Growth with surface curvature on quenched potentials

A discrete growth model driven by the Laplacian of the surface curvature in quenched random media is discussed. The interface width W at the saturated regime obeys scaling W approximately Lalpha with alpha approximately 2.3, where L is the system size. Starting from an initial sine wave condition of a selected wavelength, we measure an autocorrelation function, and obtain the dynamic critical exponent z approximately 3.1. The model is expected to be described by the quenched Mullins-Herring equations.