Spheres and prolate and-oblate ellipsoids from an analytical solution of the spontaneous-curvature fluid-membrane model

摘要

An analytic solution for the Helfrich spontaneous curvature membrane model [H. Naito, M.Okuda, and pu-Yang Zhong-Can,Phys. Rev. E 48, 2304 (1993); 54, 2816 (1996)], which has the conspicuous feature of representing a circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as (i) a flat plane (trivial case), (ii) a sphere, (iii) a prolate ellipsoid, (iv) a capped cylinder, (v) an oblate ellipsoid, (vi) a circular biconcave shape, (vii) a self-intersecting inverted circular biconcave shape, and (viii) a self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with a minimum of local curvature energy. [S1063-651X(49)00309-8]. [References: 21]