具常负曲率弹性曲面的分布分支点与曲面形状
Distributed branch points and the shape of elastic surfaces with constant negative curvature
摘要：
我们开发了一个理论，分布的分支点，并调查他们的作用，在确定的形状和影响薄双曲物体的力学。我们表明，分支点是双曲面的自然拓扑缺陷，它们携带的拓扑指数，这给他们一定程度的鲁棒性，他们可以影响一个双曲曲面的整体形态，而不集中能量。提出了一种离散微分几何（DDG）方法来研究具有分布分支点的双曲物体的变形。我们提出的证据表明，测地半径$R$包含分支点的表面的最大曲率增长的次指数，$O(e^{c\sqrt{R}})$相反的指数增长性$O(e^{c' R})$的表面没有分支点。我们认为，优化规范的曲率，即弯曲能量，分布分支点是积极的首选足够大的伪球面。此外，它们是分布的，因此它们导致类似分形的递归屈曲模式。
英文摘要：
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.
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。
