双凹盘形解开口膜泡形状的解析法研究

随着开口膜泡在实验上的发现,对开口泡形状的数值及解析研究逐渐成为该领域的一个热点.讨论了如何由欧阳双凹盘形闭合解构造开口泡的解析解的问题.首先将开口泡要满足的三个不独立的边界条件简化为两个独立的边界条件,给出高斯测地曲率kg=-2,边界条件2可满足,然后由边界条件1得到确定膜泡边界的几何方程.进而讨论了由欧阳双凹盘解可构造的开口泡的各种可能形状,得到了三类管型拓扑解,它们是外凸管形解、类环管形解、类悬链面管形解.

An analytical solution for opening-up vesicle based on the circular biconcave shape

The numerical and the analytical studies of the opening-up vesicles have become hot topics since the experimental observation by A. Saitoh et al. This paper deals with how to obtain the analytical solution of an opening-up shape from the Ouyang biconcave analytical solution. We find only two of the three boundary conditions for the vesicle rims to be independent. The second boundary condition can be satisfied by the Gaussian bending modulus k_g=-2, then we obtain the geometric equation for the rims of an opening-up vesicle from the first boundary condition. By analyzing the Ouyang analytic solutions for a closed circular biconcave vesicle and periodic noduloidlike vesicle, we obtain three kinds of shapes with tube topology, which are the convex tube, the toruslike tube, and the catenoidlike tube.