Avalanche statistics and intermittency in topological defect-mediated flows

TL;DR

This paper investigates the velocity fluctuations in topological defect-mediated flows, revealing power-law distributions with specific exponents and connecting these to avalanche phenomena in materials.

Contribution

It introduces a systematic approach to derive velocity fluctuation distributions and links these to avalanche scaling in defect-driven material flows.

Findings

Velocity distribution has power-law tails with exponent -3 at high velocities.

Intermediate velocities follow a power-law with exponent -2.

The results connect fluctuation statistics to avalanche scaling exponents.

Abstract

Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling arguments and a systematic cluster expansion method to account for density correlations. We find that the distribution has power-law tails with an exponent that takes the value -3 for $v\rightarrow \infty$, but a value -2 for intermediate values of $v$. We relate these regimes to the theory of avalanches, by directly computing the known avalanche scaling exponents.