Theoretical and Applied Discrete Geometry

这个项目的研究涉及将刚体和非刚体框架理论和十段理论应用于离散几何问题。例如，扩展了首席研究员关于中心收缩下球盘的并或交的体积的克内塞-波尔森问题的结果，涉及弹性表面限制的体积不变的波纹管问题，机器人手臂的张开，某些稳定的高度对称的张拉整体结构的编目，以及涉及颗粒材料堆积的稳定性问题。考虑颗粒材料，在雪崩，沙子，岩石堆，M&A；M‘s，药丸，谷物，种子，粉末，以及小行星和行星上的风化。应用上述理论的一个很好的例子是当外力施加到颗粒材料上时。了解力在整个材料中的传递方式很重要，刚性结构的数学理论可以用来证明、阐明和简化这些力的计算。

Research on this project involves applying the theory of rigid and non-rigid frameworks and tensegrities to problems in discrete geometry. Examples involve extending the principle investigator's results on the Kneser-Poulsen problem concerning the volume of the union or intersection of spherical disks under contractions of their centers, bellows problems involving the invariance of the volume bounded by flexible surfaces, the opening of robot arms, the cataloguing of certain stable highly symmetric tensegrity structures, and stability questions involving packings of granular materials.Consider granular materials, which are seen in avalanches, sand, rock piles, piles of M&M's, pills, grain, seeds, powders, and the regolith on asteroids and planets. A good example of an application of the theory above is when an external force is applied to a granular material. Understanding the way that force is transmitted throughout the material is important, and the mathematical theory of rigid structures can be used to justify, elucidate, and simplify the calculations of these forces.