Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different r...Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different regions and gullies reveal that cumulative curve of grain composition, in particular for debris flows of high density, ρ5〉2 g/cm^3, can be fitted well by exponential function with exponents varying with regions and gullies. Debris flows fall into a narrow-valued domain of the exponent, as evidenced by Jiangjiagou Gully （JJG） with high occurrence frequency of debris flows. Furthermore, fractality of grain composition and porosity have been derived from cumulative curves in a certain size range, a range that determines the upper limit of grains constituting the matrix of debris flows. One can conclude that fractal structure of porosity plays crucial roles in soil fluidization that initiates debris flows, and debris flows occur at some range of fractal dimension, in coincidence with field observations.展开更多
On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.T...On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.These results are compared with experimental and calculated data of other authors.The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging,as a manifestation of the fractality property of living systems.展开更多
<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exp...<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exponent can be explained by optimizing the overall energy distribution in the tumor, assuming that the target is four-dimensional. There are two possible ways of approximating the metabolic rate of the malignant tumor: 1) the volume blood-supply remains, but the surface and the length of the vessel network are modified;or 2) assuming that the malignant cell clusters try to maximize their metabolic rate to energize their proliferation by the longer length of the vessels. Our objective is to study how vascular fractality changes due to the greater demand for nutrients due to the proliferation of cancerous tissue. <strong>Results: </strong>It is shown that when a malignant tumor remains in expected four-dimensional volumetric conditions, it has a lower metabolic rate than the maximal metabolic potential in the actual demand of the proliferating cancer tissue. By maximizing the metabolic rate in malignant conditions, the allometric exponent will be smaller than 3/4, so the observed “dimensionality” of the metabolic rate versus mass becomes greater than four. The first growing period is exponential and keeps the “four-dimensional volume”, but the growth process turns to the sigmoidal phase in higher metabolic demand, and the tumor uses other optimizing strategies, further lowering the scaling exponent of metabolic rate. <strong>Conclusion:</strong> It is shown that a malignant cellular cluster changes its metabolic scaling exponent when maximizing its energy intake in various alimentary conditions.展开更多
We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientat...We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientated sensitivity of the telescope. Meanwhile, on the grounds of NASA Science Working Group Report in 1984, we reexamine the strategy of Search for Extraterrestrial Intelligence(SETI).A mathematical analysis of the radar equation will be performed in the first section, aiming to make it convenient to design a receiver system that can detect activities of an extraterrestrial civilization, according to the observable region of the narrowband. Taking advantage of the inherent potential of FAST, we simulate the theoretical detection of a Kardashev Type I civilization by a snowflake-selected reflecting area(Drake et al.).展开更多
To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with g...To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.展开更多
Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and intro...Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.展开更多
In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth su...In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surface or a real crack profile,the crack is taken as a fractal one,and then the real asymptotic form at the crack tip is developed by applying Griffith's energy balance principle and fractal geometry.Through the developed asymptotic form,it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.展开更多
The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution ki...The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.展开更多
Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregat...Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregate.The five combinations,in which 10%,32%,and 48%Wollastonite were added,were made for scanning using both scanning electron microscopy(SEM)and computed tomography scan technology(CT).Then,the 2D SEM pictures and the 3D pore distribution curves are obtained before and after the freezing and thawing processes,where the micro-pores in the CCM materials are shown.The fractal dimension is used to quantify the topography image in two dimensions,as well as the pore distribution in three dimensions.This method allows for the determination of both surface porosity and volume porosity,both of which show an increase in response to an escalation of freeze-thaw cycles.It is also found that the micro-damage in the concrete is of self-similarity,and in the context of the fractal dimension,the pore evolution can be quantitatively characterized across different sizes,ranging from local to global levels,before and after freezing and thawing.展开更多
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal...As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.展开更多
The accurate identification of microporosity is crucial for the characterization of hydrocarbon reservoir permeability and production.Scanning electron microscopy(SEM)is among the limited number of methods available t...The accurate identification of microporosity is crucial for the characterization of hydrocarbon reservoir permeability and production.Scanning electron microscopy(SEM)is among the limited number of methods available to directly observe the microscopic structure of the hydrocarbon reservoir rocks.Nevertheless,precise segmentation of microscopic pores at different depths in SEM images remains an unsolved challenge,known as the‘depth-related resolution loss'problem.Therefore,in this study,a 3D reconstruction technique for regions of interest(ROI)was developed for in-depth pixel analysis and differentiation among various depths of SEM images.The processed SEM images,together with the processing outcomes of this technique,were used as the input database to train a stochastic depth with multi-channel residual pathways(SdstMcrp)deep learning model programmed in Python to develop a tool for segmenting the microscopic pore spaces in SEM images obtained from the Beibuwan Basin.The more accurate segmentation helped to detect an average of 1.2 times more microporosity in SEM images,accounting for about 1.6 times more pixels and 1.2 times more pore surface area.Finally,the impact of the accurate segmentation on the calculation of permeability,a significant reservoir production property,was investigated using fractal geometry models and sensitivity analysis.The results showed that the obtained permeability values would vary by a factor of 6,which represents a considerable difference.These findings demonstrate that the proposed models can effectively identify features across a wide range of grayscale values in SEM images.展开更多
To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with...To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with rectangular,circular,and D-shaped holes.Asθincreases from 0°to 60°in the rectangular hole,the left failure location shifts from the left corner to the left sidewall,the left corner,and then the floor,while the right failure location shifts from the right corner to the right sidewall,right roof corner,and then the roof.Furthermore,the initial failure vertical stress first decreases and then increases.In comparison,the failure severity in the rectangular hole decreases for variousθvalues as 30°>45°>60°>0°.With increasingθ,the fractal dimension(D)of rock slices first increases and then decreases.For the rectangular and D-shaped holes,whenθ=0°,30°,and 90°,D for the rectangular hole is less than that of the D-shaped hole.Whenθ=45°and 60°,D for the rectangular hole is greater than that of the D-shaped hole.Theoretical analysis indicates that the stress concentration at the rectangular and D-shaped corners is greater than the other areas.The failure location rotates with the rotation ofθ,and the failure occurs on the side with a high concentration of compressive stress,while the side with the tensile and compressive stresses remains relatively stable.Therefore,the fundamental reason for the rotation of failure location is the rotation of stress concentration,and the external influencing factor is the rotation ofθ.展开更多
Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature ...Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.展开更多
The predictive model and design of heavy-duty metal rubber shock absorber for the powertrains of heavy-load mining vehicles were investigated.The microstructural characteristics of the wire mesh were elucidated using ...The predictive model and design of heavy-duty metal rubber shock absorber for the powertrains of heavy-load mining vehicles were investigated.The microstructural characteristics of the wire mesh were elucidated using fractal graphs.A numerical model based on virtual fabrication technique was established to propose a design scheme for the wire mesh component.Four sets of wire mesh shock absorbers with various relative densities were prepared and a predictive model based on these relative densities was established through mechanical testing.To further enhance the predictive accuracy,a variable transposition fitting method was proposed to refine the model.Residual analysis was employed to quantitatively validate the results against those obtained from an experimental control group.The results show that the improved model exhibits higher predictive accuracy than the original model,with the determination coefficient(R^(2))of 0.9624.This study provides theoretical support for designing wire mesh shock absorbers with reduced testing requirements and enhanced design efficiency.展开更多
Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potentia...Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.展开更多
Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the...Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the self-affine,self-similarity,and iterative generation characteristics of fractal geometry,the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane,facade,and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre.The research shows that the geometric complexity of Wuzhen Grand Theater in the“fifth façade”and multi-faceted façade is significantly higher than that of Harbin Grand Theater,and its morphological design is more inclined to echo the texture of the surrounding water towns.The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines.The research proves that fractal dimension can effectively quantify the complexity of architectural form,provide a scientific basis for the form design,environmental integration,and form interpretation of performance architecture,and expand the mathematical analysis dimension of architectural form design.展开更多
Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishe...Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.展开更多
WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphol...WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphological Division and Fractal Models”,Acta Geologica Sinica-English Edition(Accepted Article):https://doi.org/10.1111/1755-6724.15094.展开更多
To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based...To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.展开更多
基金N ationalN aturalScience Foundation ofChina,N o.40101001N o.40025103
文摘Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different regions and gullies reveal that cumulative curve of grain composition, in particular for debris flows of high density, ρ5〉2 g/cm^3, can be fitted well by exponential function with exponents varying with regions and gullies. Debris flows fall into a narrow-valued domain of the exponent, as evidenced by Jiangjiagou Gully （JJG） with high occurrence frequency of debris flows. Furthermore, fractality of grain composition and porosity have been derived from cumulative curves in a certain size range, a range that determines the upper limit of grains constituting the matrix of debris flows. One can conclude that fractal structure of porosity plays crucial roles in soil fluidization that initiates debris flows, and debris flows occur at some range of fractal dimension, in coincidence with field observations.
文摘On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.These results are compared with experimental and calculated data of other authors.The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging,as a manifestation of the fractality property of living systems.
文摘<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exponent can be explained by optimizing the overall energy distribution in the tumor, assuming that the target is four-dimensional. There are two possible ways of approximating the metabolic rate of the malignant tumor: 1) the volume blood-supply remains, but the surface and the length of the vessel network are modified;or 2) assuming that the malignant cell clusters try to maximize their metabolic rate to energize their proliferation by the longer length of the vessels. Our objective is to study how vascular fractality changes due to the greater demand for nutrients due to the proliferation of cancerous tissue. <strong>Results: </strong>It is shown that when a malignant tumor remains in expected four-dimensional volumetric conditions, it has a lower metabolic rate than the maximal metabolic potential in the actual demand of the proliferating cancer tissue. By maximizing the metabolic rate in malignant conditions, the allometric exponent will be smaller than 3/4, so the observed “dimensionality” of the metabolic rate versus mass becomes greater than four. The first growing period is exponential and keeps the “four-dimensional volume”, but the growth process turns to the sigmoidal phase in higher metabolic demand, and the tumor uses other optimizing strategies, further lowering the scaling exponent of metabolic rate. <strong>Conclusion:</strong> It is shown that a malignant cellular cluster changes its metabolic scaling exponent when maximizing its energy intake in various alimentary conditions.
基金supported by the National Natural Science Foundation of China(Grant No.11929301)National Key R&D Program of China(2017YFA0402600)。
文摘We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientated sensitivity of the telescope. Meanwhile, on the grounds of NASA Science Working Group Report in 1984, we reexamine the strategy of Search for Extraterrestrial Intelligence(SETI).A mathematical analysis of the radar equation will be performed in the first section, aiming to make it convenient to design a receiver system that can detect activities of an extraterrestrial civilization, according to the observable region of the narrowband. Taking advantage of the inherent potential of FAST, we simulate the theoretical detection of a Kardashev Type I civilization by a snowflake-selected reflecting area(Drake et al.).
基金Funded by the National Natural Science Foundation of China(Nos.5226804252468035)。
文摘To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.
基金financially supported by the China Scholarship Council(CSC)。
文摘Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.
基金Supported by the National Natural Science Foundation of China (Grant Nos.50539030,50539010,50539110 and 50579010)the National Science and Technology Supporting Program (Grant No.2006BAC14B03)the National Science Foundation of Hohai University (Grant No.2008426811)
文摘In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surface or a real crack profile,the crack is taken as a fractal one,and then the real asymptotic form at the crack tip is developed by applying Griffith's energy balance principle and fractal geometry.Through the developed asymptotic form,it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.
基金supported by Independent Research Project of State Key Laboratory of Advanced Special Steel,Shanghai Key Laboratory of Advanced Ferrometallurgy,Shanghai University(SKLASS-2023-Z13)the Science and Technology Commission of Shanghai Municipality(No.19DZ2270200)+1 种基金A portion of the work was performed at US National High Magnetic Field Laboratory,which is supported by the National Science Foundation(Cooperative Agreement No.DMR-1157490 and DMR-1644779)the State of Florida.Thanks also to Mary Tyler for editing.
文摘The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.
文摘Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregate.The five combinations,in which 10%,32%,and 48%Wollastonite were added,were made for scanning using both scanning electron microscopy(SEM)and computed tomography scan technology(CT).Then,the 2D SEM pictures and the 3D pore distribution curves are obtained before and after the freezing and thawing processes,where the micro-pores in the CCM materials are shown.The fractal dimension is used to quantify the topography image in two dimensions,as well as the pore distribution in three dimensions.This method allows for the determination of both surface porosity and volume porosity,both of which show an increase in response to an escalation of freeze-thaw cycles.It is also found that the micro-damage in the concrete is of self-similarity,and in the context of the fractal dimension,the pore evolution can be quantitatively characterized across different sizes,ranging from local to global levels,before and after freezing and thawing.
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
基金financially supported by the National Key R&D Program of China(No.2022YFE0121300)the National Natural Science Foundation of China(No.52374376)the Introduction Plan for High-end Foreign Experts(No.G2023105001L)。
文摘As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.
基金the Natural Science Foundation of Shandong Province of China(Nos.ZR2022QD080 , ZR2025MS575)the National Natural Science Foundation of China(Nos.W25322063,42250410333,52250410357)+1 种基金the Fundamental Research Funds for the Central Universities,CHD(No.300102263103)the Young Talent Fund of Association for Science and Technology in Shaanxi,China(No.20230703)。
文摘The accurate identification of microporosity is crucial for the characterization of hydrocarbon reservoir permeability and production.Scanning electron microscopy(SEM)is among the limited number of methods available to directly observe the microscopic structure of the hydrocarbon reservoir rocks.Nevertheless,precise segmentation of microscopic pores at different depths in SEM images remains an unsolved challenge,known as the‘depth-related resolution loss'problem.Therefore,in this study,a 3D reconstruction technique for regions of interest(ROI)was developed for in-depth pixel analysis and differentiation among various depths of SEM images.The processed SEM images,together with the processing outcomes of this technique,were used as the input database to train a stochastic depth with multi-channel residual pathways(SdstMcrp)deep learning model programmed in Python to develop a tool for segmenting the microscopic pore spaces in SEM images obtained from the Beibuwan Basin.The more accurate segmentation helped to detect an average of 1.2 times more microporosity in SEM images,accounting for about 1.6 times more pixels and 1.2 times more pore surface area.Finally,the impact of the accurate segmentation on the calculation of permeability,a significant reservoir production property,was investigated using fractal geometry models and sensitivity analysis.The results showed that the obtained permeability values would vary by a factor of 6,which represents a considerable difference.These findings demonstrate that the proposed models can effectively identify features across a wide range of grayscale values in SEM images.
基金supported by the National Natural Science Foundation of China (Grant Nos.52304227 and 52104133)Scientific and Technological Research Platform for Disaster Prevention and Control of Deep Coal Mining (Anhui University of Science and Technology) (Grant No.DPDCM2208).
文摘To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with rectangular,circular,and D-shaped holes.Asθincreases from 0°to 60°in the rectangular hole,the left failure location shifts from the left corner to the left sidewall,the left corner,and then the floor,while the right failure location shifts from the right corner to the right sidewall,right roof corner,and then the roof.Furthermore,the initial failure vertical stress first decreases and then increases.In comparison,the failure severity in the rectangular hole decreases for variousθvalues as 30°>45°>60°>0°.With increasingθ,the fractal dimension(D)of rock slices first increases and then decreases.For the rectangular and D-shaped holes,whenθ=0°,30°,and 90°,D for the rectangular hole is less than that of the D-shaped hole.Whenθ=45°and 60°,D for the rectangular hole is greater than that of the D-shaped hole.Theoretical analysis indicates that the stress concentration at the rectangular and D-shaped corners is greater than the other areas.The failure location rotates with the rotation ofθ,and the failure occurs on the side with a high concentration of compressive stress,while the side with the tensile and compressive stresses remains relatively stable.Therefore,the fundamental reason for the rotation of failure location is the rotation of stress concentration,and the external influencing factor is the rotation ofθ.
基金supported by The National Natural Science Foundation of China(Grant Nos.12272411 and 42007259).
文摘Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.
基金National Natural Science Foundation of China(12262028)Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT22085)Inner Mongolia Autonomous Region Science and Technology Plan Project(2021GG0437)。
文摘The predictive model and design of heavy-duty metal rubber shock absorber for the powertrains of heavy-load mining vehicles were investigated.The microstructural characteristics of the wire mesh were elucidated using fractal graphs.A numerical model based on virtual fabrication technique was established to propose a design scheme for the wire mesh component.Four sets of wire mesh shock absorbers with various relative densities were prepared and a predictive model based on these relative densities was established through mechanical testing.To further enhance the predictive accuracy,a variable transposition fitting method was proposed to refine the model.Residual analysis was employed to quantitatively validate the results against those obtained from an experimental control group.The results show that the improved model exhibits higher predictive accuracy than the original model,with the determination coefficient(R^(2))of 0.9624.This study provides theoretical support for designing wire mesh shock absorbers with reduced testing requirements and enhanced design efficiency.
文摘Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.
基金Jiangxi Province Intelligent Building Engineering Research Center Open Fund Project,Fractal Theory of Performing Architectural Form Design Research(Project No.:EZ202111440).
文摘Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the self-affine,self-similarity,and iterative generation characteristics of fractal geometry,the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane,facade,and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre.The research shows that the geometric complexity of Wuzhen Grand Theater in the“fifth façade”and multi-faceted façade is significantly higher than that of Harbin Grand Theater,and its morphological design is more inclined to echo the texture of the surrounding water towns.The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines.The research proves that fractal dimension can effectively quantify the complexity of architectural form,provide a scientific basis for the form design,environmental integration,and form interpretation of performance architecture,and expand the mathematical analysis dimension of architectural form design.
基金funded by the National Key R&D Program of China,China(Grant No.2023YFB4005500)National Natural Science Foundation of China,China(Grant Nos.52379113 and 52379114).
文摘Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.
文摘WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphological Division and Fractal Models”,Acta Geologica Sinica-English Edition(Accepted Article):https://doi.org/10.1111/1755-6724.15094.
基金funded by the National Key Research and Development ProgramFund for Young Scientists(No.2021YFC2900400)+5 种基金the National Natural Science Foundation of China(No.52304123)Fundamental Research Funds for the Central Universities(No.2024CDJXY025)Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(No.CSTB2024TIAD-CYKJCXX0016)Postdoctoral Research Foundation of China(No.2023M730412)Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(No.GZB20230914)Chongqing Outstanding Youth Science Foundation Program(No.CSTB2023NSCQ-JQX0027)。
文摘To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.
