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

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

在 (2 +1)维情况下 ,利用数值模拟研究了Kuramoto Sivashinsky (K S)与Karda Parisi Zhang (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 .

We have studied the evolution of (2 + 1)-dimensional surface morphology in the Kuramoto-Sivashinsky (K-S) and Karda-Parisi-Zhang (KPZ) models by using the numerical simulation approach. The results show that the surface morphology has the self-affine fractal properties in both the models and exhibits a cellular structure after long-time growth in K-S model. With numerical correlation, dynamic scaling characteristics are observed explicitly in both models, and the roughness exponent, the growth exponent and the dynamic exponent are all obtained. From the simulation 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.