arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0909.0156cond-mat.softcond-mat.otherphysics.bio-phq-bio.QM
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自由边脂膜形状方程与边界条件的相容性

Compatibility between shape equation and boundary conditions of lipid membranes with free edges

Z. C. Tu

摘要:

只有满足脂膜形状方程的特殊开曲面才能与边界条件相容。由于这种相容性,形状方程的第一个积分应消失轴对称脂膜,其中两个定理的不存在性得到验证:(i)没有轴对称的开放膜的一部分环面满足形状方程;(ii)没有轴对称的开放膜的一部分的双凹盘状表面满足形状方程。此外,由于这种兼容性,形状方程被简化为二阶微分方程,而边界条件则被简化为两个方程。简化形状方程和边界条件的数值解与实验值符合得很好[A. Saitoh \emph{et al.},Proc. Natl. Acad. Sci. USA \textbf{95},1026(1998)]。

英文摘要:

Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions. As a result of this compatibility, the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation; (ii) There is no axisymmetric open membrane being a part of a biconcave discodal surface satisfying the shape equation. Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this compatibility. Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh \emph{et al.}, Proc. Natl. Acad. Sci. USA \textbf{95}, 1026 (1998)].

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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