Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spontaneous free-boundary structure in crumpled membranes   We investigate the strong curvature that appears at the boundaries of a thin
crumpled elastic membrane. We account for these high-curvature regions in terms
of the stretching-ridge singularity believed to dominate the structure of
strongly deformed elastic membranes. Using a membrane fastened to itself to
form a bag shape with a single stretching ridge, we show that the creation of
points of high boundary curvature lowers the interior ridge's energy. In the
limit of small thickness, the induced curvature becomes arbitrarily strong on
the scale of the object size and results in sharp edges connecting interior
vertices to the boundary. REVISED: We analyze these edges as conical sectors
with no stretching. As the membrane size diverges, the edge energy grows as the
square root of the central ridge energy. For comparison, we discuss the effect
of truncating a stretching ridge at its ends. The effect of truncation becomes
appreciable when the truncation length is comparable to the width of the
untruncated ridge.

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The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: eess
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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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: atom-ph
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The categories of this paper are: mtrl-th