Growth and Structure of Random Fibre Clusters and Cluster Networks

TL;DR

This paper investigates the growth, structure, and correlations of 2D fibre clusters and networks formed by deposition, deriving formulas to analyze their internal and inter-cluster properties.

Contribution

It introduces a new analytical expression for the two-point density autocorrelation function of fibre networks, linking internal cluster structure with network correlations.

Findings

Derived an expression for the two-point density autocorrelation function.

Analyzed the scaling properties of single fibre clusters.

Provided a framework to study nontrivial correlations in fibre networks.

Abstract

We study the properties of 2D fibre clusters and networks formed by deposition processes. We first examine the growth and scaling properties of single clusters. We then consider a network of such clusters, whose spatial distribution obeys some effective pair distribution function. In particular, we derive an expression for the two-point density autocorrelation function of the network, which includes the internal structure of a cluster and the effective cluster-cluster pair distribution function. This formula can be applied to obtain information about nontrivial correlations in fibre networks.