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A series representation of the nonlinear equation for axisymmetrical fluid membrane shape | | B. Hu
; Q. H. Liu J. X. Liu
; X. Wang
; H. Zhang
; O. Y. Zhong-Can
; | | Date: |
31 Jul 2000 | | Subject: | Soft Condensed Matter | cond-mat.soft | | Affiliation: | 1,and 2), Q. H. Liu (1,3,and 4) J. X. Liu , X. Wang , H. Zhang, O. Y. Zhong-Can (,Department of Physics and the Center for Nonlinear Studies, Hong Kong Baptist University; ,Department of Physics, University of Houston; ,Department of Applied Physics, H | | Abstract: | Whatever the fluid lipid vesicle is modeled as the spontaneous-curvature, bilayer-coupling, or the area-difference elasticity, and no matter whether a pulling axial force applied at the vesicle poles or not, a universal shape equation presents when the shape has both axisymmetry and up-down symmetry. This equation is a second order nonlinear ordinary differential equation about the sine $sinpsi (r)$ of the angle $psi (r)$ between the tangent of the contour and the radial axis $r$. However, analytically there is not a generally applicable method to solve it, while numerically the angle $psi (0)$ can not be obtained unless by tricky extrapolation for $r=0$ is a singular point of the equation. We report an infinite series representation of the equation, in which the known solutions are some special cases, and a new family of shapes related to the membrane microtubule formation, in which $sinpsi (0)$ takes values from 0 to $pi /2$, is given. | | Source: | arXiv, cond-mat/0007489 | | Services: | Forum | Review | PDF | Favorites | |
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