悬垂窗帘中褶皱的粗化
The coarsening of folds in hanging drapes
摘要：
我们考虑悬垂物的弹性能--一个薄的弹性片，被重力拉下，在顶部有精细的折叠，实现近似均匀的限制。在薄弹性片材中的能量驱动图案形成的该示例特别令人感兴趣，因为折叠的长度尺度随高度而变化。我们重点讨论了最小弹性能如何依赖于物理参数。当薄板厚度为零时，极限能量是由于重力，这相对容易理解。我们的主要成就是确定了由于正厚度引起的校正的“标度律”。我们这样做是通过（i）证明一个上界，通过考虑几个结构的能量，并采取最好的;（ii）证明一个ansatz自由的下界，这与上界一致的参数无关的前因子。最近的物理学文献中也考虑了悬垂物中褶皱的粗化，使用了一种自相似结构，其基本单元被称为“褶皱”。“我们的结果补充和扩展了这项工作，通过显示自相似粗化在一定的参数范围内实现了最佳标度律，并通过显示其他结构（涉及片材的横向扩展）在参数空间的其他区域中做得更好。我们的分析使用几何线性Föppl-vonKármán模型的弹性能量，并限制在泊松比为零的情况下。
英文摘要：
We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern formation in a thin elastic sheet is of particular interest because the length scale of folding varies with height. We focus on how the minimum elastic energy depends on the physical parameters. As the sheet thickness vanishes, the limiting energy is due to the gravitational force and is relatively easy to understand. Our main accomplishment is to identify the "scaling law" of the correction due to positive thickness. We do this by (i) proving an upper bound, by considering the energies of several constructions and taking the best; (ii) proving an ansatz-free lower bound, which agrees with the upper bound up to a parameter-independent prefactor. The coarsening of folds in hanging drapes has also been considered in the recent physics literature, using a self-similar construction whose basic cell has been called a "wrinklon." Our results complement and extend that work, by showing that self-similar coarsening achieves the optimal scaling law in a certain parameter regime, and by showing that other constructions (involving lateral spreading of the sheet) do better in other regions of parameter space. Our analysis uses a geometrically linear Föppl-von Kármán model for the elastic energy, and is restricted to the case when Poisson's ratio is zero.
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。
