Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar patter...Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.展开更多
Fractal theory is becoming an increasingly useful tool to describe soil structure dynamics for a better understanding of the performance of soil systems. Changes in land use patterns significantly affect soil physical...Fractal theory is becoming an increasingly useful tool to describe soil structure dynamics for a better understanding of the performance of soil systems. Changes in land use patterns significantly affect soil physical, chemical and biological properties. However, limited information is available on the fractal characteristics of deep soil layers under different land use patterns. In this study, the fractal dimensions of particle size distribution(PSD) and micro-aggregates in the 0–500 cm soil profile and soil anti-erodibility in the 0–10 cm soil profile for 10 typical land use patterns were investigated in the Zhifanggou Watershed on the Loess Plateau, China. The 10 typical land use patterns were: slope cropland, two terraced croplands, check-dam cropland, woodland, two shrublands, orchard, artificial and natural grasslands. The results showed that the fractal dimensions of PSD and micro-aggregates were all significantly influenced by soil depths, land use patterns and their interaction. The plantations of shrubland, woodland and natural grassland increased the amount of larger micro-aggregates, and decreased the fractal dimensions of micro-aggregates in the 0–40 cm soil profile. And they also improved the aggregate state and aggregate degree and decreased dispersion rate in the 0–10 cm soil profile. The results indicated that fractal theory can be used to characterize soil structure under different land use patterns and fractal dimensions of micro-aggregates were more effective in this regard. The natural grassland may be the best choice for improving soil structure in the study area.展开更多
An automatic three-dimensional(3D) reconstruction method based on four-view stereo vision using checkerboard pattern is presented. Mismatches easily exist in traditional binocular stereo matching due to the repeatable...An automatic three-dimensional(3D) reconstruction method based on four-view stereo vision using checkerboard pattern is presented. Mismatches easily exist in traditional binocular stereo matching due to the repeatable or similar features of binocular images. In order to reduce the probability of mismatching and improve the measure precision, a four-camera measurement system which can add extra matching constraints and offer multiple measurements is applied in this work. Moreover, a series of different checkerboard patterns are projected onto the object to obtain dense feature points and remove mismatched points. Finally, the 3D model is generated by performing Delaunay triangulation and texture mapping on the point cloud obtained by four-view matching. This method was tested on the 3D reconstruction of a terracotta soldier sculpture and the Buddhas in the Mogao Grottoes. Their point clouds without mismatched points were obtained and less processing time was consumed in most cases relative to binocular matching. These good reconstructed models show the effectiveness of the method.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
Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix.The sparingly soluble salt formed,displays a beautiful stratification of disc...Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix.The sparingly soluble salt formed,displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis.The Liesegang structures are analyzed from the viewpoint of their fractal nature.Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time,band spacing and band width laws.The dependence of the band spacing on the initial concentrations of diffusing(outer)and immobile(inner)electrolytes(A0 and B0,respectively)is taken to follow the Matalon-Packter law.Both mathematical fractal dimensions and box-count dimensions are calculated.The fractal dimension is found to increase with increasing A0 and decreasing B0.We also analyze mosaic patterns with random distribution of crystallites,grown under different conditions than the classical Liesegang gel method,and report on their fractal properties.Finally,complex Liesegang patterns wherein the bands are grouped in multiplets are studied,and it is shown that the fractal nature increases with the multiplicity.展开更多
Under biaxial pressure, the microcrack patterns of concrete samples with hard inclusion are as followings: Microcracks generate around the sample at the early pressured period, and gap is formed in the middle part wit...Under biaxial pressure, the microcrack patterns of concrete samples with hard inclusion are as followings: Microcracks generate around the sample at the early pressured period, and gap is formed in the middle part with the increase of σ 1; microcrack gap is becoming smaller gradually with σ 1 increase again; microcracks become active within the original gap, but they in an original active area become small. Approaching the main fracture, microcracks form as a belt and jump back and forth in the belt. The spatial fractal D s of microcracks changes from small to big, but turns decrease when approaching the main fracture. All of the features were seldom mentioned in the past experiment, however, which have some similarities with the long seismicity patterns before strong earthquakes. In this paper, Lancang Gengma earthquake was taken as an example to analyse.〖KH*2D]展开更多
Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyze...Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyzed the fracture surface characteristics induced by supercritical carbon dioxide(SC-CO_(2))and water in open-hole and perforation completion conditions under triaxial stresses.A simple calculation method was proposed to quantitatively analyze the fracture surface area and roughness in macro-level based on three-dimensional(3D)scanning data.In micro-level,scanning electron micrograph(SEM)was used to analyze the features of fracture surface.The results showed that the surface area of the induced fracture increases with perforation angle for both SC-CO_(2)and water fracturing,and the surface area of SC-CO_(2)-induced fracture is 6.49%e58.57%larger than that of water-induced fracture.The fractal dimension and surface roughness of water-induced fractures increase with the increase in perforation angle,while those of SC-CO_(2)-induced fractures decrease with the increasing perforation angle.A considerable number of microcracks and particle peeling pits can be observed on SC-CO_(2)-induced fracture surface while there are more flat particle surfaces in water-induced fracture surface through SEM images,indicating that fractures tend to propagate along the boundary of the particle for SC-CO_(2)fracturing while water-induced fractures prefer to cut through particles.These findings are of great significance for analyzing fracture mechanism and evaluating fracturing stimulation performance.展开更多
To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested...To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested: geometric patterns, fractal patterns, reptile-skin patterns, and patterns of circular cylinders arranged in a lattice and in a zigzag manner. A suitable pattern for adaptive control of flow is one that generates longitudinal vortices with nonconstant distances. The preferred instability mode of a laminar boundary layer is expected to be selected automatically from fluctuations involving many frequencies and caused by fractal patterns. Snake- and reptile-skin patterns may have a similar ability as fractal patterns because they consist of multiscale patterns. The longitudinal vortices generated from peculiar positions and concave corners in patterns were observed. The distance between these vortices is not constant because the onset of vortices is at concave corners in fractal patterns. These vortices have differing strengths and easily cause nonlinear interactions, so they can disturb a laminar boundary layer with several higher-harmonic frequencies. The velocity profiles of the laminar boundary-layer flow over the fractal patterns were measured by using hydrogen bubbles. The results show the down-wash flow between the longitudinal vortices, which means that the vortices may effectively suppress the boundary layer separation in an adverse pressure gradient.展开更多
The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of a...The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of as fractals as they exhibit self-similarity within the range of scale considered. Their fractal dimensions are not integer but fractional, ranging from 1.04 to 1.51. The unoccupied dimensions change from 0.49 to 0.96. The combined conditions of population density, pattern type and aggregation intensity together influence the values of fractal dimensions of patterns. The box counting is a useful and efficient method to investigate the complexity of patterns. Fractal dimension may be a most desirable and appropriate index for quantifying the horizontal spatial microstructure and fractal behaviors of patterns over a certain range of scales.展开更多
Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometr...Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.展开更多
The researches about reed growth were mainly concentrated on seasonal dynamics, investigation of reed resource, and comparison of different ecotypes of reed. By means of fractal geometric theory of non linear science...The researches about reed growth were mainly concentrated on seasonal dynamics, investigation of reed resource, and comparison of different ecotypes of reed. By means of fractal geometric theory of non linear science, the fractal character of growth pattern of reed, for the purpose of quantitatively exploring the mechanism of reed growth was studied. The way to calculate fractal dimension of reed growth is box dimension (BD) and information dimension (ID). The results showed that the difference between two samplings in May and those among three samplings in June and later were not remarkable for both BD or ID. It was noted that the difference between samplings in and after May is significant. It was demonstrated that the fractal dimension of size distribution of reed ranged from 0 6235 to 0 8761 The distribution pattern could be statistically divided as two significant periods: the size of reed is quite well distributed at the beginning of reed growth (fractal dimension>0 8), but is irregular in the middle and later growth season (fractal dimension<0 7). These results are benefit to reach the goal of rational use of reed resources and to protect the biodiversity in wetland ecosystem.展开更多
A series of laboratory investigations are conducted to analyze the effect of flocculant type on the spatial morphology and microstructural characteristics of flocs during the flocculation and settling of tailings.Four...A series of laboratory investigations are conducted to analyze the effect of flocculant type on the spatial morphology and microstructural characteristics of flocs during the flocculation and settling of tailings.Four flocculant types(i.e.,ZYZ,JYC-2,ZYD,and JYC-1)are considered in this study.The fractal characteristics and internal structures of tailings flocs with different flocculant types and settlement heights are analyzed by conducting scanning electron microscopy and X-ray micro-computed tomography scanning experiments based on the fractal theory.Results show that unclassified tailings flocs are irregular clusters with fractal characteristics,and the flocculation effect of the four flocculant types has the following trend:ZYZ>JYC-2>ZYD>JYC-1.The size and average grayscale value of tailings flocs decrease with the increase in settlement height.The average grayscale values at the top and bottom are 144 and 103,respectively.The settlement height remarkably affects the pore distribution pattern,as reflected in the constructed three-dimensional pore model of tailings flocs.The top part of flocs has relatively good penetration,whereas the bottom part of flocs has mostly dispersed pores.The number of pores increases exponentially with the increase in settlement height.By contrast,the size of pores initially increases and subsequently decreases with the increase in settlement height.展开更多
Expo 2010 Shanghai China was a successful, splendid, and unforgettable event, leaving us with valuable experi- ences. The visitor flow pattern of the Expo is investigated in this paper. The Hurst exponent, the mean va...Expo 2010 Shanghai China was a successful, splendid, and unforgettable event, leaving us with valuable experi- ences. The visitor flow pattern of the Expo is investigated in this paper. The Hurst exponent, the mean value, and the standard deviation of visitor volume indicate that the visitor flow is fractal with long-term stability and correlation as well as obvious fluctuation in a short period. Then the time series of visitor volume is converted into a complex network by using the visibility algorithm. It can be inferred from the topological properties of the visibility graph that the network is scale-free, small-world, and hierarchically constructed, confirming that the time series are fractal and a close relationship exists among the visitor volumes on different days. Furthermore, it is inevitable that will be some extreme visitor volumes in the original visitor flow, and these extreme points may appear in a group to a great extent. All these properties are closely related to the feature of the complex network. Finally, the revised linear regression is performed to forecast the next-day visitor volume based on the previous 10-day data.展开更多
文摘Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.
基金supported by the Strategic Technology Project of Chinese Academy of Sciences (XDA05060300)the Science and Technology R&D Program of Shaanxi Province (2011KJXX63)
文摘Fractal theory is becoming an increasingly useful tool to describe soil structure dynamics for a better understanding of the performance of soil systems. Changes in land use patterns significantly affect soil physical, chemical and biological properties. However, limited information is available on the fractal characteristics of deep soil layers under different land use patterns. In this study, the fractal dimensions of particle size distribution(PSD) and micro-aggregates in the 0–500 cm soil profile and soil anti-erodibility in the 0–10 cm soil profile for 10 typical land use patterns were investigated in the Zhifanggou Watershed on the Loess Plateau, China. The 10 typical land use patterns were: slope cropland, two terraced croplands, check-dam cropland, woodland, two shrublands, orchard, artificial and natural grasslands. The results showed that the fractal dimensions of PSD and micro-aggregates were all significantly influenced by soil depths, land use patterns and their interaction. The plantations of shrubland, woodland and natural grassland increased the amount of larger micro-aggregates, and decreased the fractal dimensions of micro-aggregates in the 0–40 cm soil profile. And they also improved the aggregate state and aggregate degree and decreased dispersion rate in the 0–10 cm soil profile. The results indicated that fractal theory can be used to characterize soil structure under different land use patterns and fractal dimensions of micro-aggregates were more effective in this regard. The natural grassland may be the best choice for improving soil structure in the study area.
基金Project(2012CB725301)supported by the National Basic Research Program of ChinaProject(201412015)supported by the National Special Fund for Surveying and Mapping Geographic Information Scientific Research in the Public Welfare of ChinaProject(212000168)supported by the Basic Survey-Mapping Program of National Administration of Surveying,Mapping and Geoinformation of China
文摘An automatic three-dimensional(3D) reconstruction method based on four-view stereo vision using checkerboard pattern is presented. Mismatches easily exist in traditional binocular stereo matching due to the repeatable or similar features of binocular images. In order to reduce the probability of mismatching and improve the measure precision, a four-camera measurement system which can add extra matching constraints and offer multiple measurements is applied in this work. Moreover, a series of different checkerboard patterns are projected onto the object to obtain dense feature points and remove mismatched points. Finally, the 3D model is generated by performing Delaunay triangulation and texture mapping on the point cloud obtained by four-view matching. This method was tested on the 3D reconstruction of a terracotta soldier sculpture and the Buddhas in the Mogao Grottoes. Their point clouds without mismatched points were obtained and less processing time was consumed in most cases relative to binocular matching. These good reconstructed models show the effectiveness of the method.
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Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix.The sparingly soluble salt formed,displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis.The Liesegang structures are analyzed from the viewpoint of their fractal nature.Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time,band spacing and band width laws.The dependence of the band spacing on the initial concentrations of diffusing(outer)and immobile(inner)electrolytes(A0 and B0,respectively)is taken to follow the Matalon-Packter law.Both mathematical fractal dimensions and box-count dimensions are calculated.The fractal dimension is found to increase with increasing A0 and decreasing B0.We also analyze mosaic patterns with random distribution of crystallites,grown under different conditions than the classical Liesegang gel method,and report on their fractal properties.Finally,complex Liesegang patterns wherein the bands are grouped in multiplets are studied,and it is shown that the fractal nature increases with the multiplicity.
文摘Under biaxial pressure, the microcrack patterns of concrete samples with hard inclusion are as followings: Microcracks generate around the sample at the early pressured period, and gap is formed in the middle part with the increase of σ 1; microcrack gap is becoming smaller gradually with σ 1 increase again; microcracks become active within the original gap, but they in an original active area become small. Approaching the main fracture, microcracks form as a belt and jump back and forth in the belt. The spatial fractal D s of microcracks changes from small to big, but turns decrease when approaching the main fracture. All of the features were seldom mentioned in the past experiment, however, which have some similarities with the long seismicity patterns before strong earthquakes. In this paper, Lancang Gengma earthquake was taken as an example to analyse.〖KH*2D]
基金National Natural Science Foundation of China(Grant No.51804318)the China Postdoctoral Science Foundation Founded Project(Grant No.2019M650963)National Key Basic Research and Development Program of China(Grant No.2014CB239203).
文摘Morphology of hydraulic fracture surface has significant effects on oil and gas flow,proppant migration and fracture closure,which plays an important role in oil and gas fracturing stimulation.In this paper,we analyzed the fracture surface characteristics induced by supercritical carbon dioxide(SC-CO_(2))and water in open-hole and perforation completion conditions under triaxial stresses.A simple calculation method was proposed to quantitatively analyze the fracture surface area and roughness in macro-level based on three-dimensional(3D)scanning data.In micro-level,scanning electron micrograph(SEM)was used to analyze the features of fracture surface.The results showed that the surface area of the induced fracture increases with perforation angle for both SC-CO_(2)and water fracturing,and the surface area of SC-CO_(2)-induced fracture is 6.49%e58.57%larger than that of water-induced fracture.The fractal dimension and surface roughness of water-induced fractures increase with the increase in perforation angle,while those of SC-CO_(2)-induced fractures decrease with the increasing perforation angle.A considerable number of microcracks and particle peeling pits can be observed on SC-CO_(2)-induced fracture surface while there are more flat particle surfaces in water-induced fracture surface through SEM images,indicating that fractures tend to propagate along the boundary of the particle for SC-CO_(2)fracturing while water-induced fractures prefer to cut through particles.These findings are of great significance for analyzing fracture mechanism and evaluating fracturing stimulation performance.
文摘To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested: geometric patterns, fractal patterns, reptile-skin patterns, and patterns of circular cylinders arranged in a lattice and in a zigzag manner. A suitable pattern for adaptive control of flow is one that generates longitudinal vortices with nonconstant distances. The preferred instability mode of a laminar boundary layer is expected to be selected automatically from fluctuations involving many frequencies and caused by fractal patterns. Snake- and reptile-skin patterns may have a similar ability as fractal patterns because they consist of multiscale patterns. The longitudinal vortices generated from peculiar positions and concave corners in patterns were observed. The distance between these vortices is not constant because the onset of vortices is at concave corners in fractal patterns. These vortices have differing strengths and easily cause nonlinear interactions, so they can disturb a laminar boundary layer with several higher-harmonic frequencies. The velocity profiles of the laminar boundary-layer flow over the fractal patterns were measured by using hydrogen bubbles. The results show the down-wash flow between the longitudinal vortices, which means that the vortices may effectively suppress the boundary layer separation in an adverse pressure gradient.
基金The paper is supported by grants from the NSFC (No. 39825106 and 39860023).
文摘The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of as fractals as they exhibit self-similarity within the range of scale considered. Their fractal dimensions are not integer but fractional, ranging from 1.04 to 1.51. The unoccupied dimensions change from 0.49 to 0.96. The combined conditions of population density, pattern type and aggregation intensity together influence the values of fractal dimensions of patterns. The box counting is a useful and efficient method to investigate the complexity of patterns. Fractal dimension may be a most desirable and appropriate index for quantifying the horizontal spatial microstructure and fractal behaviors of patterns over a certain range of scales.
基金Project supported by the Natural Science Foundation of Zhejiang Province (No. M603228), Zhejiang Science and Technology Plan Project, and Ningbo Science Foundation for Doctor, China
文摘Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.
文摘The researches about reed growth were mainly concentrated on seasonal dynamics, investigation of reed resource, and comparison of different ecotypes of reed. By means of fractal geometric theory of non linear science, the fractal character of growth pattern of reed, for the purpose of quantitatively exploring the mechanism of reed growth was studied. The way to calculate fractal dimension of reed growth is box dimension (BD) and information dimension (ID). The results showed that the difference between two samplings in May and those among three samplings in June and later were not remarkable for both BD or ID. It was noted that the difference between samplings in and after May is significant. It was demonstrated that the fractal dimension of size distribution of reed ranged from 0 6235 to 0 8761 The distribution pattern could be statistically divided as two significant periods: the size of reed is quite well distributed at the beginning of reed growth (fractal dimension>0 8), but is irregular in the middle and later growth season (fractal dimension<0 7). These results are benefit to reach the goal of rational use of reed resources and to protect the biodiversity in wetland ecosystem.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51974012 and 51804017)the National Key Research and Development Program of China(No.2018YFC0604602)+1 种基金the Fundamental Research Funds for the Central Universities,China(No.FRF-BD-19-005A)the Opening Fund of State Key Laboratory of Nonlinear Mechanics(No.LNM202009).
文摘A series of laboratory investigations are conducted to analyze the effect of flocculant type on the spatial morphology and microstructural characteristics of flocs during the flocculation and settling of tailings.Four flocculant types(i.e.,ZYZ,JYC-2,ZYD,and JYC-1)are considered in this study.The fractal characteristics and internal structures of tailings flocs with different flocculant types and settlement heights are analyzed by conducting scanning electron microscopy and X-ray micro-computed tomography scanning experiments based on the fractal theory.Results show that unclassified tailings flocs are irregular clusters with fractal characteristics,and the flocculation effect of the four flocculant types has the following trend:ZYZ>JYC-2>ZYD>JYC-1.The size and average grayscale value of tailings flocs decrease with the increase in settlement height.The average grayscale values at the top and bottom are 144 and 103,respectively.The settlement height remarkably affects the pore distribution pattern,as reflected in the constructed three-dimensional pore model of tailings flocs.The top part of flocs has relatively good penetration,whereas the bottom part of flocs has mostly dispersed pores.The number of pores increases exponentially with the increase in settlement height.By contrast,the size of pores initially increases and subsequently decreases with the increase in settlement height.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70871082)the Shanghai Leading Academic Discipline Project, China (Grant No. S30504)the Science and Technology Innovation Foundation of Shanxi Agricultural University, China (Grant No. 201208)
文摘Expo 2010 Shanghai China was a successful, splendid, and unforgettable event, leaving us with valuable experi- ences. The visitor flow pattern of the Expo is investigated in this paper. The Hurst exponent, the mean value, and the standard deviation of visitor volume indicate that the visitor flow is fractal with long-term stability and correlation as well as obvious fluctuation in a short period. Then the time series of visitor volume is converted into a complex network by using the visibility algorithm. It can be inferred from the topological properties of the visibility graph that the network is scale-free, small-world, and hierarchically constructed, confirming that the time series are fractal and a close relationship exists among the visitor volumes on different days. Furthermore, it is inevitable that will be some extreme visitor volumes in the original visitor flow, and these extreme points may appear in a group to a great extent. All these properties are closely related to the feature of the complex network. Finally, the revised linear regression is performed to forecast the next-day visitor volume based on the previous 10-day data.