  A continuum Landau theory for the micro-elasticity of membranes is discussed,
which incorporates a coupling between the bilayer thickness variation and the
difference in the two monolayers' tilts. This coupling stabilizes a new phase
with a rippled micro-structure. Interactions among membrane inclusions combine
a dilation-induced attraction and a tilt-difference-induced repulsion that
yield 2D crystal phases, with possible coexistence of different lattice
spacings for large couplings. Inclusions favoring crystals are those with
either a long-convex or a short-concave hydrophobic core.
