科赫分形基底上受限固-固模型动力学标度行为的数值研究

Numerical investigations of dynamic behaviors of the restricted solid-on-solid model for Koch fractal substrates

为分析基底结构对离散生长模型动力学性质的影响,本文在随机游走指数十分接近而分形维数和谱维数均不相同的科赫格子和科赫曲线分形基底上对受限固-固(restricted solid-on-solid)模型的生长过程进行数值模拟研究.通过分析表面宽度和饱和表面极值高度的统计行为发现:随机游走的动力学指数能够对饱和粗化表面的动力学行为起主要贡献.尽管分形基底具有不同的分形维数和谱维数,但是在两种分形基底上得到了在误差范围内相同的粗造度指数.两种分形基底上饱和表面相对生长高度极大(小)值分布分别可以很好的塌缩在一起,且很好的满足Asym2Sig函数分布.

In order to investigate the influence of structures of substrates on the dynamic properties of a discrete growth model, the restricted solid-on-solid model for Koch lattice and Koch curve fractal substrates, which have different fractal dimensions and spectrum dimensions but the same walk dimensions, is studied by means of numerical simulations. Surface width and distribution of the extremal height of the saturated surface are calculated. Results show that the random walk exponent plays the determinative part in the saturated regime. Although the fractal substrates have different fractal dimensions and spectral dimensions, the value of roughness exponents for the two substrates are almost the same within the error. The data of maximal height distributions （minmal height distribution） on the width of the saturated surface for the two fractal substrates can be well collapsed together and fitted by Asym2Sig distribution.