  Many systems exhibit a phase where the order parameter is spatially
modulated. These patterns can be the result of a frustration caused by the
competition between interaction forces with opposite effects. In all models
with local interactions, these ordered phases disappear in the strong
segregation regime (low temperature). It is expected however that these phases
should persist in the case of long range interactions, which can't be correctly
described by a Ginzburg-Landau type model with only a finite number of spatial
derivatives of the order parameter. An alternative approach is to study the
dynamics of the phase transition or pattern formation. While, in the usual
process of Ostwald ripening, succession of doubling of the domain size leads to
a total segregation, or macro-segregation, C. Misbah and P. Politi have shown
that long-range interactions could cause an interruption of this coalescence
process, stabilizing a pattern which then remains in a micro-structured state
or super-crystal. We show that this is the case for a modified Cahn-Hilliard
dynamics due to Oono which includes a non local term and which is particularly
well suited to describe systems with a modulated phase.
