由Helfrich能量导出的“膜形方程”的局部灵敏度分析
Local sensitivity analysis of the `Membrane shape equation' derived from the Helfrich energy
摘要：
在膜力学中，Helfrich能量通常用于模拟脂双层的弹性弯曲能。膜的形状的某些几何特征的控制微分方程可以通过将变分方法（最小化原理）应用于Helfrich能量泛函而获得，并且在轴对称框架中得到了很好的研究。然而，Helfrich能量泛函和由此产生的微分方程涉及一些参数，并且在文献中很少有关于参数选择的解释，特别是关于出现在泛函中的“自发曲率”项的选择。在本文中，我们提出了一个仔细的分析和数值研究的某些方面的参数敏感性的Helfrich的使用模拟特定的模型系统，我们证明了我们的计划的应用程序形成的球形芽和珍珠形状的膜囊泡。
英文摘要：
The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well-studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the "spontaneous curvature" term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrich's Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.
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