三扭转莫比乌斯带的沉降动力学：几何与拓扑的较量
Sedimentation dynamics of triply-twisted Möbius bands: Geometry versus topology
AI总结：
本文通过实验和数值模拟研究具有三重旋转对称性的三扭转莫比乌斯带沉降动力学，发现其旋转方向不仅取决于扭转方向，还随纵横比变化，揭示了流体阻力与惯性效应的共同作用机制。
摘要：
手性物体一直吸引着数学、晶体学、化学和生物学等多个学科的科学家。莫比乌斯带是一种具有标志性的手性结构，可以通过将一条带子的两端在施加奇数个扭转后连接而成。传统上，扭转方向决定其在流体中沉降时的旋转行为。在此，我们展示了具有三重旋转对称性的三扭转莫比乌斯带的实验和计算研究，这些研究挑战了这一主流认识。我们探索了三种具有不同曲率的带子，每种带子由其构造方法定义。实验观察表明，所有三种带子在沉降过程中均沿轴向排列并表现出旋转运动。令人惊讶的是，只有一种带子的旋转方向（手性流体动力学响应）偏离了预期；它并非仅由扭转方向决定，而是随带子的纵横比变化。数值模拟证实了这一观察结果，并且对每种带子的阻力张量进行的深入分析揭示了这种转变的可能原因。我们提出，流体诱导阻力的变化与惯性效应共同构成了这一现象的基础。我们的研究挑战了现有的手性物体流体动力学知识，丰富了我们对于复杂流体动力学的理解。此外，它在多个领域提供了变革性的潜力，有望推动混合、分离过程以及新型被动游动装置的发展。
英文摘要：
Chiral objects have intrigued scientists across several disciplines, including mathematics, crystallography, chemistry, and biology. A Möbius band, an emblematic chiral structure, can be made by connecting the ends of a strip after applying an odd number of twists. Traditionally, the direction of the twist governs its rotational behaviour during sedimentation in a fluid. Here, we present experimental and computational investigations of triply-twisted Möbius bands boasting threefold rotational symmetry that challenge this prevailing understanding. We explore three types of bands with different curvatures, each defined by its construction method. Experimental observations reveal that all three types of bands align axially and exhibit rotational motion during sedimentation. Surprisingly, for only one type of band the spinning direction (chiral hydrodynamic response) departs from expectations; it is not solely determined by the twist direction but changes with the aspect ratio of the band. Numerical simulations corroborate this observation, and an in-depth analysis of the resistance tensors of each type of band sheds light on the possible causes of this transition. We propose that modifications in fluid-induced drag, combined with inertial effects, underpin this phenomenon. Our study challenges existing knowledge of chiral object hydrodynamics, enriching our understanding of complex fluid dynamics. Moreover, it offers transformative potential across diverse fields, promising advancements in mixing, separation processes, and innovative passive swimmers.
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