Dynamic scaling and the surface structure of Eden clusters

Abstract

The evolution of the surface of two-dimensional Eden deposits grown in a strip of width L is related to the dynamics of a set of ‘‘normal modes’’ of wave number q. Monte Carlo simulations show striking similarities with critical phenomena. The amplitude squared of the modes relax in the long-time limit (t→∞) to a value S(q)∼$q^{\mathrm{-}2}$, and the relaxation towards the steady state is dominated by a relaxation time scaling as τ(q)∼$q^{\mathrm{-}z}$ with z=1.55±0.15. This implies that the surface width has the scaling from ξ(t,L)∼$L^{1/2}$G(t/$L^z$) with G(x)→G(∞)≠0 as x→∞ and G(x)∼$x^{1/\left(2z\right)}$ for x→0.