Title: Energy Variational Modeling and Numerical Simulation of Open Membranes in Stokes Flow Show Chinese title

Title: 开放膜在斯托克斯流中的能量变分建模与数值模拟

Abstract: Lipid bilayer membranes are fundamental biological structures that serve as cellular boundaries, mediating transport, signaling, and maintaining structural integrity. This study introduces a novel mathematical model for open membranes immersed in Stokes flows, accounting for membrane elasticity, line tension at the open edge, and fluid-membrane interactions. The model is derived from an energy functional that incorporates Helfrich bending energy and a line energy associated with the open edge. By balancing dissipation in both the bulk fluid and the membrane surface, following the maximal dissipation principle, we derive the governing equations within an energy variational framework. Assuming axisymmetry and employing a boundary integral reduction, we transform the 3D problem into an effectively 1D problem, for which we develop a finite element-based numerical method to solve the resulting moving boundary problem. Several numerical examples are provided to validate the model and compare the results with existing studies. Show Chinese abstract

Abstract: 脂质双层膜是基本的生物结构，作为细胞边界，介导运输、信号传递和维持结构完整性。 本研究介绍了一种用于沉浸在斯托克斯流中的开放膜的新数学模型，考虑了膜的弹性、开放边缘的线张力以及流体-膜相互作用。 该模型来源于一个包含赫尔里奇弯曲能和与开放边缘相关的线能的能量泛函。 通过平衡体流和膜表面的耗散，遵循最大耗散原理，我们在能量变分框架内推导出控制方程。 假设轴对称性并采用边界积分约简，我们将三维问题转化为一个有效的一维问题，并开发了一种基于有限元的数值方法来解决由此产生的移动边界问题。 提供了几个数值示例来验证模型，并将结果与现有研究进行比较。