Universal Power Law in the Noise from a Crumpled Elastic Sheet

TL;DR

This study investigates the crackling sounds from crumpled mylar sheets, revealing a universal power-law distribution in click energies and a stretched exponential autocorrelation, indicating underlying scale-invariant dynamics.

Contribution

It demonstrates the universality of the power-law distribution of click energies in crumpled sheets across different sizes and materials.

Findings

Click energies span six orders of magnitude.

Energy autocorrelation follows a stretched exponential form.

Power-law distribution p(E) ~ E^{-1} is universal.

Abstract

Using high-resolution digital recordings, we study the crackling sound emitted from crumpled sheets of mylar as they are strained. These sheets possess many of the qualitative features of traditional disordered systems including frustration and discrete memory. The sound can be resolved into discrete clicks, emitted during rapid changes in the rough conformation of the sheet. Observed click energies range over six orders of magnitude. The measured energy autocorrelation function for the sound is consistent with a stretched exponential C(t) ~ exp(-(t/T)^{b}) with b = .35. The probability distribution of click energies has a power law regime p(E) ~ E^{-a} where a = 1. We find the same power law for a variety of sheet sizes and materials, suggesting that this p(E) is universal.