Multifractality in domain wall dynamics of a ferromagnetic film

Scale-free distribution of silences

Soundscape studies help us understand ecological processes, biodiversity distribution, anthropic influences, and even urban quality, across a wide variety of places and time periods. In this work, instead of looking for differences, we ask if there are common characteristics shared by all soundscapes. Based on our results, we propose a universal distribution of quiet-time (background noise) and sound-time (acoustic energy bursts) in audio recordings. We analyzed one continuous hour during daylight and one at night, from ten randomly selected days in each environment: urban, dry forest, savanna, rupestrian field, Atlantic forest, marine, and freshwater. We found that the histograms of the quiet-time followed a power law for all scenarios analyzed, they present fractal events or scale-free distributions. This distribution covers up to four orders of magnitude, with an exponent of 1.6≤α≤2.0 for all soundscapes. By contrast, the sound-time distribution in all environments followed a log-normal or timescale dependence, with a typical time for the duration of sounds (0.06-0.12 s). Such time duration limitation can be related to the physiology of sound emission in animals.

Waiting-time statistics in magnetic systems

Many complex systems, from earthquakes and financial markets to Barkhausen effect in ferromagnetic materials, respond with a noise consisting of discrete avalanche-like events with broad range of sizes and durations, separated by waiting times. Here we focus on the waiting-time statistics in magnetic systems. By investigating the Barkhausen noise in amorphous and polycrystalline ferromagnetic films having different thicknesses, we uncover the form of the waiting-time distribution in time series recorded from the irregular and irreversible motion of magnetic domain walls. Further, we address the question of if the waiting-time distribution evolves with the threshold level, as well as with the film thickness and structural character of the materials. Our results, besides informing on the temporal avalanche correlations, disclose the waiting-time statistics in magnetic systems also bring fingerprints of the universality classes of Barkhausen avalanches and a dimensional crossover in the domain wall dynamics.

Maximum entropy principle in recurrence plot analysis on stochastic and chaotic systems

The recurrence analysis of dynamic systems has been studied since Poincaré's seminal work. Since then, several approaches have been developed to study recurrence properties in nonlinear dynamical systems. In this work, we study the recently developed entropy of recurrence microstates. We propose a new quantifier, the maximum entropy (S_max). The new concept uses the diversity of microstates of the recurrence plot and is able to set automatically the optimum recurrence neighborhood (ϵ-vicinity), turning the analysis free of the vicinity parameter. In addition, ϵ turns out to be a novel quantifier of dynamical properties itself. We apply S_max and the optimum ϵ to deterministic and stochastic systems. The S_max quantifier has a higher correlation with the Lyapunov exponent and, since it is a parameter-free measure, a more useful recurrence quantifier of time series.

Playing with universality classes of Barkhausen avalanches

Many systems crackle, from earthquakes and financial markets to Barkhausen effect in ferromagnetic materials. Despite the diversity in essence, the noise emitted in these dynamical systems consists of avalanche-like events with broad range of sizes and durations, characterized by power-law avalanche distributions and typical average avalanche shape that are fingerprints describing the universality class of the underlying avalanche dynamics. Here we focus on the crackling noise in ferromagnets and scrutinize the traditional statistics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films having different thicknesses. We show how scaling exponents and average shape of the avalanches evolve with the structural character of the materials and film thickness. We find quantitative agreement between experiment and theoretical predictions of models for the magnetic domain wall dynamics, and then elucidate the universality classes of Barkhausen avalanches in ferromagnetic films. Thereby, we observe for the first time the dimensional crossover in the domain wall dynamics and the outcomes of the interplay between system dimensionality and range of interactions governing the domain wall dynamics on Barkhausen avalanches.

Universal temporal characteristics and vanishing of multifractality in Barkhausen avalanches

Barkhausen effect in ferromagnetic materials provides an excellent area for investigating scaling phenomena found in disordered systems exhibiting crackling noise. The critical dynamics is characterized by random pulses or avalanches with scale-invariant properties, power-law distributions, and universal features. However, the traditional Barkhausen avalanches statistics may not be sufficient to fully characterize the complex temporal correlation of the magnetic domain walls dynamics. Here we focus on the multifractal scenario to quantify the temporal scaling characteristics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films with thicknesses from 50 to 1000 nm. We show that the multifractal properties are dependent on film thickness, although they seem to be insensitive to the structural character of the materials. Moreover, we observe for the first time the vanishing of the multifractality in the domain walls dynamics. As the thickness is reduced, the multifractal behavior gives place to a monofractal one over the entire range of time scales. This reorganization in the temporal scaling characteristics of Barkhausen avalanches is understood as a universal restructuring associated to the dimensional crossover, from three- to two-dimensional magnetization dynamics.

Mouse activity across time scales: fractal scenarios

In this work we devise a classification of mouse activity patterns based on accelerometer data using Detrended Fluctuation Analysis. We use two characteristic mouse behavioural states as benchmarks in this study: waking in free activity and slow-wave sleep (SWS). In both situations we find roughly the same pattern: for short time intervals we observe high correlation in activity - a typical 1/f complex pattern - while for large time intervals there is anti-correlation. High correlation of short intervals ( to : waking state and to : SWS) is related to highly coordinated muscle activity. In the waking state we associate high correlation both to muscle activity and to mouse stereotyped movements (grooming, waking, etc.). On the other side, the observed anti-correlation over large time scales ( to : waking state and to : SWS) during SWS appears related to a feedback autonomic response. The transition from correlated regime at short scales to an anti-correlated regime at large scales during SWS is given by the respiratory cycle interval, while during the waking state this transition occurs at the time scale corresponding to the duration of the stereotyped mouse movements. Furthermore, we find that the waking state is characterized by longer time scales than SWS and by a softer transition from correlation to anti-correlation. Moreover, this soft transition in the waking state encompass a behavioural time scale window that gives rise to a multifractal pattern. We believe that the observed multifractality in mouse activity is formed by the integration of several stereotyped movements each one with a characteristic time correlation. Finally, we compare scaling properties of body acceleration fluctuation time series during sleep and wake periods for healthy mice. Interestingly, differences between sleep and wake in the scaling exponents are comparable to previous works regarding human heartbeat. Complementarily, the nature of these sleep-wake dynamics could lead to a better understanding of neuroautonomic regulation mechanisms.

Multifractal detrended fluctuation analysis to characterize phase couplings in seahorse (Hippocampus kuda) feeding clicks

Nonlinear phenomena in animal vocalizations fundamentally includes known features, namely, frequency jump, subharmonics, biphonation, and deterministic chaos. In the present study, the multifractal detrended fluctuation analysis (MFDFA) has been employed to characterize the phase couplings revealed in the feeding clicks of Hippocampus kuda yellow seahorse. The fluctuation function Fq(s), generalized Hurst exponent h(q), multifractal scaling exponent τ(q), and the multifractal spectrum f(α) calculated in the procedure followed were analyzed to comprehend the underlying nonlinearities in the seahorse clicks. The analyses carried out reveal long-range power-law correlation properties in the data, substantiating the multifractal behavior. The resulting h(q) spectrum exhibits a distinct characteristic pattern in relation to the seahorse sex and size, and reveals a spectral blind spot in the data that was not possible to detect by conventional spectral analyses. The corresponding multifractal spectrum related width parameter Δh(q) is well clustered, defining the individual seahorse clicks. The highest degree of multifractality is evident in the 18 cm male seahorse, signifying greater heterogeneity. A further comparison between the seahorse body size and weight (wet) with respect to the width parameter Δh(q) and the second-order Hurst exponent h(q=2) underscores the versatility of MFDFA as a robust statistical tool to analyze bioacoustic observations.

Statistical properties of Barkhausen noise in amorphous ferromagnetic films

We investigate the statistical properties of the Barkhausen noise in amorphous ferromagnetic films with thicknesses in the range between 100 and 1000 nm. From Barkhausen noise time series measured with the traditional inductive technique, we perform a wide statistical analysis and establish the scaling exponents τ,α,1/σνz, and ϑ. We also focus on the average shape of the avalanches, which gives further indications on the domain-wall dynamics. Based on experimental results, we group the amorphous films in a single universality class, characterized by scaling exponents τ=1.28±0.02,α=1.52±0.3, and 1/σνz=ϑ=1.83±0.03, values compatible with that obtained for several bulk amorphous magnetic materials. Besides, we verify that the avalanche shape depends on the universality class. By considering the theoretical models for the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium found in literature, we interpret the results and identify an experimental evidence that these amorphous films, within this thickness range, present a typical three-dimensional magnetic behavior with predominant short-range elastic interactions governing the domain-wall dynamics. Moreover, we provide experimental support for the validity of a general scaling form for the average avalanche shape for non-mean-field systems.

Multifractal properties of ball milling dynamics

This work focuses on the dynamics of a ball inside the reactor of a ball mill. We show that the distribution of collisions at the reactor walls exhibits multifractal properties in a wide region of the parameter space defining the geometrical characteristics of the reactor and the collision elasticity. This feature points to the presence of restricted self-organized zones of the reactor walls where the ball preferentially collides and the mechanical energy is mainly dissipated.

Universal properties of magnetization dynamics in polycrystalline ferromagnetic films

We investigate the scaling behavior in the statistical properties of Barkhausen noise in ferromagnetic films. We apply the statistical treatment usually employed for bulk materials in experimental Barkhausen noise time series measured with the traditional inductive technique in polycrystalline ferromagnetic films having different thickness from 100 to 1000 nm and determine the scaling exponents. Based on this procedure, we group the samples in a single universality class, since the scaling behavior of Barkhausen avalanches is characterized by exponents τ∼1.5, α∼2.0, and 1/σνz∼ϑ∼2.0 for all the films. We interpret these results in terms of theoretical models and provide experimental evidence that a well-known mean-field model for the dynamics of a ferromagnetic domain wall in three-dimensional ferromagnets can be extended for films. We identify that the films present an universal three-dimensional magnetization dynamics, governed by long-range dipolar interactions, even at the smallest thicknesses, indicating that the two-dimensional magnetic behavior commonly verified for films cannot be generalized for all thickness ranges.