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