Search

Incorporating nanomaterials into hydrogels allows for the creation of versatile materials with properties that can be precisely tailored by manipulating their nanoscale structures, leading to a wide range of bulk properties. Investigating the structural and property characteristics of composite hydrogels is crucial in tailoring their performance for specific applications. This study focuses on investigating the correlation between the structural arrangement and properties of a composite hydrogel of thermoresponsive polymer, gelatin, and light-responsive antimicrobial porous gold nanorods (PAuNRs). The rheomechanical properties of the composite hydrogels are correlated with their nanoscale structural characteristics, investigated using small-angle neutron scattering (SANS). Analysis of SANS data reveals a decrease in the fractal dimension of PAuNRs incorporated hydrogel matrix, as compared to pure gelatin. Incorporating PAuNRs results in the formation of a softer composite hydrogel, as evident from the decrease in viscoelastic moduli, critical yield strain, denaturation temperature, and swelling ratio. Our results demonstrate that the structural modulation at the nanoscale can be precisely controlled through adjusting PAuNRs concentration and temperature, providing a fabrication mechanism for hydrogels with desired elastic properties. The reduced elasticity of the composite hydrogel and light-sensitive/antimicrobial property of the PAuNRs make this system suitable for specific biomedical applications, such as tissue engineering, device fabrication, and stimuli-based controlled drug delivery devices. [ABSTRACT FROM AUTHOR]

A scaling law for the osmotic pressure of quasi-two-dimensional polymer melts as a function of concentration is obtained, which shows fractal characteristics. Structural properties such as the chains' contour length and their inner-monomer pair distribution function display fractal scaling properties as well. These predictions are confirmed with mesoscale numerical simulations. The chains are swollen and highly entangled, yet Flory's exponent is always ν = 1/2. The melt can be considered a fluid of "blobs" whose size becomes renormalized in terms of the contour's length while the fractal dimension df increases monotonically between 5/4 and 2, as the monomer concentration is increased. The semidilute scaling of the pressure is recovered when df = 1. Our results agree with recent experiments and with numerical reports on quasi-2d melts. This work provides a new paradigm to study and interpret thermodynamic and structural data in low-dimensional polymer melts, namely as fractal macromolecular objects. [ABSTRACT FROM AUTHOR]

Hardness of thin films is a noteworthy property in the electronic and mechanical industry and is generally observed to be dependent on the degree of roughening facilitated from surface heights' surface spatial heterogeneity at the mesoscopic observation scale. Nonetheless, owing to enhanced scale fluctuations and higher-order central moments, conventional parameters provide limitations and errors in capturing the spatial heterogeneity of surfaces. Herein, we have utilized scale-independent fractal parameters to analyze the spatial heterogeneity of surface heights in Ti1−xSixN ternary hard films deposited with varying Si doping concentrations using sputtering technique. The fractal dimension, lacunarity coefficient, Moran index, surface entropy, Otsu's separability, and fractal succolarity were computed to provide an overarching understanding of the surface heights' spatial heterogeneity. Principal component analysis was employed on the data sets to identify the parameter(s) accounting for the maximum variance and accordingly, the structure–property relation between spatial heterogeneity of surface and hardness is analyzed and discussed in the context of the fractal dimension of surface heights. The results indicate the possibility of mesoscopic surface engineering and, consequently, tuning of hardness and modulus of elasticity in Ti1−xSixN hard films by mere changing of surface spatial heterogeneity facilitated by the fractal dimension of surface heights. [ABSTRACT FROM AUTHOR]

The high thermal expansion coefficient exhibited by magnesia particles typically results in significant volume changes under extreme cooling and heating conditions, thereby exacerbating thermal stress and accelerating the damage to MgO-C refractories. To mitigate the thermal stress in the vicinity of magnesia particles, flake graphite coated magnesia (MgO@FG) particles with a core shell structure were prepared. Subsequently, the MgO and MgO@FG particles were utilized as aggregates for preparing MgO-C refractories. The thermal shock resistances of these materials were compared using the oil quenching method, and their fracture behaviours before and after the thermal shock test were investigated using the Brazilian splitting test combined with the digital image correlation method and acoustic emission technique. The results indicated that the addition of MgO@FG particles reduced the thermal expansion coefficient of the MgO-C refractories and mitigated their microstructural deterioration during the thermal shock test. Furthermore, the crack branching or deflection induced by the reduced interfacial bonding properties between MgO@FG particles and matrix; the relatively decreased graphite content within the matrix; and more ceramic phases generation (MgAl 2 O 4 , AlN), collectively contributed to the strengthening and toughening of MgO-C refractories. Moreover, the addition of the MgO@FG particles resulted in an increase in the fractal dimension of the fracture surface and enhanced the resistance to deformation failure of the MgO-C refractories, thereby improving their energy dissipating capability. [ABSTRACT FROM AUTHOR]

Wavelet scattering is a recent time-frequency transform that shares the convolutional architecture with convolutional neural networks, but it allows for a faster training and it often requires smaller training sets. It consists of a multistage non-linear transform that allows us to compute the deep spectrum of a signal by cascading convolution, non-linear operator and pooling at each stage, resulting a powerful tool for signal classification when embedded in machine learning architectures. One of the most delicate parameters in convolutional architectures is the temporal sampling that strongly affects the computational load as well as the classification rate. In this paper the role of sampling in the wavelet scattering transform is studied for signal classification purposes. In particular, the role of subdivision schemes in properly compensating the information lost when using sampling at each stage of the transform is investigated. Preliminary experimental results show that, starting from coarse grids, interpolatory subdivision schemes reproduce copies of the original scattering coefficients at a fixed full grid that still represent distinctive features for signal classes. In fact, thanks to the ability of the scheme in reproducing similar fractal properties of the transform through an efficient iterative refinement procedure, the reproduced coefficients enable to obtain classification rates similar to those provided by the native wavelet scattering transform. The relationships between the tension parameter of the scheme and the fractal dimension of its limit curve are also investigated. • Interpolatory subdivision schemes are used to increase the number of wavelet scattering samples. • Interpolated wavelet scattering coefficients are used for machine-learning based classification purposes. • Fractal schemes replicate the fractal dimension of the scattering matrix and compensate the information lost during sampling. • Bounds for the fractal dimension of the limit curve of a 4-points scheme depending on the tension parameter are provided. [ABSTRACT FROM AUTHOR]

Investigating the disparities in brain activity between healthy individuals and those with intellectual and developmental disorders (IDD) is pivotal in biomedical research. In this study, we delved into these differences by employing a complexity-based analysis of electroencephalogram (EEG) signals. Specifically, we computed the fractal dimension (FD), approximate entropy, and sample entropy (SampEn) of EEG signals for both control (healthy) subjects and IDD individuals during rest and stimulation with music. Our findings revealed that IDD subjects exhibited higher complexity in both rest and stimulation scenarios compared to control subjects, indicative of heightened brain activity complexity among IDD individuals. This analysis not only sheds light on the variations in brain activity associated with IDD, but also underscores its potential applicability in assessing brain activity alterations across various disorders compared to healthy counterparts. [ABSTRACT FROM AUTHOR]

It is argued that there are a set of orthonormal basis states, which appear as highly degenerate ground states arising from spontaneous symmetry breaking with a type-B Goldstone mode, and they are scale-invariant, with a salient feature that the entanglement entropy S (n) scales logarithmically with the block size n in the thermodynamic limit. As it turns out, the prefactor is half the number of type-B Goldstone modes N B . This is achieved by performing an exact Schmidt decomposition of the orthonormal basis states, thus unveiling their self-similarities in the real space—the essence of a fractal. Combining with a field-theoretic prediction (Castro-Alvaredo and Doyon 2012 Phys. Rev. Lett. 108 120401), we are led to the identification of the fractal dimension d f with the number of type-B Goldstone modes N B for the orthonormal basis states in quantum many-body systems undergoing spontaneous symmetry breaking. [ABSTRACT FROM AUTHOR]

Objective. Patients with pulmonary fibrosis (PF) often experience long waits before getting a correct diagnosis, and this delay in reaching specialized care is associated with increased mortality, regardless of the severity of the disease. Early diagnosis and timely treatment of PF can potentially extend life expectancy and maintain a better quality of life. Crackles present in the recorded lung sounds may be crucial for the early diagnosis of PF. Approach. This paper describes an automated system for differentiating lung sounds related to PF from other pathological lung conditions using the average number of crackles per breath cycle (NOC/BC). The system is divided into four main parts: (1) pre-processing, (2) separation of crackles from normal breath sounds using the iterative envelope mean fractal dimension filter, (3) crackle verification and counting, and (4) estimating NOC/BC. The system was tested on a dataset consisting of 48 (24 fibrotic and 24 non-fibrotic) subjects and the results were compared with an assessment by two expert respiratory physicians. The set of high-resolution computed tomography images, reviewed by two expert radiologists for the presence or absence of PF, was used as the ground truth for evaluating the PF and non-PF classification performance of the system. Main results. The overall performance of the automatic classifier based on receiver operating curve-derived cut-off value for average NOC/BC of 18.65 (AUC = 0.845, 95% CI 0.739–0.952, p < 0.001; sensitivity = 91.7%; specificity = 59.3%) compares favourably with the averaged performance of the physicians (sensitivity = 83.3%; specificity = 56.25%). Significance. Although radiological assessment should remain the gold standard for diagnosis of fibrotic interstitial lung disease (ILD), the automatic classification system has strong potential for diagnostic support, especially in assisting general practitioners in the auscultatory assessment of lung sounds to prompt further diagnostic work up of patients with suspect of ILD. [ABSTRACT FROM AUTHOR]

The Chang 7 sandstone is characterized by complex micro-pore structures, strong heterogeneity, and differential fluid distribution. These characteristics result in low oil recovery. In this paper, various techniques, including high-pressure mercury intrusion, nuclear magnetic resonance, scanning electron microscope, thin section, and X-ray diffraction, are employed to quantitatively evaluate the occurrence characteristics and influencing factors of movable fluids in Chang 7 sandstone reservoirs from the Heshui Block with different fractal structures. Results show that the dominant sandstone type is feldspar lithic fragment sandstone. Chang 7 reservoir has been divided into three types (types I, II, and III) based on capillary pressure curves and pore structure parameters. These reservoirs are characterized by various fractal structures and different movable fluids distribution. Multiple possible factors affecting the movable fluid distribution are analyzed, including physical properties, pore structure, pore size distribution, mineral content, and heterogeneity. Movable fluid saturation is positively correlated with physical properties, weighted average pore-throat radius, median pore-throat radius, final residual mercury saturation, and maximum mercury withdrawal saturation. In contrast, it is negatively correlated with displacement pressure and has no obvious correlation with the sorting coefficient. Micron- and submicron-scale pores are beneficial to the movable fluid occurrence, while nano-scale pores are vice versa. The influence of mineral content on movable fluid occurrence varies with mineral types. Quartz is conducive to the movable fluid occurrence in submicron-scale pores, while carbonate cementation inhibits the movable fluid occurrence in submicron-scale pores. The inhibition of clay on the movable fluid occurrence is mainly reflected in submicron- and nano-scale pores and varies with clay mineral types. The influence of heterogeneity on the movable fluid occurrence is mainly reflected in submicron-scale pores. The occurrence models of movable fluid vary with reservoir types. [ABSTRACT FROM AUTHOR]

Let ν be a Borel probability measure on ℝ d and q , t ∈ ℝ . This study takes a broad approach to the multifractal and fractal analysis problem and proposes an intrinsic definition of the general Hausdorff and packing measures by taking into account sums of the type ∑ i h - 1 ⁢ (q ⁢ h ⁢ (ν ⁢ (B ⁢ (x i , r i))) + t ⁢ g ⁢ (r i) ) for some prescribed functions h and g. The aim of this paper is to study the descriptive set-theoretic complexity and measurability of these measures and related dimension maps. [ABSTRACT FROM AUTHOR]

Marstrand's projection theorem from 1954 states that if K ⊂ R³ is an analytic set, then, for H² almost every e ∈ S², the orthogonal projection φe(K) of K to the line spanned by e has Hausdorff dimension min{dimHK,1}. This paper contains the following sharper version of Marstrand's theorem. Let V ⊂ R³ be any 2-plane, which is not a subspace. Then, for H¹ almost every e ∈ S² ∩V, the projection πe(K) has Hausdorff dimension min{dimHK, 1}. For 0 ≤ t < dimHK, we also prove an upper bound for the Hausdorff dimension of those vectors e ∈ S² ∩ V with dimH ρe(K) ≤ t < dimH K. [ABSTRACT FROM AUTHOR]

The moisture content of flotation clean coal products is a critical factor influencing their calorific value, making dewatering research vital for the efficient utilization of coal. In this study, cationic polyacrylamide (CPAM) was employed as a high molecular weight flocculant and filter aid to investigate the mechanisms by which the anionic sodium dodecyl sulfate (SDS), cationic dodecyltrimethylammonium bromide (DTAB), and nonionic polyoxyethylene lauryl ether (Brij L23) affect the dewatering of flotation clean coal. The influence of these surfactants on the dewatering performance of flotation clean coal in conjunction with CPAM was examined through filter aid experiments, density functional theory, zeta potential measurements, agglomeration of flotation clean coal particles, and Nuclear Magnetic Resonance (NMR) analysis. The results indicated that DTAB and SDS exhibited a larger positive electrostatic potential compared to Brij L23, demonstrating stronger electrostatic adsorption on the molecules of flotation clean coal. However, the -OSO3 groups in SDS interacted more strongly with the molecules of flotation clean coal than the tertiary amine groups in DTAB. The ether and hydroxyl groups in Brij L23 interacted weakly with the molecules of flotation clean coal. The surfactants increased the compactness and structural complexity between particles within the flocs, leading to an increase in the fractal dimension of the flocs. Additionally, the surfactants enlarged the pores within the filter cake of flotation clean coal, which was beneficial for the removal of moisture. [ABSTRACT FROM AUTHOR]

[Objective] By analyzing the effects of different mixed forest patterns on the soil particle characteristics of the Kubuqi Desert, this study provides scientific basis for the efficient and sustainable management of sandy land forests. [Methods] Four representative mixed-forest configuration patterns along the section of the Yellow River in Kubuzi Desert were selected. Soil samples were taken from 0—80 cm soil depth. The laser particle size method was used for the determination of soil particle size and calculation of the mean soil particle size (Mz), sorting coefficient (δ), skewness (SK), kurtosis (KG), and fractal dimensional characteristics. [Results] (1) The dominant grain sizes in the study area were fine sand and medium sand. The four different vegetation configuration patterns had a significant refining effect on soil grain size, and the content of clay, silt, and very fine sand increased by 141.37%～415.38%, 105.75%～724.73%, and 64.93%～1597.36%, respectively, compared with the control group CK. (2) After the camping of the four vegetation configuration modes, the average grain size of the soil layer at different depths increased significantly, ranging from 2.44%～20.33%. (3) After comparing the grain size parameters of the soil under different configuration modes, it was found that the value of fractal dimension was positively correlated with the value of kurtosis and negatively correlated with the average grain size. [Conclusion] The degree of soil particle size refinement is related to the configuration mode. Different plant configuration modes on soil particle size refinement are mainly concentrated in the surface layer, and the effect of refinement gradually reduces with the increase of soil layer depth. The average particle size of soil layer at different depths increases significantly, the sorting grade of soil particles decreases, and the particle distribution becomes more discrete. The distribution of soil particles shows a gradual tendency to be broad and flat. The soil particles develop toward positive bias. The fractal dimension of soil particles at different depths of soil layer increases significantly (p＜0.05). [ABSTRACT FROM AUTHOR]

The content of coral powder in coral aggregates significantly impacts the quality of coral mortars using coral aggregates, ultimately affecting various properties of coral mortars. Hence, to elucidate the role of coral powder in coral mortars, this paper explores its impact on the properties of coral mortars. Additionally, mercury intrusion porosimetry, thermogravimetric analysis, and Fourier transform infrared spectroscopy are employed to unveil the underlying mechanisms through which coral powder enhances or diminishes the properties of coral mortars. The results illustrate that coral powder reduces the fluidity and increases the dynamic yield stress of coral mortars. Furthermore, due to its filling effect, coral powder facilitates enhancements in both the flexural and compressive strength of coral mortars. However, the refinement of pore size by coral powder, in turn, influences the shrinkage behavior of coral mortars. Simultaneously, coral powder diminishes the hydration and content of hydration products in coral mortar to a certain extent. The pore surface fractal dimension (Ds) was found to serve as a crucial indicator of strength. Notably, it displays a strong positive linear correlation with both compressive strength and flexural strength. Moreover, the composite exponential model proposed in this paper provides a more accurate simulation of the shrinkage behavior of coral mortars. [ABSTRACT FROM AUTHOR]

The article aims to develop a fractional-order proportional integral derivative (PID) controller to monitor insulin and glucose levels in humans under the influences of stress, excitement, and trauma. A novel fractional-order diabetes mellitus model is proposed, incorporating a nonsingular, nonlocal kernel (Mittag-Leffler function) to account for the effect of epinephrine on suppressing insulin secretion and the dynamics of beta-cell mass. As beta-cell mass increases in the presence of adrenaline, the system remains highly responsive to rising blood glucose and falling insulin levels, driven by the hormone's suppressive effects. The key advantage of this model is its ability to incorporate these physiological stressors and use fractional-order derivatives to describe the nonlocal dynamics within the system. The innovations of this work include a fractional-order diabetes mellitus model that captures the biological memory and hereditary effects of glucose regulation under stress, and a fractional-order PID controller that offers greater stability and robustness compared to conventional controllers, particularly in managing adrenaline-induced hyperglycemia. The model's positivity, boundedness, and equilibrium solutions are rigorously analyzed to ensure feasibility. Additionally, a new theorem is proven using fixed-point theory, confirming the existence and uniqueness of the fractional-order model. Ulam–Hyers stability analysis further demonstrates the model's robustness and well-posedness, while qualitative properties are explored. Numerical simulations to explore which is done by solutions with a two-step Lagrange polynomial for generalized Mittag Leffler kernel showed that prolonged and severe hyperglycemia was caused by regular release of adrenaline into the blood at different fractional order values and fractal dimensions by changing initial values for normal and diabetes patients. PID and controller results are analyzed to increase the stability of the system to monitor and assess of glucose–insulin system with beta cell mass to control the hyperglycemia. Lastly, the results are obtained and visually shown using graphical representations, which provide empirical evidence in support of our theoretical findings. At the end comparison of numerical simulations is constructed to show the efficiency, convergence, and accuracy of proposed techniques at different fractional values with power law and exponential kernels. Numerical simulations, mathematical modeling, and analysis work together to shed light on the dynamics of diabetes mellitus and make important advances in the knowledge and treatment of this common disease. [ABSTRACT FROM AUTHOR]

The application of phase change materials in concrete can effectively improve the thermal performance of concrete. Form-stable phase change (FSPC) particles can be used to prepare FSPC concrete to achieve this objective. However, the influence of FSPC particles on the thermal conductivity of FSPC concrete is not yet clear. In this study, the relationship between the particle gradation and thermal conductivity of FSPC concrete was analyzed based on fractal and gray correlation theory. The results show that the thermal conductivity of FSPC concrete with a fine aggregate replacement rate of 10%, 20%, and 30% was 9.16%, 13.12%, and 28.31%, respectively, lower than that of ordinary concrete. The FSPC particles have self-similarity in the fractal dimension range of 0.49–1.68. Increasing the amount of FSPC particles of 4–5, 5–6, and 8–10 mm can reduce the thermal conductivity of FSPC concrete. The use of fractal theory and gray correlation theory can effectively establish the relationship between thermal conductivity and particle size distribution of FSPC concrete. [ABSTRACT FROM AUTHOR]

Liquid nitrogen fracturing is an efficient stimulation technique for exploiting hot dry rock geothermal energy. Understanding the physical and mechanical damage characteristics of high-temperature reservoir rocks under liquid nitrogen cooling is crucial for the application of liquid nitrogen fracturing technology. Therefore, nuclear magnetic resonance technology, acoustic wave velocity measurement technique, acoustic emission (AE) technology, and 3D scanning technology were used to explore changes in the physical and mechanical properties of high-temperature granite under liquid nitrogen cooling from macroscopic and microscopic perspectives. Our research findings show that, as treatment temperature increased, the internal pore structure of the sample changed gradually, with decrease in proportion of micropores and increase in proportion of macropores. The number of pores of various sizes increased gradually. In particular, after treating the granite to a treatment of 600℃, there was a significant increase in the quantity of pores within the granite, primarily manifested by an increase in macropores. From 25 to 600℃, the compressive strength decreased from 160.79 to 68.44 MPa, a reduction of 57.44%; the tensile strength decreased from 11.13 to 6.02 MPa, a reduction of 45.91%. The fractal dimension of the fracture surface of Brazilian disk samples was calculated using the box-counting method, and the results indicated that an increase in treatment temperature would lead to an increase in roughness of the sample's fracture surface. During the uniaxial compression tests, the AE parameter rise angle (RA) suddenly increased near the peak load. The straight line relationship (average frequency = 11RA + 60) was used to classify the AE signals generated during uniaxial compression of samples. With increase in treatment temperature, the shear signal increased gradually, which is highly consistent with the macroscopic failure characteristics of the samples. [ABSTRACT FROM AUTHOR]

As the depth of coal mining in China continues to increase, the fracturing of coal rock masses has an increasingly complex impact on the surrounding rock roadways. The majority of the mine's roadways run through coal rock masses with hard roofs and soft bottoms, which typically exhibit complex dynamic behaviour. To further research the mechanical behaviour and fracture evolution of coal rock masses under hard-roof and soft-floor conditions, the study is based on the majority of working faces in a mine, which have hard roofs and soft floors. Uniaxial compression tests were utilized to study the mechanical properties of coal rock masses under hard-roof and soft-floor circumstances, using acoustic emission monitoring, whole-process imaging technologies, and fractal dimension analysis. The experimental results are as follows: The uniaxial compressive strength of the coal rock mass is significantly higher than that of its weakest component. The results of the experiment are as follows: The uniaxial compressive strength of coal rock mass is significantly higher than that of its weakest component. Samples with different soft rock strengths exhibited dissipated energy greater than the accumulated energy before the stress maximum, accompanied by volume expansion and the formation of shear surfaces. Samples with higher soft rock strengths tend to exhibit brittle failure, while weaker samples show stress-softening behaviour. Internal fracture complexity varies amongst samples with varying soft rock strengths. A fractal study of the acoustic emission parameters was carried out utilizing MATLAB programming. The fractal analysis results show that acoustic emission ringing counts and energy time series of coal rock masses under hard-roof and soft-floor settings have good fractal properties. The fractal analysis results show that acoustic emission ringing counts and energy time series of coal rock masses under hard-roof and soft-floor settings have good fractal characteristics. Acoustic emission ringing counts tend to have a larger correlation dimension than acoustic emission energy. However, while the sample is fracturing on a vast scale, the ringing count correlation dimension fluctuates very little. The correlation dimension distribution of samples with lower strength is more concentrated after the stress maximum, implying that the deformation and fracturing of the floor rock in highways under hard-roof and soft-floor circumstances are more complex. Both the correlation dimension D of acoustic emission ringing counts and energy indicate a continuous fall before peak stress, which can be used to anticipate coal rock mass fracture. This study, based on the mechanical behaviour and fracture evolution of coal rock masses under hard-roof and soft-floor conditions, provides a foundation for disaster avoidance by controlling the stability and structural deformation of floor rock in hard-roof and soft-floor highways. [ABSTRACT FROM AUTHOR]

Understanding the correlation between the brain’s activity and the physiological responses of other organs under varying conditions is a crucial area of research that holds significant potential for advancing our knowledge of human physiology. In this study, we focused on investigating the interaction between the heart and brain by employing advanced complexity analysis techniques, specifically examining the fractal dimension and approximate entropy of electroencephalogram (EEG) and R-R interval time series. The analysis was conducted on data collected from 12 subjects who were observed under three distinct conditions: baseline (normal resting state) and two collaborative activities performed both with and without the presence of noise. Our findings revealed that the complexity patterns of EEG and R-R signals showed similar trends in alterations across all conditions, suggesting a strong coupling between the brain’s and heart’s responses. This observed coupling highlights the potential for a coordinated physiological interaction between these two critical systems. Furthermore, our approach, which successfully decoded the heart–brain correlation, offers a promising framework for extending this analysis to explore correlations between the brain and other organs, thereby contributing to a deeper understanding of the complex networks that underlie human health and adaptive physiological responses. [ABSTRACT FROM AUTHOR]

The study of correlations between different organs under various conditions is a prominent field in biomedical science and engineering. This paper explores the relationship between brain and muscle activities during rest and various limb movements including plantar flexion and knee flexion. We employed complexity measures, calculating the fractal dimension (FD) and sample entropy (SampEn) of electroencephalogram (EEG) and electromyogram (EMG) signals, which serve as indicators of brain and muscle activities, respectively. Our analysis focused on how the complexity variations in these signals correlate across different tasks. The results revealed opposite trends in the complexity of EEG and EMG signals. Specifically, the complexity of EEG signals increased from initial rest to final rest, plantar flexion, and knee flexion, suggesting heightened neural activity likely due to motor planning and execution. Conversely, the complexity of EMG signals decreased, indicating more synchronized and consistent muscle contractions during these movements, reflecting coordinated motor control and reduced variability in muscular activity. This analytical approach can be applied to study the correlations between different organs’ reactions and brain activity across various tasks. [ABSTRACT FROM AUTHOR]

Based on the multi-domain fractal theory, the distribution characteristics of each granularity level of coal particles during hydrophobic flocculation were analyzed. The fractal dimension of fine-grained increased from 1.07 to 1.33, indicating that the particle size distribution range was wide, and the internal difference was significant. The fractal dimension of middle-grained decreased from 2.71 to 2.03, showing that the particle size growth noticeable and the morphology of flocs tended to be regular. The fractal dimension of the coarse-grained changes slightly around 2.90, demonstrating that the flocs had a relatively stable spatial structure under the dynamic balance of fragmentation and reaggregation. By introducing the fractal dimension of each granularity level into the flocculation kinetic equation, the conservation relationship between the median particle size and the standard deviation of the floc was quantified, and the analysis of the particle distribution characteristics of the hydrophobic flocculation system at any time was realized. [ABSTRACT FROM AUTHOR]

To explore the internal bearing characteristics and fracture evolution laws of discontinuous jointed rock mass in deep roadways, the −600 m main roadway in Xin 'an Coal Mine was used as the research background. The fracture fractal dimension D was employed to characterize the joint density, and an intermittent jointed roadway model, both without support and with anchor cable support, was modeled using the particle flow software PFC2D. The internal stress, deformation, and fracture characteristics of intermittent jointed surrounding rock in tunnels with different support methods and joint densities were studied from a microscopic perspective. The results indicate that during the bearing process of the bolt anchor support and unsupported roadway discontinuous jointed rock mass model, the main bearing area of both models transferred from the surface rock mass to the deep rock mass. The tensile cracks of the anchor cable support model were reduced by 57.7% compared with the unsupported model, effectively suppressed the tensile failure of the surrounding rock, and the convergence of the surrounding rock was substantially reduced. The density of intermittent joints was negatively correlated with the bearing capacity of the surrounding rock mass of roadways, and the increase of joint density the overall failure of the surrounding rock, and the possibility of roadway destabilization was increased. Importantly, the number and distribution of intermittent joints in the surface surrounding rock were closely related to the rupture characteristics of the roadways. When the load exceeded the ultimate load of the deep surrounding rock, stress fluctuation occurred due to the stress drop caused by its destruction. This fluctuation promoted the development of intermittent joints in the surface surrounding rock, increasing the risk of roadway destabilization. [ABSTRACT FROM AUTHOR]

Dimension interpolation is a novel programme of research which attempts to unify the study of fractal dimension by considering various spectra which live in between well-studied notions of dimension such as Hausdorff, box, Assouad and Fourier dimension. These spectra often reveal novel features not witnessed by the individual notions and this information has applications in many directions. In this survey article, we discuss dimension interpolation broadly and then focus on applications to the dimension theory of orthogonal projections. We focus on three distinct applications coming from three different dimension spectra, namely, the Fourier spectrum, the intermediate dimensions, and the Assouad spectrum. The celebrated Marstrand–Mattila projection theorem gives the Hausdorff dimension of the orthogonal projection of a Borel set in Euclidean space for almost all orthogonal projections. This result has inspired much further research on the dimension theory of projections including the consideration of dimensions other than the Hausdorff dimension, and the study of the exceptional set in the Marstrand–Mattila theorem. [ABSTRACT FROM AUTHOR]

Human emotion classification without bias and unfairness is challenging because most existing image-based methods are directly or indirectly affected by subjectivity. Therefore, we propose an EEG (Electroencephalogram) based model for an accurate emotion classification without the effect of subjectivity. The captured EEG signals are converted into Delta, Theta, Alpha, Beta, and Gama frequency bands. As emotions change, the frequency bands change and provide unique patterns for each emotion irrespective of different persons. With this observation, the statical features, namely, mean, standard deviation, variance, and kurtosis, and frequency-based features, namely, Power Spectral Density (PSD) and Petrosian Fractal Dimension (PFD) are extracted. To integrate the strength of spatial and frequency-based features, the features are supplied to quadratic discriminative analysis for the final classification. The experiments on the benchmark datasets, DEAP and SEED-IV, achieve 99.40% and 91.97% accuracy, respectively. A comparison with state-of-the-art methods shows that the method performs very well on some datasets. [ABSTRACT FROM AUTHOR]

AbstractPurpose/aim: The developing brain undergoes a remarkable process of synaptic changes. Material and methods: To investigate the developmental changes in glutamatergic synaptic connections using the whole-cell patch clamp method, evoked excitatory postsynaptic currents (eEPSCs) were recorded from locus coeruleus (LC) neurons, a brain region crucial for cognitive functions, in rats at ages 7, 14, and 21 days. We employed fractal analysis to compute fractal dimensions of AMPA and NMDA receptors, serving as markers for synaptic maturation. Results: Our findings revealed a significant increase in fractal dimensions during the third postnatal week and hence a developmental chenge of synaptic connections. A strong positive correlation between amplitude and fractal dimensions, in Pearson correlation analysis suggested that the synaptic currents’ amplitude is closely related to the fractal properties of the receptors. A linear relationship between fractal dimensions and age indicated that fractal analysis can be a robust tool for predicting developmental changes. Additionally, we employed machine learning techniques to predict developmental changes based on AMPA and NMDA receptors. Support Vector Machine (SVM) models outperformed random forest models in accurately predicting age-dependent developmental changes, as indicated by the area under the curve (AUC) values. SVM achieved an AUC of 0.89 for AMPA receptors and 0.86 for NMDA receptors, demonstrating the effectiveness of fractal-based features in characterizing synaptic maturation. Conclusion: This study offers valuable insights into synaptic development in the LC nucleus and demonstrates the potential of fractal analysis as a tool to understand brain plasticity and early development. Fractal dimensions play a crucial role in characterizing the maturation of glutamatergic synapses and neural circuitry development. [ABSTRACT FROM AUTHOR]

Hamiltonian maps are considered a class of dynamical systems that hold meticulous properties used to model a large number of complex dynamical systems. When time flows in dynamical systems with two-dimensional degrees of freedom, the trajectories in phase space can be analyzed within bidimensional surfaces known as Poincaré sections. The Chirikov–Taylor standard map for two canonical dynamical variables (momentum and coordinate) is the most renewed map characterized by a family of area-preserving maps with a single parameter that controls the degree of chaos. In this study, a generalization of the standard map for two different problems is presented and discussed. The first problem deals with the higher-order derivative Hamiltonian system (up to the fourth order) since the fourth-order characteristic provides the possibility of chaotic behavior at all scales including nanoscales where high-order derivatives take place in nanosystems. The second problem concerns the time-dependent δ -kicked rotor in fractal dimensions characterized by a time-dependent potential due to its important implications in quantum chaos. This study shows that higher-order derivative maps and fractal dimensional δ -kicked rotor maps apparently exhibit a large number of chaotic orbits and fractal patterns, including the spiral fractal patterns comparable to the Julia set. Moreover, these problems are characterized by additional parameters which can be used to control chaos. Some of these parameters lead to chaos, and others lead to fractal patterns. [ABSTRACT FROM AUTHOR]

The pressure on coal affects the pore fracture structure, altering the seepage characteristics of fluids such as gas or water. A special pseudo-triaxial loading nuclear magnetic gripper was used for uniaxial compression testing of the coal body. The T2 map of the lignite was tested online, and MRI imaging was performed. The correlation between the pore fracture structure evolution and seepage characteristics of lignite was studied. The results show that (1) there are three stages, namely, compression, pore development, and post-peak failure, which promote the development and evolution of medium pore and macropores in lignite. (2) Under uniaxial compression, the permeability of the lignite sample shows a "V-shaped" trend, first decreasing and then increasing. When the axial pressure reaches approximately 3.0 MPa, the mutation of the MRI signal increases, and the enhancement of the MRI signal of the sample is due to the cumulative effect of mutation after aggregation. The aggregation of water image signals reflects the distribution area of pores that dominate seepage. (3) Under uniaxial compression, the pore change rate Si slightly decreased. The pore change rate Si of medium pores and macropores showed a positive correlation with axial pressure, which is consistent with the total pore change trend. The compressibility coefficient Cp of the porous pores (medium pores and macropores) and the permeability stress sensitivity coefficient Cf exhibited a linear correlation. The fractal dimension D2 and D3 values of pores in the medium and macropores scale range are close to 3, with the maximum value of D2 being 2.971. This indicates significant fractal characteristics, suggesting that medium pores are the most developed in this scale range. Researches show that that the middle pore has a greater stress sensitivity and shows obvious fractal characteristics during the load failure. The compressibility of the large pore is correlated with the permeability sensitivity, These results show can help elucidate the influence of the pores fracture structure on the seepage evolution of lignite. [ABSTRACT FROM AUTHOR]

Objective: To examine the relationship between retinal vascular geometry and silent brain infarction (SBI) in the Chinese population. Methods: We conducted a cross-sectional study that retrospectively analyzed the fundus photographs, MRI and other clinical data of 227 SBIs and 227 controls who visited Shanghai Health And Medical Center for physical examination. The retinal vessel fractal dimension (FD), retinal artery fractal dimension (FDa), retinal vein fractal dimension (FDv), central retinal artery diameter in the region from 0.5 ~ 1.0 disc diameter (DD) from the disc margin (CRAEB), central retinal artery diameter in the region from 1.0 ~ 2.0 DD from the disc margin (CRAEC), central retinal vein diameter in the region from 0.5 ~ 1.0 DD from the disc margin (CRVEB), central retinal vein diameter in the region from 1.0 ~ 2.0 DD from the disc margin (CRVEC), retinal arteriovenous diameter ratio in the region from 0.5 ~ 1.0 DD from the disc margin (AVRB), and retinal arteriovenous diameter ratio in the region from 1.0 ~ 2.0 DD from the disc margin (AVRC) were accessed by the Singapore "I" Vessel Assessment (SIVA) software. Results: FD, FDa, FDv, CRAEB, CRAEC, CRVEB, CRVEC and AVRB in SBI subjects were 1.25 (1.21–1.28), 1.11 (1.08–1.14), 1.09 (1.06–1.13), 168.78 ± 19.39, 163.55 ± 18.97, 235.77 (222.64-254.08), 224.39 ± 23.29, 0.72 ± 0.06, respectively, significantly lower than those of control subjects [1.30 (1.28–1.32), 1.15 (1.13–1.18), 1.14 (1.12–1.16), 196.81 ± 27.94, 183.81 ± 25.46, 273.03 (247.59–296.30), 249.59 ± 32.03, and 0.73 ± 0.08]. Logistic regression results showed that higher FD (OR, 0.04), FDa (OR, 0.07), FDv (OR, 0.06), CRAEB (OR, 0.02), CRAEC (OR, 0.04), CRVEB (OR, 0.03), CRVEC (OR, 0.06), and AVRB (OR, 0.55) were associated with a lower of SBI. There was no significant difference in AVRC between the two groups. Conclusion: Our study shows the association between retinal vascular geometry and SBI, and the results may provide new biomarkers for the early detection of SBI. [ABSTRACT FROM AUTHOR]

Background: This study aimed to evaluate the location of retinal fractal dimension (FD) abnormalities in individuals with diabetes mellitus (DM) and hypertension (HTN) without retinopathy. Methods: The annular zone of 6 mm × 6 mm OCTA images centered on the fovea was partitioned into thin annuli and analyzed using fractal analysis to measure FDs. Results: The cohort (n = 114) had an average age of 55.7 years, with 87% self-identifying as male; 29% (n = 33) had HTN, 8% (n = 9) had DM, and 11% (n = 12) had both. Individuals with DM showed significantly lower FDs in the C5 partition of the deep vascular plexus (DVP), located 1.77 mm to 2.14 mm from the foveal center compared to controls without DM (1.57 ± 0.003 vs. 1.58 ± 0.006; p = 0.014). Those with both DM and HTN exhibited significantly lower FDs in the entire superficial vascular plexus (SVP) annulus (1.84 ± 0.01 vs. 1.85 ± 0.007; p = 0.006), as well as the C3 (1.58 ± 0.02 vs. 1.60 ± 0.02; p = 0.008), C4 (1.57 ± 0.002 vs. 1.57 ± 0.01; p = 0.036), C5 (1.56 ± 0.01 vs. 1.57 ± 0.008; p < 0.001), and C6 (1.58 ± 0.01 vs. 1.59 ± 0.008; p < 0.001) partitions of the SVP (1.03 mm to 2.50 mm from the foveal center) and the C4 (1.57 ± 0.008 vs. 1.58 ± 0.008; p = 0.015) and C5 (1.57 ± 0.01 vs. 1.58 ± 0.006; p = 0.012) partitions of the DVP (1.40 mm to 1.77 mm from the foveal center) compared to the controls with neither DM nor HTN. Conclusions: While our study examined FDs in a predominantly male veteran population, our findings align with prior studies that reported lower FDs in DM and HTN cohorts. Our study further localizes these microvascular changes, with the most prominent differences occurring at C5 and C6 of the SVP, representing an area between 1.77 and 2.50 mm from the center of the fovea. These data lay the groundwork for developing screening protocols to identify individuals at risk of developing vasculopathies. [ABSTRACT FROM AUTHOR]

This article systematically investigated the improvement effect of polypropylene fiber (PPF) on the mechanical and freeze–thaw properties of alkali-activated fly ash slag concrete (AAFSC) with high fly ash content and cured at room temperature. Fly ash and slag were used as precursors, with fly ash accounting for 80% of the total mass. A mixed solution of sodium hydroxide and sodium silicate was used as alkali activator, and short-cut PPF was added to improve the performance of AAFSC. Firstly, the strength characteristics of AAFSC at different curing ages were studied. Then, key indicators such as morphology, residual compressive strength, weight loss, relative dynamic modulus of elasticity (RDME), and pore characteristics of AAFSC after different freeze–thaw cycles were tested and analyzed. The strength performance analysis showed that the optimal dosage of PPF was 0.90%. When the alkali equivalent of the alkali activator was increased from 4% to 6%, the frost resistance of AAFSC could be improved. Furthermore, adding 0.90% PPF could increase the freeze–thaw cycle number of AAFSC by about 50 times (measured by RDME). With the increase in freeze–thaw cycles, the porosity of AAFSC increased, the fractal dimension decreased, and the proportion of harmless and less harmful pores decreased, while the proportion of harmful and multiple harmful pores increased. The relationship model between the porosity and compressive strength of AAFSC after freeze–thaw cycles was established. [ABSTRACT FROM AUTHOR]

In tunnel engineering, joint shear slip caused by external disturbances is a key factor contributing to landslides, instability of surrounding rock masses, and related hazards. Therefore, accurately characterizing the macromechanical properties of joints is essential for ensuring engineering safety. Given the significant influence of rock joint morphology on mechanical behavior, this study employs the frequency spectrum fractal dimension (D) and the frequency domain amplitude integral (Rq) as quantitative descriptors of joint morphology. Using Fourier transform techniques, a reconstruction method is developed to model joints with arbitrary shape characteristics. The numerical model is calibrated through 3D printing and direct shear tests. Systematic parameter analysis validates the selected quantitative indices as effective descriptors of joint morphology. Furthermore, multiple machine learning algorithms are employed to construct a robust predictive model. Machine learning, recognized as a rapidly advancing field, plays a pivotal role in data-driven engineering applications due to its powerful analytical capabilities. In this study, six algorithms—Random Forest (RF), Support Vector Regression (SVR), BP Neural Network, GA-BP Neural Network, Genetic Programming (GP), and ANN-based MCD—are evaluated using 300 samples. The performance of each algorithm is assessed through comparative analysis of their predictive accuracy based on correlation coefficients. The results demonstrate that all six algorithms achieve satisfactory predictive performance. Notably, the Random Forest (RF) algorithm excels in rapid and accurate predictions when handling similar training data, while the ANN-based MCD algorithm consistently delivers stable and precise results across diverse datasets. [ABSTRACT FROM AUTHOR]

Green tide area is a crucial indicator for monitoring green tide dynamics. However, scale effects arising from differences in image resolution can lead to estimation errors. Current pixel-level and sub-pixel-level methods often overlook the impact of morphological differences across varying resolutions. To address this, our study examines the influence of morphological diversity on green tide area estimation using GF-1 WFV data and the Virtual-Baseline Floating macroAlgae Height (VB-FAH) index at a 16 m resolution. Green tide patches were categorized into small, medium, and large sizes, and morphological features such as elongation, compactness, convexity, fractal dimension, and morphological complexity were designed and analyzed. Machine learning models, including Extra Trees, LightGBM, and Random Forest, among others, classified medium and large patches into striped and non-striped types, with Extra Trees achieving outstanding performance (accuracy: 0.9844, kappa: 0.9629, F1-score: 0.9844, MIoU: 0.9637). The results highlighted that large patches maintained stable morphological characteristics across resolutions, while small and medium patches were more sensitive to scale, with increased estimation errors at lower resolutions. Striped patches, particularly among medium patches, were more sensitive to scale effects compared to non-striped ones. The study suggests that incorporating morphological features of patches, especially in monitoring striped and small patches, could be a key direction for improving the accuracy of green tide monitoring and dynamic change analysis. [ABSTRACT FROM AUTHOR]

Mullite ceramic fibre membranes are prepared by a gel casting freeze-drying method, using transition phase rho alumina (ρ-Al 2 O 3) and alkaline silica (SiO 2) sol as a novel gel system and mullite fibres as the three-dimensional reticular skeleton. This strategy results in high-strength (5.73 ± 0.1–20.29 ± 0.2 MPa) green structures suitable for processing. Moreover, the prepared porous mullite membranes possess uniform pore size distribution (11–43 μm), suitable fractal dimension (2.53845–2.61954), high apparent porosity (55.95 % ± 0.1%–64.69 % ± 0.1 %), low bulk density (1.109 ± 0.01–1.385 ± 0.01 g/cm3), extremely low linear shrinkage (1.51 % ± 0.06%–2.03 % ± 0.035 %), low thermal conductivity (0.194 ± 0.006–0.436 ± 0.006 W/m⋅K), relatively high compressive strength (1.25 ± 0.1–6.42 ± 0.12 MPa), low pressure drop (0.626–8.062 hPa), high gas permeability coefficient (2.79 × 10−11±8 × 10−13-6.52 × 10−11±3 × 10−12 m2), and gas permeance (5.5 × 10−3±2 × 10−4-1.28 × 10−2±5 × 10−4 mol m−2 s−1·Pa−1). The high-strength green structures make processing convenient; the extremely low linear shrinkage makes the near-net shape moulding possible; and the low thermal conductivity, high apparent porosity, and high gas permeance enable broad application prospects of the prepared mullite ceramic membranes in high-temperature flue gas filtration. This new gel system is anticipated to provide a new route to achieve near-net shape forming of ceramics with high porosity suitable for flue gas filtration. [ABSTRACT FROM AUTHOR]

Hydrogels prepared from self-assembled cellulose nanofibrils (CNFs) are widely used in biomedicine, electronics and environmental technology. Their ability to serve as inks for extrusion-based 3D printing is conventionally evaluated by means of rheological tests. A model is developed that describes the response of CNF gels in small- and large-amplitude oscillatory tests in a unified manner. The model involves a reasonably small number of material parameters, ensures good agreement between results of simulation and observations in oscillatory tests and correctly predicts the stress–strain Lissajous curves, experimental data in hysteresis loop tests, and measurements of the steady-state viscosity. The model is applied to analyze how composition and preparation conditions for CNF gels affect transition from shear thinning to weak strain overshoot in large-amplitude shear oscillatory tests. Based on the model, simple relations are derived for the fractal dimension of CNF clusters and the storage modulus of gels prepared in aqueous solutions of multivalent salts. The validity of these equations is confirmed by comparison of their predictions with observations in independent tests.   [ABSTRACT FROM AUTHOR]

In deep brine oil and gas injection–production operations, the combined long-term effects of brine and carbon dioxide on rock mechanical properties are not clear. In order to solve this problem, the influence of long-term salt–CO2 environment on the mechanical properties of sandstone is discussed. The mechanism of interaction evolution and fracture propagation was studied in detail by NMR, the triaxial compression test and a CT scan. The results show that the triaxial compressive strength and mass of sandstone decrease first and then increase with the prolonging of soaking time. The proportion of micropores first decreased and then increased, while the proportion of medium and large pores first increased and then decreased. The pores obtained by Avizo's segmentation of the threshold value of CT sections first increased and then decreased, and the fractal dimensions obtained first increased and then decreased. In particular, the calcium ions in the immersion solution increased first and then decreased. The reaction rate was obtained and verified according to the changes in calcium carbonate mass and calcium ion mineralization at different times. The failure mode of the sample gradually changed from /-shaped failure to V-shaped composite failure, then to local /-shaped failure, and finally to X-shaped composite failure. On this basis, the process of sandstone was divided into the dissolution stage, precipitation stage and secondary dissolution stage, and the rock microstructure change model under a salt–CO2 environment was established. The mechanics, temperature, chemical interaction mechanism and fracture propagation mechanism of sandstone under a salt–CO2 environment are discussed. [ABSTRACT FROM AUTHOR]

The Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickness and Hausdorff dimension zero. In this article—written 50 years after the conjecture was first proposed—we review progress on some new variants of the original problem, namely the bi-Lipschitz variant, the topological variant, and a variant "in the large". These problems were recently studied by the authors and their collaborators. Each of them offers new perspectives on the original conjecture. [ABSTRACT FROM AUTHOR]

The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets. The Black–Scholes model for pricing stock options has been applied to various payoff structures, and options trading is based on Black and Scholes' principle of dynamic hedging to estimate and assess option prices over time. However, the Black–Scholes model requires severe constraints, assumptions, and conditions to be applied to real-life financial and economic problems. Several methods and approaches have been developed to approach these conditions, such as fractional Black–Scholes models based on fractional derivatives. These fractional models are expected since the Black–Scholes equation is derived using Ito's lemma from stochastic calculus, where fractional derivatives play a leading role. Hence, a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected. However, these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations. Nevertheless, it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model. The relationship between fractional calculus and fractals is well-known in the literature. This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing. In our analysis, we consider power-laws properties for volatility, interest rated, and dividend payout, which emerge in several empirical regularities in quantitative finance and economics. We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space. Our model can be used to obtain the prices of many pay-off models. We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that, for fractal dimensions much smaller than unity, the call option increases significantly. We prove that fractal dimensions are a powerful tool to obtain new results. Further details are analyzed and discussed. [ABSTRACT FROM AUTHOR]

Millions of patients each year are impacted by critical‐size bone tissue defects, the repair of which involves inflammation and the formation of new tissue. In this study, a fractal biomimetic design for a 3D‐printed scaffold that combined 3D printing with high‐energy plasma tantalum alloy fabrication, enabling easy production on an industrial scale is proposed. The fractal bionic design leverages the principles of fractal geometry, employing self‐affine patterns and random fractals to attain self‐affine surface design on 3D scaffolds. This approach aimed to emulate the fractal dimensions observed in natural bone structures closely. While the surface roughness of implants plays a critical role in restoration outcomes, this findings suggest that incorporating the surface fractal dimension may hold greater significance than mere roughness. A rat skull‐defect model is utilized to assess the osteogenic potential of the three scaffolds, and photoacoustic technology is first employed for long‐term, in situ monitoring of physiological signals during the bone repair process. Results from both cell and animal experiments demonstrated that fractal bionic scaffolds offer notable advantages over surface‐modified scaffolds and 3D‐printed scaffolds. This experimental results showed that the bionic scaffold group manifested a better bone‐promoting process. [ABSTRACT FROM AUTHOR]

Traditional chemical additives inevitably pollute, damage, and destroy the ecological environment and natural resources while simultaneously addressing the requirements of engineering construction in loess areas. Additionally, freeze–thaw cycles exert a substantial influence on the long‐term durability of engineering structures located in areas with loess deposits. Thus, it is a considerable benefit to identify and utilize materials that are beneficial to the environment and which will augment the engineered performance and freeze–thaw resistant capacity of loess. The purpose of this research is to evaluate the impact of freezing and thawing cycles on the mesostructural attributes using loess reinforced with lignin fiber and to elucidate an effect of varying fiber doses in relation to the response of loess to freezing and thawing. The findings illustrate that the incorporation of fiber effectively eliminates the presence of overhead pores in the loess. Furthermore, the freeze–thaw action induces the formation of long‐narrow pores along the fiber surface in the reinforced loess. Adding the fiber reduces the characteristic parameters of the loess mesostructure. On the other hand, the freezing and thawing action increases the apparent void ratio, the mean pore area, and the area probability distribution index of the reinforced loess, while decreasing the probability entropy and bringing the fractal dimension very close. Freeze–thaw has the least effect on the apparent void ratio and microfine pore area ratio of 1% fiber loess. The filling and bridge effects of lignin fiber serve as the primary means of enhancing the strength of loess. Through its control of water, fiber bears the influence of some loess particles and pores, thus improving the freeze–thaw resistant capacity of loess. [ABSTRACT FROM AUTHOR]

Monitoring the performance of reinforced concrete structures, particularly in terms of strength reduction, presents significant challenges due to the practical limitations of traditional detection methods. This study introduces an innovative framework that incorporates a non-destructive technique using electromagnetic waves (EM-waves) transmitted via Radio Frequency Identification (RFID) technology, combined with two-dimensional (2-D) Fourier transform, fractal dimension analysis, and deep learning techniques to predict reductions in structural strength. Experiments were conducted on three reinforced concrete beam (RCB) specimens exhibiting various levels of reinforcement corrosion. From these, a dataset of 1,800 EM-wave images was generated and classified into "normal" and "reduced strength" categories. These categories were used to train and validate a Convolutional Neural Network (CNN), which demonstrated robust performance, achieving a high accuracy of 0.91 and an F1-score of 0.93 in classifying instances of reduced structural strength. This approach offers a promising solution for detecting strength reduction in reinforced concrete infrastructures, enhancing both safety and maintenance efficiency. [ABSTRACT FROM AUTHOR]

This paper uses the unified solver process to acquire soliton outcomes for the fractional Phi-4 model. The dynamic characteristic of the governing model is investigated for its planar dynamical system by applying the bifurcation method. Under the given parameters, 2D and 3D phase portraits, time series, return map, Lyapunov exponent, recurrence plot, strange attractor, bifurcation diagram, and fractal dimension plot are provided. These plots show the periodic, quasi-periodic, and chaotic nature of the suggested nonlinear problem. Moreover, the sensitivity and multistability assessments of the stated model are studied for a clear understanding of chaotic behavior. To understand the system's long-term behavior, we also test the stability of our results. Our results agree with previous results and may help researchers better understand the behavior of nonlinear systems. Furthermore, other fields such as biology, economics, and engineering can apply our results. [ABSTRACT FROM AUTHOR]

The dynamic erosion effect of the corrosive medium formed by aqueous solution and CO2 gas on rock will lead to the decline of the mechanical properties of rock and seriously threaten the long-term stability and durability of rock mass in the reservoir area. In this paper, a dynamic erosion test method of CO2 solution on rock mass is proposed to study the deterioration effect of CO2 solution on rock, based on the gas–liquid cycle. A total of 210 limestone samples were tested under various dynamic erosion cycles (0, 5, 10, 15, 20, 25, and 30 cycles). A systematic analysis of key physical properties related to the degradation behavior of rock (Young's modulus, uniaxial compressive strength, tensile strength, shear strength, cohesion, and internal friction angle) was performed. Additionally, the changes in dissipated energy, fractal dimension, and micro-pore evolution during the solution erosion process were examined. The results indicate that with the increase in erosion cycles, the mechanical parameters of the samples gradually decreased, while both the proportion of dissipated energy and the fractal dimension of fragmentation increased nonlinearly by 29.58% and decreased by 9.95%, respectively. The porosity of the samples increased from 0.04% to 6.89%, and their multifractal spectrum gradually shifted to the right, indicating the development of internal pores and decreased microscopic structural stability. Finally, a limit analysis method for time-varying bearing capacity analysis of limestone pile foundation was established to analyze the time-varying evolution characteristics of pile capacity based on the deterioration effect of solution on rock. [ABSTRACT FROM AUTHOR]

Adsorption temperature, pressure, and pore structure parameters are the key factors affecting gas adsorption in porous media. However, an adsorption dynamics model has not been established that comprehensively couples adsorption temperature, adsorption pressure, and pore structure parameters. In this study, the methane adsorption and pore structure measurements are conducted, and a novel fractal dynamics model of gas adsorption in porous media is proposed. The research results show the proposed model is a function of adsorption temperature (T), adsorption pressure (P), pore size parameters (γmax and γmin), fractal dimension (Df) for pore size, and fractal dimension (DT) for pore tortuosity. The error analysis indicates the predicted adsorption amount from the proposed model matches the measured adsorption amount. The proposed model achieves the determination of the critical point of gas absorption's temperature and pressure effects through a temperature-pressure dynamics analysis. This model provides a methodological basis for clean production based on the adsorption principle and also establishes a significant foundation for the fractal design strategies of novel materials. [ABSTRACT FROM AUTHOR]

We advance the understanding of inertial clustering and the role of sling events in high-Reynolds number (Re) particle-laden turbulence. To this end, we perform one-way coupled particle tracking in flow fields obtained from direct numerical simulations (DNS) of forced homogeneous isotropic turbulence. Additionally, we examine the impact of filtering utilized in large eddy simulations by applying a sharp spectral filter to the DNS fields. Our analysis reveals that while instantaneous clustering through the centrifuge mechanism explains clustering at early times, the path history effect—the sampling of fluid flow along particle trajectories—becomes important later on. The filtered fields expose small-scale fractal clustering that cannot be predicted by the instantaneous flow field. We show that there exists a filter-effective Stokes number that governs the degree of fractal clustering and preferential sampling, revealing scale-similarity in the spatial distributions and fractal dimensions. Sling events are prevalent throughout our simulations and impose prominent patterns on the particle fields. In pursuit of investigating the sling dynamics, we compute the relative velocity, averaged over proximal neighboring particles, to identify particles undergoing caustics. As postulated in recent theories, we find that in fully resolved, high-Re turbulence, sling events occur in thin sheets of high strain, situated between turbulent vortices. This behavior is driven by rare, extreme events of compressive straining, manifested by characteristic fluctuations of the flow velocity gradients. [ABSTRACT FROM AUTHOR]