空间分数阶Edwards-Wilkinson方程的数值研究

Numerical simulations of the space-fractional Edwards-Wilkinson equation

为了探讨空间分数阶随机生长模型的动力学标度行为,利用Grümwald-Letnikov分数阶导数定义方法求解空间分数阶Edwards-Wilkinson(SFEW)方程在1+1维情况下的数值解,得到了在不同分数阶导数值时的生长指数、粗糙度指数、动力学指数和局域粗糙度指数,这些结果与标度分析得到的结果是一致的。研究结果表明SFEW模型没有出现奇异动力学行为,仍然遵守Family-Vicsek正常标度规律。同时结果也显示,非局域相互作用对SFEW方程的动力学标度行为有着显著的影响。

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 Griimwald-Letnikov type fractional derivative was numerically simulated. The scaling exponents including growth exponent, roughness expo- nent, 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.