薄膜生长的多重分形谱的计算

计算物理 ›› 2001, Vol. 18 ›› Issue (3): 247-252.

薄膜生长的多重分形谱的计算

孙霞¹, 傅竹西², 吴自勤¹

1. 中国科学技术大学基础物理中心, 安徽合肥 230026;
2. 中国科学技术大学物理系, 安徽合肥 230026

收稿日期:1999-12-07 修回日期:2000-05-15 出版日期:2001-05-25 发布日期:2001-05-25
作者简介:孙霞(1971-),女,江苏泰兴,博士后,从事分形在薄膜生长中的应用方面的研究.

MULTIFRACTAL CALCULATION OF THIN FILM GROWTH

SUN Xia¹, FU Zhu-xi², WU Zi-qin¹

1. Fundamental Physics Centre, University of Science and Technology of China, Hefei 230026, P R China;
2. Physics Department University of Science and Technology of China, Hefei 230026, P R China

Received:1999-12-07 Revised:2000-05-15 Online:2001-05-25 Published:2001-05-25

摘要/Abstract

摘要： 规则分形具有理想的标度不变性,而随机分形(如薄膜生长)概率分布曲线及标度不变性的范围与计算方法有关:以偏离平均高度的方差值求概率,标度不变性不好,多重分形谱也不光滑;而以薄膜平均底面为基准面求概率得到的标度不变性可延伸到3个数量级,多重分形谱光滑.采用外延的方法修正灰度设置的偏移可以对多重分形谱有所改善.另外,讨论了权重因子q取值范围的影响,确定了q的取值范围.

关键词: 多重分形谱, 标度不变性, 权重因子

Abstract: Regular fractal has ideal scale-invariance.But the probability distribution curve and the range of scale-invariance of random fractal (for example thin film growth) are related to the calculation method.The scale-invariance is not good and the multifractal spectrum is not smooth when the probability is calculated by variance from average height.The range of scale-invariance can be extend to 3 orders of magnitude and the multifractal spectrum is smooth when the probability is calculated by height based on the bottom of the film.An extending method is here used to correct the deviation of gray level setting-up so as to improve the multifractal spectrum.The effect of the range of the moment order q is discussed as well.

Key words: multifractal spectra, scale-invariant, the moment order

中图分类号:

O484.5

孙霞, 傅竹西, 吴自勤. 薄膜生长的多重分形谱的计算[J]. 计算物理, 2001, 18(3): 247-252.

SUN Xia, FU Zhu-xi, WU Zi-qin. MULTIFRACTAL CALCULATION OF THIN FILM GROWTH[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2001, 18(3): 247-252.