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Similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure. (English) Zbl 0939.74004
Summary: We examine some modern scaling and fractal approaches to the characterization of surface roughness. A new mathematical model of a multilevel profile suitable for flexible simulation of roughness is presented as a development from these approaches. We describe an iterative construction of the model, and show that the profile is a hierarchical structure with self-affine and fractal features. Its geometrical properties are studied both analytically and numerically, and some of them are proved to be of the renormalization type. The profile contour length can be finite or infinite, depending on the chosen values of the structural parameters. We calculate some characteristics including the bearing curve and the upper volume function of the profile and the corresponding prestructures.
MSC:
74A50Structured surfaces and interfaces, coexistent phases
28A80Fractals