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
Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics frompartic...Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics fromparticle-size distribution data. Predictive capabilities of three fractal models, i.e, Tyler-Wheatcraft model,Rieu-Sposito model, and Brooks-Corey model, were fully evaluated in this work using experimental datafrom an international database and literature. Particle-size distribution data were firstly interpolated into20 classes using a van Genuchten-type equation. Fractal dimensions of the tortuous pore wall and the poresurface were then calculated from the detailed particle-size distribution and incorporated as a parameter infractal water retention models. Comparisons between measured and model-estimated water retention cha-racteristics indicated that these three models were applicable to relatively different soil textures and pressurehead ranges. Tyler-Wheatcraft and Brooks-Corey models led to reasonable agreements for both coarse- andmedium-textured soils, while the latter showed applicability to a broader texture range. In contrast, Rieu-Sposito model was more suitable for fine-textured soils. Fractal models produced a better estimation of watercontents at low pressure heads than at high pressure heads.展开更多
Mapping mineral prospectivity in vegetated areas is a challenge. For this reason, we aimed to map spatial distribution characteristics of linear structures detected in remote sensing images using fractal and multifrac...Mapping mineral prospectivity in vegetated areas is a challenge. For this reason, we aimed to map spatial distribution characteristics of linear structures detected in remote sensing images using fractal and multifractal models. The selected study area was the Pinghe District of the Fujian Province（China）, located in the Shanghang-Yunxiao polymetallic and alunite ore belt（within the Wuyishan polymetallic belt）, where mineral resources such as copper, molybdenum, gold, silver, iron, lead, zinc, alunite and pyrophyllite have been discovered. The results of our study showed that：（1） the values of fractal dimension for all lineaments, NW-trending lineaments, and NE-trending lineaments, are 1.36, 1.32, and 1.23, respectively, indicating that these lineaments are statistically self-similar;（2） the fractal dimensions of the spatial distribution of the linear structures in the four selected hydrothermal-type ore deposits of the Pinghe District, named Zhongteng, Panchi, Xiaofanshan and Fanshan, are 1.43, 1.52, 1.37 and 1.37, respectively, which are higher than the mean value in South China;（3） the spatial distribution of the linear structures extracted from the remote sensing image and displayed by the contour map of fractal dimensions, correlates well with the known hydrothermal ore deposits; and（4） the results of the anomaly map decomposed by the spectrum-area（S-A） multifractal model is much better than the original fractal dimension contour map, which showed most of the known hydrothermal-type deposits occur in the high anomalous area. It is suggested that a high step tendency possibly matches with the boundary of the volcanic edifice and the deep fault controlling the development of the rock mass and the volcanic edifice. The complexity of the spatial distribution of mapped lineations（faults） in the Pinghe District, characterized by high values in the anomaly map, may be associated with the hydrothermal polymetallic ore mineralization in the study area.展开更多
The target in this investigation is separation and delineation of geochemical anomalies for the single element Cu in Mesgaran mining area, eastern Iran. Mesgaran mining area is located in south part of Sarbishe county...The target in this investigation is separation and delineation of geochemical anomalies for the single element Cu in Mesgaran mining area, eastern Iran. Mesgaran mining area is located in south part of Sarbishe county with about 29 Km distance to the county center. This region is part of an Ophiolite sequence and the copper anomalies seem to be related to a volcanic massive sulfide (VMS) deposit whose main part (massive sulfide Lens) has been eroded. In order to delineate Cu anomalies, the boxplot as an Exploratory Data Analysis (EDA) method and concentration-volume (C-V) Fractal modeling are employed. Both of the methods reveal low-deep anomalies which are highly correlated with geological and geophysical studies. As the main result of this study we show that Fractal modeling in spite of the Boxplot, is not recommended for complex geological settings. The proved shallow anomalies recorded by geophysical studies and defined by the used methods are in accordance to the stringer zone of a volcanic massive sulfide (VMS) deposit in Mesgaran mining area which means this region is the bottom of a VMS deposit and geochemical anomalies are related to the remained parts of the deposit.展开更多
observations from the field and the taboratory show that en echelon fractures withinfracture zones have a foede1 within Ricdel structure’ The tensile fallure mecbanism of en echelonfractures can be described by the p...observations from the field and the taboratory show that en echelon fractures withinfracture zones have a foede1 within Ricdel structure’ The tensile fallure mecbanism of en echelonfractures can be described by the pile-ups of sbear crack-dislocations. A fractal model can be used tosimulate the Riedel within Xiedel geometry, allowing the direct rneasarement of tbe ftactal dimen sions of en echelon fractare systems. The energy dissipation of tbe en ccbe1on fracture system canbe deduced using a fracil damage evo1ution model which exptalns tbe evo1ution process of en eche lon fracture svstems. The fractal nature of the fractures can be used to dcrive an accurate estimateof total energy dissipation.展开更多
Sphalerite banding is a common texture in Jinding （金顶） Pb-Zn deposit, Yunnan （云南）, southwestern China. The frequency distribution and irregularity of sphalerite grains observed in the bandings are characterize...Sphalerite banding is a common texture in Jinding （金顶） Pb-Zn deposit, Yunnan （云南）, southwestern China. The frequency distribution and irregularity of sphalerite grains observed in the bandings are characterized quantitatively by fractal models. Fractal dimensions calculated by several fractal models including box-counting model, perimeter-area （P-A） model, and number-area （N-A） model show the gradual change from outer banding to inner banding, indicating a decrease in area percentage, in irregularity, in shape and in grain size, and an increase in the numbers of grains. These results may imply an inward growth of sphalerite during mineralization, and self-organization properties are involved in the nonlinear process of mineralization.展开更多
Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability res...Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.展开更多
Without considering the influence of heat,existing fractal contact models are not applicable to analyze the contacts when the temperature changes.For this problem,the normal load model and the normal stiffness model o...Without considering the influence of heat,existing fractal contact models are not applicable to analyze the contacts when the temperature changes.For this problem,the normal load model and the normal stiffness model of thermal elasto-plastic contact of rough surfaces are developed respectively in this paper.The proposed model is based on the normal contact mechanics model of fractal theory of anisotropic and thermal elasto-plastic contact theory which can be used to characterize the rough surface thermodynamic properties.Then the validity of the model is verified.Finally,the influence of main parameters on the total normal load and the whole normal stiffness of thermal elasto-plastic contact at the interface is analyzed by contact simulation.The results show that the total normal load of thermal elasto-plastic contact increases with the increases of temperature.The whole normal stiffness of thermal elasto-plastic contact increases with increasing coefficient of linear expansion,scale factor,temperature difference or fractal dimension,but decreases with increasing fractal roughness.This model expands basic theory and applications of traditional models,and can be used to calculate and analyze the contacts when the temperature changes.展开更多
To study the gating kinetics of voltage dependent K + channel in clonal pheochromocytoma (PC12) cells, the inward currents of K channel in PC12 cells were recorded using cell attached patch clamp technique. The fracta...To study the gating kinetics of voltage dependent K + channel in clonal pheochromocytoma (PC12) cells, the inward currents of K channel in PC12 cells were recorded using cell attached patch clamp technique. The fractal features of the open and closed time distributions were determined. The fractal dimensions and kinetic setpoints for the open and closed durations were estimated. It was found that the fractal dimension D was independent of voltage and the logarithm logA of the setpoint A was inversely proportional to the pipette potential (Vp) for the closed durations. While for the open durations the fractal dimension D was inversely proportional to the pipette potential and the logarithm logA of the setpoint A was independent of voltage. Thus, for this channel the open and closed durations and voltage dependence of the gating could be well described by the fractal model.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 damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal ...The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.展开更多
Based on the Sierpinski carpet and Menger sponge models, two categories of fractal models of rock and soil which are composed of the volume fractal model of pores, the volume fractal model of grains, pore-size or part...Based on the Sierpinski carpet and Menger sponge models, two categories of fractal models of rock and soil which are composed of the volume fractal model of pores, the volume fractal model of grains, pore-size or particle-size distribution fractal models are established and their relations are clarified in this paper. Through comparison and analysis, it is found that previous models can be unified by the two categories of fractal models, so the unified fractal models are formed. Experimental results presented by Katz indicate that the first category of fractal models can be used to express the fractal behavior of sandstone. A scanning electron microscope (SEM) will be used to study the microstructure of soft clay and it will be testified that the fractal behavior of soft clay suits the second category of fractal models.展开更多
In this investigation,the Gradient Boosting(GB),Linear Regression(LR),Decision Tree(DT),and Voting algo-rithms were applied to predict the distribution pattern of Au geochemical data.Trace and indicator elements,inclu...In this investigation,the Gradient Boosting(GB),Linear Regression(LR),Decision Tree(DT),and Voting algo-rithms were applied to predict the distribution pattern of Au geochemical data.Trace and indicator elements,including Mo,Cu,Pb,Zn,Ag,Ni,Co,Mn,Fe,and As,were used with these machine learning algorithms(MLAs)to predict Au concentration values in the Doostbigloo porphyry Cu-Au-Mo mineralization area.The performance of the models was evaluated using the Mean Absolute Percentage Error(MAPE)and Root Mean Square Error(RMSE)metrics.The proposed ensemble Voting algorithm outperformed the other models,yielding more ac-curate predictions according to both metrics.The predicted data from the GB,LR,DT,and Voting MLAs were modeled using the Concentration-Area fractal method,and Au geochemical anomalies were mapped.To compare and validate the results,factors such as the location of the mineral deposits,their surface extent,and mineralization trend were considered.The results indicate that integrating hybrid MLAs with fractal modeling signifi-cantly improves geochemical prospectivity mapping.Among the four models,three(DT,GB,Voting)accurately identified both mineral deposits.The LR model,however,only identified Deposit I(central),and its mineralization trend diverged from the field data.The GB and Voting models produced similar results,with their final maps derived from fractal modeling showing the same anomalous areas.The anomaly boundaries identified by these two models are consistent with the two known reserves in the region.The results and plots related to prediction indicators and error rates for these two models also show high similarity,with lower error rates than the other models.Notably,the Voting model demonstrated superior performance in accurately delineating mineral deposit locations and identifying realistic mineralization trends while minimizing false anomalies.展开更多
To comprehensively utilize the valuable geological map,exploration profile,borehole,and geochemical logging data and the knowledge on the formation of the Jinshan Ag-Au deposit for forecasting the exploration targets ...To comprehensively utilize the valuable geological map,exploration profile,borehole,and geochemical logging data and the knowledge on the formation of the Jinshan Ag-Au deposit for forecasting the exploration targets of concealed ore bodies,three-dimensional Mineral Prospectivity Modeling(MPM)of the deposit has been conducted using the weights-of-evidence(WofE)method.Conditional independence between evidence layers was tested,and the outline results using the prediction-volume(P-V)and Student's t-statistic methods for delineating favorable mineralization areas from continuous posterior probability map were critically compared.Four exploration targets delineated ultimately by the Student's t-statistic method for the discovery of minable ore bodies in each of the target areas were discussed in detail.The main conclusions include:(1)three-dimensional modeling of a deposit using multi-source reconnaissance data is useful for MPM in interpreting their relationships with known ore bodies;(2)WofE modeling can be used as a straightforward tool for integrating deposit model and reconnaissance data in MPM;(3)the Student's t-statistic method is more applicable in binarizing the continuous prospectivity map for exploration targeting than the PV approach;and(4)two target areas within high potential to find undiscovered ore bodies were diagnosed to guide future near-mine exploration activities of the Jinshan deposit.展开更多
The fracture of rock is dependent strongly on its microstructures and the loading situations. The rough and irregular fracture is affected by these and other complicated factors. But if the fracture is examined by mea...The fracture of rock is dependent strongly on its microstructures and the loading situations. The rough and irregular fracture is affected by these and other complicated factors. But if the fracture is examined by means of mathematical method, only a geometry of irregularity appears. B. B. Mandelbrot proposed a new geometry—fractal geometry, and he applied it to various fields to describe irregular phenomena in nature.展开更多
The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal co...The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.展开更多
Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a sin...Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.展开更多
The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer partic...The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer particle's surface is irregular and has fractalcharacteristics, which can be described by fractal parameter. The more interesting discovery is thatthe surface fractal dimension values of the polymer particles vary periodically with thepolymerization time. We call this phenomenon fractal evolution, which can be divided into the'revolution' stage and the 'evolution' stage. And then we present polymerization fractal growingmodel (PFGM), and successfully describe and/or predict the whole evolving process of thepolyethylene particle morphology under the different slurry polymerization (includingpre-polymerization) conditions without H_2.展开更多
The dynamic research of landslide is one of the key Points in landslidology. In the paper,from the view point of nonlinear dynamic theory. some features of Xintan landslide, such as the distribution regularities of sp...The dynamic research of landslide is one of the key Points in landslidology. In the paper,from the view point of nonlinear dynamic theory. some features of Xintan landslide, such as the distribution regularities of spatial and temporal fractal dimensions and their corresponding relationships to landslide occurring are researched. The accumulative principles of fractal dimension reduction is exploratively pointed out. The nonlinear dynamic equation of the landslide is built by analyzing the relationship between the correlation dimension and the phase space. Finally, the forecasted results and error analysis are listed. The research results are satisfactory.展开更多
The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical mode...The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes： elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young＇s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.展开更多
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Project supported by the National Natural Science Foundation of China (No, 49971041), the National Key Basic Research Support Foundation (NKBRSF) of China (No. G1999011803) the Director Foundation of the Institute of Soil Science, CAS (No. ISSDF0004).
文摘Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics fromparticle-size distribution data. Predictive capabilities of three fractal models, i.e, Tyler-Wheatcraft model,Rieu-Sposito model, and Brooks-Corey model, were fully evaluated in this work using experimental datafrom an international database and literature. Particle-size distribution data were firstly interpolated into20 classes using a van Genuchten-type equation. Fractal dimensions of the tortuous pore wall and the poresurface were then calculated from the detailed particle-size distribution and incorporated as a parameter infractal water retention models. Comparisons between measured and model-estimated water retention cha-racteristics indicated that these three models were applicable to relatively different soil textures and pressurehead ranges. Tyler-Wheatcraft and Brooks-Corey models led to reasonable agreements for both coarse- andmedium-textured soils, while the latter showed applicability to a broader texture range. In contrast, Rieu-Sposito model was more suitable for fine-textured soils. Fractal models produced a better estimation of watercontents at low pressure heads than at high pressure heads.
基金supported by the“Quantitative Models for Prediction of Strategic Mineral Resources in China”(No.201211022)by the Ministry of Land and Resources of China and“Integrated Prediction Theory for Mineral Resource in Desert and Grassland Covered Areas and Geoinformation Extraction of Buried Mineral Resource”(No.41430320)by the National Natural Science Foundation of China
文摘Mapping mineral prospectivity in vegetated areas is a challenge. For this reason, we aimed to map spatial distribution characteristics of linear structures detected in remote sensing images using fractal and multifractal models. The selected study area was the Pinghe District of the Fujian Province（China）, located in the Shanghang-Yunxiao polymetallic and alunite ore belt（within the Wuyishan polymetallic belt）, where mineral resources such as copper, molybdenum, gold, silver, iron, lead, zinc, alunite and pyrophyllite have been discovered. The results of our study showed that：（1） the values of fractal dimension for all lineaments, NW-trending lineaments, and NE-trending lineaments, are 1.36, 1.32, and 1.23, respectively, indicating that these lineaments are statistically self-similar;（2） the fractal dimensions of the spatial distribution of the linear structures in the four selected hydrothermal-type ore deposits of the Pinghe District, named Zhongteng, Panchi, Xiaofanshan and Fanshan, are 1.43, 1.52, 1.37 and 1.37, respectively, which are higher than the mean value in South China;（3） the spatial distribution of the linear structures extracted from the remote sensing image and displayed by the contour map of fractal dimensions, correlates well with the known hydrothermal ore deposits; and（4） the results of the anomaly map decomposed by the spectrum-area（S-A） multifractal model is much better than the original fractal dimension contour map, which showed most of the known hydrothermal-type deposits occur in the high anomalous area. It is suggested that a high step tendency possibly matches with the boundary of the volcanic edifice and the deep fault controlling the development of the rock mass and the volcanic edifice. The complexity of the spatial distribution of mapped lineations（faults） in the Pinghe District, characterized by high values in the anomaly map, may be associated with the hydrothermal polymetallic ore mineralization in the study area.
文摘The target in this investigation is separation and delineation of geochemical anomalies for the single element Cu in Mesgaran mining area, eastern Iran. Mesgaran mining area is located in south part of Sarbishe county with about 29 Km distance to the county center. This region is part of an Ophiolite sequence and the copper anomalies seem to be related to a volcanic massive sulfide (VMS) deposit whose main part (massive sulfide Lens) has been eroded. In order to delineate Cu anomalies, the boxplot as an Exploratory Data Analysis (EDA) method and concentration-volume (C-V) Fractal modeling are employed. Both of the methods reveal low-deep anomalies which are highly correlated with geological and geophysical studies. As the main result of this study we show that Fractal modeling in spite of the Boxplot, is not recommended for complex geological settings. The proved shallow anomalies recorded by geophysical studies and defined by the used methods are in accordance to the stringer zone of a volcanic massive sulfide (VMS) deposit in Mesgaran mining area which means this region is the bottom of a VMS deposit and geochemical anomalies are related to the remained parts of the deposit.
文摘observations from the field and the taboratory show that en echelon fractures withinfracture zones have a foede1 within Ricdel structure’ The tensile fallure mecbanism of en echelonfractures can be described by the pile-ups of sbear crack-dislocations. A fractal model can be used tosimulate the Riedel within Xiedel geometry, allowing the direct rneasarement of tbe ftactal dimen sions of en echelon fractare systems. The energy dissipation of tbe en ccbe1on fracture system canbe deduced using a fracil damage evo1ution model which exptalns tbe evo1ution process of en eche lon fracture svstems. The fractal nature of the fractures can be used to dcrive an accurate estimateof total energy dissipation.
基金the Open Fund of the State Key Laboratory of Geological Processes and Mineral Resources of Chinaan NSERC Discovery Research Grant (ERC-OGP0183993) NSFC (No. 40373003).
文摘Sphalerite banding is a common texture in Jinding （金顶） Pb-Zn deposit, Yunnan （云南）, southwestern China. The frequency distribution and irregularity of sphalerite grains observed in the bandings are characterized quantitatively by fractal models. Fractal dimensions calculated by several fractal models including box-counting model, perimeter-area （P-A） model, and number-area （N-A） model show the gradual change from outer banding to inner banding, indicating a decrease in area percentage, in irregularity, in shape and in grain size, and an increase in the numbers of grains. These results may imply an inward growth of sphalerite during mineralization, and self-organization properties are involved in the nonlinear process of mineralization.
基金supported by China Natural Science Foundation(Grant No.52274053)Beijing Natural Science Foundation(Grant No.3232028)Open Fund of State Key Laboratory of Offshore Oil Exploitation(Grant No.CCL2021RCPS0515KQN)。
文摘Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.
基金Project(52130501)supported by the National Natural Science Foundation of ChinaProject(LY20E050012)supported by the Natural Science Foundation of Zhejiang Province,ChinaProject(Y201942581)supported by the Scientific Research Project of Education Department of Zhejiang Province,China。
文摘Without considering the influence of heat,existing fractal contact models are not applicable to analyze the contacts when the temperature changes.For this problem,the normal load model and the normal stiffness model of thermal elasto-plastic contact of rough surfaces are developed respectively in this paper.The proposed model is based on the normal contact mechanics model of fractal theory of anisotropic and thermal elasto-plastic contact theory which can be used to characterize the rough surface thermodynamic properties.Then the validity of the model is verified.Finally,the influence of main parameters on the total normal load and the whole normal stiffness of thermal elasto-plastic contact at the interface is analyzed by contact simulation.The results show that the total normal load of thermal elasto-plastic contact increases with the increases of temperature.The whole normal stiffness of thermal elasto-plastic contact increases with increasing coefficient of linear expansion,scale factor,temperature difference or fractal dimension,but decreases with increasing fractal roughness.This model expands basic theory and applications of traditional models,and can be used to calculate and analyze the contacts when the temperature changes.
基金It is supported by the National Natural science Foundation of China(No.3 9170 2 2 2 )
文摘To study the gating kinetics of voltage dependent K + channel in clonal pheochromocytoma (PC12) cells, the inward currents of K channel in PC12 cells were recorded using cell attached patch clamp technique. The fractal features of the open and closed time distributions were determined. The fractal dimensions and kinetic setpoints for the open and closed durations were estimated. It was found that the fractal dimension D was independent of voltage and the logarithm logA of the setpoint A was inversely proportional to the pipette potential (Vp) for the closed durations. While for the open durations the fractal dimension D was inversely proportional to the pipette potential and the logarithm logA of the setpoint A was independent of voltage. Thus, for this channel the open and closed durations and voltage dependence of the gating could be well described by the fractal model.
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The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.
基金Supported by the National Natural Science Foundation of China (Grant No. 50778140)Special Research Foundation of Doctorial Subjects in Universities of China (Grant No. 20070497107)
文摘Based on the Sierpinski carpet and Menger sponge models, two categories of fractal models of rock and soil which are composed of the volume fractal model of pores, the volume fractal model of grains, pore-size or particle-size distribution fractal models are established and their relations are clarified in this paper. Through comparison and analysis, it is found that previous models can be unified by the two categories of fractal models, so the unified fractal models are formed. Experimental results presented by Katz indicate that the first category of fractal models can be used to express the fractal behavior of sandstone. A scanning electron microscope (SEM) will be used to study the microstructure of soft clay and it will be testified that the fractal behavior of soft clay suits the second category of fractal models.
文摘In this investigation,the Gradient Boosting(GB),Linear Regression(LR),Decision Tree(DT),and Voting algo-rithms were applied to predict the distribution pattern of Au geochemical data.Trace and indicator elements,including Mo,Cu,Pb,Zn,Ag,Ni,Co,Mn,Fe,and As,were used with these machine learning algorithms(MLAs)to predict Au concentration values in the Doostbigloo porphyry Cu-Au-Mo mineralization area.The performance of the models was evaluated using the Mean Absolute Percentage Error(MAPE)and Root Mean Square Error(RMSE)metrics.The proposed ensemble Voting algorithm outperformed the other models,yielding more ac-curate predictions according to both metrics.The predicted data from the GB,LR,DT,and Voting MLAs were modeled using the Concentration-Area fractal method,and Au geochemical anomalies were mapped.To compare and validate the results,factors such as the location of the mineral deposits,their surface extent,and mineralization trend were considered.The results indicate that integrating hybrid MLAs with fractal modeling signifi-cantly improves geochemical prospectivity mapping.Among the four models,three(DT,GB,Voting)accurately identified both mineral deposits.The LR model,however,only identified Deposit I(central),and its mineralization trend diverged from the field data.The GB and Voting models produced similar results,with their final maps derived from fractal modeling showing the same anomalous areas.The anomaly boundaries identified by these two models are consistent with the two known reserves in the region.The results and plots related to prediction indicators and error rates for these two models also show high similarity,with lower error rates than the other models.Notably,the Voting model demonstrated superior performance in accurately delineating mineral deposit locations and identifying realistic mineralization trends while minimizing false anomalies.
基金financially supported by the Ministry of Science and Technology of China(Nos.2022YFF0801201,2021YFC2900300)the National Natural Science Foundation of China(Nos.41872245,U1911202)the Guangdong Basic and Applied Basic Research Foundation(No.2020A1515010666)。
文摘To comprehensively utilize the valuable geological map,exploration profile,borehole,and geochemical logging data and the knowledge on the formation of the Jinshan Ag-Au deposit for forecasting the exploration targets of concealed ore bodies,three-dimensional Mineral Prospectivity Modeling(MPM)of the deposit has been conducted using the weights-of-evidence(WofE)method.Conditional independence between evidence layers was tested,and the outline results using the prediction-volume(P-V)and Student's t-statistic methods for delineating favorable mineralization areas from continuous posterior probability map were critically compared.Four exploration targets delineated ultimately by the Student's t-statistic method for the discovery of minable ore bodies in each of the target areas were discussed in detail.The main conclusions include:(1)three-dimensional modeling of a deposit using multi-source reconnaissance data is useful for MPM in interpreting their relationships with known ore bodies;(2)WofE modeling can be used as a straightforward tool for integrating deposit model and reconnaissance data in MPM;(3)the Student's t-statistic method is more applicable in binarizing the continuous prospectivity map for exploration targeting than the PV approach;and(4)two target areas within high potential to find undiscovered ore bodies were diagnosed to guide future near-mine exploration activities of the Jinshan deposit.
文摘The fracture of rock is dependent strongly on its microstructures and the loading situations. The rough and irregular fracture is affected by these and other complicated factors. But if the fracture is examined by means of mathematical method, only a geometry of irregularity appears. B. B. Mandelbrot proposed a new geometry—fractal geometry, and he applied it to various fields to describe irregular phenomena in nature.
基金supported by National Natural Science Foundation of China(No.51674279)China Postdoctoral Science Foundation(No.2016M602227)a grant from National Science and Technology Major Project(No.2017ZX05049-006)
文摘The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.
基金Supported by National Natural Science Foundation of China(Grant Nos.51105304,51475364)Shaanxi Provincial Natural Science Basic Research Plan of China(Grant No.2015JM5212)
文摘Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.
基金Supported by the National Natural Science Foundation of China (No. 29706010, No. 20203016).
文摘The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer particle's surface is irregular and has fractalcharacteristics, which can be described by fractal parameter. The more interesting discovery is thatthe surface fractal dimension values of the polymer particles vary periodically with thepolymerization time. We call this phenomenon fractal evolution, which can be divided into the'revolution' stage and the 'evolution' stage. And then we present polymerization fractal growingmodel (PFGM), and successfully describe and/or predict the whole evolving process of thepolyethylene particle morphology under the different slurry polymerization (includingpre-polymerization) conditions without H_2.
文摘The dynamic research of landslide is one of the key Points in landslidology. In the paper,from the view point of nonlinear dynamic theory. some features of Xintan landslide, such as the distribution regularities of spatial and temporal fractal dimensions and their corresponding relationships to landslide occurring are researched. The accumulative principles of fractal dimension reduction is exploratively pointed out. The nonlinear dynamic equation of the landslide is built by analyzing the relationship between the correlation dimension and the phase space. Finally, the forecasted results and error analysis are listed. The research results are satisfactory.
基金supported by National Natural Science Foundation of China (Grant Nos. 50975276,50475164)National Basic Research Program of China (973 Program,Grant No. 2007CB607605)+1 种基金Doctoral Programs Foundation of Ministry of Education of China (Grant No.200802900513)Priority Academic Program Development of Jiangsu Higher Education Institutions of China (PAPD)
文摘The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes： elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young＇s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.
