Additivity, Convexity, and Beyond: Applications of Minkowski Functionals in Statistical Physics

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Studies of crack dynamics in clay soil. I. Experimental methods, results and morphological quantification (2005, methodology): “This approach was proposed by Mecke (2000), who introduced the Minkowski functions, which are based on a transformation used in mathematical morphology, i.”
Studies of crack dynamics in clay soil. II. A physically based model for crack formation (2005, background): “These numbers comprise the area density AA=m0[L L ], the length density LA=m1[LL ] and the number density NA=m2[L ] of cracks which in the following are referred to as Minkowski densities mk (Mecke, 2000).”
Quantification of soil structure based on Minkowski functions (2010, background): “Given such a binary image, integral geometry provides a limited set of d+1 Minkowski functionals (Mecke, 2000), where d is the dimension of O, in our case d1⁄43.”
Pore‐scale displacement mechanisms as a source of hysteresis for two‐phase flow in porous media (2016, background): “In supporting information, S7, we discuss in more detail the mathematical link between percolation, as defined in Hilfer [1998, 2006], and simplicial connectivity, as defined and measured by the Euler characteristic v [Mecke, 2000; Mecke and Arns, 2005; Vogel et al., 2010].”