The Statistics of Crumpled Paper

TL;DR

This paper presents a statistical analysis of crumpled paper using a minimal 1D model, revealing how segment length distributions evolve from log-normal to Gamma laws as confinement increases, and identifying critical jamming behavior.

Contribution

It introduces a simple 1D model for crumpled paper and predicts the distribution of segment lengths and critical behavior under confinement.

Findings

Segment length distribution is log-normal at low confinement.

At high confinement, the system exhibits jamming with Gamma-distributed segment lengths.

The Gamma distribution parameter relates to the number of layers in the system.

Abstract

A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations are generated numerically and their properties are investigated. At small confinement, the distribution of segment lengths is log-normal in agreement with previous predictions and experiments. At high confinement, the system approaches a jammed state with a critical behavior, whereas the length distribution follows a Gamma law which parameter is predicted as a function of the number of layers in the system.