New dynamic scaling in increasing systems

Abstract

We report a new dynamic scaling ansatz for systems whose system size is increasing with time. We apply this new hypothesis in the Eden model in two geometries. In strip geometry, we impose the system to increase with a power law, L ∼ ha. In increasing linear clusters, if a < 1/z, where z is the dynamic exponent, the correlation length reaches the whole system, and we find two regimes: the first, where the interface fluctuations initially grow with an exponent β = 0.3, and the second, where a crossover comes out and fluctuations evolve as haα. If a ≥ 1/z, there is not a crossover and fluctuations keep on growing in a unique regimen with the same exponent β. In particular, in circular geometry, a = 1, we find this kind of regime and in consequence, a unique regime holds. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2007.