
solutions are linearly stable but they only develop if the initially circular
interface is subjected to unimodal perturbations. Conversely, the application
of non-unimodal perturbations (e.g. via the superposition of multiple linearly
unstable modes) leads to the development of complex, constantly evolving finger
patterns similar to those that are typically observed in constant-width
Hele-Shaw cells.
  [1] Z. Zheng, H. Kim, and H. A. Stone, Controlling viscous fingering using
time-dependent strategies, Phys. Rev. Lett. 115, 174501 (2015).

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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga