Dynamic scaling and the surface structure of Eden clusters

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^-2, and the relaxation towards the steady state is dominated by a relaxation time scaling as {τ}(q){~}q^-z with z=1.55±{}0.15. This implies that the surface width has the scaling from {ξ}(t,L){~}L1/2G(t/Lᶻ) with G(x){→}G({∞}){≠}0 as x{→}{∞} and G(x){~}x1/(2z) for x{→}0.