Tiling the plane with noncongruent toric focal conic domains

This paper deals with regular arrays of macroscopic defects (focal conic do mains) observed when a slab of lamellar phase is sandwiched between two sub strates imposing different orientational anchorings. We report, in particul ar, detailed observations of the texture of a lyotropic lamellar phase in c ontact with a glass substrate and a lyotropic sponge phase. We consider sev eral models fur the defects depending on the material and the substrate par ameters, Their energy has a common form, and the main features of the textu res are explained in the framework of a simple model where disks of differe nt sizes tile a plane in order to minimize a particular interface energy.