Structural invariance of stochastic fibrous networks

We use simulation and analytic modelling to probe the structural similarity reported in the literature for fibre networks with manifestly different degrees of uniformity. From simulations of point processes in the plane to represent random, clustered and disperse fibre centres, we show that the distribution of distances between pairs of centres is very insensitive to the extent of clustering. Further, we quantify the correlation between the lengths of adjacent polygon sides arising from a Poisson line process in the plane as being $\rho = 0.616 \pm 0.001$ and show that this is very insensitive to fibre orientation and only weakly influenced by clustering. The relevance of this correlation to pore geometry is discussed.In the final part we analyze simulated areal density maps and show that their variance relative to that of a random fibre network of the same constituent fibres, as quantified by the formation number, depends at small scales on the flocculation intensity only and depends at large scales on the number of fibres per floc only.