Ridge Network in Crumpled Paper

TL;DR

This study analyzes the network structure of ridges in crumpled paper sheets, revealing power-law and log-normal distributions, disassortative degree correlations, and geometric properties of facets and Voronoi diagrams.

Contribution

It introduces a detailed network analysis of ridges in crumpled paper, including distributions and correlations, providing new insights into their spatial organization.

Findings

Ridge length distribution follows a power-law tail.

Shorter ridges exhibit a log-normal distribution.

Degree distribution decays exponentially and is disassortative.

Abstract

The network formed by ridges in a straightened sheet of crumpled paper is studied using a laser profilometer. Square sheets of paper were crumpled into balls, unfolded and their height profile measured. From these profiles the imposed ridges were extracted as networks. Nodes were defined as intersections between ridges, and links as the various ridges connecting the nodes. Many network and spatial properties have been investigated. The tail of the ridge length distribution was found to follow a power-law whereas the shorter ridges followed a log-normal distribution. The degree distribution was found to have an exponentially decaying tail, and the degree correlation was found to be disassortative. The facets created by the ridges and the Voronoi diagram formed by the nodes have also been investigated.