Controlled instability and multiscaling in models of epitaxial growth

We show that discretized versions of commonly studied nonlinear growth equations have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Controlling this instability by the introduction of higher-order nonlinear terms leads to intermittent behavior characterized by multiexponent scaling of height fluctuations, similar to the "turbulent" behavior found in recent simulations of one-dimensional atomistic models of epitaxial growth.