Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of
  Spontaneous Curvature Fluid Membrane Model   An analytic solution for Helfrich spontaneous curvature membrane model (H.
Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf
54}, 2816 (1996)), which has a conspicuous feature of representing the circular
biconcave shape, is studied. Results show that the solution in fact describes a
family of shapes, which can be classified as: i) the flat plane (trivial case),
ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the
oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting
inverted circular biconcave shape, and viii) the self-intersecting nodoidlike
cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the
one with the minimum of local curvature energy.

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The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th