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arXiv 2104.09212cond-mat.soft
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气泡表面细丝的形状

Shapes of a filament on the surface of a bubble

S Ganga Prasath, Joel Marthelot, Rama Govindarajan, Narayanan Menon

AI总结:

本文结合实验、理论与数值能量最小化,研究球形气泡表面细丝在几何、弹性与重力竞争下的形态分岔及盘绕行为。

摘要:

细长弹性结构所呈现的形状,既取决于其所处空间的几何,也取决于其所承受的力。我们通过实验和理论分析,探究了被限制在球形气泡表面的细丝的形态相空间。通过改变细丝的弯曲刚度、重量以及其长度相对于气泡半径的大小,可以控制其形态。当限制几何和弹性能量占主导时,细丝沿测地线分布;而当重力能量变得显著时,会发生分岔,细丝的一部分占据一条经线,其余部分则沿一条可近似为纬线的曲线分布。在远离转变点、细丝远长于气泡直径时,它会在选定的纬向区域周围盘绕。一个将细丝形状视为两段弧线组合的简单模型能够很好地捕捉该转变;为了与分岔的亚临界性质取得更好的定量一致,我们通过数值能量最小化研究了其形态。我们对细丝形态空间的分析由一个几何参数以及另一个比较弹性能量与体积力的参数所张成,可能为在复杂表面上装填细长结构提供指导。

英文摘要:

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore by experiments and theoretical analysis, the morphological phase-space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well and for better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of filament's morphological space spanned by a geometric parameter, and one that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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