压缩弹性流体界面的形状、力与力矩：超越轴对称构型
Shapes, forces, and torques of compressed elastic fluid interfaces: beyond axisymmetric configurations
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中文总结 AI 辅助
该研究将Plateau-Douglas问题推广至非轴对称弹性流体界面，通过弱非线性分析和谱求解器分类屈曲模式，为软材料界面稳定提供理论支撑。
中文摘要 AI 辅助
受经典Plateau-Douglas问题（针对由两条闭合曲线界定的肥皂膜）启发，我们求解具有固定表面积且抵抗平面外弯曲的流体界面的类似问题。边界为平面，但无需对称或同心。平衡表面使Willmore弯曲能最小化，是悬链面等极小曲面的推广，同时呈现受限弹性界面的特征，如屈曲。我们通过弱非线性分析和开发完全非线性谱求解器，系统分类所有可能的屈曲模式和解分支。该数学框架为稳定细胞膜及其他软材料所需的力与力矩提供了新的认识，表明即使在对称系统中也可出现与物理相关的非对称状态。
英文摘要
Inspired by the classical Plateau-Douglas problem for soap films bounded by two closed curves, we solve an analogous problem for fluid interfaces with fixed surface area and resistance to out-of-plane bending. The boundaries are planar but need not be symmetric or concentric. The equilibrium surfaces minimize the Willmore bending energy and generalize minimal surfaces such as the catenoid while also exhibiting characteristic features of confined elastic interfaces such as buckling. We systematically classify all possible buckling modes and solution branches by performing a weakly nonlinear analysis and developing a fully nonlinear spectral solver. Our mathematical framework provides insight into the forces and torques required to stabilize cellular membranes and other soft materials and shows that physically relevant asymmetric states can arise even in symmetric systems.
