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Matérn's hard-core processes are valuable point process models in spatial statistics. In order to extend their field of application, Matérn's original models are generalized here, both as point processes and particle processes. The thinning rule uses a distance-dependent probability function, which controls deletion of points close together. For this general setting, explicit formulas for first-and second-order characteristics can be given. Two examples from materials science illustrate the application of the models.

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The tail correlation function (TCF) is a popular bivariate extremal dependence measure to summarize data in the domain of attraction of a max-stable process. For the class of TCFs, being largely unexplored so far, several aspects are contributed: (i) generalization of some mixing max-stable processes (ii) transfer of two geostatistical construction principles to max-stable processes, including the turning bands operator (iii) identification of subclasses of TCFs, including M3 processes based on radial monotone shapes (iv) recovery of subclasses of max-stable processes from TCFs (v) parametric classes (iv) diversity of max-stable processes sharing an identical TCF. We conclude that caution should be exercised when using TCFs for statistical inference.

In this paper, the effect of a mullite coating on a carbon-bonded alumina filter used in steel melt filtration on the mechanical properties of the cast steel G42CrMo4 (1.7231) at both quasi-static and cyclic loading is presented. The investigations cover quasi-static tensile tests at different temperatures. Additionally, cyclic tests in high-cycle fatigue (HCF) and very high-cycle fatigue (VHCF) regimes were performed. Fracture surfaces as well as cross-sections are examined by scanning electron microscopy and light microscopy to determine the non-metallic inclusions responsible for failure. In comparison to the uncoated filter, a mullite coating on the filter leads to a deterioration of deformation characteristics and fatigue lifetime of the cast steel. This effect is attributed to a higher amount of large non-metallic inclusions, which were not retained by the coated metal melt filter.