A series representation of the nonlinear equation for axisymmetrical fluid membrane shape

Details A series representation of the nonlinear equation for axisymmetrical fluid membrane shape A series representation of the nonlinear equation for axisymmetrical fluid membrane shape

2000-07-31

arxiv.org/abs/cond-mat/0007489v2

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

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 $sin\psi (r)$ 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 $sin\psi (0)$ takes values from 0 to $\pi /2$, is given.

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