We study the dynamics of large-scale flow in a system with several competing length scales. This system, when driven, is characterized by critically metastable states. When the driving force is lowered, these states ‘‘melt’’ via nucleation of a low density of slowly moving defects, which control and relate the long-time, long-distance behaviors. We demonstrate these properties with a one-dimensional lattice-dynamics model for twinning in elastic materials, including (a) a periodic substrate potential, (b) a nonconvex nearest-neighbor spring potential, and (c) a harmonic next-nearest-neighbor spring potential. This system exhibits a rich spectrum of superlattice ground states. Large-scale driving, obtained by adding a constant force and damping to the equations of motion, shows four distinct regimes: (i) At high forces a metastable inhomogeneously modulated configuration moves rigidly with a velocity given by the ratio of force to damping; (ii) as the force decreases the rigidity is lost via local nucleation of soliton defects (in the double well) and fluctuations of the velocities increase; (iii) for even lower forces the configuration ceases to translate, and the dynamics is controlled by nucleation of (sine-Gordon-like) kink-antikink pairs in the substrate; and finally (iv) at a sufficiently low force a metastable configuration, consisting of a random array of solitons (in the double-well potential), is pinned. We also observe strong hysteretic behavior at the transitions.

• Received 5 September 1989

DOI:https://doi.org/10.1103/PhysRevB.41.6703