Search Results (49)

In this work, we present a new partially coherent adjustable anomalous vortex laser beam (PCAAVLB) and introduce it into turbulent biological tissue. The equation of such PCAAVLB in turbulent biological tissue is obtained. By numerical analysis, the evolution of the intensity of such PCAAVLB in turbulent biological tissue is analyzed. It is found that the PCAAVLB in biological tissue can lose its ring shape and become a Gaussian beam, and a PCAAVLB with smaller topological charge $M$ or coherence length $\sigma$ will evolve into a Gaussian profile faster. The PCAAVLB in turbulent biological tissue with a smaller small-length-scale factor $l_0$ or larger fractal dimension $D$ will evolve into a Gaussian profile faster and have a larger intensity as z increases. The results may have potential applications in sensing under biological tissue environments and laser imaging in biology. Full article

This study systematically investigates the effect of steel fiber content on the fractal evolution characteristics of bending cracks in alkali-activated slag concrete (AASC) beams. A four-point bending test on simply supported beams, combined with digital image correlation (DIC) technology, was employed to quantitatively analyze the fractal dimension of crack propagation paths in AASC beams with steel fiber contents ranging from 0% to 1.4%, using the box-counting method. The relationship between fracture energy and fractal dimension was examined, along with the fractal control mechanisms of mid-span deflection, crack width, and the fractal evolution of fracture toughness parameters. The results revealed that as the steel fiber content increased, the crack fractal dimension decreased from 1.287 to 1.155, while the critical fracture energy of AASC beams increased by approximately 75%. Both mid-span deflection and maximum crack width were positively correlated with the crack fractal dimension, whereas the fractal dimension showed a negative correlation with critical cracking stress and fracture toughness and a positive correlation with the energy release rate. When the steel fiber content exceeded 1.2%, the performance gains began to diminish due to fiber agglomeration effects. Overall, the findings suggest that an optimal steel fiber content range of 1.0% to 1.2% provides the best crack control and mechanical performance, offering a theoretical basis for the design of AASC structures. Full article

This study investigated the fracture behavior of concrete beams with recycled coarse aggregate (RCA) and recycled fine aggregate (RFA) using the box-counting method to measure crack fractal dimensions under load. Beams with RCA showed higher fractal dimensions due to RCA’s lower elastic moduli and compressive strengths, resulting in reduced deformation resistance, ductility, and more late-stage crack propagation. A direct proportional relationship existed between RCA/RFA replacement ratios and crack fractal dimensions. Second-order and third-order polynomial trend surface-fitting techniques were applied to examine the complex relationships among RFA/RCA dosage, applied load, and crack fractal dimension. The results indicated that the RFA dosage had a negative quadratic influence, while load had a positive linear effect, with dosage impact increasing with load. A second-order functional relationship was found between mid-span deflection and crack fractal dimension, reflecting nonlinear behavior consistent with concrete mechanics. This study enhances the understanding of recycled aggregate concrete beam fracture behavior, with the crack fractal dimension serving as a valuable quantitative indicator for damage state and crack complexity assessment. These findings are crucial for engineering design and application, enabling better evaluation of structural performance under various conditions. Full article

In this article, a high-gain axisymmetric Minkowski fractal reflectarray is designed and fabricated for Ku-Band satellite internet communications. High gain is achieved here by carefully optimising the number of unit cells, their shape modifier, focal length, feed position and scan angle. The space-filling properties of Minkowski fractals help in miniaturising the fractal. The scan angle of the reflectarray varied by adjusting the fractal scaling factor for each unit cell in the array. The reflectarray is symmetric along the X-axis in its design and configuration. Initially, a Minkowski fractal unit cell is designed using iteration-1 in the simulation software. Then, its design parameters are optimised to achieve high gain, a narrow beam, and beam scan capabilities. The sensitivity of design parameters is examined individually using the array synthesis method to achieve these performance parameters. It helps to establish the maximum range of design and performance parameters for this design. The proposed reflectarray resonates at 12 GHz, achieving a gain of over 20 dB and a narrow beamwidth of less than 15 degrees. Finally, the designed fractal reflectarray is tested in real-time simulation environments using MATLAB R2023b, and its performance is evaluated in an interference scenario involving LEO and MEO satellites, as well as a ground station, under various time conditions. For real-world applicability, it is necessary to identify, analyse, and mitigate the unwanted interference signals that degrade the desired satellite signal. The proposed reflectarray, with its performance characteristics and beam scanning capabilities, is found to be an excellent choice for Ku-band satellite internet communications. Full article

In this paper a new generalized fractal equation for studying the behaviour of self-similar beams using the Timoshenko beam theory is introduced. This equation is established in fractal dimensions by applying the concept of fractal continuum calculus $F^{\alpha }$-CC introduced recently by Balankin and Elizarraraz in order to study engineering phenomena in complex bodies. Ultimately, the achieved formulation is a fourth-order fractal single equation generated by superposing a shear deformation on an Euler–Bernoulli beam. A mapping of the Timoshenko principle onto self-similar beams in the integer space into a corresponding principle for fractal continuum space is formulated employing local fractional differential operators. Consequently, the single equation that describes the stress/strain of a fractal Timoshenko beam is solved, which is simple, exact, and algorithmic as an alternative description of the fractal bending of beams. Therefore, the elastic curve function and rotation function can be described. Illustrative examples of classical beams are presented and show both the benefits and the efficiency of the suggested model. Full article

This study evaluated the combined effect of a cationic coagulant (Magnafloc 1727^®) and a high molecular weight anionic flocculant (SNF 604^®) on the settling properties, aggregate structure, and rheological behavior of synthetic tailings suspensions composed of kaolinite and quartz in industrial water at pH 11. Settling tests, focused beam reflectance measurement (FBRM), zeta potential measurement, and rheological characterization were used to analyze the system’s performance under different coagulant dosages (0–150 g/t), while keeping the flocculant dosage constant (20 g/t). The results indicated that the coagulant favored surface charge neutralization, shifting the zeta potential from −13.2 mV to +4.0 mV. This resulted in larger, more efficient flocs capturing fines, with a 46% turbidity reduction. FBRM analysis revealed a significant increase in aggregate size and a slight decrease in fractal dimension (from 2.35 to 2.20), consistent with larger volume structures and lower bulk density. Rheologically, a substantial increase in yield stress was observed, especially in 50 wt% suspensions, suggesting the development of a continuous flocculated network with greater mechanical strength. These findings highlight the importance of sequential chemical conditioning in clayey tailings and its impact on clarification efficiency and water recovery under alkaline conditions representative of industrial mining processes. Full article

Carbonate rock slopes in reservoir environments are increasingly exposed to dissolution-induced deterioration due to water level fluctuations. However, the influence of internal structures—particularly calcite veins—on dissolution behavior remains inadequately understood. The acid-induced dissolution of limestone by a sulfuric acid solution leads to the removal of soluble minerals and changes to the rock structure. Natural variation in rock structures—particularly in the presence, density, and morphology of calcite veins—can significantly affect the dissolution process and its outcomes. In this study, we obtained three types of Triassic limestone from the same host rock but with varying vein structures from the Three Gorges Reservoir area. Cylindrical rock specimens were prepared to investigate the acid-induced dissolution behavior of limestone in a sulfuric acid solution. We identified and analyzed the macrostructures on the rock specimens before and after the interaction. Additionally, SEM was employed to observe the microstructures of the specimens before and after the acid-induced dissolution, and fractal dimension analysis was conducted on the SEM images to quantify surface complexity. Furthermore, we used a focused ion beam–scanning electron microscope (FIB-SEM) with an automatic mineral identification and characterization system, as well as mineral roundness calculation, for mineral identification and analysis. Based on the experiments and analyses, we determined the following: The contact surfaces between the host rock and the calcite veins increase the dissolution areas between the limestone and the sulfuric acid solution, intensifying the dissolution reactions, enhancing the connectivity of the original microstructural planes, and generating new, highly extended dissolution fissures. The calcite veins facilitate the entry of sulfuric acid solution into the limestone, intensifying the dissolution of the edges and corners of dolomite and resulting in the gradual rounding of dolomite shapes. Quantitatively, the limestone with dense, fine calcite veins exhibited the most severe dissolution, with water absorption rates nearly twice as high as the non-veined samples (0.13% vs. 0.07%), a 2.2% reduction in fractal dimension, and a 19.53% increase in dolomite roundness with the 1 ≤ R ≤ 3 interval, indicating significantly enhanced surface complexity and mineral reshaping. In summary, the presence of more calcite veins, regardless of their width, leads to more severe rock dissolution. Full article

In order to obtain high-performance 3D printed parts, this study focuses on the key performance indicator of impact toughness. The parametric modeling software Rhino 6 is used to design impact specimens, and the laser selective melting equipment DiMetal-100, independently developed by the South China University of Technology, is used to manufacture impact specimens. Subsequently, the CoCrMo alloy parts were annealed using an MXQ1600-40 box-type atmosphere furnace and subjected to impact testing using a cantilever beam impact testing machine XJV-22. Fractal theory was applied to analyze the fractal behavior of the resulting impact fracture surfaces. The research results indicate that the 3D-printed impact specimens exhibited excellent surface quality, characterized by brightness, low roughness, and the absence of significant defects such as warping or deformation. In terms of annealing treatment, lower annealing temperatures did not improve the impact performance of SLM-formed CoCrMo alloy parts but instead led to a decrease in toughness. While increasing the annealing temperature can improve toughness to some extent, the effect is limited. Furthermore, the relationship between impact energy and heat treatment temperature exhibits a U-shaped trend. The fractal dimension analysis shows that the parts annealed in a 1200 °C furnace have the highest fractal dimension and better toughness performance. This study introduces a novel approach by comprehensively integrating advanced 3D printing technology, annealing processes, and fractal theory analysis to systematically investigate the influence of annealing temperature on the impact properties of 3D-printed CoCrMo alloy parts, thereby establishing a solid foundation for the application of high-performance 3D printed parts. Full article

With the depletion of high-grade iron ore resources, the efficient utilization of low-grade iron ore has become a critical demand in the steel industry. Due to its uniform particle size and chemical composition, pelletized iron ore significantly enhances both the utilization rate of iron ore and the efficiency of metallurgical processes. This paper presents a deep learning model based on ResUNet, which integrates three-dimensional CT images obtained through industrial computed tomography (ICT) to precisely segment hematite, liquid phase, and porosity. By incorporating residual connections and batch normalization, the model enhances both robustness and segmentation accuracy, achieving F1 scores of 98.37%, 95.10%, and 83.87% for the hematite, pores, and liquid phase, respectively, on the test set. Through 3D reconstruction and quantitative analysis, the volume fractions and fractal dimensions of each component were computed, revealing the impact of the spatial distribution of different components on the physical properties of the pellets. Systematic evaluation of model robustness demonstrated varying sensitivity to different CT artifacts, with the strongest resistance to beam hardening and highest sensitivity to Gaussian noise. Multi-scale resolution analysis revealed that segmentation quality and fractal dimension estimates exhibit phase-dependent responses to resolution changes, with the liquid phase being the most sensitive. Despite these dependencies, the relative complexity relationships among phases remained consistent across resolutions, supporting the reliability of our qualitative conclusions. The study demonstrates that the deep learning-based image segmentation method effectively captures microstructural details, reduces human error, and enhances automation, providing a scientific foundation for optimizing pellet quality and improving metallurgical performance. It holds considerable potential for industrial applications. Full article

Background: Implant-prosthetic therapy requires a detailed assessment of the bone structure before designing a personalized treatment plan. Tooth extraction at the molar level is followed by a series of bone changes dependent on the patient’s general condition and age and the area in which it was performed. The fractal analysis of cone beam computed tomography (CBCT) represents a way to assess the quality of post-extraction bone regeneration. The purpose of this study was to analyze the alveolar bone changes after tooth extraction using fractal analysis on CBCT images. Methods: This retrospective study included pre- and post-extraction CBCTs at 3 months of 60 patients who underwent 100 extractions of first and/or second molars. Fractal analysis on CBCT images was performed using ImageJ, and the data obtained from the measurements were statistically processed. A multiple regression model was used to assess factors influencing bone remodeling. Results: Fractal analysis performed on CBCT images showed that most patients experienced advanced bone remodeling, this being more pronounced in those from rural areas, in the vertical plane at the mandible and at the second molar. The multiple regression model showed that the factors that play an important role in predicting bone resorption are represented by age group (age above 56 years old is associated with less bone resorption), location (bone resorption is more pronounced at the mandible level), and molar (bone resorption for the second molar is higher). Conclusions: Post-extraction bone changes were influenced by the age of the patient and by the location of the extraction, with the maxilla and first molar having better fractal analysis values compared to the mandible and second molar. These results emphasize the importance of training implantologists in CBCT evaluation to improve personalized implant-prosthetic treatment decisions. Full article

Functional polymeric materials play a critical role in optimizing flocculation and sedimentation processes in mining tailings, where complex interactions with mineral surfaces govern polymer performance. This study examines the structure–performance relationship, which describes how the internal structure of aggregates (e.g., compactness, porosity and fractal dimension) influences sedimentation behavior, specifically for anionic polyacrylamide (SNF 704) in kaolin-quartz-pyrite suspensions at a pH of 10.5. Using focused beam reflectance measurement (FBRM) and static sedimentation tests, we demonstrate that pyrite exhibits the highest flocculant adsorption capacity, inducing a train-like polymer conformation on its surface. This reduces the formation of effective polymeric bridges, resulting in less compact and more porous aggregates that negatively impact sedimentation rates. Increasing the flocculant dosage improves the capture of fine particles; however, at high pyrite concentrations, rapid saturation of adsorption sites limits flocculation efficiency. Additionally, the fractal dimension of the aggregates decreases with increasing pyrite content, revealing more open structures that hinder consolidation. These findings underscore the importance of optimizing polymer dosage and tailoring flocculant design to the mineralogical composition, thereby enhancing water recovery and sustainability in mining operations. This study highlights the role of structure–property relationships in polymeric flocculants and their potential for next-generation tailings management solutions. Full article

(1) Background: Condylar fracture healing pattern classification in children and adolescents is primarily based on the radiological assessment of condylar morphology; however, recent studies showed the presence of a poor correlation between post-treatment radiological findings and clinical temporomandibular joint (TMJ) dysfunction. The present case series aimed to correlate the condylar morphology, shape, and trabecular bone density with the skeletal asymmetry and the clinical recovery of two growing patients with unilateral condylar fractures undergoing orthopedic treatment with the Balters Bionator appliance. (2) Methods: Pre- and post-treatment (12 months) cone-beam computed tomography (CBCT) scans of two growing patients with unilateral condylar fracture were retrieved; both patients were treated with the Balters Bionator appliance for one year. Morphological evaluation of the condylar healing pattern was carried out on CBCT reconstructions of the mandible. Condylar remodeling and skeletal asymmetry were assessed through linear measurements performed on pre- and post-treatment CBCT scans; then, fractal analysis (FA) was employed to assess the condylar trabecular bone density on orthopantomographies (OPTs). Clinical and TMJ functional evaluation were retrieved from patients’ records from before and at the end of the treatment (12 months). (3) Results: Conservative treatment of condylar fractures in growing patients led to an increased bone density of the condylar heads, regardless of the post-treatment size and morphology of the injured condyles. Patient one presented an unchanged condylar morphology on the affected side, while patient two’s condyle was slightly spherical. The qualitative results were confirmed by quantitative measurements on CBCTs. The radiological healing patterns were associated with slightly different functional outcomes. Both patients also exhibited an improvement in skeletal asymmetry and TMJ function. (4) Conclusions: According to the findings in the present study, the condylar remodeling and bone apposition after conservative treatment of condylar fractures in growing patients can exhibit different radiological and functional outcomes. Indeed, an unchanged morphology of the condylar head is more likely to determine a physiological TMJ recovery. Full article

In the design of structures involving quasi-brittle materials such as concrete, it is essential to consider the scale dependence of the mechanical properties of the material. Among the theories used to describe the phenomenon of size effect, the fractal theory proposed by Carpinteri and colleagues has attracted attention for its results in the last three decades of research. The present study employs the fractal perspective to examine the scale effect in three-point bending tests conducted on expanded polyethylene (EPS) beam specimens. The influence of size on flexural strength, fracture energy, and critical angle of rotation is investigated. Additionally, numerical simulations based on peridynamic (PD) theory are performed based on the experimental tests. The global behavior, brittleness, failure configuration, and fractal scale effect obtained numerically are evaluated. The numerical results show a good correlation with the experimental ones and, moreover, both the experimental and numerical results are in agreement with the fractal theory of scale effect. More precisely, the error of the sum of the fractal exponents, computed with respect to the theoretical one, is equal to −1.20% and −2.10% for the experimental and numerical results, respectively. Moreover, the classical dimensional analysis has been employed to demonstrate that the scale effect can be naturally described by the PD model parameters, allowing to extend the results for scales beyond those analyzed experimentally. Full article

The durability of carbonated recycled aggregate concrete (C-RAC) beams is still unclear at present. In this paper, the characteristics of corrosion-induced cracks and the steel corrosion depth of C-RAC beams were investigated through the accelerated corrosion test. The results showed that when accelerating corrosion to the 40th day, compared to the non-carbonated recycled aggregate concrete (NC-RAC) beam, the corrosion-induced cracking area of the C-RAC beam with a 100% carbonated recycled coarse aggregate (C-RCA) replacement ratio decreased by 40.00%, while the total length of the corrosion-induced cracks (CCs) increased by 51.82%. The type of probability distribution for the width of the CCs on the tension side of the C-RAC beams was a lognormal distribution. Compared with the NC-RAC beam, the mean value of the width of the CCs of the C-RAC beam with a 100% C-RCA replacement ratio decreased by 66.67%, the crack width distribution was more concentrated, and the quartiles and median were all reduced. With an increase in the C-RCA replacement ratio, the fractal dimension and the scale coefficient of CCs on the tension side of the beams showed an approximate trend of first increasing and then decreasing. The distribution of the corrosion depth of longitudinal tensile steel bars in the C-RAC beams was a mainly normal distribution. When the C-RCA replacement ratio increased from 30% to 100%, the mean value of the corrosion depth of the longitudinal tensile steel bars decreased by 33.46%, and the trend of changes in the quartiles and medians was basically the same as the trend of changes in the mean value. The research results can provide some reference for promoting the engineering application of C-RAC beams. Full article

The damage degree of a reinforced concrete structure is closely related to the generation and expansion of cracks. However, the traditional damage assessment methods of reinforced concrete structures have defects, including low efficiency of crack detection, low accuracy of crack extraction, and dependence on the experience of inspectors to evaluate the damage of structures. Because of the above problems, this paper proposes a damage assessment method for concrete members combining the U-Net convolutional neural network and crack fractal features. Firstly, the collected test crack images are input into U-Net for segmenting and extracting the output cracks. The damage to the concrete structure is then classified into four empirical levels according to the damage index (DI). Subsequently, a linear regression equation is constructed between the fractal dimension (D) of the cracks and the damage index (DI) of the reinforced concrete members. The damage assessment is then performed by predicting the damage index using linear regression. The method was subsequently employed to predict the damage level of a reinforced concrete shear wall–beam combination specimen, which was then compared with the actual damage level. The results demonstrate that the damage assessment method for concrete members proposed in this study is capable of effectively identifying the damage degree of the concrete members, indicating that the method is both robust and generalizable. Full article