Dislocation motion in cellular structures

Abstract

The slow motions of cellular structures of parallel rolls are described by the amplitude equation in the weakly nonlinear domain. As this equation has a variational structure, the Peach-Köhler force exerted on a dislocation can be computed in the same way as for usual crystals. When the cellular structure is really described by variational equations, this force keeps its variational origin (it is the gradient of some energy) and vanishes for some optimal wave number. In thermoconvection in porous layers, this variational structure of the dynamics is lost at perturbative order beyond the one giving the usual amplitude equation. Therefore, the notion of an optimal wave number loses its meaning, and the quantity equivalent to the Peach-Köhler force does not vanish anymore at the wave number of marginal stability for perpendicular diffusion, contrary to what happens in variational systems where this condition defines the optimal structure. Another consequence of this nonvariational dynamics is the occurrence of gliding motion of dislocations in uniformly curved rolls, a situation where no Peach-Köhler force exists in variational systems.