Interfacial growth in driven Ginzburg-Landau models: Short and long-time dynamics

Interfacial growth in driven systems is studied from the initial stage to the longtime regime. Numerical integrations of a Ginzburg-Landan type equation with a new flux term introduced by an external field are presented. The interfacial instabilities are induced by the external field. From the numerical results, we obtain the dispersion relation for the initial growth. During the intermediate temporal regime, fingers of a characteristic triangular shape could grow. Depending on the boundary conditions, the final state corresponds to strips, multifinger states, or a one-finger state. The results for the initial growth are interpreted by means of surface-driven and Mullins-Sekerka instabilities. The shape of the one-finger state is explained in terms of the characteristic length introduced by the external field.