Kondev J, Henley CL, Salinas DG
Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540 and Department of Physics, Princeton University, Princeton, New Jersey 08540, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):104-25. doi: 10.1103/physreve.61.104.
We develop an approach for characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e., loops of constant height. Given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops, and the exponent that characterizes their size distribution. Scaling formulas are derived, and used to relate these two geometrical exponents to the roughness exponent of a self-affine surface, thus providing independent measurements of this important quantity. Furthermore, we define the scale-dependent curvature, and demonstrate that by measuring its third moment departures of the height fluctuations from Gaussian behavior can be ascertained. These nonlinear measures are used to characterize the morphology of computer generated Gaussian rough surfaces, surfaces obtained in numerical simulations of a simple growth model, and surfaces observed by scanning-tunneling microscopes. For experimentally realized surfaces the self-affine scaling is cut off by a correlation length, and we generalize our theory of contour loops to take this into account.
我们基于对轮廓环（即等高线环）标度性质的分析，开发了一种表征粗糙表面形态的方法。给定表面的高度轮廓，我们对轮廓环的分形维数及其表征尺寸分布的指数进行独立测量。推导了标度公式，并用于将这两个几何指数与自仿射表面的粗糙度指数相关联，从而提供对这一重要量的独立测量。此外，我们定义了与尺度相关的曲率，并证明通过测量其第三矩，可以确定高度涨落偏离高斯行为的程度。这些非线性度量用于表征计算机生成的高斯粗糙表面、简单生长模型数值模拟中获得的表面以及扫描隧道显微镜观察到的表面的形态。对于实验实现的表面，自仿射标度被一个相关长度截断，我们推广了轮廓环理论以考虑这一点。
