分形基底上受限固-固模型动力学性质的数值模拟研究*

摘要

为了探讨非完整基底结构对生长表面动力学行为的影响,本文在具有相同分形维数而不同谱维数的谢尔宾斯基箭头和蟹状分形基底上对受限固-固(restricted solid-on-solid, RSOS)模型的生长过程进行了大量的数值模拟研究。通过计算表面宽度和饱和表面极值高度的统计行为对生长表面的动力学行为进行了分析。结果表明,分形基底结构对生长表面的动力学行为具有显著的影响。尽管在两种基底上受限固-固模型的表面宽度均表现出很好的动力学标度行为,仍然满足Family-Vicsek标度规律,但由此计算得到的动力学标度指数并不相同。饱和生长表面的极值高度并不能满足三种常用的极值统计分布,即Weibull, Gumbel和Frechet分布,而是能很好地符合Asym2Sig分布。%In order to investigate the effect of the structure of a non-complete substrate on the dynamic behaviors of a growing surface, the restricted solid-on-solid model on Sierpinski arrowhead and Crab fractal substrates, which have the same fractal dimensions but of different spectrum dimensions, are extensively studied by means of numerical simulations. The surface width and the maximal height of the saturated surface are calculated. It is found that the microscopic structure of the substrates affects significantly the dynamic properties of the surfaces. Although the restricted solid-on-solid model evolving on two kinds of fractal substrates exhibits dynamic scaling behavior, the standard Family-Vicsek scaling is still satisfied for different dynamic scaling exponents. The maximal height of the width of saturated surface can be fitted by Asym2Sig distribution, not by the three kinds of usual extreme statistical distribution, i.e. Weibull, Gumbel, and Frechet distributions.