论文标题
带有柔性半径的圆形包装的刚度
Rigidity of Circle Packings with Flexible Radii
论文作者
论文摘要
圆形包装是满足指定切实要求的圆圈的安排。关于圆形和球体包装的许多问题在自然界中出现在材料设计和蛋白质结构中。令人惊讶的是，关于圆形包装的稳定性和刚性知之甚少。在本文中，我们研究了代表给定平面图的圆形包装的刚度。圆的半径具有平等和不平等约束。我们提供了双重条件，以使包装在一阶上刚性。这使我们有足够的条件表明包装很严格。然后，我们将探索超出一阶刚性问题的困难。
Circle packings are arrangement of circles satisfying specified tangency requirements. Many problems about packing of circles and spheres occur in nature particularly in material design and protein structure. Surprisingly, little is known about the stability and rigidity of circle packings. In this paper, we study the rigidity of circle packings representing a given planar graph. The radii of circles are flexible with equality and inequality constraints. We provide a dual condition for the packing to be rigid in the first order. This gives us a sufficient condition to show a packing is rigid. Then we will explore the difficulties on rigidity problems beyond the first order.
