Abstract:

In order to investigate the dynamical scaling behaviour of the space-fractional stochastic growth model, the spacefractional EdwardsWilkinson (SFEW) equation in (1+1)-dimensional case based on the Grümwald-Letnikov type fractional derivative was numerically simulated. The scaling exponents including growth exponent, roughness exponent, dynamic exponent and local roughness exponent with different fractional orders were obtained, which were consistent with the corresponding scaling analysis. The results show that the anomalous dynamic behaviour does not appear in the SFEW model, which still satisfies the FamilyVicsek normal scaling. The results also imply that the nonlocal interactions affect the scaling behaviour of the SFEW equation.

Key words: space-fractional; Edwards-Wilkinson equation; surface roughness; correlation function