R. Montagne et al., MULTIPLE FRONT PROPAGATION INTO UNSTABLE STATES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(1), 1994, pp. 377-385
The dynamics of transient patterns formed by front propagation in exte
nded nonequilibrium systems is considered. Under certain circumstances
, the state left behind a front propagating into an unstable homogeneo
us state can be an unstable periodic pattern. It is found by a numeric
al solution of a model of the Freedericksz transition in nematic liqui
d crystals that the mechanism of decay of such periodic unstable state
s is the propagation of a second front which replaces the unstable pat
tern by another unstable periodic state with a larger wavelength. The
speed of this second front and the periodicity of the new state are an
alytically calculated with a generalization of the marginal stability
formalism suited to the study of front propagation into periodic unsta
ble states.