Avalanche Spatial Structure and Multivariable Scaling Functions; Sizes, Heights, Widths, and Views through Windows

TL;DR

This paper presents a systematic method to extract universal multivariable scaling functions and critical exponents from avalanche data, addressing experimental limitations like limited field of view, and applies it to simulations of avalanche dynamics.

Contribution

It introduces a new approach for analyzing avalanche spatial structures and scaling functions, including corrections and error estimates, using the novel software SloppyScaling.

Findings

Universal scaling functions for avalanche size, height, and width distributions.

Resolution of field of view distortion effects in avalanche measurements.

Development of accurate parameterizations with corrections to scaling.

Abstract

We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven quenched Kardar-Parisi-Zhang (qKPZ) equation. We fully characterize the spatial structure of these avalanches- we report universal scaling functions for size, height and width distributions, and also local front heights. Furthermore, we resolve a problem that arises in many imaging experiments of crackling noise and avalanche dynamics, where the observed distributions are strongly distorted by a limited field of view. Through artificially windowed data, we show these distributions and their multivariable scaling functions may be written in terms of two control parameters, the window size and the characteristic length scale of the dynamics. For the entire system and the windowed distributions we develop accurate parameterizations for the universal scaling functions, including corrections to scaling and systematic error bars, facilitated by a novel software environment SloppyScaling.