论文标题
分布式分支点和具有恒定负曲率的弹性表面的形状
Distributed branch points and the shape of elastic surfaces with constant negative curvature
论文作者
论文摘要
我们开发了一种用于分布式分支点的理论，并研究了它们在确定薄屈曲物体机制的形状和影响力学中的作用。我们表明，分支点是双曲线板中的自然拓扑缺陷，它们具有拓扑指数，使它们具有一定的稳健性，并且可以影响双曲线表面的整体形态而无需集中能量。我们开发了一种离散的差别几何方法（DDG）方法来研究具有分布分支点的双曲线对象的变形。我们提供了证据表明，带有大地半径$ r $包含分支点的表面的最大曲率在$ o（e^{c \ sqrt {r}}）$上，与指数级增长$ o（e^{c'r}）$相反。我们认为，要优化曲率的规范，即弯曲能，分布式分支点在足够大的伪层表面上是能量优选的。此外，它们是分布的，以便导致分形递归屈曲模式。
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic sheets, they carry a topological index which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating energy. We develop a discrete differential geometric (DDG) approach to study the deformations of hyperbolic objects with distributed branch points. We present evidence that the maximum curvature of surfaces with geodesic radius $R$ containing branch points grow sub-exponentially, $O(e^{c\sqrt{R}})$ in contrast to the exponential growth $O(e^{c' R})$ for surfaces without branch points. We argue that, to optimize norms of the curvature, i.e. the bending energy, distributed branch points are energetically preferred in sufficiently large pseudospherical surfaces. Further, they are distributed so that they lead to fractal-like recursive buckling patterns.
