Chord length analysis of the fragments of a ‘dead leaves’ tessellation
Wilfried Gille · Waves in Random and Complex Media · 2007
Let the (homogeneous) fragments of a puzzle, resulting from a ‘dead leaves’ tessellation, be embedded in a homogeneous medium (constant density). The application of elastic scattering methods allows the determination of second-order characteristics and derived functions of these particles (set covariance, geometric covariogram, chord length distribution). The second-order characteristics of the grains of the ‘dead leaves’ model, closely interrelated with those of the resulting tessellation pieces, can be considered as puzzle particles (PPs). A discussion of the behaviour of the chord length distribution of the PPs allows the origin of the shape of the PPs to be characterized. For fitting PPs, the mean small-angle scattering correlation function γ P (r) of the PPs fulfills γ P ″(0)/[γ P ′ (0)]2 = 1.