“…However, while secondary instabilities do not change the basic topology of the coupled-growth patterns [9,10], the shape transformation from lamellae to rods, and the reverse one, involve the disruption, or breakup, of the triple-junction lines (trijunctions) at which the two solids and the liquid are in contact. The lamella-rod transition is thus a discontinuous process, and gives rise to highly nonlinear, particularly complex spatio-temporal phenomena [8,17,18,19,20,21,22,23,24,25]. Among key results, the lamellar breakup was shown to result from the amplification of a propagative instability that resembles a Rayleigh-Plateau instability [17,22,26].…”