Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous elasticity, fluctuations and disorder in elastic membranes   Motivated by a freely suspended graphene and polymerized membranes in soft
and biological matter we present a detailed study of a tensionless elastic
sheet in the presence of thermal fluctuations and quenched disorder. The
manuscript is based on an extensive draft dating back to 1993, that was
circulated privately. It presents the general theoretical framework and
calculational details of numerous results, partial forms of which have been
published in brief Letters (Le Doussal and Radzihovsky 1992). The experimental
realization of atom-thin graphene sheets has driven a resurgence in this
fascinating subject, making our dated predictions and their detailed
derivations timely. To this end we analyze the statistical mechanics of a
generalized D-dimensional elastic "membrane" embedded in d dimensions using a
self-consistent screening approximation (SCSA), that has proved to be
unprecedentedly accurate in this system, exact in three complementary limits: d
--> infinity, D --> 4, and D=d. Focusing on the critical "flat" phase, for a
homogeneous two-dimensional membrane embedded in three dimensions, we predict
its universal length-scale dependent roughness, elastic moduli exponents, and a
universal negative Poisson ratio of -1/3. We also extend these results to
short- and long-range correlated random heterogeneity, predicting a variety of
glassy wrinkled membrane states. Finally, we also predict and analyze a
continuous crumpling transition in a "phantom" elastic sheet. We hope that this
detailed presentation of the SCSA theory will be useful for further theoretical
developments and corresponding experimental investigations on freely suspended
graphene.

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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
18
The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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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: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
2
The categories of this paper are: math
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The categories of this paper are: chem-ph