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
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 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
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
This research employs micro-CT scanning technology to analyze the porosity,pore fractal dimension,and spatial variability of sandstone preheated to 600℃ and subsequently cooled in water at varying temperatures(20℃,6...This research employs micro-CT scanning technology to analyze the porosity,pore fractal dimension,and spatial variability of sandstone preheated to 600℃ and subsequently cooled in water at varying temperatures(20℃,60℃,100℃).The study investigates the mechanisms by which various factors influence thermal shock damage,focusing on the effects of cooling water temperature and the boiling phase transition.The objective is to develop a method for characterizing thermal shock damage that considers spatial variability.The findings indicate that thermal shock damage is limited to a shallow depth beneath the surface,with increased severity near the surface.The boiling phase transition significantly enhances the convective heat transfer coefficient,resulting in substantially higher thermal shock damage when cooled with 100℃ boiling water compared to 20℃ and 60℃ water.Furthermore,for the entire specimen,heating damage exceeds thermal shock damage,and the influence of thermal shock diminishes as specimen size increases.This study addresses the limitations of traditional methods for assessing thermal shock damage that disregard spatial variability and provides practical guidance for engineering projects to manage thermal shock damage more effectively.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
Safe operation of underground reservoirs in coal mines is crucial for the coordinated exploitation of coal and water resources in western China.Mine water infiltration significantly influences the stability of the coa...Safe operation of underground reservoirs in coal mines is crucial for the coordinated exploitation of coal and water resources in western China.Mine water infiltration significantly influences the stability of the coal pillar.Therefore,laboratory tests were systematically carried out on coal from the Daliuta Coal Mine in Northwest China.Samples were taken in the vertical and parallel bedding directions and soaked for 0 d,2 d,4 d,or 16 d.In this study,atomic absorption spectroscopy(AAS),X-ray diffraction(XRD),and scanning electron microscopy(SEM)were used to analyze the variations in the water absorption characteristics and corresponding internal structure of the coal.Uniaxial compression tests and synchronous acoustic emission(AE)monitoring revealed the sample failure process and mechanical properties of the samples.Finally,the time-and frequency-domain characteristics of the AE signal were comprehensively analyzed using fractal dimension,fast Fourier transform,and cluster analysis.The strength and elastic modulus demonstrate significant anisotropy with different bedding planes and reveal the existence of the optimum water content.Specifically,the sample strength increases after 2 d of immersion,with increments of 23.3% and 0.6% for the vertical and parallel bedding samples,and decreases after 16 d of immersion,with decreases of 29% and 45% for the vertical and parallel samples,respectively.Additionally,shear cracks account for over 60% during the damage development of the samples.The proportion of tensile cracks is higher for samples with longer immersion times and parallel bedding planes.This research provides a theoretical basis for stability evaluation and protection of coal pillars in underground reservoirs using the AE technique.展开更多
To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(...To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(AE)monitoring is employed to analyze key parameters,establishing a multiparameter quantitative system for CCR fracture processes.The impact of lithological homogeneity on fracture evolution and energy migration is examined.Results show that CCR exhibits a three-stage mechanical response:weak contact,strong contact,and post-peak stages,each with distinct crack evolution patterns.A positive correlation is found between lithological homogeneity and tensile crack proportion.No significant correlation is observed between AE average frequency(AF)and AE counts across different lithological CCR;however,peak frequency(PF)displays clear lithology-dependent characteristics.The regulatory effect of the rock homogeneity coefficient(φ)on crack deriva tion mechanisms is quantfied,yielding mathematical relationships between fracture strength(f),crack propagation path angle(β),crack fractal dimension(D),andφ.The study highlights how different fracture modes alter energy migration pathways,confirming the coupling effect of grain distribution on mechanical response and crack propagation,and the influence of parameterφon critical energy release zones.These findings offer new insights into CCR failure mechanisms for mining safety.展开更多
Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we prop...Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we propose the FractalNet-LSTM model,which combines fractal convolutional units with recurrent long short-term memory(LSTM)layers to model time series efficiently.To test the effectiveness of the model,data with complex structures and patterns,in particular,with seasonal and cyclical effects,were used.To better demonstrate the obtained results and the formed conclusions,the model performance was shown on the datasets of electricity consumption,sunspot activity,and Spotify stock price.The result showed that the proposed model outperforms traditional approaches at medium forecasting horizons and demonstrates high accuracy for data with long-term and cyclical dependencies.However,for financial data with high volatility,the model’s efficiency decreases at long forecasting horizons,indicating the need for further adaptation.The findings suggest further adaptation.The findings suggest that integrating fractal properties into neural network architecture improves the accuracy of time series forecasting and can be useful for developing more accurate and reliable forecasting systems in various industries.展开更多
The flow characteristics of coalbed methane(CBM)are influenced by the coal rock fracture network,which serves as the primary gas transport channel.This has a significant effect on the permeability performance of coal ...The flow characteristics of coalbed methane(CBM)are influenced by the coal rock fracture network,which serves as the primary gas transport channel.This has a significant effect on the permeability performance of coal reservoirs.In any case,the traditional techniques of coal rock fracture observation are unable to precisely define the flow of CBM.In this study,coal samples were subjected to an in situ loading scanning test in order to create a pore network model(PNM)and determine the pore and fracture dynamic evolution law of the samples in the loading path.On this basis,the structural characteristic parameters of the samples were extracted from the PNM and the impact on the permeability performance of CBM was assessed.The findings demonstrate that the coal samples'internal porosity increases by 2.039%under uniaxial loading,the average throat pore radius increases by 205.5 to 36.1μm,and the loading has an impact on the distribution and morphology of the pores in the coal rock.The PNM was loaded into the finite element program COMSOL for seepage modeling,and the M3 stage showed isolated pore connectivity to produce microscopic fissures,which could serve as seepage channels.In order to confirm the viability of the PNM and COMSOL docking technology,the streamline distribution law of pressure and velocity fields during the coal sample loading process was examined.The absolute permeability of the coal samples was also obtained in order for comparison with the measured results.The macroscopic CBM flow mechanism in complex lowpermeability coal rocks can be revealed through three-dimensional reconstruction of the microscopic fracture structure and seepage simulation.This study lays the groundwork for the fine description and evaluation of coal reservoirs as well as the precise prediction of gas production in CBM wells.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.
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.
基金financially supported by the National Natural Science Foundation of China(Grant No.51874207)the Natural Science Foundation of Shanxi Province(Grant Nos.202303021211042 and 202303011222006).
文摘This research employs micro-CT scanning technology to analyze the porosity,pore fractal dimension,and spatial variability of sandstone preheated to 600℃ and subsequently cooled in water at varying temperatures(20℃,60℃,100℃).The study investigates the mechanisms by which various factors influence thermal shock damage,focusing on the effects of cooling water temperature and the boiling phase transition.The objective is to develop a method for characterizing thermal shock damage that considers spatial variability.The findings indicate that thermal shock damage is limited to a shallow depth beneath the surface,with increased severity near the surface.The boiling phase transition significantly enhances the convective heat transfer coefficient,resulting in substantially higher thermal shock damage when cooled with 100℃ boiling water compared to 20℃ and 60℃ water.Furthermore,for the entire specimen,heating damage exceeds thermal shock damage,and the influence of thermal shock diminishes as specimen size increases.This study addresses the limitations of traditional methods for assessing thermal shock damage that disregard spatial variability and provides practical guidance for engineering projects to manage thermal shock damage more effectively.
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 National Natural Science Foundation of China(Grant Nos.52174084 and U23B20146)the Open Fund for State Key Laboratory of Water Resource Protection and Utilization in Coal Mining(Grant No.WPUKFJJ2022-07)。
文摘Safe operation of underground reservoirs in coal mines is crucial for the coordinated exploitation of coal and water resources in western China.Mine water infiltration significantly influences the stability of the coal pillar.Therefore,laboratory tests were systematically carried out on coal from the Daliuta Coal Mine in Northwest China.Samples were taken in the vertical and parallel bedding directions and soaked for 0 d,2 d,4 d,or 16 d.In this study,atomic absorption spectroscopy(AAS),X-ray diffraction(XRD),and scanning electron microscopy(SEM)were used to analyze the variations in the water absorption characteristics and corresponding internal structure of the coal.Uniaxial compression tests and synchronous acoustic emission(AE)monitoring revealed the sample failure process and mechanical properties of the samples.Finally,the time-and frequency-domain characteristics of the AE signal were comprehensively analyzed using fractal dimension,fast Fourier transform,and cluster analysis.The strength and elastic modulus demonstrate significant anisotropy with different bedding planes and reveal the existence of the optimum water content.Specifically,the sample strength increases after 2 d of immersion,with increments of 23.3% and 0.6% for the vertical and parallel bedding samples,and decreases after 16 d of immersion,with decreases of 29% and 45% for the vertical and parallel samples,respectively.Additionally,shear cracks account for over 60% during the damage development of the samples.The proportion of tensile cracks is higher for samples with longer immersion times and parallel bedding planes.This research provides a theoretical basis for stability evaluation and protection of coal pillars in underground reservoirs using the AE technique.
基金support from the National Key Research and Development Plan Project(No.2022YFC3004700)the National Natural Science Foundation of China(No.52374241)+1 种基金Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX24_2924)Graduate Innovation Program of China University of Mining and Technology(No.2024WLKXJ151).
文摘To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(AE)monitoring is employed to analyze key parameters,establishing a multiparameter quantitative system for CCR fracture processes.The impact of lithological homogeneity on fracture evolution and energy migration is examined.Results show that CCR exhibits a three-stage mechanical response:weak contact,strong contact,and post-peak stages,each with distinct crack evolution patterns.A positive correlation is found between lithological homogeneity and tensile crack proportion.No significant correlation is observed between AE average frequency(AF)and AE counts across different lithological CCR;however,peak frequency(PF)displays clear lithology-dependent characteristics.The regulatory effect of the rock homogeneity coefficient(φ)on crack deriva tion mechanisms is quantfied,yielding mathematical relationships between fracture strength(f),crack propagation path angle(β),crack fractal dimension(D),andφ.The study highlights how different fracture modes alter energy migration pathways,confirming the coupling effect of grain distribution on mechanical response and crack propagation,and the influence of parameterφon critical energy release zones.These findings offer new insights into CCR failure mechanisms for mining safety.
文摘Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we propose the FractalNet-LSTM model,which combines fractal convolutional units with recurrent long short-term memory(LSTM)layers to model time series efficiently.To test the effectiveness of the model,data with complex structures and patterns,in particular,with seasonal and cyclical effects,were used.To better demonstrate the obtained results and the formed conclusions,the model performance was shown on the datasets of electricity consumption,sunspot activity,and Spotify stock price.The result showed that the proposed model outperforms traditional approaches at medium forecasting horizons and demonstrates high accuracy for data with long-term and cyclical dependencies.However,for financial data with high volatility,the model’s efficiency decreases at long forecasting horizons,indicating the need for further adaptation.The findings suggest further adaptation.The findings suggest that integrating fractal properties into neural network architecture improves the accuracy of time series forecasting and can be useful for developing more accurate and reliable forecasting systems in various industries.
基金The National Key R&D Program,Grant/Award Number:2023YFC2907203National Natural Science Foundation of China,Grant/Award Numbers:52374121,52074121。
文摘The flow characteristics of coalbed methane(CBM)are influenced by the coal rock fracture network,which serves as the primary gas transport channel.This has a significant effect on the permeability performance of coal reservoirs.In any case,the traditional techniques of coal rock fracture observation are unable to precisely define the flow of CBM.In this study,coal samples were subjected to an in situ loading scanning test in order to create a pore network model(PNM)and determine the pore and fracture dynamic evolution law of the samples in the loading path.On this basis,the structural characteristic parameters of the samples were extracted from the PNM and the impact on the permeability performance of CBM was assessed.The findings demonstrate that the coal samples'internal porosity increases by 2.039%under uniaxial loading,the average throat pore radius increases by 205.5 to 36.1μm,and the loading has an impact on the distribution and morphology of the pores in the coal rock.The PNM was loaded into the finite element program COMSOL for seepage modeling,and the M3 stage showed isolated pore connectivity to produce microscopic fissures,which could serve as seepage channels.In order to confirm the viability of the PNM and COMSOL docking technology,the streamline distribution law of pressure and velocity fields during the coal sample loading process was examined.The absolute permeability of the coal samples was also obtained in order for comparison with the measured results.The macroscopic CBM flow mechanism in complex lowpermeability coal rocks can be revealed through three-dimensional reconstruction of the microscopic fracture structure and seepage simulation.This study lays the groundwork for the fine description and evaluation of coal reservoirs as well as the precise prediction of gas production in CBM wells.
