Universal temporal characteristics and vanishing of multifractality in Barkhausen avalanches

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.

Magnetic Barkhausen Noise Transient Analysis for Microstructure Evolution Characterization with Tensile Stress in Elastic and Plastic Status

Stress affects the microstructure of the material to influence the durability and service life of the components. However, the previous work of stress measurement lacks quantification of the different variations in time and spatial features of micromagnetic properties affected by stress in elastic and plastic ranges, as well as the evolution of microstructure. In this paper, microstructure evolution under stress in elastic and plastic ranges is evaluated by magnetic Barkhausen noise (MBN) transient analysis. Based on a J-A model, the duration and the intensity are the eigenvalues for MBN transient analysis to quantify transient size and number of Barkhausen events under stress. With the observation of domain wall (DW) distribution and microstructure, the correlation between material microstructure and MBN transient eigenvalues is investigated to verify the ability of material status evaluation on the microscopic scale of the method. The results show that the duration and the intensity have different change trends in elastic and plastic ranges. The eigenvalue fusion of the duration and intensity distinguishes the change in microstructure under the stress in elastic and plastic deformation. The appearance of grain boundary (GB) migration and dislocation under the stress in the plastic range makes the duration and the intensity higher on the GB than those inside the grain. Besides, the reproducibility of the proposed method is investigated by evaluating microstructure evolution for silicon steel sheet and Q235 steel sheet. The proposed method investigates the correlation between the microstructure and transient micromagnetic properties, which has the potential for stress evaluation in elastic and plastic ranges for industrial materials.

Effect of a uniform random external magnetic field with spatiotemporal variation on compensation in Ising spin-1/2 trilayered square ferrimagnets

Trilayered spin-1/2 Ising ferrimagnets are interesting thin systems for compensation phenomenon. In this work, a Metropolis Monte Carlo study is performed on the magnetic and thermodynamic response of such a system on square Bravais lattice, driven by uniform random external magnetic field with spatiotemporal variations. In two distinct configurations, the surface layers are made up of A and the middle layer is made up of B atoms in an ABA-type stacking while in AAB-type stacking, the top layer and the middle layer is made up of A atoms while the bottom layer is made up of B atoms. The magnetic coupling between the like atoms (A-A and B-B) is ferromagnetic while between the unlike atoms (A-B), it is antiferromagnetic. For the time-dependent external uniform random field, the mean is always set to zero and the standard deviation is varied until spin-field energy is comparable to the dominant cooperative energy of the system. The findings show that the observed compensation and critical points shift and steady-state magnetic behaviors shift among N, L, P, and Q, etc., type of ferrimagnetic behaviors, depending on the strength of external uniform random field. The compensation phenomenon even vanishes after crossing a finite threshold of standard deviation of the magnetic field for particular choices of the other controlling parameters. Thus islands of ferrimagnetic phase without compensation appear within the phase area with compensation of field-free case, in the two-dimensional Hamiltonian parameter space. For both the configurations, the areas of such islands even grow with increasing standard deviation of the external field, σ, obeying a scaling relation of the form: f(σ,A(σ))=σ^{-b}A(σ) with b_{ABA}=1.958±0.122 and b_{AAB}=1.783±0.118.

Recent progress on emergent two-dimensional magnets and heterostructures

Intrinsic two-dimensional (2D) magnetic materials own strong long-range magnetism while their characteristics of the ultrathin thickness and smooth surface provide an ideal platform for manipulating the magnetic properties at 2D limit. This makes them to be potential candidates in various spintronic applications compared to their corresponding bulk counterparts. The discovery of magnetic ordering in 2D CrI₃and Gr₂Ge₂Te₆nanostructures stimulated tremendous research interest in both experimental and theoretical studies on various intrinsic magnets at 2D limit. This review gives a comprehensive overview of the recent progress on the emergent 2D magnets and heterostructures. Firstly, several kinds of typical 2D magnetic materials discovered in the last few years and their fabrication methods are summarized in detail. Secondly, the current strategies for manipulating magnetic properties in 2D materials are further discussed. Then, the recent advances on the construction of representative van der Waals magnetic heterostructures and their respective performance are provided. With the hope of motivating the researchers in this area, we finally offered the challenges and outlook on 2D magnetism.

Mechanism of subcritical avalanche propagation in three-dimensional disordered systems

We present a numerical study on necessary conditions for the appearance of infinite avalanche below the critical point in disordered systems that evolve throughout metastable states. The representative of those systems is the nonequilibrium athermal random-field Ising model. We investigate the impact on propagation of infinite avalanche of both the interface of flipped spins at the avalanche's starting point and the number of independent islands of flipped spins in the system at the moment when the avalanche starts. To deduce what effects are originated due to finite system's size, and to distinguish them from the real necessary conditions for the appearance of the infinite avalanche, we examined lattices of different sizes as well as other key parameters for the avalanche propagation.

Effects of external noise on threshold-induced correlations in ferromagnetic systems

In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent γ_{S/T} (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.

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.

Avalanche properties in striplike ferromagnetic systems

We present numerical findings on the behavior of the athermal nonequilibrium random-field Ising model of spins at the thin striplike L_{1}×L_{2}×L_{3} cubic lattices with L_{1}<L_{2}<L_{3}. Changing of system sizes highly influences the evolution and shape of avalanches. The smallest avalanches [classified as three-dimension- (3D) like] are unaffected by the system boundaries, the larger are sandwiched between the top and bottom system faces so are 2D-like, while the largest are extended over the system lateral cross section and propagate along the length L_{3} like in 1D systems. Such a structure of avalanches causes double power-law distributions of their size, duration, and energy with larger effective critical exponent corresponding to 3D-like and smaller to 2D-like avalanches. The distributions scale with thickness L_{1} and are collapsible following the proposed scaling predictions which, together with the distributions' shape, might be important for analysis of the Barkhausen noise experimental data for striplike samples. Finally, the impact of system size on external field that triggers the largest avalanche for a given disorder is presented and discussed.

Multifractal and Entropy-Based Analysis of Delta Band Neural Activity Reveals Altered Functional Connectivity Dynamics in Schizophrenia

Dynamic functional connectivity (DFC) was established in the past decade as a potent approach to reveal non-trivial, time-varying properties of neural interactions – such as their multifractality or information content –, that otherwise remain hidden from conventional static methods. Several neuropsychiatric disorders were shown to be associated with altered DFC, with schizophrenia (SZ) being one of the most intensely studied among such conditions. Here we analyzed resting-state electroencephalography recordings of 14 SZ patients and 14 age- and gender-matched healthy controls (HC). We reconstructed dynamic functional networks from delta band (0.5–4 Hz) neural activity and captured their spatiotemporal dynamics in various global network topological measures. The acquired network measure time series were made subject to dynamic analyses including multifractal analysis and entropy estimation. Besides group-level comparisons, we built a classifier to explore the potential of DFC features in classifying individual cases. We found stronger delta-band connectivity, as well as increased variance of DFC in SZ patients. Surrogate data testing verified the true multifractal nature of DFC in SZ, with patients expressing stronger long-range autocorrelation and degree of multifractality when compared to controls. Entropy analysis indicated reduced temporal complexity of DFC in SZ. When using these indices as features, an overall cross-validation accuracy surpassing 89% could be achieved in classifying individual cases. Our results imply that dynamic features of DFC such as its multifractal properties and entropy are potent markers of altered neural dynamics in SZ and carry significant potential not only in better understanding its pathophysiology but also in improving its diagnosis. The proposed framework is readily applicable for neuropsychiatric disorders other than schizophrenia.

Critical disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems

In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.

The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary

The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the time-scale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the two-dimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.

Multifractal Dynamic Functional Connectivity in the Resting-State Brain

Assessing the functional connectivity (FC) of the brain has proven valuable in enhancing our understanding of brain function. Recent developments in the field demonstrated that FC fluctuates even in the resting state, which has not been taken into account by the widely applied static approaches introduced earlier. In a recent study using functional near-infrared spectroscopy (fNIRS) global dynamic functional connectivity (DFC) has also been found to fluctuate according to scale-free i.e., fractal dynamics evidencing the true multifractal (MF) nature of DFC in the human prefrontal cortex. Expanding on these findings, we performed electroencephalography (EEG) measurements in 14 regions over the whole cortex of 24 healthy, young adult subjects in eyes open (EO) and eyes closed (EC) states. We applied dynamic graph theoretical analysis to capture DFC by computing the pairwise time-dependent synchronization between brain regions and subsequently calculating the following dynamic graph topological measures: Density, Clustering Coefficient, and Efficiency. We characterized the dynamic nature of these global network metrics as well as local individual connections in the networks using focus-based multifractal time series analysis in all traditional EEG frequency bands. Global network topological measures were found fluctuating–albeit at different extent–according to true multifractal nature in all frequency bands. Moreover, the monofractal Hurst exponent was found higher during EC than EO in the alpha and beta bands. Individual connections showed a characteristic topology in their fractal properties, with higher autocorrelation owing to short-distance connections–especially those in the frontal and pre-frontal cortex–while long-distance connections linking the occipital to the frontal and pre-frontal areas expressed lower values. The same topology was found with connection-wise multifractality in all but delta band connections, where the very opposite pattern appeared. This resulted in a positive correlation between global autocorrelation and connection-wise multifractality in the higher frequency bands, while a strong anticorrelation in the delta band. The proposed analytical tools allow for capturing the fine details of functional connectivity dynamics that are evidently present in DFC, with the presented results implying that multifractality is indeed an inherent property of both global and local DFC.

Impact of Healthy Aging on Multifractal Hemodynamic Fluctuations in the Human Prefrontal Cortex

Fluctuations in resting-state cerebral hemodynamics show scale-free behavior over two distinct scaling ranges. Changes in such bimodal (multi) fractal pattern give insight to altered cerebrovascular or neural function. Our main goal was to assess the distribution of local scale-free properties characterizing cerebral hemodynamics and to disentangle the influence of aging on these multifractal parameters. To this end, we obtained extended resting-state records (N = 2¹⁴) of oxyhemoglobin (HbO), deoxyhemoglobin (HbR) and total hemoglobin (HbT) concentration time series with continuous-wave near-infrared spectroscopy technology from the brain cortex. 52 healthy volunteers were enrolled in this study: 24 young (30.6 ± 8.2 years), and 28 elderly (60.5 ± 12.0 years) subjects. Using screening tests on power-law, multifractal noise, and shuffled data sets we evaluated the presence of true multifractal hemodynamics reflecting long-range correlation (LRC). Subsequently, scaling-range adaptive bimodal signal summation conversion (SSC) was performed based on standard deviation (σ) of signal windows across a range of temporal scales (s). Building on moments of different order (q) of the measure, σ(s), multifractal SSC yielded generalized Hurst exponent function, H(q), and singularity spectrum, D(h) separately for a fast and slow component (the latter dominating the highest temporal scales). Parameters were calculated reflecting the estimated measure at s = N (focus), degree of LRC [Hurst exponent, H(2) and maximal Hölder exponent, h_max] and measuring strength of multifractality [full-width-half-maximum of D(h) and ΔH₁₅ = H(−15)−H(15)]. Correlation-based signal improvement (CBSI) enhanced our signal in terms of interpreting changes due to neural activity or local/systemic hemodynamic influences. We characterized the HbO-HbR relationship with the aid of fractal scale-wise correlation coefficient, r_σ(s) and SSC-based multifractal covariance analysis. In the majority of subjects, cerebral hemodynamic fluctuations proved bimodal multifractal. In case of slow component of raw HbT, h_max, and Ĥ(2) were lower in the young group explained by a significantly increased r_σ(s) among elderly at high temporal scales. Regarding the fast component of CBSI-pretreated HbT and that of HbO-HbR covariance, h_max, and focus were decreased in the elderly group. These observations suggest an attenuation of neurovascular coupling reflected by a decreased autocorrelation of the neuronal component concomitant with an accompanying increased autocorrelation of the non-neuronal component in the elderly group.

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.

Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model

We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L×L×l which explain the size-driven critical crossover from two dimensions (l=const, L→∞) to three dimensions (l∝L→∞). A model of effective critical disorder R_{c}^{eff}(l,L) with a unique fitting parameter and no free parameters in the R_{c}^{eff}(l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.

Threshold-induced correlations in the Random Field Ising Model

We present a numerical study of the correlations in the occurrence times of consecutive crackling noise events in the nonequilibrium zero-temperature Random Field Ising model in three dimensions. The critical behavior of the system is portrayed by the intermittent bursts of activity known as avalanches with scale-invariant properties which are power-law distributed. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations show that the observed correlations emerge upon applying a finite threshold to the pertaining signals when defining events of interest. Such events are called subavalanches and are obtained by separation of original avalanches in the thresholding process. The correlations are evidenced by power law distributed waiting times and are present in the system even when the original avalanche triggerings are described by a random uncorrelated process.