Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Buckling transition and boundary layer in non-Euclidean plates   Non-Euclidean plates are thin elastic bodies having no stress-free
configuration, hence exhibiting residual stresses in the absence of external
constraints. These bodies are endowed with a three-dimensional reference
metric, which may not necessarily be immersible in physical space. Here, based
on a recently developed theory for such bodies, we characterize the transition
from flat to buckled equilibrium configurations at a critical value of the
plate thickness. Depending of the reference metric, the buckling transition may
be either continuous or discontinuous. In the infinitely thin plate limit,
under the assumption that a limiting configuration exists, we show that the
limit is a configuration that minimizes the bending content, amongst all
configurations with zero stretching content (isometric immersions of the
mid-surface). For small but finite plate thickness we show the formation of a
boundary layer, whose size scales with the square root of the plate thickness,
and whose shape is determined by a balance between stretching and bending
energies.

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The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph