Dislocations vis et surfaces minima dans les smectiques A

Abstract

It is shown that in the neighbourhood of a second-order smectic-nematic transition, the smectic layers fold into minimal surfaces rather than Dupin cyclides. Typical defects corresponding to this situation are screw dislocations. A hydro-dynamic analogy enables us to show that these dislocations organize themselves into domains separated by walls where the layers break sharply. Various experimental recent observations are briefly discussed in the light of this theory.