Intrinsic geometry approach to surface kinetic roughening

Abstract

A model for kinetic roughening of one-dimensional interfaces is presented within anintrinsic geometry framework that is free from the standard small-slope and no-overhangapproximations. The model is meant to probe the consequences of the latter on theKardar–Parisi–Zhang (KPZ) description of non-conserved, irreversible growth.Thus, growth always occurs along the local normal direction to the interface,with a rate that is subject to fluctuations and depends on the local curvature.Adaptive numerical techniques have been designed that are specially suited tothe study of fractal morphologies and can support interfaces with large slopesand overhangs. Interface self-intersections are detected, and the ensuing cavitiesremoved. After appropriate generalization of observables such as the global and localsurface roughness functions, the interface scaling is seen in our simulations tobe of the Family–Vicsek-type for arbitrary curvature dependence of the growthrate, KPZ scaling appearing for large system sizes and sufficiently large noiseamplitudes.