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 model. 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.

中文翻译：

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从Helfrich能量得出的“膜形状方程”的局部灵敏度分析

Helfrich能量通常用于模拟膜力学中脂质双层的弹性弯曲能。可以通过对Helfrich能量泛函应用变分方法（最小化原理）来获得膜的某些几何特征的控制微分方程，并在轴对称框架中进行了深入研究。但是，Helfrich能量泛函和所产生的微分方程涉及许多参数，文献中很少有关于参数选择的解释，特别是对于出现在函数中的“自发曲率”术语的选择。在本文中，我们对Helfrich模型的参数敏感性的某些方面进行了仔细的分析和数值研究。