Multifractal Parameters Research Articles

Heart rate variability series during physical activity analyzed with multifractal techniques

Abstract Our study uses multifractal techniques to analyze time series of heart rate variability series (RR time series) during rest and physical activity. Subsets of the RR time series data were extracted for each stage. The multifractal spectra of the RR time series data were constructed using the method developed by Chhabra and Jensen. Then, parameters such as width, symmetry, and curvature of the multifractal spectra were calculated. The multifractal spectra obtained at resting stage were broad, skewed to the right, and they had small curvatures around in the maximum. On the contrary, the subsets of the RR time series obtained during physical activity were narrow, skewed to the left, and showed an increased curvature value around the maximum. In addition, these multifractal spectrum parameters shown significant differences in series of subjects who perform physical activity regularly and sedentary. Furthermore, the results obtained from this study were compared with data from previous works involving patients with congestive heart failure and healthy subjects.

Impact of surface-roughness and fractality on electrical conductivity of SnS thin films

Mono- and multi-fractal geometry have been used to explore the surface characteristics of scanning electron microscopy (SEM) micrographs of the SnS films with thicknesses of 100nm (SnS1) to 600nm (SnS4), respectively. For this investigation, the SnS thin films have been grown on fluorine-doped tin oxide (FTO)-coated glass substrate through the thermal evaporation route, and surface morphologies are captured by SEM. Two-dimensional multi-fractal detrended fluctuation analysis (MFDFA) based on the partition function is used to examine whether the surfaces have a multi-fractal nature or not. The partition function is applied to extract the generalized Hurst exponent from the segment size. It has been found that surfaces with higher surface roughness induce substantial nonlinearity and a wider width of the multi-fractal spectrum. The multi-fractal spectrum acquired from the analysis of the geometry and shape of the singularity spectrum is used to quantify the irregularity and complexity of surfaces. Minkowski functionals (MFs) parameters such as volume, boundary, and connectivity were measured for each thin film. Moreover, we tried to correlate the electrical conductivity with the mono- and multi-fractal parameters such as fractal dimension (Df), singularity strength function (Δα), singularity spectrum Δf(α), and it is observed that the conductivity of a thin film decreases with decreasing fractal dimension. The minimum (maximum) resistivity (conductivity) was observed for the surface having a larger fractal dimension. The present investigation suggests that such SnS surfaces, having minimal resistivity and maximum conductivity on the roughest surface, indicate enhanced light trapping capacity and can be utilized as active layers for advanced optoelectronics devices.

Multifractal structure and Gutenberg–Richter parameter associated with volcanic emissions of high energy in Colima, Mexico (years 2013–2015)

Abstract. The evolution of multifractal structures in various physical processes, such as climatology, seismology, or volcanology, serves as a crucial tool for detecting changes in corresponding phenomena. In this study, we explore the evolution of the multifractal structure of volcanic emissions with varying energy levels (observed at Colima, Mexico, during the years 2013–2015) to identify clear indicators of imminent high-energy emissions nearing 8.0×108 J. These indicators manifest through the evolution of six multifractal parameters: the central Hölder exponent (α0); the maximum and minimum Hölder exponents (αmax, αmin); the multifractal amplitude (W=αmax-αmin); the multifractal asymmetry (γ=[αmax-α0]/[α0-αmin]); and the complexity index (CI), calculated as the sum of the normalized values of α0, W, and γ. Additionally, the results obtained from adapting the Gutenberg–Richter seismic law to volcanic energy emissions, along with the corresponding skewness and standard deviation of the volcanic emission data, further support the findings obtained through multifractal analysis. These results, derived from multifractal structure analysis, adaptation of the Gutenberg–Richter law to volcanic emissions, and basic statistical parameters, hold significant relevance in anticipating potential volcanic episodes of high energy. Such anticipation can be further quantified using an appropriate forecasting algorithm.

Multifractal Characteristics of Low-Field Nuclear Magnetic Resonance of Different Rank Coals and Its Permeability Predicting Method.

The permeability of methane in coal is a crucial factor in the production of coal-bed methane (CBM), which is dependent on the pore size distribution (PSD) of coal. The transverse relaxation time cutoff value (T2C) is a crucial parameter in nuclear magnetic resonance (NMR) techniques for converting NMR data into an absolute PSD. To investigate an appropriate approach for predicting the T2C and permeability of different rank coals, this study first revealed, through centrifuge experiments with a centrifugal force of 1.38 MPa, the T2C values of five coal samples: anthracite coal (3 ms), lean coal (8 ms), coking coal (12 ms), fat coal (11 ms), and lignite coal (13 ms). These T2C values were then employed to obtain the absolute PSD values of the coal samples. The results demonstrated that the pore structure characteristics of these coal samples are essentially identical, with micropores constituting the majority, varying between 63.47% and 93.74%. Subsequently, the multifractal analysis method was introduced to establish a new T2C value calculation model. A comparison of the model-calculated T2C values with those obtained from centrifugal experiments revealed an average deviation of only 5.26%. Finally, a new permeability model was developed by conducting multiple regressions on permeability and multifractal parameters. In comparison to classical models, such as the Timur-Coates (TC) model and the Schlumberger Dauer Research Center (SDR) model, the developed permeability model offers more accurate predictions. These results are applicable to pore structure characterization and methane permeability prediction in coal reservoirs of varying rank and other unconventional gas reservoirs.

Novel multifractal-based classification model for the quality grades of surrounding rock within tunnels

Understanding the variation patterns of tunnel boring machine (TBM) operational parameters is crucial for assessing engineering geological conditions and quality grades of surrounding rock within tunnels. Studying the multifractal characteristics of the TBM operational parameters can help identify the patterns, but the relevant research has not yet been explored. This paper proposed a novel classification model for quality grades of surrounding rock in TBM tunnels based on multifractal analysis theory. Initially, the statistical characteristics of eight TBM cycle data with different grades of surrounding rock were explored. Subsequently, the method of calculating and analyzing the multifractal characteristic parameters of the TBM operational data was deduced and summarized. The research results showed that the TBM operational parameters of cutterhead torque, total thrust, advance rate, and cutterhead rotation speed have significant multifractal characteristics. Its multifractal dimension, midpoint slope of the generalized fractal spectrum, and singularity strength range can be used to evaluate the surrounding rock grades of the tunnel. Finally, a novel classification model for the tunnel surrounding rocks based on the multifractal characteristic parameters was proposed using the multiple linear regression method, and the model was verified through four TBM cycle data containing different surrounding rock grades. The results showed that the proposed multifractal-based classification model for tunnel surrounding rocks has high accuracy and applicability. This study not only achieves multifractal feature representation and surrounding rock classification for TBM operational parameters but also holds the potential for adaptive adjustment of TBM operational parameters and automated tunneling applications.

Pore-Fracture System Distribution Heterogeneity by Using the T2 Spectral Curve under a Centrifugal State

In this paper, 12 sandstone samples are collected from the Taiyuan Formation in Qinshui Basin, and sample types using the T2 spectral under LF-NMR saturation and centrifugation conditions are classified. Moreover, single and multifractal models were used to calculate fractal parameters of saturated and centrifugal T2 spectra, and the correlation between different fractal parameters, pore structure, T2cutoff value, and pore permeability parameters was studied. The results are as follows. (1) According to the T2 spectrum curves under centrifugation and saturation conditions, all the samples can be divided into three types. There are significant differences in the uniform pore size distribution. However, the non-uniformity of small pore distribution in type B samples is stronger than that of other types, while heterogeneity of large pore distribution is weaker than that of different types. The centrifugal T2 spectrum curve exhibits both single-fold and multifractal characteristics. The results of a single fractal by using a centrifugal T2 spectrum are consistent with those of a saturated T2 spectrum, indicating that single fractal features by using centrifugal and saturated T2 spectra are consistent. Unlike the single fractal parameters, the correlation between the saturation and centrifugal T2 spectrum’s multifractal parameters is weak. This suggests that the physical significance conveyed by the centrifugal T2 spectrum’s multifractal parameters differs from that of the saturated T2 spectrum.

Multifractal of acoustic emission for the multi-scale fracture behavior of diatomite modified concrete

It has been attempted to determine how supplemental cementitious materials (SCMs) affects concrete's resistance to fracture. Nevertheless, acoustic emission (AE) has not been used to investigate the impact of diatomite, an SCMs, on the fracture characteristics of concrete. In this investigation, the aim was to assess the fracture behavior of concrete with variable loadings of diatomite (0 %, 1 %, 2 %, 3 %). Three-point bending is performed along with continuous AE monitoring for concrete with various contents of diatomite to obtain AE information. The fracture behavior (fracture parameters, fracture mode, multi-scale fracture and damage) is determined by analyzing AE parameters and corresponding statistical indicators such as Multifractal Detrended Fluctuation Analysis(MF-DFA) and Weibull theory. The results show that the addition of diatomite enhances the fracture property of concrete especially the optimal 2 % content. Then, the high RA value and tensile crack ratio suggest the improvement of the tensile resistance of diatomite. Moreover, a novel quantitative index called multifractal parameter is proposed to evaluate the multi-scale fracture. The finding contributes to a novel method for quantifying multi-scale cracking. The low multifractal parameter in diatomite modified concrete implies a small cracking scale in comparison with the ordinary concrete. Finally, the presence of diatomite slowed down the development of fracture damage in concrete.

The Pore Structure Multifractal Evolution of Vibration-Affected Tectonic Coal and the Gas Diffusion Response Characteristics

Vibrations caused by downhole operations often induce coal and gas outburst accidents in tectonic zone coal seams. To clarify how vibration affects the pore structure, gas desorption, and diffusion capacity of tectonic coal, isothermal adsorption-desorption experiments under different vibration frequencies were carried out. In this study, high-pressure mercury intrusion experiments and low-pressure liquid nitrogen adsorption experiments were conducted to determine the pore structures of tectonic coal before and after vibration. The pore distribution of vibration-affected tectonic coal, including local concentration, heterogeneity, and connectivity, was analyzed using multifractal theory. Further, a correlation analysis was performed between the desorption diffusion characteristic parameters and the pore fractal characteristic parameters to derive the intrinsic relationship between the pore fractal evolution characteristics and the desorption diffusion characteristics. The results showed that the vibration increased the pore volume of the tectonic coal, and the pore volume increased as the vibration frequency increased in the 50 Hz range. The pore structure of the vibration-affected tectonic coal showed multifractal characteristics, and the multifractal parameters affected the gas desorption and diffusion capacity by reflecting the density, uniformity, and connectivity of the pore distribution in the coal. The increases in the desorption amount (Q), initial desorption velocity (V0), initial diffusion coefficient (D0), and initial effective diffusion coefficient (De) of the tectonic coal due to vibration indicated that the gas desorption and diffusion capacity of the tectonic coal were improved at the initial desorption stage. Q, V0, D0, and De had significant positive correlations with pore volume and the Hurst index, and V0, D0, and De had negative correlations with the Hausdorff dimension. To a certain extent, vibration reduced the local density regarding the pore distribution in the coal. As a result, the pore size distribution was more uniform, and the pore connectivity was improved, thereby enhancing the gas desorption and diffusion capacity of the coal.

Multifractal characteristics on pore structure of Longmaxi shale using nuclear magnetic resonance (NMR)

The efficient exploration and extraction of shale gas is essential for China's energy structure as a replacement for natural gas. In this research, shale samples from the Longmaxi Formation in Changning, Sichuan Province were investigated for their pore structure. To achieve this, X-ray diffraction (XRD) and nuclear magnetic resonance (NMR) experiments were performed on the samples. Fractal theory was employed to characterize the pore structure and fractal features of the shale reservoirs. The fractal characteristics of reservoir rocks were correlated with physical parameters and mineral components to identify the controlling factors for the multifractal dimension. The results indicate the following: ① Quartz predominates in the mineral composition of shale in the study area, while clay minerals are the least abundant. ② The primary pore types observed in the samples are bound fluid pores, primarily controlled by mesopores (2 nm ≤ r ≤ 50 nm). ③ The calculated multifractal parameters show that the heterogeneous pore structure exhibits multifractal characteristics. ④ The low probability multifractal parameters Dmin-D0 and αmax-α0 were found to be negatively correlated with reservoir porosity, permeability, and clay mineral content, while the high probability multifractal parameters D0-Dmax and α0-αmin were found to be positively correlated with them. The comprehensive fractal characterization of reservoir rocks demonstrates the applicability of multifractal dimensions in characterizing the heterogeneity of shale reservoir pore structures, which holds potential promise for coal methane exploration.

Effect of NO2 on SO2–SO42- conversion in atmosphere: Evidence from long-term precipitation

Sulfate aerosol (SO42−) is an important factor leading to acid rain and aggravating atmospheric particulate pollution. SO42− is mainly converted from gaseous SO2, in which the oxidant gas NO2 may play a key role. In real atmosphere with complexity and nonlinearity, the impact of NO2 on SO2–SO42- conversion exhibits scale dependence due to the combined effect of meteorology, atmospheric chemistry, and pollution emission. Here, based on the long-term atmospheric precipitation data from 2014 to 2021 of Nanchong City in the Sichuan Basin, the Extended Ensemble Empirical Mode Decomposition (EEMD) and Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) methods have been employed to analyze the nonlinear correlations between gaseous SO2 and SO42− in rainwater at different time scales. A multifractal parameter Δh has been described as the scaling features of SO2–SO42- conversion efficiency in the real atmosphere. Then, the impact of NO2 on SO2–SO42- conversion in cold and warm seasons has been quantified, using sliding window analysis and Pearson correlation analysis. The results show that NO2 significantly promoted SO2–SO42- conversion in the cold season, but had little effect on it in the warm season. As direct evidence from atmospheric precipitation analysis, this finding has provided a new theoretical basis for evaluating the impact of NO2 on secondary aerosol generation.

Multi-fractal characteristics of pore system in deep organic-rich shales of the Wufeng-Longmaxi formation in the Sichuan Basin and their geological significance

The heterogeneity of pore system of deep shale reservoir determines the occurrence, enrichment and migration behavior of shale gas within shales. In this study, multi-fractal analysis was applied to analyze CO2 and N2 adsorption data for obtaining multi-fractal parameters including Hurst index and multi-fractal spectrum (D5--D5+) of the deep Wufeng-Longmaxi shales collected from the Sichuan Basin, China, in order to study the connectivity and heterogeneity of micropore pores and meso-macropores as well as their influencing factors. The results showed that pore system of the Wufeng-Longmaxi deep shale exhibits distinct multifractal nature. There exists significant differences in the pore volume (PV) of micropores (<2 nm), mesopore (2–50 nm), and macropore (>50 nm) across different shale lithofacies due to their differences in TOC content and mineral composition. The heterogeneity and connectivity of micropores and meso-macropores within deep shales in the Sichuan Basin are controlled by multiple factors including shale lithofacies, burial depth, and pressure coefficients. Notably, siliceous shale (SL) and calcareous/argillaecous siliceous shale (C/ASL), known as sweet spot for current shale gas exploitation, exhibits characteristics such as relative low micropore connectivity, high micropore heterogeneity, high micropore PV and low meso-macropore connectivity. These suggest that isolated pressure-sealing compartment is easier formed within the overpressured SL and C/ASL. Thus, pressure in these shales is less likely to release during the Yanshanian-Xishanian tectonic uplift process, favoring the preservation of organic matter (OM) pores and residual interparticle pores, which is conducive to the accumulation of deep shale gas dominated by free gas.

Investigation on vibration characteristics induced by gas–liquid two-phase flows in a horizontal pipe

The intrinsic characteristics of multiphase flow inevitably result in vibrations within the pipe structure. The evolution of vibration characteristics is crucial for monitoring the stability of the multiphase flow pipelines. However, under high liquid velocity condition, the influence of flow pattern on the gas–liquid two-phase flow-induced vibration (GTFIV) of the pipe remains unclear. In this paper, the vibration signals in the horizontal pipe under different flow patterns at high liquid velocity are measured by a vibration test system. Synchronously, images inside the pipe are captured to illustrate the flow mechanism. The results show that the α stable distribution model holds higher fitting accuracy than the standard normal distribution for the GTFIV. The random behavior of small-scale bubbles determines the structural richness of the GTFIV. The multifractal characteristics of the GTFIV are strongly dependent on the flow pattern. The formation of the gas plug leads to significant unevenness in the fractal structure of the GTFIV. The multifractal strength of the GTFIV gradually increases as the flow pattern transforms from dispersed bubble flow to slug flow. Some multifractal spectrum parameters of the vibration signal can be applied for the identification of flow patterns in the pipe.

Fractal and Multifractal Analysis of Microscopic Pore Structure of UHPC Matrix Modified with Nano Silica

Nano silica (NS) has been found to have a positive impact on enhancing the microporous structure of Ultra-High-Performance Concrete (UHPC). However, there is a lack of effective methods to accurately characterize the regulatory improvement mechanism of NS on the pore structure of UHPC. In this study, our objective is to investigate the influence of NS on various characteristic parameters of the pore structure in UHPC, including porosity, average pore size, box fractal dimension, and multifractal spectral parameters. To analyze these effects, we employ a combination of X- CT image processing techniques and fractal theory. Furthermore, we conducted regression analysis using linear functions to explore the correlation between these parameters and the 28d compressive strength of UHPC. The experimental results demonstrate that NS promotes the refinement of matrix pore size, leading to a denser microstructure of the matrix. Fractal analysis revealed that the pore structure of NS-modified UHPC exhibited favorable fractal characteristics. The fractal dimension and multiple fractal parameters provided complementary insights into the pore structure of NS-modified UHPC from different perspectives. The fractal dimension described the global information, indicating that NS improved matrix defects and reduced the complexity of the pore structure. On the other hand, the multiple fractal parameters supplemented local information, highlighting how the increase in micropores contributed to the heterogeneity of the pore structure. The results of the correlation analysis indicate that the developed mathematical model has a good fit with the 28d compressive strength of UHPC.

Multifractal characterization of fried foods pore microstructure

This study aimed to unravel the multifractal properties of internal microstructure in relation to textural evolution of meat-analog (MA) based coated fried foods. Wheat and rice flour-based batters were used to coat MA model that was deep fried at 180 °C for 2, 4 and 6 min in canola oil. Internal pore microstructures were investigated by X-ray microtomography based multifractal analysis (MFA) and texture were assessed by mechanical texture analyzer. Results showed that batter coatings greatly influenced the formation of internal microstructure during frying as well as post-frying mass redistribution and textural evolution. The frying time impacted the evolution of micropores, and porosity showed a positive correlation with the fat content of MA-based fried products. Porous, low-moisture and high-fat containing coated fried MA-based product demonstrated higher textural stability. Internal microstructure (pore distribution) of fried MAs were heterogenous and possessed multifractal scaling behavior, as depicted by MFA outcomes (Singularity & Rényi spectra). Strong correlation observed between moisture-fat, texture, porosity and selected multifractal parameters (Δα, Δfα, R-L, D1, D2, ΔD).

Experimental investigation into grain size effect on failure behavior and nonlinear time-varying acoustic emission series of granite

This study aims to investigate the grain size effect on mechanical properties and failure mechanisms of hard rock. Thus, a series of uniaxial compression experiments were carried out on granites with various grain sizes, and acoustic emission (AE) signals were synchronously collected in the experimental process for further nonlinear analysis. The results show that the four characteristic stresses of granite (σcc, σci, σcd, and σc) significantly decrease with the increase of grain size. The ratio of σcd/σc basically remains a constant of 0.8; the ratio of σci/σc increases gradually from 0.6 to about 0.7; the ratio of σcc/σc also shows a rising trend overall. With the increase of grain size, the AE energy level rises; the proportion of high-frequency tensile signals is reduced; the multi-fractal parameters Δα (non-uniformity of signals) and Δf (frequency difference between minimum and maximum signals) decrease. During the loading process, the time-varying value of Δα changes between 0.0 and 0.35, and that of Δf changes within the range from −0.2 to 0.5, showing a ‘rise-fall-rise-fall’ mode. The grain size effect on the influence of crack evolution is further discussed based on the nonlinear time-varying AE analysis. All these results reflect the mechanisms of grain size effect on granite. Large grain size weakens grain boundaries, facilitating shear slip along weak planes between crystal particles. In addition, the enhanced local stress concentration and initial defects in rock with large grain size could activate the crack coalescences of intra-crystalline cracks and weak boundary planes more easily in a relatively low-stress state.

Study on the multifractal characterization and seepage of the shale matrix: A case study of the Longmaxi Formation in southwestern Sichuan Basin, China

The pore structure and heterogeneity of shale significantly impact the occurrence and permeability of shale gas. Studying these aspects is beneficial for exploring and developing shale gas. In this study, organic-rich shale from the Longmaxi Formation in the Luzhou-Changning area was selected as the research subject. Experiments, including spontaneous imbibition, pressure saturation, and nuclear magnetic resonance, were conducted to characterize the pore structure and heterogeneity of the shale in this area. Using multifractal theory, we analyzed and discussed the multifractal characteristics of pores with different connectivities in relation to permeability. The results indicate that the T2 cutoff value (T2f) of the shale is greater than the T2c value, suggesting that the pore size of connected pores exceeds that of pores retaining bound water. The sizes of connected pores primarily range from 1 to 30 nm, predominantly between 1 and 10 nm. Significant differences were observed in the multifractal spectrum functions under dry, spontaneous imbibition, and water-saturated conditions, reflecting varying degrees of heterogeneity. The multifractal parameters differ, with higher ΔD values under water-saturated conditions, indicating that pores with weaker connectivity enhance the overall heterogeneity of the shale when saturated. Conversely, lower ΔD values under dry conditions suggest less heterogeneity in pores containing bound water. Total organic carbon (TOC) and clay content were identified as the main factors influencing the development of connected pores. Based on these findings, a discriminant 3D diagram correlating permeability with porosity, tortuosity, and multifractal parameters (D0-Dmax) of strongly connected pores was established for the Luzhou-Changning area. This diagram serves as an effective tool for evaluating the flow capacity of shale reservoirs and offers guidance for identifying sweet spots within the reservoir.

Promoting Sustainable Coal Mining: Investigating Multifractal Characteristics of Induced Charge Signals in Coal Damage and Failure Process

Monitoring and preventing coal–rock dynamic disasters are essential for ensuring sustainable and safe mining. Induced charge monitoring, as a geophysical method, enables sustainable monitoring of coal–rock deformation and failure. The induced charge signal contains crucial information regarding damage evolution, making it imperative and important to explore its temporal characteristics for effective monitoring and early warnings of dynamic disasters in deep mining. This paper conducted induced charge monitoring tests at different loading rates, investigating the multifractal characteristics of induced charge signals during the early and late stages of loading. It proposed the maximum generalized dimension D(q)max, multifractal spectrum width Δα, and height difference Δf as multifractal parameters for induced charge signals. Additionally, quantitative characterization of coal damage was performed, studying the variation patterns of signal multifractal characteristic parameters with coal damage evolution. This study revealed the induced charge signal of the coal body multifractal characteristics in the whole loading process. In the late loading stage, the double logarithmic curve demonstrated some nonlinearity compared to the previous period, indicating the higher non-uniformity of the induced charge time series. D(q)max and Δα in the late loading stage were higher than those in the early stage and increased with loading rates. As coal damage progressed, there were significant jumps of D(q)max in both the early and late stages of damage, with larger jumps indicating richer fracture events in the coal. The width Δα showed an overall trend of increase–decrease–increase with coal damage evolution, while the height difference Δf fluctuated around zero in the early stage of damage development but increased significantly during severe damage and destruction. By studying the multifractal characteristics of induced charge signals, this study provides insights for the early identification of coal–rock dynamic disasters.

Characteristics of Soil Particle Sizes and Fractal Parameters under Different Plantation Types of Populus alba

Vegetation plays a leading role in restoring desert ecosystems and increasing productivity. In this study, we elucidate the improvement effects of different restoration areas of Populus alba on the soil particle distribution, sedimentation environment, and fractal characteristics. We selected the restoration areas of P. alba × Caragana korshinskii (YN), P. alba × Hedysarum leave (YY), and P. alba × Hedysarum scoparium (YH), which have a history of twenty-one years. We analyzed the soil nutrients, soil particle size, soil particle size parameters, soil fractal dimension (D) values, and soil multifractal parameters at soil depths of 0–80 cm. We found that the YN, YY, and YH significantly increased the soil nutrients and soil fine particles (p < 0.05) and changed the deposition pattern of the soil particles in the sandy area. The YN, YY, and YH promote soil particle refinement and reduce the sorting performance of the soil particles. The vegetation promotes extremely positive-skewed and very leptokurtic soil particle distributions. The D values in the YN, YY, and YH restoration areas increased by 7.62%–27.94%, 7.36%–26.28%, and 7.10%–17.92%, respectively, relative to those of the LS. The construction of the different restoration areas of P. alba has made the distribution of the soil particles nonuniform. Compared with the YY and YH plantations, the distribution range of the soil particles in the YN plantation is wider, and the distribution heterogeneity is greater. In addition, we found that the fractal parameters are influenced by the soil physicochemical properties, the depositional environment, and vegetation factors. Therefore, we believe that D values and multifractal parameters are necessary as additional information for desert soil texture improvement. The results of this study provide a scientific and theoretical basis for the future revegetation of deserts.

Dynamic multifractal characteristics of acoustic emission about composite samples with different stress loading and unloading conditions

Studying the failure characteristics of the common composite strata structure in western China is essential for evaluating stope stability and predicting coal mine dynamic disasters. To investigate the influence of different stress loading and unloading conditions on the instability characteristics of composite samples, three triaxial loading and unloading test schemes simulating different in-situ mining depths were designed. Complex triaxial tests were conducted on 12 sets of composite samples, and the bearing capacity, acoustic emission (AE) parameters and dynamic multifractal characteristics of the samples under different stress loading or unloading conditions were analyzed. The results indicate that samples tested by stress schemes simulating greater mining depths exhibit less damage, and the failure mode is a tensile-shear mixed failure, but the tensile failure is the main failure mode. The multifractal spectral parameters Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\alpha$$\\end{document} of AE time series during the failure of composite samples tested with triaxial loading and unloading schemes simulating different mining depths show a decreasing trend in Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\alpha$$\\end{document} values with increasing mining depth, while the change rules of Δfα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta f\\left( \\alpha \\right)$$\\end{document} values are the opposite. The multifractal parameter changes degree in four-layer rock structure composite samples under different stress conditions are lower than those in three-layer rock structure composite samples, indicating that the microcrack propagation process in the three-layer composite sample is more complex, resulting in higher levels of damage. The dynamic change of multifractal parameters Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\alpha$$\\end{document} and Δfα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta f\\left( \\alpha \\right)$$\\end{document} during different stress loading and unloading stages reflects the influence of axial pressure or confining pressure changes on crack propagation in composite samples. Compared to the initial stress stage, the non-uniformity of AE signals increases in the residual stress stage, and the proportion of large signals becomes more prominent, signifying a complex micro-fracture process in the composite samples.

Pallidal multifractal complexity is a new potential physiomarker of dystonia

ObjectiveLow-frequency 4–12 Hz pallidal oscillations are being considered as potential physiomarkers for dystonia. We suggest investigating the multifractal properties of pallidal activity as an additional marker. MethodsWe employed local field potentials (LFP) recordings from 23 patients with dystonia who were undergoing deep brain stimulation (DBS) surgery to explore the connection between disease severity and the multifractal characteristics of pallidal activity. Furthermore, we performed an analysis of LFP recordings from four patients, following the externalization of DBS lead electrodes, to investigate the impact of DBS and neck muscle vibration on multifractal parameters. ResultsGreater dystonia severity exhibited a correlation with a narrower multifractal spectrum width but higher multifractal spectral asymmetry. Both GPi DBS and muscle vibration in dystonia patients expanded the multifractal spectrum width while restoring multifractal spectral symmetry. Notably, the threshold peak intensities for an increase in multifractal spectrum width substantially overlapped with the optimal volume of tissue activated. A broader multifractal spectrum during DBS corresponded to more favorable clinical outcomes. ConclusionsMultifractal properties of pallidal neuronal activity serve as indicators of neural dysfunction in dystonia. SignificanceThese findings suggest the potential of utilizing multifractal characteristics as predictive factors for the DBS outcome in dystonia.