Scaling structure in simple screening models for columnar growth

Abstract

Several versions of a simplified oblique incidence ballistic deposition model introduced by Nagatani [J. Phys. A 24, L449 (1991)] have been explored using computer simulations and theoretical approaches. In these models self-similar columnar patterns characterized by an algebraic distribution of heights evolve as a consequence of the competition among columns for the incoming flux. The growth rate of each column is a nonlinear function of its height. The competition is driven by the shot noise in the deposition process or, for a deterministic version of the model, by the amplification of disorder in the initial state of the surface. We find excellent agreement between simulation results and the theoretical analysis. However, our results appear to differ substantially from those obtained by Nagatani using smaller-scale simulations and a Monte Carlo renormalization-group analysis. In particular, we indicate how a spurious dependence of the height distribution exponent on the angle of incidence may arise from crossover effects. In the deterministic case the height distribution exponent depends continuously on the distribution of initial disorder. © 1992 The American Physical Society.