Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nematic director fields and topographies of shells of revolution   We solve the forward and inverse problems associated with the transformation
of flat sheets to surfaces of revolution with non-trivial topography, including
Gaussian curvature, without a stretch elastic cost. We deal with systems
slender enough to have a small bend energy cost. Shape change is induced by
light or heat causing contraction along a non-uniform director field in the
plane of an initially flat nematic sheet. The forward problem is, given a
director distribution, what shape is induced? Along the way, we determine the
Gaussian curvature and the evolution with induced mechanical deformation of the
director field and of material curves in the surface (proto-radii) that will
become radii in the final surface. The inverse problem is, given a target
shape, what director field does one need to specify? Analytic examples of
director fields are fully calculated that will, for specific deformations,
yield catenoids and paraboloids of revolution. The general prescription is
given in terms of an integral equation.

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The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
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The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: math