Growth, Percolation, and Correlations in Disordered Fiber Networks

Details Growth, Percolation, and Correlations in Disordered Fiber Networks Growth, Percolation, and Correlations in Disordered Fiber Networks

1996-11-06

arxiv.org/abs/cond-mat/9611046v1

Physics

Condensed Matter

Statistical Mechanics

30 pages, 24 PostScript figures, to be published in J. Stat. Phys. also available at http://www.physics.helsinki.fi/tft/tft_pr

Scientific paper

10.1007/BF02181493

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.

Affiliated with

Also associated with

No associations

Rating

Growth, Percolation, and Correlations in Disordered Fiber Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Growth, Percolation, and Correlations in Disordered Fiber Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth, Percolation, and Correlations in Disordered Fiber Networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-695934