Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morphological transitions of sliding drops: Dynamics and bifurcations   We study fully three-dimensional droplets that slide down an incline by
employing a thin-film equation that accounts for capillarity, wettability, and
a lateral driving force in small-gradient (or long-wave) approximation. In
particular, we focus on qualitative changes in the morphology and behavior of
stationary sliding drops. We employ the inclination angle of the substrate as
control parameter and use continuation techniques to analyze for several fixed
droplet sizes the bifurcation diagram of stationary droplets, their linear
stability, and relevant eigenmodes. The obtained predictions on existence
ranges and instabilities are tested via direct numerical simulations that are
also used to investigate a branch of time-periodic behavior (corresponding to
repeated breakup-coalescence cycles, where the breakup is also denoted as
pearling) which emerges at a global instability, the related hysteresis in
behavior, and a period-doubling cascade. The nontrivial oscillatory behavior
close to a Hopf bifurcation of drops with a finite-length tail is also studied.
Finally, it is shown that the main features of the bifurcation diagram follow
scaling laws over several decades of the droplet size.

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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con