1999/06/03 by Quan-Hui Liu, Quanhui Liu, Zhou Haijun +4
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Medicine · Physics and Astronomy · #Axial ratio #Chemistry #Classical mechanics #Curvature #Cylinder #Ellipsoid #Erythrocyte Function and Pathophysiology #Geometry #Lipid Membrane Structure and Behavior #Mathematics #Oblate spheroid #Optics #Physics #Plane (geometry) #Prolate spheroid #SPHERES #Spheroid #Surfactants and Colloidal Systems #cond-mat.soft
paper · pdf · doi:10.1103/physreve.60.3227
11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999)
arxiv created 1999/06/03 · openalex publication_date 1999/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An analytic solution for the Helfrich spontaneous curvature membrane model [H. Naito, M.Okuda, and Ou-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.