Statistics of approximately self-affine fractals: Random corrugated surface and time series
Statistics of approximately self-affine fractals: Random corrugated surface and time series
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DOI：
10.1103/physreve.53.5749
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发表时间：
1996-06-01
影响因子：
2.4
通讯作者：
Kant, R
中科院分区：
文献类型：
--
作者：
Kant, R
粗糙波纹表面或时间序列建模为一维，平稳，高斯随机过程与幂律功率谱在有限的频率范围内，并与随机过程的技术进行分析。具有小尺度和大尺度截断的幂律谱的表面表现出近似自仿射分形行为。有两个交叉尺度，即，一个较低的交叉尺度和一个较高的交叉尺度，分别用于非分形到分形和分形到非分形的过渡。我们找到了各种统计特性的精确表示，即，均方（MS）宽度、MS斜率、MS曲率、平均曲线长度（面积）、平均过零密度、相关函数以及这些类别的曲线或波纹表面的结构函数。强调了粗糙度指数、上、下截止尺度以及幂律谱与非幂律谱的交叉对近似自仿射分形统计性质的重要性。在两个交叉尺度之间的区域中的各种统计特性的标度行为进行了讨论。提出了几种提取分形维数的方法。最后，我们将我们的结果应用到一个颗粒流实验来描述这个问题的各种时间尺度和总的统计测量。
Rough corrugated surfaces or time series are modeled as one-dimensional, stationary, Gaussian random processes with power-law power spectra over a limited range of frequencies and analyzed with the techniques of random processes. Surfaces with power-law spectra with small- and large-scale cutoffs exhibit approximate self-affine fractals behavior. There are two crossover scales, viz., a lower crossover scale and an upper crossover scale for nonfractal to fractal and fractal to nonfractal transition, respectively. We find the exact representation for the various statistical properties, viz., the mean square (MS) width, the MS slope, the MS curvature, the mean curve length (area), the mean zero crossing density the correlation function, and the structure function for these class of curves or corrugated surfaces. The importance of roughness exponent, upper and lower cutoff scales, and crossover of power-law spectra to non-power-law spectra to statistical properties of approximately self-affine fractal is emphasized. The scaling behavior of various statistical properties in the region between the two crossover scales is discussed. We suggest several methods for extracting fractal dimension. Finally, we apply our results to a granular flow experiment to characterize various time scales and gross statistical measure in this problem.