Structural properties of disordered fibre networks

We study the growth, percolation, and correlations in models of disordered fibre networks. We introduce a 2D deposition model with a parameter p which controls the degree of fibre clustering. For p = 1, the deposited fibre networks is uniformly random, while for p = 0 only a single connected cluster grows. For p = 0, we examine the growth law for the average size of the cluster as well as its mass density profile. For p > 0, we examine the dependence of the percolation threshold on p numerically, and derive a mean-field expression for it near p = 0 and p = 1. Fibre networks produced by our model are shown to display nontrivial density correlations. These results are discussed in the context of experimental density correlations of paper sheets.