Kinetic super-roughening and anomalous dynamic scaling in nonequilibrium growth models

We argue that recently introduced models of surface-diffusion-driven nonequilibrium growth that are characterized by critical roughness exponents ({α}) exceeding unity (``super-rough'' growth) exhibit an ``anomalous'' form of dynamic scaling whose asymptotic behavior is different from the usual scaling behavior of self-affine kinetic growth models with {α}1. We propose a generalized scaling function for super-rough ({α}>1) growth and demonstrate its applicablity to several discrete nonequilibrium super-rough models.