GROWTH, PERCOLATION, AND CORRELATIONS IN DISORDERED FIBER NETWORKS

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition mod el with effective fiber-fiber interactions represented by a parameter p which controls the degree of clustering. For p = I the deposited net work is uniformly random, while for p = 0 only a single connected clus ter can grow. For p = 0 we first derive the growth law for the average size of the cluster as well ss a formula for its mass density profile . For p > 0 we carry out extensive simulations on fibers, and also nee dles and disks, to study the dependence of the percolation threshold o n p. We also derive a mean-field theory for the threshold near p = 0 a nd p = 1 and find good qualitative agreement with the simulations. The fiber networks produced by the model display nontrivial density corre lations for p < 1. We study these by deriving an approximate expressio n for the pair distribution function of the model that reduces to the exactly known case of a uniformly random network. We also show that th e two-point mass density correlation function of the model has a nontr ivial form, and discuss our results in view of recent experimental dat a on mss density correlations in paper sheets.