The stability of several triply periodic surfaces

The stability of six triply periodic surfaces of constant mean curvature (CMC) is investigated. The relative energy and curvature values of the surfaces comprising the P (Pm (3) over barm), I-WP (Im (3) over barm), and G (I4(1)32) families are numerically calculated with K. Brakke's Surface Evolver. Regions where the I-WP surface can exist metastable to a complementary I-WP surface are found. This type of metastability is also found in the F-RD surface. Bifurcation points marking the stability limits of the P, I-WP, and G families are also calculated with Evolver. Modes of instability which may occur in the six CMC families are classified. Bifurcations in the P, G, I-WP, C(P), D, and F-RD families are attributed to fundamental instabilities. Lattices of spheres (LOS) are possible extremal surfaces at the bifurcations. It is determined that both the CMC surfaces and the LOS configurations are unstable to coarsening. Because the variation in curvature is lowest for the G family, it is the most robust of the six families to coarsening when the surfaces are otherwise equivalent.