流体动力学欧拉 - 弹性体：斯托克斯流中弹性细丝动态屈曲的形状转变
The hydrodynamic Euler-elastica: shape transitions in the dynamical buckling of elastic filaments in Stokes flow
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中文总结 AI 辅助
研究斯托克斯流中弹性细丝动态屈曲的形状转变，用粗粒度数值模型揭示三种形态状态，由无量纲屈曲数主导，傅里叶分析表明状态转变源于曲率模式竞争，发现不同形状对小扰动敏感，弥合了静态和动态屈曲理论。
中文摘要 AI 辅助
粘性流体中弹性细丝的屈曲现象在鞭毛、微管和DNA等生物系统中普遍存在，长期以来一直由静态欧拉 - 弹性体描述。然而，当细丝动态屈曲时，其形状与静态预测不同，表现出复杂、不可预测的行为。本文使用粗粒度数值模型探索斯托克斯流中细丝屈曲的长时间尺度动力学，揭示了翻转、环和结三种不同的形态状态。每种状态的主导主要由无量纲屈曲数Bu控制。傅里叶分析表明，形状状态之间的转变源于前三个曲率模式之间的竞争，高阶模式衰减符合指数规律。在某些参数范围内，相近初始条件下不同形状共存，表明对小扰动具有确定性敏感性。这些发现弥合了静态和动态屈曲理论，对生物推进和微尺度细长游泳者的设计具有重要意义。
英文摘要
The buckling of elastic filaments in viscous fluids, ubiquitous in biological systems like flagella, microtubules, and DNA, has long been described by the static Euler-elastica. Yet, when such filaments buckle dynamically, their shapes defy static predictions, exhibiting complex, unpredictable behaviours. Here, we use a coarse-grained numerical model to explore the long-timescale dynamics of filament buckling in Stokes flow, revealing three distinct morphological regimes, termed flip, loop, and knot. The dominance of each regime is primarily governed by the dimensionless buckling number $\mathrm{Bu}$. Fourier analysis shows that these transitions between shape regimes arise from competition between the first three curvature modes, with high-order modes decay fitting an exponential law. In some parameter ranges, distinct shapes coexist for close initial conditions, indicating deterministic sensitivity to small perturbations. These findings bridge static and dynamic buckling theories, with implications for biological propulsion and the design of microscale slender swimmers.
