Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
1999-06-03
Physics
Condensed Matter
Soft Condensed Matter
11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999)
Scientific paper
10.1103/PhysRevE.60.3227
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.
Haijun Zhou
Liu Ji-Xing
Liu Quan-Hui
Zhong-Can Ou-Yang
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