Anomalous diffusion on crumpled wires in two dimensions

TL;DR

This study investigates the anomalous diffusion of random walks on real two-dimensional crumpled wire structures, revealing diffusion behavior similar to two-dimensional percolation thresholds and discussing implications for physical systems.

Contribution

It provides the first experimental analysis of random walks on actual crumpled wire configurations, linking their diffusion properties to percolation theory.

Findings

Diffusion is anomalous with an exponent close to 2D percolation threshold

Crumpled wire structures exhibit complex hierarchical topology

Results have implications for understanding transport in disordered systems

Abstract

It is investigated the statistical properties of random walks evolving on real configurations of a crumpled wire rigidly jammed in two dimensions. These crumpled hierarchical structures with complex topology are obtained from a metallic wire injected at a constant rate into a transparent planar cell of 20cm of diameter. The observed diffusion is anomalous with an exponent very close to that obtained at the threshold of two dimensional percolation. A comparison of the system studied in this paper with other systems of physical interest is also made, and an experimental consequence of our results is discussed.