Kuramoto-Sivashinsky与Karda-Parisi-Zhang模型中生长界面分形特性研究

在（2＋1）维情况下，利用数值模拟研究了Kuramoto-Sivashinsky (K-S)与Karda-Parisi-Z hang (KPZ)模型所决定的非平衡态界面生长演化过程.结果表明，KPZ与K-S模型都表现出明 显的时间和空间标度特性.相对于KPZ模型而言，K-S模型所对应的表面具有更明显的颗粒特 征，当生长时间较长时，生长界面呈现蜂窝状结构.通过数值相关分析得到了生长界面的粗 糙度指数、生长指数和动态标度指数等参数.从两种模型对应的表面形貌特征和表面参数来 看，在(2+1)维情况下，KPZ与K-S模型所决定的表面具有完全不同的动态标度行为，属于不 同的两类物理模型. 关键词： Kuramoto-Sivashinsky (K-S)模型 Karda-Parisi-Zhang(KPZ)模型 分形 数值模拟

The study of two-dimensional growth interface in Kuramoto-Sivashinsky and Karda- Parisi-Zhang models

We have studied the evolution of (2+1)-dimensional surface morphology in the Kur amoto-Sivashinsky (K-S) and Karda-Parisi-Zhang (KPZ) models by using the numeric al simulation approach. The results show that the surface morphology has the sel f-affine fractal properties in both the models and exhibits a cellular structure after long-time growth in K-S model. With numerical correlation, dynamic scalin g characteristics are observed explicitly in both models, and the roughness expo nent, the growth exponent and the dynamic exponent are all obtained. From the si mulation results we suggest that the two models have the different properties in present time and space scale, and are not in the same universality class.