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Drought is characterized by a moisture deficit that can adversely impact the environment, economy, and society. In North America, like many regions worldwide, predicting the timing of drought events is challenging. However, our novel study in climate research explores whether the Drought Monitor database exhibits fractal characteristics, represented by a single scaling exponent. This database categorizes drought areas by intensity, ranging from D0 (abnormally dry) to D4 (exceptional drought). Through vibration analysis using power spectral densities (PSD), we investigate the presence of power-law scaling in various statistical moments across different scales within the database. Our multi-fractal analysis estimates the multi-fractal spectrum for each category, and the Higuchi algorithm assesses the fractal complexity, revealing that D4 follows a multi-fractal pattern with a wide range of exponents, while D0 to D3 exhibit a mono-fractal nature with a narrower range of exponents.

Thanks to the continuous development of light-curing resin composites it is now possible to print permanent single-tooth restorations. The purpose of this study was to compare resin composites for milling -Gandio Blocks (GR), Brilliant Crios (CR) and Enamic (EN) with resin composite for 3D printing—Varseo Smile Crown plus (VSC). Three-point bending was used to measure flexural strength (σf) and flexural modulus (Ef). The microhardness was measured using a Vickers method, while fractographic, microstructural, texture and fractal dimension (FD) analyses were performed using SEM, optical microscope and picture analysis methods. The values of σf ranged from 118.96 (±2.81) MPa for EN to 186.02 (±10.49) MPa for GR, and the values of Ef ranged from 4.37 (±0.8) GPa for VSC to 28.55 (±0.34) GPa for EN. HV01 ranged from 25.8 (±0.7) for VSC to 273.42 (±27.11) for EN. The filler content ranged from 19–24 vol. % for VSC to 70–80 vol. % for GR and EN. The observed fractures are typical for brittle materials. The correlation between FD of materials microstructure and Ef was observed. σf of the printed resin depends on layers orientation and is significantly lower than σf of GR and CR. Ef of the printed material is significantly lower than Ef of blocks for milling.

Root fractal analysis is instrumental in comprehending the intricate structures of plant root systems, offering insights into root morphology, branching patterns, and resource acquisition efficiency. We conducted a field experiment on paddy–wheat root systems under varying nitrogen fertilizer strategies to address the need for quantitative standardization in root fractal analysis. The study evaluated the impact of nitrogen fertilizer heterogeneity on root length and number. We established functional relationships and correlations among root fractal characteristics and root length across different box dimension scales and various root placement angles at 2.5, 5, 10, 20, 40, and 80 box dimension scales. Results indicated that nitrogen fertilizer had a limited impact on paddy–wheat axile roots, with a coefficient of variation below 0.35 among samples. Box dimension scale influenced 3D fractal dimension (FD) and fractal abundance (FA), with strong correlations (>78%) among 3D fractal features and low sample errors (<6%). The linear correlation coefficient exceeded 72% between 3D FA and root length and 50% between FA and FD. Different axile root placement angles significantly impacted planar fractal results, particularly at a 10° angle. This stability was maintained throughout the sampling period, with high correlation coefficients (>0.76 for FA and >0.5 for FD) and low sample errors (<1.5% for FA and <4.5% for FD). In conclusion, for calculating the 3D fractal characteristics of paddy–wheat axile roots during the seedling stage, box dimension scales of 2.5, 5, 10, 20, 40, and 80, as well as 2, 5, 10, 20, 50 and 100 and 3, 6, 12, 24, 48 and 96, were suitable. When computing the planar fractal characteristics of paddy–wheat axile roots during this stage, a 10° placement angle between axile root systems yields lower errors. These findings enhance root quantification methods, standardize root analysis, and promote the comparability of crop root system fractal data across different varieties and regions, thereby advancing root-related research.

This study explores the multi-fractal properties of cosmic-ray (CR) counts collected from two mid-latitude neutron-monitor stations, Newark (NEWK) and Irkutsk 3 (IRK3), and two high-latitude stations, Thule (THUL) and Inuvik (INVK), during periods of severe geomagnetic storms. By employing multi-fractal along with time-series analysis, we did an in-depth examination of CR count variations to demonstrate the effectiveness of these methods in analyzing complex signals associated with astrophysical and solar phenomena. The findings reveal that CR count rates across stations at different latitudes exhibit multi-fractal characteristics, reflecting a range of scaling exponents that capture varying degrees of correlation and variability within the system. The results underscore that solar activity, geomagnetic events, and interactions with Earth’s magnetic field play a more crucial role in determining multi-fractality than the geographic location of the measurement station. Moreover, the study shows that geomagnetic events exert a stronger influence on the multi-fractal properties of CR count rate than the geographic location of station, underscoring the impact of solar storms and Earth’s magnetic field on the distribution and intensity of CRs. This work emphasizes the value of multi-fractal analysis as a powerful tool for investigating the complex nature of CR counts and its sensitivity to both extraterrestrial and terrestrial factors.

Identification of geochemical anomalies is of particular importance for tracing the footprints of anomalies. This can be implemented by advanced techniques of exploratory data analysis, such as fractal/multi-fractal approaches based on priori or posteriori distribution of geochemical elements. The latter workflow involves analysis of 2D/3D produced maps, which can be mostly obtained by geostatistical algorithms. There are two challenging issues for such an analysis. The first one corresponds to handling the cross-correlation structures among the data, and the second one relates to the compositional nature of data. To tackle these problems, this paper investigates the application of Gaussian co-simulation for modeling the cross-correlated compositional data in order to recognize the multivariate geochemical anomalies in integration with fractal analysis. In this context, an innovative algorithm, namely co-simulated size number (CoSS-N), is introduced for this purpose. The compositional nature of data is addressed by additive log-ratio transformation of original data while the Gaussian co-simulation handles the reproduction of cross-correlation among the components. The co-simulated outputs are then taken into account for capturing different geochemical populations, showing different levels of backgrounds and anomalies. The algorithm is illustrated via a real case study located in Philippine wherever seven geochemical components are required to be considered. The accuracy of results is examined by statistical validation techniques, indicating the capability of the CoSS-N algorithm for multivariate identification of geochemical anomalies.

This study reports a fractal analysis of one-year radon in groundwater disturbances from five stations in China amidst the catastrophic Wenchuan (Mw = 7.9) earthquake of 12 May 2008 (day 133). Five techniques are used (DFA, fractal dimensions with Higuchi, Katz, Sevcik methods, power-law analysis) in segmented portions glided throughout each signal. Noteworthy fractal areas are outlined in the KDS, GS, MSS data, whilst the portions were non-significant for PZHS and SPS. Up to day 133, critical epoch DFA-exponents are 1.5≤α<2.0, with several above 1.8. The fractal dimensions exhibit Katz’s D around 1.0–1.2, Higuchi’s D between 1.5 and 2.0, and Sevcik’s D between 1.0 and 1.5. Several power-law exponents are above 1.7, and numerous are above 2.0. All fractal results of the KDS-GS-MSS are further analysed using a novel computerised methodology that locates the exact out-of-threshold fractal areas and combines the outcomes of different methods per five, four, three, and two (maximum 13 combinations) versus nineteen Mw≥ 5.5 earthquakes of the greater area. Most coincidences using different techniques are before the great Wenchuan earthquake and after the earthquake. This is not only with one method but with 13 different methods. Other interpretations are also discussed.

The paper considers a generalized approach to the time series multifractal analysis. The focus of research is on the correct estimation of multifractal characteristics from short time series. Based on numerical modeling and estimating, the main disadvantages and advantages of the sample fractal characteristics obtained by three methods: the multifractal fluctuation detrended analysis, wavelet transform modulus maxima and multifractal analysis using discrete wavelet transform are studied. The generalized Hurst exponent was chosen as the basic characteristic for comparing the accuracy of the methods. A test statistic for determining the monofractal properties of a time series using the multifractal fluctuation detrended analysis is proposed. A generalized approach to estimating the multifractal characteristics of short time series is developed and practical recommendations for its implementation are proposed. A significant part of the study is devoted to practical applications of fractal analysis. The proposed approach is illustrated by the examples of multifractal analysis of various real fractal time series.

Barite mineralization is visible as veins in the Kuik‒Qureq area, southern part of Sanandaj zone, Western Iran. Geological and structural maps of the area were prepared using remote sensing data and field achievements. Statistical analysis of fractures included the ratio of distance and length to abundance, and also the calculation of the fractal dimension of fractures. This analysis indicates the role of structural controls on the barite mineralization in the region. Petro-fabrics were used to determine displacement and contribution of faults in barite mineralization. Geometric analysis using rose diagrams determined that the trends of the dominant fractures are N‒S and NN‒S, NNW‒SSE, WNW‒ESE and NNE‒SSW, and the main barite mineralization was formed along these faults. A tectonic model is presented for the region based on classifying fractures by azimuth and features observed in thin section. According to the proposed model, at least four stages of tectonic deformation affected the region and during these the direction of the σ 1 axis changed in a clockwise direction. Barite mineralization mainly occurred in two stages: the first and main stage when first order fractures formed with the N‒S trend, and during the third deformation stage when secondary barite was deposited in third order fractures with an E‒W trend.

Analyzing and fusing information layers of exploratory parameters is a crucial stride for increasing the accuracy of pinpointing mineral potential zones in the reconnaissance stage of mineral exploration. Remote sensing, geophysical, geochemical, and geology data were analyzed and fused for identify metallic mineralization in the Kodegan-Basiran region (East Iran). Landsat 7 Enhanced Thematic Mapper Plus (ETM+), aeromagnetic data, geological data, and geochemical stream sediment samples were utilized. The study area contains some copper indices and mines. Thus, the main focus of this study was identifying the zones with high potential for metallic copper mineralization. A two-stage methodology was implemented in this study: First, extraction of the exploratory parameters related to metallic mineralization and second is data fusion by the hybrid fuzzy-analytic hierarchy process (Fuzzy-AHP) method. Hydrothermal alterations and iron oxides in the area were mapped by applying the optimum index factor (OIF), band ratio (BR), and least squared fit (LS-Fit) to ETM+ data. Intrusive masses were positioned as one of the effective parameters in identifying metallic mineralization zones using the gradient tensor method to assess aeromagnetic data. In order to determine the threshold concentration and the location of mineralization anomalies, the K-means clustering algorithm, vertical geochemical zonality (Vz) index, as well as concentration-area (C-A) multi fractal and singularity analysis were implemented on the geochemical data. In conclusion, the potential zones of metallic mineralization in the Kodegan-Basiran region were displayed in a mineral prospectivity map (MPM) derived from the Fuzzy-AHP decision-making method. Finally, to validate the prospectivity map of metallic mineralization, a control area was selected and surveyed by collecting mineralogical, petrological, and stream sediment samples. Field works confirmed the mineralization of Cu and Fe sulfides, oxides, and hydroxides. The high potential areas identified in the MPM can be considered as targets for future Cu exploration in the Kodegan-Basiran area.

This paper reports one-month 3 kHz EM disturbances recorded at Kardamas, Ilia, Greece after a strong M L = 6.6 earthquake occurred on 2018/10/25 near Zakynthos and Ilia. During this period 17 earthquakes occurred with magnitudes M L = 4.5 and M L = 5.5 and depths between 3 km and 17 km, all near Zakynthos and Ilia. A two-stage, fully computational methodology was applied to the outcomes of five different time-evolving chaos analysis techniques (DFA, fractal dimension analysis through Higuchi, Katz and Sevcik methods and power-law analysis). Via literature-based thresholds, the out-of-threshold results of all chaos analysis methods were located and from these, the common time instances of 13 selected combinations per five, four, three and two methods. Numerous persistent segments were located with DFA exponents between 1.6 ≤ α ≤ 2.0 , fractal dimensions between 1.4 ≤ D ≤ 2.0 and power-law exponents between 2.2 ≤ β ≤ 3.0 . Out of the 17 earthquakes, six earthquakes were jointly matched by 13 selected combinations of five, four, three and two chaos analysis methods, four earthquakes by all combinations of four, three and two, while the remaining seven earthquakes were matched by at least one combination of three methods. All meta-analysis matches are within typical forecast periods.