Laplacian Needle Growth

Publisher Website
Google Scholar
Abstract
We study the scaling properties of a forest of one-dimensional needles that grow from a d-dimensional substrate by the aggregation of individual random walkers. Using opacity arguments we establish the existence of an upper critical dimension dc such that for d ≥ dc the decay of the needle density ρ(h) as a function of the height h above the substrate is correctly described by a continuum mean-field theory. Below dc the decay of the density profile can be inferred from the competition between two needles. Scaling arguments in combination with a conformal mapping calculation indicate that ρ(h) ~ ln h/h in d = 1, in agreement with extensive simulations.

This publication has 20 references indexed in Scilit: