Twist-grain-boundary phases in smectics are the geometrical analogs of the
Abrikosov flux lattice in superconductors. At large twist angles, the nonlinear
elasticity is important in evaluating their energetics. We analytically
construct the height function of a pi/2 twist-grain-boundary phase in smectic-A
liquid crystals, known as Schnerk's first surface. This construction, utilizing
elliptic functions, allows us to compute the energy of the structure
analytically. By identifying a set of heretofore unknown defects along the
pitch axis of the structure, we study the necessary topological structure of
grain boundaries at other angles, concluding that there exist a set of
privileged angles and that the \pi/2 and \pi/3 grain boundary structures are
particularly simple.Comment: 13 pages, 7 figure
