Noise-Reduced Diffusion-Limited Deposition

To investigate the role of fluctuations in diffusion-limited growth the authors apply the noise reduction algorithm to the problem of two-dimensional deposition on a substrate consisting of a straight line. The authors consider the scaling of the height and the width of trees growing on the square lattice. For the sizes studied they find two length scales characterised by different exponents depending on the noise reduction parameter m. Using these exponents the effective fractal dimension Deff of trees is calculated and for m>>1 they obtain Deff approximately=1.57. The density profile in the direction of growth and the scaling properties of the lateral correlation function are also determined.