Measuring geometric frustration in twisted inextensible filament bundles
Measuring geometric frustration in twisted inextensible filament bundles
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DOI：
10.1103/physreve.95.052503
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发表时间：
2017-05-31
影响因子：
2.4
通讯作者：
Kudrolli, Arshad
中科院分区：
文献类型：
--
作者：
Panaitescu, Andreea;Grason, Gregory M.;Kudrolli, Arshad
我们调查与实验和映射的结构，一个六角有序的纤维束，是在其两端附近举行，并围绕其中心轴逐渐扭曲。长丝相对于彼此自由滑动，并且进一步保持在无张力边界条件下。测量束包装与微X射线成像，我们发现，长丝开发的螺旋旋转欧米茄强加在边界。然后，我们表明，所观察到的结构是一致的映射的灯丝的位置，磁盘上的双重非欧几里德表面与高斯曲率增加扭曲。我们进一步证明，平均丝间距是最小的表面上，这可以近似为一个半球的有效曲率K-eff = 3 Ω（2）。检查包装的双重表面上，我们分析了几何挫折的包装在扭曲的束，并发现核心保持相对六角有序的纤维间应变从束中心的增长，驱动形成的缺陷在外部的高度扭曲的束。
We investigate with experiments and mapping the structure of a hexagonally ordered filament bundle that is held near its ends and progressively twisted around its central axis. The filaments are free to slide relative to each other and are further held under tension-free boundary conditions. Measuring the bundle packing with micro x-ray imaging, we find that the filaments develop the helical rotation Omega imposed at the boundaries. We then show that the observed structure is consistent with a mapping of the filament positions to disks packed on a dual non-Euclidean surface with a Gaussian curvature which increases with twist. We further demonstrate that the mean interfilament distance is minimal on the surface, which can be approximated by a hemisphere with an effective curvature K-eff = 3 Omega(2). Examining the packing on the dual surface, we analyze the geometric frustration of packing in twisted bundles and find the core to remain relatively hexagonally ordered with interfilament strains growing from the bundle center, driving the formation of defects at the exterior of highly twisted bundles.