Wavelet transforms in a critical interface model for Barkhausen noise

TL;DR

This paper applies wavelet transforms to a critical interface model for Barkhausen noise, revealing scale-dependent roughness and correlation properties, and analyzing effects of finite driving rates on avalanche dynamics.

Contribution

It introduces wavelet analysis to study Barkhausen noise in a critical interface model, highlighting scale-dependent roughness and correlation behaviors, especially under finite driving rates.

Findings

Effective interface roughness exponent $0$ on short scales.

Waiting times between avalanches are uncorrelated, showing white noise behavior.

Correlation scaling as $1/f^{1.5}$ at intermediate frequencies under finite driving.

Abstract

We discuss the application of wavelet transforms to a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of surface tension), the effective interface roughness exponent $\zeta$ is $\simeq 1.20$, close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times between avalanches are fully uncorrelated, as the wavelet transform of their autocorrelations scales as white noise. Similarly, detrended size-size correlations give a white-noise wavelet transform. Consideration of finite driving rates, still deep within the intermittent regime, shows the wavelet transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies. This behavior is ascribed to intra-avalanche correlations.