Characterization of Surface Morphology

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 23)


An important characteristics of morphology of disordered multiphase materials is the structure of their surface, and in particular their surface roughness. The concepts of modern statistical physics of disordered media can now quantify the roughness in terms of self-affine fractals, and the roughness or Hurst exponent. The dynamics of growth of such surfaces can also be described by dynamical scaling, discrete models of material growth, and suitable continuum differential equations. Moreover, fractal geometry, and the associated power-law correlation functions, point to the fundamental role of length scale and long-range correlations in the macroscopic homogeneity of a heterogeneous material. If the largest relevant length scale of the material, e.g., its linear size, is less than the length scale at which it can be considered homogeneous, then the classical equations that describe transport processes in the material must be fundamentally modified.


Fractal Dimension Fractional Brownian Motion Hurst Exponent Dynamical Exponent Direct Correlation Function 
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© Springer-Verlag New York, Inc. 2003

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