Ropelength for periodic links (A12)

绳长问题研究的是（理想的）绳系紧时的结和环的形状。我们考虑三环体中的链路的长度，即空间中三周期的细丝网络。这种网络在材料科学中随处可见，例如聚合物和蛋白质。我们将长度临界理论扩展到这种周期情况，并将努力理解当周期格变化时最小值的行为。我们已经列举了单周期链接，并将此列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进一步情况，并将研究更复杂的数值例子。

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.