Ropelength for periodic links (A12)

周期性连接的绳索长度 (A12)

• 批准号: 315965799
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: CRC/Transregios
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/315965799?language=en
• 关键词: Ropelength; periodic; links; A12

The ropelength problem studies the shape of knots and links when tied tight in (idealized) rope. We consider ropelength for links in the three-torus, that is, for triply periodic networks of filaments in space. Such networks arise throughout materials science, for instance in polymers and proteins. We have extended the theory of ropelength criticality to this periodic case and will work to understand the behavior of minimizers as the lattice of periodicity is varied. We have enumerated singly periodic links, and will extend this enumeration to the doubly and triply periodic cases. We will search for further cases where tight shapes can be described exactly, and will investigate more complicated examples numerically.

绳长问题研究在（理想的）绳子上系紧时结和链节的形状。我们考虑三圆环中的链接的绳索长度，即空间中细丝的三周期网络。这种网络出现在整个材料科学中，例如在聚合物和蛋白质中。我们已将绳长临界性理论扩展到这种周期性情况，并将努力理解最小化器在周期性网格变化时的行为。我们已经枚举了单周期链接，并将将此枚举扩展到双周期和三周期情况。我们将寻找可以精确描述紧密形状的更多情况，并将以数值方式研究更复杂的示例。