论文标题
$ \ mathbb {z}^2 $配置的稳定性
Stability of $\mathbb{Z}^2$ configurations in 3D
论文作者
论文摘要
受分子结构稳定性问题的启发，我们研究了有关具有两体和三体贡献的构型能量集合的严格最小值。我们的主要重点是表征那些在没有第一个邻居成对的第一个邻居或角度之间的距离或角度之间无法变形的配置。此类配置称为{\ it Angle-rigid}。 我们在$ \ mathbb {z}^2 $中的有限配置类别中解决了这个问题，被视为平面三维点集。提出了足够的防止角rigities的条件。当仅限于特定的配置子类时，这种情况也被证明是必要的。
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-body contributions. Our main focus is on characterizing those configurations which cannot be deformed without changing distances between first neighbors or angles formed by pairs of first neighbors. Such configurations are called {\it angle-rigid}. We tackle this question in the class of finite configurations in $\mathbb{Z}^2$, seen as planar three-dimensional point sets. A sufficient condition preventing angle-rigidity is presented. This condition is also proved to be necessary when restricted to specific subclasses of configurations.
