Hyperbolic non-Euclidean elastic strips and almost minimal surfaces
Hyperbolic non-Euclidean elastic strips and almost minimal surfaces
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DOI：
10.1103/physreve.83.046602
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发表时间：
2011-04-13
影响因子：
2.4
通讯作者：
Kupferman, Raz
中科院分区：
文献类型：
--
作者：
Efrati, Efi;Sharon, Eran;Kupferman, Raz
研究了细长非欧几里得弹性条的平衡构型，该弹性条具有沿条不变的双曲二维参考度量(a)。在消失的厚度极限下，能量最小值是通过最小化(a) / bar的所有等距嵌入的平均曲率平方的积分来获得的。对于窄条，无论度规的具体形式如何，这些最小值都非常接近最小表面。我们研究了这些“几乎最小”表面的性质，发现了丰富的三维稳定构型。我们提供了一些明确的解决方案，以及一个框架，以纳入额外的力量和约束。
We study equilibrium configurations of thin and elongated non-Euclidean elastic strips with hyperbolic two-dimensional reference metrics (a) over bar which are invariant along the strip. In the vanishing thickness limit energy minima are obtained by minimizing the integral of the mean curvature squared among all isometric embeddings of (a) over bar. For narrow strips these minima are very close to minimal surfaces regardless of the specific form of the metric. We study the properties of these "almost minimal" surfaces and find a rich range of three-dimensional stable configurations. We provide some explicit solutions as well as a framework for the incorporation of additional forces and constraints.