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
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
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
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
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
During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is ...During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is needed to replace the standard perturbation model of structure formation. Recently, we have been developing a model of cosmology that accounts for a large number of the observed properties of the universe. A key component of this model is that fractal structures that later regulated the creation of both matter and radiation came into existence during the initial Planck-era inflation. Initially, the vacuum was the only existence and since time, distance, and energy were uncertain, its only property, the curvature (or energy), was most likely distributed randomly. Everything that happened after the Planck era can be described by the known laws of physics so the remaining fundamental problem is to discover how such a random beginning could organize itself into the hierarchy of highly non-random self-similar structures on all length scales that are necessary to explain the existence of all cosmic structures. In this paper, we present a variation of the standard sandpile model that points to a solution. Incidental to our review of the distributions of cosmic structures, we discovered that the apparent transition from a fractal to a homogeneous distribution of structures at a distance of about 150 Mpc is a consequence of the finite size of the universe rather than a change in the underlying statistics of the distributions.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
With the rapid advancements in technology and science,optimization theory and algorithms have become increasingly important.A wide range of real-world problems is classified as optimization challenges,and meta-heurist...With the rapid advancements in technology and science,optimization theory and algorithms have become increasingly important.A wide range of real-world problems is classified as optimization challenges,and meta-heuristic algorithms have shown remarkable effectiveness in solving these challenges across diverse domains,such as machine learning,process control,and engineering design,showcasing their capability to address complex optimization problems.The Stochastic Fractal Search(SFS)algorithm is one of the most popular meta-heuristic optimization methods inspired by the fractal growth patterns of natural materials.Since its introduction by Hamid Salimi in 2015,SFS has garnered significant attention from researchers and has been applied to diverse optimization problems acrossmultiple disciplines.Its popularity can be attributed to several factors,including its simplicity,practical computational efficiency,ease of implementation,rapid convergence,high effectiveness,and ability to address singleandmulti-objective optimization problems,often outperforming other established algorithms.This review paper offers a comprehensive and detailed analysis of the SFS algorithm,covering its standard version,modifications,hybridization,and multi-objective implementations.The paper also examines several SFS applications across diverse domains,including power and energy systems,image processing,machine learning,wireless sensor networks,environmental modeling,economics and finance,and numerous engineering challenges.Furthermore,the paper critically evaluates the SFS algorithm’s performance,benchmarking its effectiveness against recently published meta-heuristic algorithms.In conclusion,the review highlights key findings and suggests potential directions for future developments and modifications of the SFS algorithm.展开更多
In the concurrent extraction of coal and gas,the quantitative assessment of evolving characteristics in mining-induced fracture networks and mining-enhanced permeability within coal seams serves as the cornerstone for...In the concurrent extraction of coal and gas,the quantitative assessment of evolving characteristics in mining-induced fracture networks and mining-enhanced permeability within coal seams serves as the cornerstone for effective gas extraction.However,representing mining-induced fracture networks from a three-dimensional(3D)sight and developing a comprehensive model to evaluate the anisotropic mining-enhanced permeability characteristics still pose significant challenges.In this investigation,a field experiment was undertaken to systematically monitor the evolution of borehole fractures in the coal mass ahead of the mining face at the Pingdingshan Coal Mining Group in China.Using the testing data of borehole fracture,the mining-induced fracture network at varying distances from the mining face was reconstructed through a statistical reconstruction method.Additionally,utilizing fractal theory,a model for the permeability enhancement rate(PER)induced by mining was established.This model was employed to quantitatively depict the anisotropic evolution patterns of PER as the mining face advanced.The research conclusions are as follows:(1)The progression of the mining-induced fracture network can be classified into the stage of rapid growth,the stage of stable growth,and the stage of weak impact;(2)The PER of mining-induced fracture network exhibited a typical progression that can be characterized with slow growth,rapid growth and significant decline;(3)The anisotropic mining-enhanced permeability of the reconstructed mining-induced fracture networks were significant.The peak PER in the vertical direction of the coal seam is 6.86 times and 4446.38 times greater than the direction perpendicular to the vertical thickness and the direction parallel to the advancement of the mining face,respectively.This investigatione provides a viable approach and methodology for quantitatively assessing the anisotropic PER of fracture networks induced during mining,in the concurrent exploitation of coal and gas.展开更多
The pore structure of rocks significantly influences the porosity and permeability of reservoirs and the migration ability of oil and gas,and being the key task on the development of volcanic gas reservoirs.Nine volca...The pore structure of rocks significantly influences the porosity and permeability of reservoirs and the migration ability of oil and gas,and being the key task on the development of volcanic gas reservoirs.Nine volcanic rock samples from the Yingcheng Formation and Huoshiling Formation in the Longfengshan area of the Changling Fault Depression in the Songliao Basin were selected for this study.The pore structures of the volcanic rocks in the study area were investigated using high-pressure mercury injection,X-ray diffraction combined with fractal theory.The relationships between the fractal dimension and physical properties characteristics,pore structure parameters,and mineral content were analyzed to provide guidance for the development of volcanic rock gas reservoirs.The results show that the reservoir can be divided into 3 types(I,II,and III)based on the shape of the capillary pressure curve,and the physical properties deteriorate successively.Different types of reservoirs exhibit different fractal characteristics.For typesⅠ,ⅡandⅢ,the average total fractal dimensions were 2.3418,2.6850,and 2.9203,respectively.The larger the fractal dimension,the stronger the heterogeneity of reservoir.A small number of macro-pores primarily contributed to permeability.The fractal dimension was negatively correlated with porosity and permeability.The fractal dimension of the rock was strongly correlated with quartz and feldspar contents,and the mineral composition and content are closely related to the pore evolution of the reservoir,which are the internal factors affecting the fractal dimension of volcanic rock.展开更多
The contact stiffness of the tool-holder assembly interface affects the overall dynamic performance of the milling system.Currently,the contact parameters are primarily established by minimizing the frequency response...The contact stiffness of the tool-holder assembly interface affects the overall dynamic performance of the milling system.Currently,the contact parameters are primarily established by minimizing the frequency response in modal tests and through dynamic simulation results.However,alterations in the structure or material of the tool-holder system necessitate multiple modal tests,thereby increasing computational costs.This study aims to streamline the process of determining contact stiffness and enhance accuracy by developing an analytical model that considers tool-holder contact properties.Initially,the microstructure of the contact surface is characterized via fractal theory to determine its fractal parameters.Then the contact coefficient is introduced to precisely depict the area distribution function of the microcontact.Building upon this,a contact stiffness model is established which is verified by the modal tests.The test results indicate that utilizing this model can reduce the structural modal frequency calculation error to 0.56%.Finally,the Monte Carlo algorithm is employed to investigate the sensitivity of fractal parameters and radial interference on contact characteristics.The findings demonstrate that the fractal dimension has the greatest influence on the dynamic behavior of the tool-holder structure.This study proposes a milling tool-holder contact stiffness modeling method from a microscopic perspective,which offers sufficient computational accuracy to provide a theoretical basis for the selection of milling tool-holder structures in practical machining.展开更多
The high-pressure mercury intrusion (HPMI) experiment is widely used to assess the pore architecture oftight sandstone reservoirs. However, the conventional analysis of the high- pressure mercury intrusionhas always f...The high-pressure mercury intrusion (HPMI) experiment is widely used to assess the pore architecture oftight sandstone reservoirs. However, the conventional analysis of the high- pressure mercury intrusionhas always focused on the mercury injection curves themselves, neglecting the important geologicalinformation conveyed by the mercury ejection curves. This paper quantitatively describes the fractalcharacteristics of ejection curves by using four fractal models, i.e.,. Menger model, Thermodynamicmodel, Sierpinski model, and multi- fractal model. In comparison with mercury injection curves, weexplore the fractal significance of mercury ejection curves and define the applicability of different fractalmodels in characterizing pore architectures. Investigated tight sandstone samples can be divided intofour types (Types A, B, C and D) based on porosity, permeability, and mercury removal efficiency. Type Dsamples are unique in that they have higher permeability (>0.6 mD) but lower mercury removal effi-ciency (<35%). Fractal studies of the mercury injection curve show that it mainly reflects the pore throatcharacteristics, while the mercury ejection curve serves to reveal the pore features, and porosity andpermeability correlate well with the fractal dimension of the injection curve, while mercury removalefficiency correlates only with the Ds' value of the ejection curve. The studies on the mercury ejectioncurves also reveal that the small pores and micropores of the Type C and Type D samples are moredeveloped, with varying pore architecture. The fractal dimension Ds' value of Type D samples is greaterthan that of Type C samples, and the dissolution of Type D samples is more intense than that of Type Csamples, which further indicates that the Type D samples are smaller in pore size, rougher in surface, andwith greater difficulty for the hydrocarbon to enter, resulting in their reservoir capacity probably lessthan that of Type C samples. In this regard, the important information characterized by the mercuryejection curve should be considered in evaluating the tight sandstone reservoirs. Finally, the Menger andThermodynamic models prove to be more suitable for describing the total pore architecture, while theSierpinski model is better for characterizing the variability of the interconnected pores.展开更多
Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements.However,these surveys often involve compositional data,the weight concentrations,which do not meet the requirements ...Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements.However,these surveys often involve compositional data,the weight concentrations,which do not meet the requirements of statistical methods due to the closure effect.In this study,we applied an integrated approach combining compositional data,multifractal,and multivariate statistical analyses to identify the nonlinear complexity of the spatial distributions of elemental concentrations in the Er’renshan ore field.Initially,the raw concentrations were transformed into log-ratios following the principles of composition data theory to alleviate the impact of the closure effect.Multifractal analysis was then conducted to characterise the nonlinear complexity of the concentration distributions.Furthermore,principal component analysis(PCA)and factor analysis(FA)were applied to identify spurious correlations and the potential factors controlling the distribution patterns.The results demonstrate that:a)the raw data are biased,while the log-ratio data are unbiased and more reliable;b)the spatial distributions of elemental concentrations exhibit nonlinear complexity;and c)the elemental distribution in the study area is largely controlled by structural factors.展开更多
Fractal theory provides a new strategy for equipment design.In this work,we propose a novel H-like fractal(HLF)impeller to improve the uniformity of the distribution of hydrodynamics in stirred tanks.The impellers are...Fractal theory provides a new strategy for equipment design.In this work,we propose a novel H-like fractal(HLF)impeller to improve the uniformity of the distribution of hydrodynamics in stirred tanks.The impellers are constructed by replacing two vertical blades or four legs with two or four H-like subblades by fractal iterations,respectively.Flow characteristics including velocity and turbulent kinetic energy(TKE)distributions,vortices,power number,are predicted by large eddy simulation.Compared with Rushton turbine(RT)impeller when H/T=1(or dual RTs when H/T=1.5,triple RTs when H/T=2),the HLF impeller can produce a flow field with more uniform distributions of larger velocities and TKE level.The impeller with more fractal iteration times can further improve the distribution uniformity of hydrodynamics in the case of high H/T.Power analysis shows that this is mainly due to the improved energy utilization efficiency by the fractal structure design.展开更多
Complex evidence theory is a generalized Dempster-Shafer evidence theory,which has the ability to express uncertain information.One of the key issues is the uncertainty measure of Complex Basic Belief Assignment(CBBA)...Complex evidence theory is a generalized Dempster-Shafer evidence theory,which has the ability to express uncertain information.One of the key issues is the uncertainty measure of Complex Basic Belief Assignment(CBBA).However,the research on the uncertainty measure of complex evidence theory is still an open issue.Therefore,in this paper,first,the Fractal-based Complex Belief(FCB)entropy as a generalization of Fractal-based Belief(FB)entropy,which has superiority in uncertainty measurement of CBBA,is proposed.Second,on the basis of FCB entropy,we propose Fractal-based Supremum Complex Belief(FSCB)entropy and Fractal-based Infimum Complex Belief(FICB)entropy,with FSCB entropy as the upper bound and FICB entropy as the lower bound.They are collectively called the proposed FCB entropy.Furthermore,we analyze the properties,physical interpretation and numerical examples to prove the rationality of the proposed method.Finally,a practical information fusion application is proposed to prove that the proposed FCB entropy can reasonably measure the uncertainty of CBBA.The results show that,the proposed FCB entropy can handle the uncertainty measure of CBBA,which can be a reasonable way for uncertainty measure in complex evidence theory.展开更多
Tight oil is the most viable target for unconventional oil and gas exploration, but the complexity of micro-/nanopore throat systems significantly affects the oil content of reservoirs. To investigate the causes of he...Tight oil is the most viable target for unconventional oil and gas exploration, but the complexity of micro-/nanopore throat systems significantly affects the oil content of reservoirs. To investigate the causes of heterogeneity in oil-bearing reservoirs, a high-pressure mercury injection experiment combined with fractal theory was conducted to analyze the micro pore throat structure characteristics of the tight sandstone of Chang 7 Member reservoirs in the Ordos Basin. The factors controlling the variations in oil content among tight sandstone samples were identified based on mineral composition characteristics. The results indicate that the pore throat radius distribution is mainly unimodal an bimodal. In oil-bearing samples, the pore throat distributions align well with the corresponding permeability contribution curves, while in oil-free samples, there is a clear deviation from these curves. Mesopore throats exert the greatest influence on seepage capacity. Differences in fractal characteristics are primarily reflected in D1 values, with oil-free samples exhibiting D1 values close to 3, indicating an extremely nonuniform pore throat structure at this scale. The content of quartz, plagioclase, and chlorite is significantly higher in oil-bearing samples than in oil-free samples, whereas calcite content is lower in oil-bearing samples. There is a positive correlation between the contents of quartz, plagioclase, and chlorite with D1;their increased presence contributes to a more favorable pore throat structure.Conversely, the calcite contents show an inverse relationship with D1. Cementation increases the complexity of pore throat structures, while multiple diagenetic processes simultaneously control these characteristics, leading to variations in oil content.展开更多
To investigate the influence of dynamic loading and freeze-thaw cycles(F-T)on the energy evolution and damage characteristics of multi-walled carbon nanotubes(MWCNTs)reinforced concrete specimens,impact compression te...To investigate the influence of dynamic loading and freeze-thaw cycles(F-T)on the energy evolution and damage characteristics of multi-walled carbon nanotubes(MWCNTs)reinforced concrete specimens,impact compression tests were conducted.These tests used a split-Hopkinson pressure bar(SHPB)apparatus with a diameter of 50 mm and were performed on MWCNTs concrete samples that had undergone different numbers of F-T cycles.The impact pressures applied were 0.40,0.50,and 0.60 MPa,respectively.The effects of impact pressure and F-T number on the fractal dimension(D_(f))of the fractured blocks and absorbed energy(W_s)of MWCNTs concrete were investigated.The results indicate that the D_(f) of the fractured blocks in MWCNTs concrete increases with the increase of impact pressure and F-T number,and under the same experimental conditions,the D_(f) of MWCNTs concrete is lower than that of ordinary concrete.The variation in W_s is different:the W_s of MWCNTs concrete under impact load increases with increasing impact pressure but decreases with increasing F-T number.Additionally,under the same experimental conditions,the W_s of MWCNTs concrete is greater than that of ordinary concrete.The incorporation of MWCNTs significantly enhances the impact resistance of the concrete.展开更多
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.
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.
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.
文摘During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is needed to replace the standard perturbation model of structure formation. Recently, we have been developing a model of cosmology that accounts for a large number of the observed properties of the universe. A key component of this model is that fractal structures that later regulated the creation of both matter and radiation came into existence during the initial Planck-era inflation. Initially, the vacuum was the only existence and since time, distance, and energy were uncertain, its only property, the curvature (or energy), was most likely distributed randomly. Everything that happened after the Planck era can be described by the known laws of physics so the remaining fundamental problem is to discover how such a random beginning could organize itself into the hierarchy of highly non-random self-similar structures on all length scales that are necessary to explain the existence of all cosmic structures. In this paper, we present a variation of the standard sandpile model that points to a solution. Incidental to our review of the distributions of cosmic structures, we discovered that the apparent transition from a fractal to a homogeneous distribution of structures at a distance of about 150 Mpc is a consequence of the finite size of the universe rather than a change in the underlying statistics of the distributions.
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 Prince Sattam bin Abdulaziz University for funding this research work through the project number(2024/RV/06).
文摘With the rapid advancements in technology and science,optimization theory and algorithms have become increasingly important.A wide range of real-world problems is classified as optimization challenges,and meta-heuristic algorithms have shown remarkable effectiveness in solving these challenges across diverse domains,such as machine learning,process control,and engineering design,showcasing their capability to address complex optimization problems.The Stochastic Fractal Search(SFS)algorithm is one of the most popular meta-heuristic optimization methods inspired by the fractal growth patterns of natural materials.Since its introduction by Hamid Salimi in 2015,SFS has garnered significant attention from researchers and has been applied to diverse optimization problems acrossmultiple disciplines.Its popularity can be attributed to several factors,including its simplicity,practical computational efficiency,ease of implementation,rapid convergence,high effectiveness,and ability to address singleandmulti-objective optimization problems,often outperforming other established algorithms.This review paper offers a comprehensive and detailed analysis of the SFS algorithm,covering its standard version,modifications,hybridization,and multi-objective implementations.The paper also examines several SFS applications across diverse domains,including power and energy systems,image processing,machine learning,wireless sensor networks,environmental modeling,economics and finance,and numerous engineering challenges.Furthermore,the paper critically evaluates the SFS algorithm’s performance,benchmarking its effectiveness against recently published meta-heuristic algorithms.In conclusion,the review highlights key findings and suggests potential directions for future developments and modifications of the SFS algorithm.
基金supported by the National Natural Science Foundation of China (Grant No.42377143)Sichuan Natural Science Foundation (Grant No.2024NSFSC0097)the Open Fund of State Key Laboratory of Coal Mining and Clean Utilization,China (Grant No.2021-CMCU-KFZD001).
文摘In the concurrent extraction of coal and gas,the quantitative assessment of evolving characteristics in mining-induced fracture networks and mining-enhanced permeability within coal seams serves as the cornerstone for effective gas extraction.However,representing mining-induced fracture networks from a three-dimensional(3D)sight and developing a comprehensive model to evaluate the anisotropic mining-enhanced permeability characteristics still pose significant challenges.In this investigation,a field experiment was undertaken to systematically monitor the evolution of borehole fractures in the coal mass ahead of the mining face at the Pingdingshan Coal Mining Group in China.Using the testing data of borehole fracture,the mining-induced fracture network at varying distances from the mining face was reconstructed through a statistical reconstruction method.Additionally,utilizing fractal theory,a model for the permeability enhancement rate(PER)induced by mining was established.This model was employed to quantitatively depict the anisotropic evolution patterns of PER as the mining face advanced.The research conclusions are as follows:(1)The progression of the mining-induced fracture network can be classified into the stage of rapid growth,the stage of stable growth,and the stage of weak impact;(2)The PER of mining-induced fracture network exhibited a typical progression that can be characterized with slow growth,rapid growth and significant decline;(3)The anisotropic mining-enhanced permeability of the reconstructed mining-induced fracture networks were significant.The peak PER in the vertical direction of the coal seam is 6.86 times and 4446.38 times greater than the direction perpendicular to the vertical thickness and the direction parallel to the advancement of the mining face,respectively.This investigatione provides a viable approach and methodology for quantitatively assessing the anisotropic PER of fracture networks induced during mining,in the concurrent exploitation of coal and gas.
基金Supported by Key Scientific and Technological Projects of Sinopec(No.P21104-2).
文摘The pore structure of rocks significantly influences the porosity and permeability of reservoirs and the migration ability of oil and gas,and being the key task on the development of volcanic gas reservoirs.Nine volcanic rock samples from the Yingcheng Formation and Huoshiling Formation in the Longfengshan area of the Changling Fault Depression in the Songliao Basin were selected for this study.The pore structures of the volcanic rocks in the study area were investigated using high-pressure mercury injection,X-ray diffraction combined with fractal theory.The relationships between the fractal dimension and physical properties characteristics,pore structure parameters,and mineral content were analyzed to provide guidance for the development of volcanic rock gas reservoirs.The results show that the reservoir can be divided into 3 types(I,II,and III)based on the shape of the capillary pressure curve,and the physical properties deteriorate successively.Different types of reservoirs exhibit different fractal characteristics.For typesⅠ,ⅡandⅢ,the average total fractal dimensions were 2.3418,2.6850,and 2.9203,respectively.The larger the fractal dimension,the stronger the heterogeneity of reservoir.A small number of macro-pores primarily contributed to permeability.The fractal dimension was negatively correlated with porosity and permeability.The fractal dimension of the rock was strongly correlated with quartz and feldspar contents,and the mineral composition and content are closely related to the pore evolution of the reservoir,which are the internal factors affecting the fractal dimension of volcanic rock.
基金Supported by National Science and Technology Major Project of China(Grant No.J2019-VII-0001-0141).
文摘The contact stiffness of the tool-holder assembly interface affects the overall dynamic performance of the milling system.Currently,the contact parameters are primarily established by minimizing the frequency response in modal tests and through dynamic simulation results.However,alterations in the structure or material of the tool-holder system necessitate multiple modal tests,thereby increasing computational costs.This study aims to streamline the process of determining contact stiffness and enhance accuracy by developing an analytical model that considers tool-holder contact properties.Initially,the microstructure of the contact surface is characterized via fractal theory to determine its fractal parameters.Then the contact coefficient is introduced to precisely depict the area distribution function of the microcontact.Building upon this,a contact stiffness model is established which is verified by the modal tests.The test results indicate that utilizing this model can reduce the structural modal frequency calculation error to 0.56%.Finally,the Monte Carlo algorithm is employed to investigate the sensitivity of fractal parameters and radial interference on contact characteristics.The findings demonstrate that the fractal dimension has the greatest influence on the dynamic behavior of the tool-holder structure.This study proposes a milling tool-holder contact stiffness modeling method from a microscopic perspective,which offers sufficient computational accuracy to provide a theoretical basis for the selection of milling tool-holder structures in practical machining.
基金The research project was co-funded by the National Natural Science Foundation of China(No.42072172,No.41772120)Shandong Province Natural Science Fund for Distinguished Young Scholars(No.JQ201311)the Graduate Scientific and Technological Innovation Project Financially Supported by Shandong University of Science and Technology(No.SDKDYC190313).
文摘The high-pressure mercury intrusion (HPMI) experiment is widely used to assess the pore architecture oftight sandstone reservoirs. However, the conventional analysis of the high- pressure mercury intrusionhas always focused on the mercury injection curves themselves, neglecting the important geologicalinformation conveyed by the mercury ejection curves. This paper quantitatively describes the fractalcharacteristics of ejection curves by using four fractal models, i.e.,. Menger model, Thermodynamicmodel, Sierpinski model, and multi- fractal model. In comparison with mercury injection curves, weexplore the fractal significance of mercury ejection curves and define the applicability of different fractalmodels in characterizing pore architectures. Investigated tight sandstone samples can be divided intofour types (Types A, B, C and D) based on porosity, permeability, and mercury removal efficiency. Type Dsamples are unique in that they have higher permeability (>0.6 mD) but lower mercury removal effi-ciency (<35%). Fractal studies of the mercury injection curve show that it mainly reflects the pore throatcharacteristics, while the mercury ejection curve serves to reveal the pore features, and porosity andpermeability correlate well with the fractal dimension of the injection curve, while mercury removalefficiency correlates only with the Ds' value of the ejection curve. The studies on the mercury ejectioncurves also reveal that the small pores and micropores of the Type C and Type D samples are moredeveloped, with varying pore architecture. The fractal dimension Ds' value of Type D samples is greaterthan that of Type C samples, and the dissolution of Type D samples is more intense than that of Type Csamples, which further indicates that the Type D samples are smaller in pore size, rougher in surface, andwith greater difficulty for the hydrocarbon to enter, resulting in their reservoir capacity probably lessthan that of Type C samples. In this regard, the important information characterized by the mercuryejection curve should be considered in evaluating the tight sandstone reservoirs. Finally, the Menger andThermodynamic models prove to be more suitable for describing the total pore architecture, while theSierpinski model is better for characterizing the variability of the interconnected pores.
基金supported by the Doctoral Research Start-up Fund,East China University of Technology(DHBK2019313)the Open Research Fund Program of Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring(Central South University),the Ministry of Education(2020YSJS10)+1 种基金the Open Research Fund Program of Shandong Provincial Engineering Laboratory of Application and Development of Big Data for Deep Gold Exploration(SDK202224)the Basic Scientific Research Fund of the Institute of Geophysical and Geochemical Exploration,Chinese Academy of Geological Sciences(AS2022P03).
文摘Geochemical surveys are essential for understanding the spatial distribution of ore-forming elements.However,these surveys often involve compositional data,the weight concentrations,which do not meet the requirements of statistical methods due to the closure effect.In this study,we applied an integrated approach combining compositional data,multifractal,and multivariate statistical analyses to identify the nonlinear complexity of the spatial distributions of elemental concentrations in the Er’renshan ore field.Initially,the raw concentrations were transformed into log-ratios following the principles of composition data theory to alleviate the impact of the closure effect.Multifractal analysis was then conducted to characterise the nonlinear complexity of the concentration distributions.Furthermore,principal component analysis(PCA)and factor analysis(FA)were applied to identify spurious correlations and the potential factors controlling the distribution patterns.The results demonstrate that:a)the raw data are biased,while the log-ratio data are unbiased and more reliable;b)the spatial distributions of elemental concentrations exhibit nonlinear complexity;and c)the elemental distribution in the study area is largely controlled by structural factors.
基金the financial support from the National Natural Science Foundation of China(22078058)。
文摘Fractal theory provides a new strategy for equipment design.In this work,we propose a novel H-like fractal(HLF)impeller to improve the uniformity of the distribution of hydrodynamics in stirred tanks.The impellers are constructed by replacing two vertical blades or four legs with two or four H-like subblades by fractal iterations,respectively.Flow characteristics including velocity and turbulent kinetic energy(TKE)distributions,vortices,power number,are predicted by large eddy simulation.Compared with Rushton turbine(RT)impeller when H/T=1(or dual RTs when H/T=1.5,triple RTs when H/T=2),the HLF impeller can produce a flow field with more uniform distributions of larger velocities and TKE level.The impeller with more fractal iteration times can further improve the distribution uniformity of hydrodynamics in the case of high H/T.Power analysis shows that this is mainly due to the improved energy utilization efficiency by the fractal structure design.
基金supported by the National Natural Science Foundation of China (No. 62473067)Chongqing Talents: Exceptional Young Talents Project, China (No. cstc2022ycjh-bgzxm0070)Chongqing Overseas Scholars Innovation Program, China (No. cx2022024)
文摘Complex evidence theory is a generalized Dempster-Shafer evidence theory,which has the ability to express uncertain information.One of the key issues is the uncertainty measure of Complex Basic Belief Assignment(CBBA).However,the research on the uncertainty measure of complex evidence theory is still an open issue.Therefore,in this paper,first,the Fractal-based Complex Belief(FCB)entropy as a generalization of Fractal-based Belief(FB)entropy,which has superiority in uncertainty measurement of CBBA,is proposed.Second,on the basis of FCB entropy,we propose Fractal-based Supremum Complex Belief(FSCB)entropy and Fractal-based Infimum Complex Belief(FICB)entropy,with FSCB entropy as the upper bound and FICB entropy as the lower bound.They are collectively called the proposed FCB entropy.Furthermore,we analyze the properties,physical interpretation and numerical examples to prove the rationality of the proposed method.Finally,a practical information fusion application is proposed to prove that the proposed FCB entropy can reasonably measure the uncertainty of CBBA.The results show that,the proposed FCB entropy can handle the uncertainty measure of CBBA,which can be a reasonable way for uncertainty measure in complex evidence theory.
基金supported by the National Natural Science Foundation of China (Grant No. 42002139)the Basic Prospective Project of SINOPEC (Grant No. P23240-3)。
文摘Tight oil is the most viable target for unconventional oil and gas exploration, but the complexity of micro-/nanopore throat systems significantly affects the oil content of reservoirs. To investigate the causes of heterogeneity in oil-bearing reservoirs, a high-pressure mercury injection experiment combined with fractal theory was conducted to analyze the micro pore throat structure characteristics of the tight sandstone of Chang 7 Member reservoirs in the Ordos Basin. The factors controlling the variations in oil content among tight sandstone samples were identified based on mineral composition characteristics. The results indicate that the pore throat radius distribution is mainly unimodal an bimodal. In oil-bearing samples, the pore throat distributions align well with the corresponding permeability contribution curves, while in oil-free samples, there is a clear deviation from these curves. Mesopore throats exert the greatest influence on seepage capacity. Differences in fractal characteristics are primarily reflected in D1 values, with oil-free samples exhibiting D1 values close to 3, indicating an extremely nonuniform pore throat structure at this scale. The content of quartz, plagioclase, and chlorite is significantly higher in oil-bearing samples than in oil-free samples, whereas calcite content is lower in oil-bearing samples. There is a positive correlation between the contents of quartz, plagioclase, and chlorite with D1;their increased presence contributes to a more favorable pore throat structure.Conversely, the calcite contents show an inverse relationship with D1. Cementation increases the complexity of pore throat structures, while multiple diagenetic processes simultaneously control these characteristics, leading to variations in oil content.
基金Funded by the Gansu Provincial Key Research and Development Plan-Industrial Project(No.25YFGA029)。
文摘To investigate the influence of dynamic loading and freeze-thaw cycles(F-T)on the energy evolution and damage characteristics of multi-walled carbon nanotubes(MWCNTs)reinforced concrete specimens,impact compression tests were conducted.These tests used a split-Hopkinson pressure bar(SHPB)apparatus with a diameter of 50 mm and were performed on MWCNTs concrete samples that had undergone different numbers of F-T cycles.The impact pressures applied were 0.40,0.50,and 0.60 MPa,respectively.The effects of impact pressure and F-T number on the fractal dimension(D_(f))of the fractured blocks and absorbed energy(W_s)of MWCNTs concrete were investigated.The results indicate that the D_(f) of the fractured blocks in MWCNTs concrete increases with the increase of impact pressure and F-T number,and under the same experimental conditions,the D_(f) of MWCNTs concrete is lower than that of ordinary concrete.The variation in W_s is different:the W_s of MWCNTs concrete under impact load increases with increasing impact pressure but decreases with increasing F-T number.Additionally,under the same experimental conditions,the W_s of MWCNTs concrete is greater than that of ordinary concrete.The incorporation of MWCNTs significantly enhances the impact resistance of the concrete.
