Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media withi...Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.展开更多
The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the...The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.展开更多
Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short w...Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.展开更多
Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This ...Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This paper proposes a successive shift box-counting method,in which the studied object is divided into small sub-objects that are composed of a series of gridsaccording to its characteristic scaling. The terrain fractal dimensions in the grids are calculatedwith the successive shift box-counting method and the scattered points with values of fractaldimensions are obtained. The present research shows that the planar variation of fractal dimensionsis well consistent with fault traces and geological boundaries.展开更多
In this paper, the box-counting dimension is used to derive an explicit formula for the dimension of a fractal constructed using several contractions or by combining fractals. This dimension agrees with the Hausdorff ...In this paper, the box-counting dimension is used to derive an explicit formula for the dimension of a fractal constructed using several contractions or by combining fractals. This dimension agrees with the Hausdorff dimension in the particular case when the scales factors considered are all the same. A more general sufficient condition for the box-counting dimension and the Hausdorff dimension to be the same is given. It is also shown that the dimension of the fractal obtained by combining two fractals is the weighted average of the dimensions of the two fractals.展开更多
In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set ar...In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.展开更多
Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This p...Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This puts high constraints and challenges on the design of such networks.Structural changing of the network is one of such challenges that affect the network performance,includ-ing the required quality of service(QoS).The fractal dimension(FD)is consid-ered one of the main indicators used to represent the structure of the communication network.To this end,this work analyzes the FD of the network and its use for telecommunication networks investigation and planning.The clus-ter growing method for assessing the FD is introduced and analyzed.The article proposes a novel method for estimating the FD of a communication network,based on assessing the network’s connectivity,by searching for the shortest routes.Unlike the cluster growing method,the proposed method does not require multiple iterations,which reduces the number of calculations,and increases the stability of the results obtained.Thus,the proposed method requires less compu-tational cost than the cluster growing method and achieves higher stability.The method is quite simple to implement and can be used in the tasks of research and planning of modern and promising communication networks.The developed method is evaluated for two different network structures and compared with the cluster growing method.Results validate the developed method.展开更多
The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was d...The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was developed based on the fractal theory and the computer image processing technology, was explored to describe the pore structure of porous metal materials. Furthermore, the fractal dimension of pore structure was calculated by the soft and the effects of magnification and porosity on ffactal dimension were also discussed. The results show that the fractal dimension decreases with increase in the magnification, while it increases continuously with the porosity enhancing. The interrelationship between the fractal dimension and the magnification or porosity can be presented by the equation of D=α_0exp(-x/α_1)+α_2和D=k_2-(k_1-k_2)/[1+exp((θ-k_0)/k_3)], respectively.展开更多
[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the ...[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.展开更多
Surface electromyogram (EMG) signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers' right forearm flexor respectively in the process of forearm su...Surface electromyogram (EMG) signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers' right forearm flexor respectively in the process of forearm supination (FS) and forearm pronation (FP).After the raw action surface EMG (ASEMG) signal was decomposed into several sub-signals with wavelet packet transform (WPT),five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.展开更多
A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpi...A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.展开更多
The loess area in the northern part of Baoji City, Shaanxi Province, China is a region with frequently landslide occurrences. The main aim of this study is to quantitatively predict the extent of landslides using the ...The loess area in the northern part of Baoji City, Shaanxi Province, China is a region with frequently landslide occurrences. The main aim of this study is to quantitatively predict the extent of landslides using the index of entropy model(IOE), the support vector machine model(SVM) and two hybrid models namely the F-IOE model and the F-SVM model constructed by fractal dimension. First, a total of 179 landslides were identified and landslide inventory map was produced, with 70%(125) of the landslides which was optimized by 10-fold crossvalidation being used for training purpose and the remaining 30%(54) of landslides being used for validation purpose. Subsequently, slope angle, slope aspect, altitude, rainfall, plan curvature, distance to rivers, land use, distance to roads, distance to faults, normalized difference vegetation index(NDVI), lithology, and profile curvature were considered as landslide conditioning factors and all factor layers were resampled to a uniform resolution. Then the information gain ratio of each conditioning factors was evaluated. Next, the fractal dimension for each conditioning factors was calculated and the training dataset was used to build four landslide susceptibility models. In the end, the receiver operating characteristic(ROC) curves and three statistical indexes involving positive predictive rate(PPR), negative predictive rate(NPR) and accuracy(ACC) were applied to validate and compare the performance of these four models. The results showed that the F-SVM model had the highest PPR, NPR, ACC and AUC values for training and validation datasets, respectively, followed by the F-IOE model.Finally, it is concluded that the F-SVM model performed best in all models, the hybrid model built by fractal dimension has advantages than original model, and can provide reference for local landslide prevention and decision making.展开更多
Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studi...Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studies examining soil particle volume fractal dimension in alpine grasslands.To study the volume fractal dimension of soil particles (D) and its relationships with soil salt,soil nutrient and plant species diversity,we conducted an experiment on an alpine grassland under different disturbance degrees:non-disturbance (N0),light disturbance (L),moderate disturbance (M) and heavy disturbance (H).The results showed that (1) Ds varied from 2.573 to 2.635 among the different disturbance degrees and increased with increasing degrees of disturbance.(2) Shannon-Wiener diversity index,Pielou's evenness index and Margalef richness index reached their highest values at the M degree,indicating that moderate disturbance is beneficial to the increase of plant species diversity.(3) In the L and M degrees,there was a significant positive correlation between D and clay content and a significant negative correlation between D and soil organic matter (SOM).In the H degree,D was significantly and positively correlated with total salt (TS).The results suggested that to a certain extent,D can be used to characterize the uniformity of soil texture in addition to soil fertility characteristics.(4) For the L degree,there was a significant negative correlation between D and the Shannon-Wiener diversity index; while for the M degree,there was a significant negative correlation between D and Pielou's evenness index.展开更多
We describe the fractal analysis of three differently sized coal samples(0.350-0.833 mm,0.245-0.350 mm,and 0.198-0.245 mm).The influence of fractal dimension on CH 4 adsorption capacity is investigated.The physical pa...We describe the fractal analysis of three differently sized coal samples(0.350-0.833 mm,0.245-0.350 mm,and 0.198-0.245 mm).The influence of fractal dimension on CH 4 adsorption capacity is investigated.The physical parameters of the samples were determined via the Brunauer-Emmett-Teller(BET) theory.A CH 4 adsorption study over the pressures range from 0 to 5 MPa was carried out with a new volumetric measurement system.The CH 4 adsorption was measured using the differently sized coal.Two fractal dimensions,D 1 and D 2 were determined over the pressure ranges from 0 to 0.5 MPa and from 0.5 to 1 MPa,using the Frenkel-Halsey-Hill(FHH) method.We conclude that the two fractal dimensions correlate with the CH 4 adsorption capacity of the coal:increasing CH 4 adsorption capacity occurs with a corresponding increase in fractal dimension.Furthermore,D 1 and D 2 are positively correlated with surface area,pore volume,and samples size.The size distribution of the samples has fractal characteristics.展开更多
Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the h...Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the help of intrinsically safe borehole video instrument.And according to the geology of this working face,a discrete element model was calculated by UDEC.Combining in situ experimental data with numerical results,the relationship between the fractal dimension of boreholes'wall and the distribution of advanced abutment pressure was studied under the condition of mining advance.The results show that the variation tendency of fractal dimension and the abutment pressure has the same characteristic value.The distance between working face and the peak value of the abutment pressure has a slight increasing trend with the advancing of mining-face.When the working face is set as the original point,the trend of fractal dimension from the far place to the origin can be divided into three phases:constant,steady increasing and constant.And the turning points of these phases are the max-influencing distance(50 m)and peak value(15 m)of abutment pressure.展开更多
The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitativel...The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.展开更多
Food dye Brilliant Blue was introduced as the tracer in a dye-tracing experiment to obtain dye profile patterns of sandy loam soil, aeolian sandy soil, percolating paddy soil and permeable paddy soil. The dyed soil pr...Food dye Brilliant Blue was introduced as the tracer in a dye-tracing experiment to obtain dye profile patterns of sandy loam soil, aeolian sandy soil, percolating paddy soil and permeable paddy soil. The dyed soil profiles were then photographed and the photos were scanned into a computer. Edited with certain software, only the dyed areas were left on the profile photos, which indicted the preferential flow paths for water and solute transport. Fractal dimensions of the dye patterns were calculated according to Arnold's function. Soil particle size distribution was analyzed by pipette method. The regression analysis showed that there was significant relationship between soil clay content and fractal dimension D of the dye pattern of soil profile. Based on the experiment results, the possibility of introducing fractal dimension to estimation of soil sensitivity to preferential flow is discussed.展开更多
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
基金supported by the National Natural Science Foundation of China (Nos.52374078 and 52074043)the Fundamental Research Funds for the Central Universities (No.2023CDJKYJH021)。
文摘Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.
文摘The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.
文摘Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.
文摘Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This paper proposes a successive shift box-counting method,in which the studied object is divided into small sub-objects that are composed of a series of gridsaccording to its characteristic scaling. The terrain fractal dimensions in the grids are calculatedwith the successive shift box-counting method and the scattered points with values of fractaldimensions are obtained. The present research shows that the planar variation of fractal dimensionsis well consistent with fault traces and geological boundaries.
文摘In this paper, the box-counting dimension is used to derive an explicit formula for the dimension of a fractal constructed using several contractions or by combining fractals. This dimension agrees with the Hausdorff dimension in the particular case when the scales factors considered are all the same. A more general sufficient condition for the box-counting dimension and the Hausdorff dimension to be the same is given. It is also shown that the dimension of the fractal obtained by combining two fractals is the weighted average of the dimensions of the two fractals.
文摘In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2022R66),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This puts high constraints and challenges on the design of such networks.Structural changing of the network is one of such challenges that affect the network performance,includ-ing the required quality of service(QoS).The fractal dimension(FD)is consid-ered one of the main indicators used to represent the structure of the communication network.To this end,this work analyzes the FD of the network and its use for telecommunication networks investigation and planning.The clus-ter growing method for assessing the FD is introduced and analyzed.The article proposes a novel method for estimating the FD of a communication network,based on assessing the network’s connectivity,by searching for the shortest routes.Unlike the cluster growing method,the proposed method does not require multiple iterations,which reduces the number of calculations,and increases the stability of the results obtained.Thus,the proposed method requires less compu-tational cost than the cluster growing method and achieves higher stability.The method is quite simple to implement and can be used in the tasks of research and planning of modern and promising communication networks.The developed method is evaluated for two different network structures and compared with the cluster growing method.Results validate the developed method.
基金Project(2011CB610302) supported by the National Basic Research Program of ChinaProjects(51074130,51134003) supported by the National Natural Science Foundation of ChinaProject(20110491699) supported by the National Science Foundation for Post-doctoral Scientists of China
文摘The FeCrA1 fiber was used to prepare porous metal materials with air-laid technology, and then followed by sintering at 1300 ℃ for a holding period of 2 h in the vacuum. In addition, a novel fractal soft, which was developed based on the fractal theory and the computer image processing technology, was explored to describe the pore structure of porous metal materials. Furthermore, the fractal dimension of pore structure was calculated by the soft and the effects of magnification and porosity on ffactal dimension were also discussed. The results show that the fractal dimension decreases with increase in the magnification, while it increases continuously with the porosity enhancing. The interrelationship between the fractal dimension and the magnification or porosity can be presented by the equation of D=α_0exp(-x/α_1)+α_2和D=k_2-(k_1-k_2)/[1+exp((θ-k_0)/k_3)], respectively.
基金Supported by National Natural Science Fund Program(40705038)~~
文摘[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.
基金The National Natural Science Foundation of China(No.60171006)the National Basic Research Programof China (973 Pro-gram) (No.2005CB724303).
文摘Surface electromyogram (EMG) signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers' right forearm flexor respectively in the process of forearm supination (FS) and forearm pronation (FP).After the raw action surface EMG (ASEMG) signal was decomposed into several sub-signals with wavelet packet transform (WPT),five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.
基金Supported by Visiting Scholar Foundation of Key Laboratory.inUniversity
文摘A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.
基金funded by National Key Research and Development Program of China (Grant No. 2017YFC0504700)
文摘The loess area in the northern part of Baoji City, Shaanxi Province, China is a region with frequently landslide occurrences. The main aim of this study is to quantitatively predict the extent of landslides using the index of entropy model(IOE), the support vector machine model(SVM) and two hybrid models namely the F-IOE model and the F-SVM model constructed by fractal dimension. First, a total of 179 landslides were identified and landslide inventory map was produced, with 70%(125) of the landslides which was optimized by 10-fold crossvalidation being used for training purpose and the remaining 30%(54) of landslides being used for validation purpose. Subsequently, slope angle, slope aspect, altitude, rainfall, plan curvature, distance to rivers, land use, distance to roads, distance to faults, normalized difference vegetation index(NDVI), lithology, and profile curvature were considered as landslide conditioning factors and all factor layers were resampled to a uniform resolution. Then the information gain ratio of each conditioning factors was evaluated. Next, the fractal dimension for each conditioning factors was calculated and the training dataset was used to build four landslide susceptibility models. In the end, the receiver operating characteristic(ROC) curves and three statistical indexes involving positive predictive rate(PPR), negative predictive rate(NPR) and accuracy(ACC) were applied to validate and compare the performance of these four models. The results showed that the F-SVM model had the highest PPR, NPR, ACC and AUC values for training and validation datasets, respectively, followed by the F-IOE model.Finally, it is concluded that the F-SVM model performed best in all models, the hybrid model built by fractal dimension has advantages than original model, and can provide reference for local landslide prevention and decision making.
基金financially supported by the National Basic Research Program of China(2009CB825103)
文摘Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studies examining soil particle volume fractal dimension in alpine grasslands.To study the volume fractal dimension of soil particles (D) and its relationships with soil salt,soil nutrient and plant species diversity,we conducted an experiment on an alpine grassland under different disturbance degrees:non-disturbance (N0),light disturbance (L),moderate disturbance (M) and heavy disturbance (H).The results showed that (1) Ds varied from 2.573 to 2.635 among the different disturbance degrees and increased with increasing degrees of disturbance.(2) Shannon-Wiener diversity index,Pielou's evenness index and Margalef richness index reached their highest values at the M degree,indicating that moderate disturbance is beneficial to the increase of plant species diversity.(3) In the L and M degrees,there was a significant positive correlation between D and clay content and a significant negative correlation between D and soil organic matter (SOM).In the H degree,D was significantly and positively correlated with total salt (TS).The results suggested that to a certain extent,D can be used to characterize the uniformity of soil texture in addition to soil fertility characteristics.(4) For the L degree,there was a significant negative correlation between D and the Shannon-Wiener diversity index; while for the M degree,there was a significant negative correlation between D and Pielou's evenness index.
基金funded by the State Key Basic Research Program of China(No.2011CB201202)
文摘We describe the fractal analysis of three differently sized coal samples(0.350-0.833 mm,0.245-0.350 mm,and 0.198-0.245 mm).The influence of fractal dimension on CH 4 adsorption capacity is investigated.The physical parameters of the samples were determined via the Brunauer-Emmett-Teller(BET) theory.A CH 4 adsorption study over the pressures range from 0 to 5 MPa was carried out with a new volumetric measurement system.The CH 4 adsorption was measured using the differently sized coal.Two fractal dimensions,D 1 and D 2 were determined over the pressure ranges from 0 to 0.5 MPa and from 0.5 to 1 MPa,using the Frenkel-Halsey-Hill(FHH) method.We conclude that the two fractal dimensions correlate with the CH 4 adsorption capacity of the coal:increasing CH 4 adsorption capacity occurs with a corresponding increase in fractal dimension.Furthermore,D 1 and D 2 are positively correlated with surface area,pore volume,and samples size.The size distribution of the samples has fractal characteristics.
基金financial support from the State Key Basic Research Program of China(Nos.2011CB201201and 2010CB226802)the National Natural Science Foundation of China(No.51204112)
文摘Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the help of intrinsically safe borehole video instrument.And according to the geology of this working face,a discrete element model was calculated by UDEC.Combining in situ experimental data with numerical results,the relationship between the fractal dimension of boreholes'wall and the distribution of advanced abutment pressure was studied under the condition of mining advance.The results show that the variation tendency of fractal dimension and the abutment pressure has the same characteristic value.The distance between working face and the peak value of the abutment pressure has a slight increasing trend with the advancing of mining-face.When the working face is set as the original point,the trend of fractal dimension from the far place to the origin can be divided into three phases:constant,steady increasing and constant.And the turning points of these phases are the max-influencing distance(50 m)and peak value(15 m)of abutment pressure.
基金Projects(51822403,51827901)supported by the National Natural Science Foundation of ChinaProject(2019ZT08G315)supported by the Department of Science and Technology of Guangdong Province,China。
文摘The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.
基金Project supported by the National Key Basic Research Support FOundation(NKBRSF) of China(No.G19990ll708) and the Guangxi Uni,rsitv Science funds China(No.1701).
文摘Food dye Brilliant Blue was introduced as the tracer in a dye-tracing experiment to obtain dye profile patterns of sandy loam soil, aeolian sandy soil, percolating paddy soil and permeable paddy soil. The dyed soil profiles were then photographed and the photos were scanned into a computer. Edited with certain software, only the dyed areas were left on the profile photos, which indicted the preferential flow paths for water and solute transport. Fractal dimensions of the dye patterns were calculated according to Arnold's function. Soil particle size distribution was analyzed by pipette method. The regression analysis showed that there was significant relationship between soil clay content and fractal dimension D of the dye pattern of soil profile. Based on the experiment results, the possibility of introducing fractal dimension to estimation of soil sensitivity to preferential flow is discussed.
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.