Search Results (178)

The quasisymmetric minimality for fractal sets is a hot research topic for scholars focused on the fractal geometry and quasisymmetric mappings. In this paper, we study the quasisymmetric minimality on packing dimension for homogeneous perfect sets. By using some mathematical tools such as the mass distribution principle, we find that a special class of homogeneous perfect sets with packing dimension 1 is quasisymmetrically packing minimal. Our result generalizes the results in the references. Full article

Wet–dry cycles are a key factor aggravating the durability degradation of foam concrete. To address this issue, this study prepared bentonite slurry–steel slag foam concrete (with steel slag and cement as main raw materials, and bentonite slurry as admixture) using the physical foaming method. Based on 7-day unconfined compressive strength tests with different mix proportions, the optimal mix proportion was determined as follows: mass ratio of bentonite to water 1:15, steel slag content 10%, and mass fraction of bentonite slurry 5%. Based on this optimal mix proportion, dry–wet cycle tests were carried out in both water and salt solution environments to systematically analyze the improvement effect of steel slag and bentonite slurry on the durability of foam concrete. The results show the following: steel slag can act as fine aggregate to play a skeleton role; after fully mixing with cement paste, it wraps the outer wall of foam, which not only reduces foam breakage but also inhibits the formation of large pores inside the specimen; bentonite slurry can densify the interface transition zone, improve the toughness of foam concrete, and inhibit the initiation and propagation of matrix cracks during the dry–wet cycle process; the composite addition of the two can significantly enhance the water erosion resistance and salt solution erosion resistance of foam concrete. The dry–wet cycle in the salt solution environment causes more severe erosion damage to foam concrete. The main reason is that, after chloride ions invade the cement matrix, they erode hydration products and generate expansive substances, thereby aggravating the matrix damage. Scanning Electron Microscopy (SEM) analysis shows that, whether in water environment or salt solution environment, the fractal dimension of foam concrete decreased slightly with an increasing number of wet–dry cycle times. Based on fractal theory, this study established a compressive strength–porosity prediction model and a dense concrete compressive strength–dry–wet cycle times prediction model, and both models were validated against experimental data from other researchers. The research results can provide technical support for the development of durable foam concrete in harsh environments and the high-value utilization of steel slag solid waste, and are applicable to civil engineering lightweight porous material application scenarios requiring resistance to dry–wet cycle erosion, such as wall bodies and subgrade filling. Full article

With the increase in energy density of power batteries, the risk of thermal runaway significantly increases under extreme working conditions. Therefore, this article proposes a biomimetic liquid cooling plate design based on the fractal structure of fir needle leaf veins, combined with Murray’s mass transfer law, which has significantly improved the heat dissipation performance under extreme working conditions. A multi-field coupling model of electrochemistry fluid heat transfer was established using ANSYS 2022 Fluent, and the synergistic mechanism of environmental temperature, coolant parameters, and heating power was systematically analyzed. Research has found that compared to traditional serpentine channels, leaf vein biomimetic structures can reduce the maximum temperature of batteries by 11.78 °C at a flow rate of 4 m/s and 5000 W/m³. Further analysis reveals that there is a critical flow rate threshold of 2.5 m/s for cooling efficiency (beyond which the effectiveness of temperature reduction decreases by 86%), as well as a thermal saturation temperature of 28 °C (with a sudden increase in temperature rise slope by 284%). Under low-load conditions of 2600 W/m ³, the system exhibits a thermal hysteresis plateau of 40.29 °C. To predict the battery temperature in advance and actively intervene in cooling the battery pack, based on the experimental data and thermodynamic laws of the biomimetic liquid cooling system mentioned above, this study further constructed a support vector machine (SVM) prediction model to achieve real-time and accurate prediction of the highest temperature of the battery pack (validation set average relative error 1.57%), providing new ideas for intelligent optimization of biomimetic liquid cooling systems. Full article

The article presents research on concrete creep in bridge structures, focusing on the influence of concrete mix composition and the use of advanced rheological models with fractional-order derivatives. Laboratory tests were performed on nine mixes varying in blast furnace slag content (0%, 25%, and 75% of cement mass) and air-entrainment. The results were used to calibrate fractal rheological models—Kelvin–Voigt and Huet–Sayegh—where the viscous element was replaced with a fractal element. These models showed high agreement with experimental data and improved the accuracy of creep prediction. Comparison with Eurocode 2 revealed discrepancies up to 64%, especially for slag-free concretes used in prestressed bridge structures. The findings highlight the important role of mineral additives in reducing creep strains and the need to consider individual mix characteristics in design calculations. In the context of modern bridge construction technologies, such as balanced cantilever or incremental launching, reliable modeling of early-age creep is particularly important. The proposed modeling approach may enhance the precision of long-term structural behavior analyses and contribute to improved safety and durability of concrete infrastructure. Full article

Prefabricated Ultra-High-Performance Concrete (UHPC) and cast-in-place Normal Concrete (NC) composite members are increasingly used in bridge engineering because they combine high performance with cost-effectiveness. The bond at the UHPC-NC interface is critical as it directly impacts the composite structure’s safety. This study employed 3D laser scanning acquired the UHPC substrate geometry, utilized fractal dimension analysis to quantify the interface roughness, and adopted the slant shear test to evaluate the effects of retarder application mass and hydration delay duration on roughness and bond strength. The research results indicate that the failure modes of UHPC-NC specimens can be categorized into interface shear failure and NC splitting tensile failure. With the extension of hydration delay duration, both the interface roughness and bond strength show a decreasing trend. The influence of retarder dosage on interface roughness and bond strength exhibits a threshold effect. This study also confirms the effectiveness of fractal dimension as a quantitative tool for characterizing the macroscopic roughness features of the bonding interface. The findings of this paper provide a solid theoretical basis and quantitative support for optimizing key process parameters such as retarder dosage and precisely controlling hydration delay duration, offering significant engineering guidance for enhancing the interface bonding performance of UHPC-NC composite structures. Full article

This study investigated the interplay of bodily degrees of freedom (DoFs) governing the collective variable comprising the center of pressure (CoP) and center of mass (CoM) in postural control through the analytical lens of multiplicative interactions across scales. We employed a task combination involving a wobble board, introducing mechanical instability mainly along the mediolateral (ML) axis and the Trail Making Task (TMT), which imposes precise visual demands primarily along the anteroposterior (AP) axis. Using Multiscale Regression Analysis (MRA), a novel analytical method rooted in Detrended Fluctuation Analysis (DFA), we scrutinized CoP-to-CoM and CoM-to-CoP effects across multiple timescales ranging from $100\mathrm{ms}$ to $10\mathrm{s}$. CoP was computed from ground reaction forces recorded via a force plate, and CoM was derived from full-body 3D motion capture using a biomechanical model. We found that the wobble board attenuated CoM-to-CoP effects across timescales ranging from $100\mathrm{to}400\mathrm{ms}$. Further analysis revealed nuanced changes: while there was an overall reduction, this encompassed an accentuation of CoM-to-CoP effects along the AP axis and a decrease along the ML axis. Importantly, these alterations in CoP’s responses to CoM movements outweighed any nonsignificant effects attributable to the TMT. CoM exhibited no sensitivity to CoP movements, regardless of the visual and mechanical task demands. In addition to identifying the characteristic timescales associated with bodily DoFs in facilitating upright posture, our findings underscore the critical significance of directionally challenging biomechanical constraints, particularly evident in the amplification of CoP-to-CoM effects along the AP axis in response to ML instability. These results underscore the potential of wobble board training to enhance the coordinative and compensatory responses of bodily DoFs to the shifting CoM by prompting appropriate adjustments in CoP, thereby suggesting their application for reinstating healthy CoM–CoP dynamics in clinical populations with postural deficits. Full article

To explore the influence of mine roof on the damage and failure of sandstone surrounding rock under different pressure rates, mechanical experiments with different strain rates were carried out on sandstone rock samples. The strength, deformation, failure, energy and damage characteristics of rock samples with different strain rates were also discussed. The research results show that with the increases in the strain rate, peak stress, and elastic modulus show a monotonically increasing trend, while the peak strain decreases in the reverse direction. At a low strain rate, the proportion of the mass fraction of complete rock blocks in the rock sample is relatively high, and the shape integrity is good, while rock samples with a high strain rate retain more small-sized fragmented rock blocks. This indicates that under high-rate loading, the bifurcation phenomenon of secondary cracks is obvious. The rock samples undergo a failure form dominated by small-sized fragments, with severe damage to the rock samples and significant fractal characteristics of the fragments. At the initial stage of loading, the primary fractures close, and the rock samples mainly dissipate energy in the forms of frictional slip and mineral fragmentation. In the middle stage of loading, the residual fractures are compacted, and the dissipative strain energy keeps increasing continuously. In the later stage of loading, secondary cracks accelerate their expansion, and elastic strain energy is released sharply, eventually leading to brittle failure of the rock sample. Under a low strain rate, secondary cracks slowly expand along the clay–quartz interface and cause intergranular failure of the rock sample. However, a high strain rate inhibits the stress relaxation of the clay, forces the energy to transfer to the quartz crystal, promotes the penetration of secondary cracks through the quartz crystal, and triggers transgranular failure. A constitutive model based on energy damage was further constructed, which can accurately characterize the nonlinear hardening characteristics and strength-deformation laws of rock samples with different strain rates. The evolution process of its energy damage can be divided into the unchanged stage, the slow growth stage, and the accelerated growth stage. The characteristics of this stage reveal the sudden change mechanism from the dissipation of elastic strain energy of rock samples to the unstable propagation of secondary cracks, clarify the cumulative influence of strain rate on damage, and provide a theoretical basis for the dynamic assessment of surrounding rock damage and disaster early warning when the mine roof comes under pressure. Full article

In recent years, droughts and extreme weather events have witnessed increasing frequency around the globe, leading to a growing number of issues related to soil cracking that severely impact the stability of engineering projects and ecological environments. This study mainly investigates the cracking of clay in arid areas of Xinjiang. An experiment is conducted in a climate simulation laboratory, in which we explored the evolution of soil drying cracks under different (straight/curved) boundary constraints. The crack development process is quantitatively described through the use of digital imaging technology and by combining parameters such as crack rate, fractal dimension, and water-holding performance at different boundaries. The following conclusions were drawn: Under curved boundary conditions, cracks expand in a curve-like manner, and the cracks in the boundary area are densely distributed. However, under straight boundary conditions, penetrating straight cracks are formed, and the soil blocks present as regular polygons. Boundary conditions significantly impact the residual water content. Under straight boundary conditions, the residual masses of strongly and weakly bound water are significantly higher than those under curved boundary conditions. The complexity of the crack network under the curved boundary condition is higher, and its fractal dimension is significantly greater than that under the straight boundary condition. A quantitative analysis based on the use of digital image processing technology indicates that the boundary geometry has a significant controlling effect on the crack propagation path. This research provides guidance on the prevention and control of soil engineering cracking and damage in arid regions. Full article

Repeated mining under insufficiently collapsed gobs is a complex process in underground mining and is associated with safety hazards such as ground collapse and subsidence. The effect of layer spacing on the fracture network evolution and fluid transport mechanisms in rock strata during this process has not been systematically studied. In this work, the discrete element method was employed to analyze the fracture development and seepage evolution of surrounding rocks in the Nanliang coal mine across varying layer spacings (5, 20, 35, 50, and 65 m). A systematic evaluation of the rock mass integrity was conducted through damage coefficient quantification. The key findings revealed that an increase in the layer spacing progressively reduced the damage coefficients in both the overburden strata above the goaf and in the interlayer formations ahead of the working face, accompanied by reduced fracture propagation intensity. Shear failure mechanisms dominated throughout the mining process. Fractal characteristics of the fractures intensified with the advance of the working face, while the hydraulic conductivity and interstitial pressure in the interlayer strata exhibited declining trends with reduced attenuation rates. Our findings provide critical insights for ensuring the safety and improving the efficiency of repeated mining under insufficiently collapsed gobs. Full article

To explore how the water–cement ratio affects the mechanical behavior of concrete subjected to freeze–thaw cycles, four sets of concrete samples with water–cement ratios of 0.41, 0.44, 0.47, and 0.50 were prepared for laboratory analysis. These samples underwent varying numbers of freeze–thaw cycles (0, 10, 20, and 30) before being tested using the split Hopkinson pressure bar (SHPB) system for dynamic compression. The experimental data show that the mass of the concrete specimens follows a non-monotonic trend during freeze–thaw cycling, initially rising and then gradually declining. Simultaneously, key dynamic mechanical properties, such as compressive strength and elastic modulus, markedly deteriorate, as evidenced by rightward shifts in the stress–strain curves. Importantly, the extent of degradation differs notably depending on the water–cement ratio. Additional analysis highlights a strong association between the fractal nature of the fracture patterns and the effects of freeze–thaw cycles: under consistent freeze–thaw conditions not only does the fractal dimension consistently increase with the number of cycles, but it also positively correlates with the water–cement ratio. Full article

To address the low resource utilization of copper tailings and high environmental impact of conventional river sand, this study innovatively integrates Box–Behnken design (BBD) with fractal theory to systematically investigate the performance optimization mechanisms of cement mortar incorporating copper tailings sand. A three-factor interaction model was developed through BBD experimental design, considering water–cement ratio (0.38–0.48), replacement ratio (10–30%), and binder–sand ratio (0.3–0.4), to elucidate the macroscopic performance evolution under multiparameter coupling effects. Fractal dimension analysis was employed to quantitatively characterize microstructural evolution. Experimental results demonstrate that the optimal parameters (water–cement ratio: 0.43, replacement ratio: 20%, binder–sand ratio: 0.35) yield superior performance, with 28-day compressive/flexural strengths reaching 61.88/7.14 MPa (12.3%/9.8% enhancement over the control group), and sulfate attack resistance showing 0.74% mass loss after 30 cycles. Microstructural analysis reveals reduced fractal dimension (D = 2.31) in copper tailings-modified specimens, indicating improved pore structure homogeneity. The enhanced performance is attributed to synergistic effects of micro-aggregate filling and pozzolanic reaction-driven C-S-H gel densification. This research establishes a novel multiscale methodology overcoming the limitations of conventional single-factor analysis, providing theoretical and technical support for high-value utilization of industrial solid wastes in construction materials. Full article

The geometry of rock mass fractures is typically characterized through geological and geotechnical investigations. Detailed descriptions of granitic host rock can yield valuable data for constructing fracture network models. However, significant discrepancies often arise between data representing the mechanical and hydraulic properties of rocks. At the study site, fracture geometry data were gathered through surface and underground surveying, borehole logging, and underground mapping. Three-dimensional photogrammetry was utilized alongside traditional rock mass classification methods (Q-system, RMR, GSI) to derive key parameters of fracture networks, such as orientation, size, and intensity. This study focuses on Rock Quality Designation (RQD), a measure of fracture density derived from tunnel face mapping. Findings indicate that variations in fracture frequency are significantly affected by how fracture sets are defined and by the orientation distribution of fractures. Furthermore, using the D parameter (the 2D fractal dimension of fracture frequency) as a validation measure for RQD may lead to misleading interpretations if it aggregates fracture sets on the tunnel scale. Full article

Corals in the Galápagos present diverse reef configurations from biogenic coral reefs to coral communities growing on rocks and sand. These corals have experienced decades of disturbances including recurring El Niño and mass bleaching events. However, traditional methods in ecology have limited capacity in describing coral demographic trends across large spatial scales. Photogrammetry—a form of 3D imaging, has emerged over the past decade as a popular method for benthic surveys. However, the majority of protocols in the field utilize the 2D products of photogrammetry, ignoring overhangs and leaving significant information unexploited. We surveyed seven reef sites across the archipelago using underwater photogrammetry and developed new methods for 3D annotation and fractal dimension calculation. Our findings reveal variation in coral cover, diversity, and structural complexity across the archipelago. Our results align with previous studies in the region and add important information on reef structural complexity which was not measured here before. We release a unique dataset: Galápagos_3D, including seven 3D models and over 17,000 annotated images. This study establishes an important baseline for long-term monitoring, research, and conservation in the Galápagos, potentially informing evidence-based policies and advancing our understanding of coral resilience and recovery. Full article

Hydraulic concrete is subject to severe durability challenges when abraded by the high-speed flow of sandy water. Conventional concrete frequently needs to be repaired because of its high brittleness and insufficient abrasion resistance, while granular rubber can easily be dislodged from the matrix during abrasion, forming a new source of abrasion and increasing the damage to the matrix. For this reason, we used fibrous rubber concrete to systematically study the mechanisms of the influence of the dosage of nitrile rubber (5%, 10%, and 15%) and fiber length (6, 12, and 18 mm) on resistance to impact and abrasion performance. Through mechanical tests, underwater steel ball abrasion tests, three-dimensional morphology measurements, and fractal dimension analysis, the law behind the damage evolution of fibrous rubber concrete was revealed. The results show that concrete with 15% NBR and 12 mm fibers yielded the best performance, and its 144-hour abrasion resistance reached 25.0 h/(kg/m²), which is 163.7% higher than that for the baseline group. Fractal dimension analysis (D = 2.204 for the optimum group vs. 2.356 for the benchmark group) showed that the fiber network effectively suppressed surface damage extension. The long-term mass loss rate was only 2.36% (5.82% for the benchmark group), and the elastic energy dissipation mechanism remained stable under dynamic loading. The results of a microanalysis showed that the high surface roughness of NBR enhances interfacial bonding, which synergizes with crack bridging and stress dispersion and, thus, forms a multiscale anti-impact abrasion barrier. This study provides a new material solution for the design of durable concrete for use in high-impact and high-abrasion environments, which combines mechanical property preservation and resource recycling value. However, we did not systematically examine the evolution of the performance of fiber rubber concrete concrete under long-term environmental coupling conditions, such as freeze–thaw cycles, ultraviolet aging, or chemical attacks, and there are limitations to our assessment of full life-cycle durability. Full article

The most hydrodynamic swimming position occurs with the head submerged, highlighting the benefit of reduced breathing frequency for efficiency. This study aimed to characterize and compare kinematics between two breaststroke breathing patterns—breathing every cycle and breathing every two cycles—while also analyzing intra-cyclic velocity variation (dv) and fractal dimension. In the breathing every cycle pattern, each cycle included a breath. In the breathing every cycle pattern, swimmers breathed once per cycle. In the breathing every two cycles pattern, breathing occurred every second cycle, resulting in three types of cycles: breathing, non-breathing, and the breathing cycle following a non-breathing cycle. To ensure familiarity with the new breathing pattern, swimmers underwent a six-week intervention program. They then performed three maximal 25 m bouts in each breathing pattern. Kinematic data were collected using a dual-media optoelectronic system (Qualisys AB, Sweden), integrating underwater and dry-land camera recordings. The results showed minimal differences between the three cycle types. The non-breathing cycle had the shallowest and deepest head positions, the lowest horizontal head amplitude out of water, and the smallest vertical head amplitude. It also had the fastest maximum vertical velocity of the feet and maximum center of mass velocity in the swimming direction. Full article