Fractal evolution characteristics of fracture meso-damage in uniaxial compression rock masses using bonded block model.

With regard to deep mining in metal mines, an investigation into the failure mode of deep fractured rock masses and their corresponding acoustic emission signal characteristics is conducted via uniaxial compression tests. Subsequently, a fractal damage renormalization group mechanical model is developed to explain the behavior of those fractured rock masses. Employing the bonded block model (BBM) numerical simulation method, fracture process in synthetic rock samples is analyzed, thereby validating the efficacy of the mechanical model. The numerical simulations highlight the critical role of fractures expansion in underlying the deterioration of rock mass strength. As the peak load decreases, the fracture fractal dimension increases, leading to a significant 14.2% reduction in compressive strength accompanied by an approximate 8.7% rise in average fracture fractal dimension. A comparative analysis of tetrahedral and voronoi block synthetic rock samples reveals the tetrahedral block samples exhibit a superior ability to depict the fracture behavior of fractured rock masses. Specifically, they offer a more accurate simulation of acoustic emission characteristics and failure modes. Furthermore, variations in the fracture fractal dimension with respect to the hole defect's position are observed, with the maximum value occurring along the vertical axis of the hole defect. This observation underscores the potential utility of visually monitoring deep rock fracture dynamics as an effective mean for quantitatively evaluating fracture damage and strength degradation in deep rock formations.

Study on full-scale pores characterization and heterogeneity of coal based on low-temperature nitrogen adsorption and low-field nuclear magnetic resonance experiments.

The characteristics and heterogeneity of coal pores are crucial for understanding the production mechanism of coalbed methane (CBM). In this study, coal samples with varying degrees of metamorphism (0.58% ≤ RO, max ≤ 3.44%) were collected. The characteristics of pore development and the heterogeneous properties of pores were revealed through low-temperature nitrogen adsorption (LTNA) and low-field nuclear magnetic resonance (NMR) experiments. The results indicate that pores with varying diameters exhibit favorable development in low-rank coals, along with favorable pores connectivity. The micropores composition of middle-rank coals was found to be 73.56%, however, the connectivity among transitional, meso, and macropores was observed to be poor. In high-rank coals, the proportion of micropores was 92.74%, with numerous micropores being closed or semi-closed. This resulted in inferior connectivity between micropores and transitional pores. As coal metamorphism progressed, the DL1 (characterizing the roughness of adsorption pores (AP) surface, ranging from 2.13 to 2.45) and DL2 (characterizing the complexity of AP structure, ranging from 2.56 to 2.77) initially decreased and then increased, whereas the DN (characterizing the heterogeneity of seepage pores (SP), ranging from 2.92 to 2.95) consistently improved. Furthermore, the roughness of pore surface and the complexity of pore structure in AP increased as the specific surface area and volume of pores increased. On the contrary, as the SP content increased, the uniformity of the pore structure improved. When the volume of SP remained constant, the complexity of the pore structure decreased due to increased pore connectivity.

Experimental Study on the Flexural Performance of Steel-Polyvinyl Alcohol Hybrid Fiber-Reinforced Concrete.

This paper explores the impact of steel-PVA hybrid fibers (S-PVA HF) on the flexural performance of panel concrete via three-point bending tests. Crack development in the concrete is analyzed through Digital Image Correlation (DIC) and Scanning Electron Microscope (SEM) experiments, unveiling the underlying mechanisms. The evolution of cracks in concrete is quantitatively analyzed based on fractal theory, and a predictive model for flexural strength (PMFS) is established. The results show that the S-PVA HF exhibits a synergistic effect in enhancing and toughening the concrete at multi-scale. The crack area of steel-PVA hybrid fiber concrete (S-PVA HFRC) is linearly correlated with deflection (δ), and it further reduces the crack development rate and crack area compared to steel fiber-reinforced concrete (SFRC). The S-PVA HF improves the proportional ultimate strength (fL) and residual flexural strength (fR,j) of concrete, and the optimal flexural performance of concrete is achieved when the steel fiber dosage is 1.0% and the PVA fiber dosage is 0.2%. The established PMFS of hybrid fiber-reinforced concrete (HFRC) can effectively predict the flexural strength of concrete.

Proposal for New Method for Calculating Sedimentation Process Efficiency in Water Treatment Plants.

An important aspect of water treatment is removing fine-grain materials from water. Due to the properties of fine-grain materials, they are difficult to remove from water. During the sedimentation process, which takes place in settling tanks, such materials are removed. The sedimentation process is often accompanied by coagulation and flocculation processes, which form aggregates of particles (flocs) from the fine-grained material particles in a suspension (non-grainy suspension). This kind of suspension (consisting of aggregates of particles or flocs) shows a different behaviour when falling compared with classic grainy suspensions. The main goal and novelty of this article are to propose (and test) a modification of the often used Stokes' formula with the addition of fractal geometry into the calculation of the terminal velocity of free-falling particles in order to overcome Stokes' formula's limitation, thus obtaining the sedimentation process efficiency. Because of this fractal modification, it is possible to use the simple and elegant Stokes' formula in order to calculate better the terminal velocity of non-grainy particles-aggregates or flocs-and thus obtain the sedimentation efficiency for the whole range of suspensions, both non-grainy and grainy. The results obtained in this article show that the sedimentation process efficiency calculated by using the modified formula based on the fractal geometry morphology of particles (the proposed fractal method) describes and agrees more with the data from the experiment than the sedimentation efficiency calculated only based on particle size (classic method).

Prediction of formation abrasiveness under the action of a PDC bit based on the fractal dimension of a rock surface.

During rock drilling, a drill bit will wear as it breaks the rock. However, there is no uniform grading standard for rock abrasiveness. To solve this problem, the wear mechanisms of a polycrystalline diamond compact (PDC) bit and the formation it is drilling into are analyzed in depth, and an abrasiveness evaluation method based on the fractal dimension of the rock surface topography is established. Initially, a three-dimensional digital model is generated from a scanning electron microscope image of the rock after drilling; next, an evaluation of the irregularities on the rock surface is performed using an adapted Weierstrass-Mandelbrot (W-M) function to ascertain the fractal dimensionality. Then, the microcontact characteristics of the contact surface between the formation and the PDC bit are analyzed, and the distribution of the microconvex contact points of the two-body friction pair in a region is obtained. Because the sliding friction between the drill bit and the rock produces a large amount of heat, according to the contact area formula of the friction surface and heat conduction theory, the temperature rise and overall temperature distribution of the formation and PDC bit under the condition of sliding friction are revealed, and the real contact area between the formation and the drill bit within a certain temperature range is obtained. Finally, the evaluation index of rock abrasiveness under sliding conditions is established by adopting the wear weight loss of the rock cutting tool per unit volume as the index of rock abrasiveness, and the model is verified by a microdrilling experiment. The research in this paper is highly important for improving the rock-breaking efficiency and bit service life during drilling.

Experimental, theoretical and numerical simulation-based investigations on the fabricated Cu2ZnSn thin-film-based Schottky diodes with enhanced electron transport for solar cell.

Copper-zinc-tin Cu2ZnSn (CZT) thin films are promising materials for solar cell applications. This thin film was deposited on a fluorine-doped tin oxide (FTO) using an electrochemical deposition hierarchy. X-ray diffraction of thin-film studies confirms the variation in the structural orientation of CZT on the FTO surface. As the pH of the solution is increased, the nature of the CZT thin-film aggregate changes from a fern-like leaf CZT dendrite crystal to a disk pattern. The FE-SEM surface micrograph shows the dendrite fern leaf and sharp edge disks. The 2-D diffusion limitation aggregation under slippery conditions for ternary thin films was performed for the first time. The simulation showed that by changing the diffusing species, the sticking probability was responsible for the pH-dependent morphological change. Convincingly, diffusion-limited aggregation (DLA) simulations confirm that the initial structure of copper is responsible for the final structure of the CZT thin films. An experimental simulation with pH as a controlled parameter revealed phase transition in CZT thin films. The top and back contact of Ag-CZT thin films based on Schottky behavior give a better electronic mechanism in superstrate and substrate solar cells.

Research on the enhancement material and culture method of soil aggregates composed of feldspathic sandstone and sand.

The Mu Us Sandy Land is a region characterized by wind-blown sand and soil erosion in northern China. To enhance the soil quality of this area, various organic materials were incorporated into the mixed soil at a volume ratio of 1:2 for feldspathic sandstone to sand. Culture was conducted in the field and under constant temperature conditions in laboratory culture chambers. Four treatments were established in the experiment, each calculated based on weight ratio and controlled (with no organic material added, CK); single application of straw (5% straw, P1); single application of biochar (5% biochar, P2); combined application of biochar and straw (5% biochar + 5% straw, P3). After 90 days of culture, soil samples were collected for analysis of various indicators such as soil aggregate particle size distribution, water stability of soil aggregates, mean weight diameter, mean geometric diameter, and fractal dimension using dry sieving and wet sieving methods. The objective is to establish a scientific basis and provide technical support for addressing the challenges associated with compound soil and implementing rational fertilization measures. The research results indicate that: (1) The quantity of aggregates > 0.25 mm under different treatments follows the order CK < P1 < P2 < P3, and the differences between treatments are significant (P < 0.05); (2) Soil water stability, mean weight diameter (MWD), mean geometric diameter (GMD), and fractal dimension of soil aggregates in compound soil with different organic material additions are superior to the control, and the effect of biochar on improving soil aggregates is better than that of corn straw. The combined application of both significantly improves the effect compared to single applications. In both culture modes, under wet sieving, the P3 treatment shows the highest MWD and GMD of soil aggregates, with an increase ranging from 3.45% to 85% and 4.55% to 38.46%, respectively, compared to other treatments. (3) The trend of fractal dimension among treatments is consistent: P3 < P2 < P1 < CK, and the differences between treatments are significant (P < 0.05). Moreover, there is a good negative correlation linear equation relationship between the fractal dimension (y) and WR > 0.25 (x) of compound soil, with a correlation coefficient of up to 0.9851. In conclusion, the incorporation of organic materials can effectively enhance the proportion of macroaggregates in compound soil consisting of Feldspathic sandstone and sand, thereby improving soil stability and erosion resistance. The optimal outcome is achieved through the combined application of biochar and straw. Indoor culture proves to be more effective than field culture, while wet sieving accurately reflects the structural characteristics of compound soil under both dry and wet sieving treatments.

Unique algorithm for the evaluation of embryo photon emission and viability.

Living cells have spontaneous ultraweak photon emission derived from metabolic reactions associated with physiological conditions. The ORCA-Quest CMOS camera (Hamamatsu Photonics, Japan) is a highly sensitive and essential tool for photon detection; its use with a microscope incubator (Olympus) enables the detection of photons emitted by embryos with the exclusion of harmful visible light. With the application of the second law of thermodynamics, the low-entropy energy absorbed and used by embryos can be distinguished from the higher-entropy energy released and detectable in their environment. To evaluate higher-entropy energy data from embryos, we developed a unique algorithm for the calculation of the entropy-weighted spectral fractal dimension, which demonstrates the self-similar structure of the energy (photons) released by embryos. Analyses based on this structure enabled the distinction of living and degenerated mouse embryos, and of frozen and fresh embryos and the background. This novel detection of ultra-weak photon emission from mouse embryos can provide the basis for the development of a photon emission embryo control system. The ultraweak photon emission fingerprints of embryos may be used for the selection of viable specimens in an ideal dark environment.

Radiographic texture of the trabecular bone of the proximal phalanx in horses with metacarpophalangeal osteoarthritis.

Osteoarthritis (OA) is a prevalent condition in horses, leading to changes in trabecular bone structure and radiographic texture. Although fractal dimension (FD) and lacunarity have been applied to quantify these changes in humans, their application in horses remains nascent. This study evaluated the use of FD, bone area fraction (BA/TA), and lacunarity in quantifying trabecular bone differences in the proximal phalanx (P1) in 50 radiographic examinations of equine metacarpophalangeal joints with varying OA degrees. In the dorsopalmar view, regions of interest were defined in the trabecular bone of the proximal epiphysis, medial and lateral to the sagittal groove of P1. Lower BA/TA values were observed medially in horses with severe OA (P=0.003). No significant differences in FD and lacunarity were found across OA degrees (P>0.1). FD, BA/TA, and lacunarity were not effective in identifying radiographic texture changes in the P1 trabecular bone in horses with different metacarpophalangeal OA degrees.

Optimum study of fractional polio model with exponential decay kernel.

This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics. Our findings reveal distinct disease-free equilibrium (DFE) and endemic equilibrium (EE) points, shedding light on the disease's stability. Furthermore, graphical representations and numerical simulations demonstrate the behavior of the disease under various parameter values, enhancing our understanding of polio transmission dynamics. In conclusion, this study offers valuable insights into the spread of polio and contributes to the broader understanding of infectious disease dynamics.

Magnetization Dynamics in Quasiperiodic Magnonic Crystals.

Quasiperiodic magnonic crystals, in contrast to their periodic counterparts, lack strict periodicity which gives rise to complex and localised spin wave spectra characterized by numerous band gaps and fractal features. Despite their intrinsic structural complexity, quasiperiodic nature of these magnonic crystals enables better tunability of spin wave spectra over their periodic counterparts and therefore holds promise for the applications in reprogrammable magnonic devices. In this article, we provide an overview of magnetization reversal and precessional magnetization dynamics studied so far in various quasiperiodic magnonic crystals, illustrating how their quasiperiodic nature gives rise to tailored band structure, enabling unparalleled control over spin waves. The review is concluded by highlighting the possible potential applications of these quasiperiodic magnonic crystals, exploring potential avenues for future exploration followed by a brief summary.

Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator.

COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to determine the disease's status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MATLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVID-19 affects people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.

Tracking and modeling the movement of Queensland fruit flies, Bactrocera tryoni, using harmonic radar in papaya fields.

Determining movement parameters for pest insects such as tephritid fruit flies is critical to developing models which can be used to increase the effectiveness of surveillance and control strategies. In this study, harmonic radar was used to track wild-caught male Queensland fruit flies (Qflies), Bactrocera tryoni, in papaya fields. Experiment 1 continuously tracked single flies which were prodded to induce movement. Qfly movements from this experiment showed greater mean squared displacement than predicted by both a simple random walk (RW) or a correlated random walk (CRW) model, suggesting that movement parameters derived from the entire data set do not adequately describe the movement of individual Qfly at all spatial scales or for all behavioral states. This conclusion is supported by both fractal and hidden Markov model (HMM) analysis. Lower fractal dimensions (straighter movement paths) were observed at larger spatial scales (> 2.5 m) suggesting that Qflies have qualitatively distinct movement at different scales. Further, a two-state HMM fit the observed movement data better than the CRW or RW models. Experiment 2 identified individual landing locations, twice a day, for groups of released Qflies, demonstrating that flies could be tracked over longer periods of time.

Combination of optical coherence tomography-derived shape and texture features are associated with development of sub-foveal geographic atrophy in dry AMD.

Geographic atrophy (GA) is an advanced form of dry age-related macular degeneration (AMD) that leads to progressive and irreversible vision loss. Identifying patients with greatest risk of GA progression is important for targeted utilization of emerging therapies. This study aimed to comprehensively evaluate the role of shape-based fractal dimension features ( F fd ) of sub-retinal pigment epithelium (sub-RPE) compartment and texture-based radiomics features ( F t ) of Ellipsoid Zone (EZ)-RPE and sub-RPE compartments for risk stratification for subfoveal GA (sfGA) progression. This was a retrospective study of 137 dry AMD subjects with a 5-year follow-up. Based on sfGA status at year 5, eyes were categorized as Progressors and Non-progressors. A total of 15 shape-based F fd of sub-RPE surface and 494 F t from each of sub-RPE and EZ-RPE compartments were extracted from baseline spectral domain-optical coherence tomography scans. The top nine features were identified from F fd and F t feature pool separately using minimum Redundancy maximum Relevance feature selection and used to train a Random Forest (RF) classifier independently using three-fold cross validation on the training set ( S t , N = 90) to distinguish between sfGA Progressors and Non-progressors. Combined F fd and F t was also evaluated in predicting risk of sfGA progression. The RF classifier yielded AUC of 0.85, 0.79 and 0.89 on independent test set ( S v , N = 47) using F fd , F t , and their combination, respectively. Using combined F fd and F t , the improvement in AUC was statistically significant on S v with p-values of 0.032 and 0.04 compared to using only F fd and only F t , respectively. Combined F fd and F t appears to identify high-risk patients. Our results show that FD and texture features could be potentially used for predicting risk of sfGA progression and future therapeutic response.

FDI: A MATLAB tool for computing the fractal dimension index of sources reconstructed from EEG data.

BACKGROUND: The fractal dimension (FD) is a valuable tool for analysing the complexity of neural structures and functions in the human brain. To assess the spatiotemporal complexity of brain activations derived from electroencephalogram (EEG) signals, the fractal dimension index (FDI) was developed. This measure integrates two distinct complexity metrics: 1) integration FD, which calculates the FD of the spatiotemporal coordinates of all significantly active EEG sources (4DFD); and 2) differentiation FD, determined by the complexity of the temporal evolution of the spatial distribution of cortical activations (3DFD), estimated via the Higuchi FD [HFD(3DFD)]. The final FDI value is the product of these two measurements: 4DFD × HFD(3DFD). Although FDI has shown utility in various research on neurological and neurodegenerative disorders, existing literature lacks standardized implementation methods and accessible coding resources, limiting wider adoption within the field. METHODS: We introduce an open-source MATLAB software named FDI for measuring FDI values in EEG datasets. RESULTS: By using CUDA for leveraging the GPU massive parallelism to optimize performance, our software facilitates efficient processing of large-scale EEG data while ensuring compatibility with pre-processed data from widely used tools such as Brainstorm and EEGLab. Additionally, we illustrate the applicability of FDI by demonstrating its usage in two neuroimaging studies. Access to the MATLAB source code and a precompiled executable for Windows system is provided freely. CONCLUSIONS: With these resources, neuroscientists can readily apply FDI to investigate cortical activity complexity within their own studies.

Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative.

Alzheimer's disease stands as one of the most widespread neurodegenerative conditions associated with aging, giving rise to dementia and posing significant public health challenges. Mathematical models are considered as valuable tools to gain insights into the mechanisms underlying the onset, progression, and potential therapeutic approaches for AD. In this paper, we introduce a mathematical model for AD that employs the fractal fractional operator in the Caputo sense to characterize the temporal dynamics of key cell populations. This model encompasses essential elements, including amyloid-ß ($\mathbb{ A_\beta }$), neurons, astroglia and microglia. Using the fractal fractional operator, we have established the existence and uniqueness of solutions for the model under consideration, employing Leray-Schaefer's theorem and the Banach fixed-point methods. Utilizing functional techniques, we have analyzed the proposed model stability under the Ulam-Hyers condition. The suggested model has been numerically simulated by using a fractional Adams-Bashforth approach, which involves a two-step Lagrange polynomial. For numerical simulations, different ranges of fractional order values and fractal dimensions are considered. This new fractal fractional operator in the form of the Caputo derivative was determined to yield better results than an ordinary integer order. Various outcomes are shown graphically by for different fractal dimensions and arbitrary orders.

Dynamic topological data analysis: a novel fractal dimension-based testing framework with application to brain signals.

Topological data analysis (TDA) is increasingly recognized as a promising tool in the field of neuroscience, unveiling the underlying topological patterns within brain signals. However, most TDA related methods treat brain signals as if they were static, i.e., they ignore potential non-stationarities and irregularities in the statistical properties of the signals. In this study, we develop a novel fractal dimension-based testing approach that takes into account the dynamic topological properties of brain signals. By representing EEG brain signals as a sequence of Vietoris-Rips filtrations, our approach accommodates the inherent non-stationarities and irregularities of the signals. The application of our novel fractal dimension-based testing approach in analyzing dynamic topological patterns in EEG signals during an epileptic seizure episode exposes noteworthy alterations in total persistence across 0, 1, and 2-dimensional homology. These findings imply a more intricate influence of seizures on brain signals, extending beyond mere amplitude changes.

Morphology, aspect ratio, and surface elemental composition of primary aerosol particles at urban region of India.

The PM2.5 and PM10 particles were characterized in terms of morphology (size and shape) and surface elemental composition at two different (traffic and industrial) locations in urban region of India and further linked to different morphological defining parameters. The overall PM2.5 and PM10 showed significant daily variability indicating higher PM10 as compared to PM2.5. PM2.5/PM10 ratio was found to be 0.58 ± 0.10 indicating the abundance of PM2.5. Soot aggregates, aluminosilicates, and brochosomes particles were classified based on morphology, aspect ratio (AR), and surface elemental composition of single particles. The linear regression analysis indicates the significant correlation between area equivalent (Daeq) and feret diameter (Dfd) (R2 0.86-0.98). Higher aspect ratio (1.48 ± 0.87-1.43 ± 0.50) was noted at traffic site as compared to industrial site (1.33 ± 0.58-1.29 ± 0.30), while circularity showed the opposite trend. Fractal dimension (Df) of soot aggregates estimated by the soot parameters method (SPM) were found to be 1.70, 1.72, and 1.88, mainly attributed to vehicular emissions, biomass, and industrial emission/coal burning, respectively. This further inferred that freshly emitted soot particles exhibited lacey in nature with spherical shape (Df 1.70) at traffic site, while at industrial location, they were different with compact shapes (Df 1.88) due to particle aging processes. This study inferred the synoptic changes in mass, chemical characteristics, and morphology of aerosol particles which provide the new insights into individual atmospheric particle and their dynamic nature.

Development, Application and Utility of a Machine Learning Approach for Melanoma and Non-Melanoma Lesion Classification Using Counting Box Fractal Dimension.

The diagnosis and identification of melanoma are not always accurate, even for experienced dermatologists. Histopathology continues to be the gold standard, assessing specific parameters such as the Breslow index. However, it remains invasive and may lack effectiveness. Therefore, leveraging mathematical modeling and informatics has been a pursuit of diagnostic methods favoring early detection. Fractality, a mathematical parameter quantifying complexity and irregularity, has proven useful in melanoma diagnosis. Nonetheless, no studies have implemented this metric to feed artificial intelligence algorithms for the automatic classification of dermatological lesions, including melanoma. Hence, this study aimed to determine the combined utility of fractal dimension and unsupervised low-computational-requirements machine learning models in classifying melanoma and non-melanoma lesions. We analyzed 39,270 dermatological lesions obtained from the International Skin Imaging Collaboration. Box-counting fractal dimensions were calculated for these lesions. Fractal values were used to implement classification methods by unsupervised machine learning based on principal component analysis and iterated K-means (100 iterations). A clear separation was observed, using only fractal dimension values, between benign or malignant lesions (sensibility 72.4% and specificity 50.1%) and melanoma or non-melanoma lesions (sensibility 72.8% and specificity 50%) and subsequently, the classification quality based on the machine learning model was ≈80% for both benign and malignant or melanoma and non-melanoma lesions. However, the grouping of metastatic melanoma versus non-metastatic melanoma was less effective, probably due to the small sample size included in MM lesions. Nevertheless, we could suggest a decision algorithm based on fractal dimension for dermatological lesion discrimination. On the other hand, it was also determined that the fractal dimension is sufficient to generate unsupervised artificial intelligence models that allow for a more efficient classification of dermatological lesions.