Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relaxation and Intermediate Asymptotics of a Rectangular Trench in a
  Viscous Film   The surface of a thin liquid film with nonconstant curvature flattens as a
result of capillary forces. While this leveling is driven by local curvature
gradients, the global boundary conditions greatly influence the dynamics. Here,
we study the evolution of rectangular trenches in a polystyrene nanofilm.
Initially, when the two sides of a trench are well separated, the asymmetric
boundary condition given by the step height controls the dynamics. In this
case, the evolution results from the leveling of two noninteracting steps. As
the steps broaden further and start to interact, the global symmetric boundary
condition alters the leveling dynamics. We report on full agreement between
theory and experiments for: the capillary-driven flow and resulting time
dependent height profiles; a crossover in the power-law dependence of the
viscous energy dissipation as a function of time as the trench evolution
transitions from two noninteracting to interacting steps; and the convergence
of the profiles to a universal self-similar attractor that is given by the
Green's function of the linear operator describing the dimensionless linearized
thin film equation.

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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci