A non-gaussian model for random surfaces

Abstract
The central concern of this paper is to develop for rough (two-dimensional, metallic) surfaces a model other than the Gaussian one usually used. An analysis, via the notion of ‘upcrossing characteristics’, of some new data on abraded stainless steel, as well as a new look at some old data, indicates the need for such a model. The model adopted is of a form that gives X 2 -type marginal height distributions for the surface. After the new model has been introduced and motivated, its properties are investigated in some detail. In particular, the properties of the surface and its profiles at local maxima are studied by examining, for example, the height distribution and the surface curvature at such points. Phenomena are observed that are notably, qualitatively, different to what happens in the Gaussian model. Although the model introduced here is motivated by problems in the study of metallic surfaces, we believe it to be useful in other areas. Consequently, those sections of the paper that investigate the properties of the model are written so as to be independent of the original motivation. The paper also reintroduces, in an applied setting, the idea of examining surfaces via their upcrossing characteristics.

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