Search for universal roughness distributions in a critical interface model

Wavelet transforms in a critical interface model for Barkhausen noise

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 the surface tension), the effective interface roughness exponent zeta is approximately 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.

Fractional Laplacian in bounded domains

The fractional Laplacian operator -(-delta)(alpha/2) appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely, hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalue spectrum are also obtained.

Roughness of time series in a critical interface model

We study roughness probability distribution functions (PDFs) of the time signal for a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. Starting with time "windows" of data collection much larger than the system's internal "loading time" (related to demagnetization effects), we show that the initial Gaussian shape of the PDF evolves into a double-peaked structure as window width decreases. We advance a plausible physical explanation for such a structure, which is broadly compatible with the observed numerical data. Connections to experiment are suggested.