Experiments were performed to study the pitting corrosion morphology of 304 stainless steel exposed to FeCl 3 environments and SEM micrographs of the pitting corrosion morphology were obtained. The image processing te...Experiments were performed to study the pitting corrosion morphology of 304 stainless steel exposed to FeCl 3 environments and SEM micrographs of the pitting corrosion morphology were obtained. The image processing technique combining with the fractal method was employed to analyze these pitting corrosion images and the self-similarity of pits morphology was observed. It indicates that fractal characteristics exist in pitting corrosion of 304 stainless steel. The self-similarity and complexity of the pitting morphology phenomenon were described in terms of fractal dimension which can also be an important parameter related to characterize pitting morphology qualitatively and quantitatively.展开更多
Fractal theory was applied to a preliminary discussion of the fractal character and formation mechanism of the coastline of the bedrock coast of China on the basis of GIS (Geographical Information System). Some signif...Fractal theory was applied to a preliminary discussion of the fractal character and formation mechanism of the coastline of the bedrock coast of China on the basis of GIS (Geographical Information System). Some significant conclusions were drawn:(1) The fractal dimensions of the coastline and linear structures of Liaodong Peninsula are 1.0093 and 1.0246 respectively, those of Shandong Peninsula are 1.019 and 1.021 respectively, etc.(2) The fractal dimensions of coastlines of Liaodong Peninsula, Shandong Peninsula, Zhejiang and Fujian-Guangdong tend to increase with the spatial change from north to south.(3)The regional linear structures(including faults)control the basic trends and fractal dimensions of coastlines as a whole in the regions of the bedrock coast of China:the more the controlling effect of linear structures, the smaller the fractal dimensions of coastlines.(4)The substantial constituents of coast and biologic function both play an important role in affecting the fractal dimensions of coastlines of Liaodong Peninsula, Shandong Peninsula, Zhejiang, Fujian-Guangdong and Taiwan Island.展开更多
MANDELBROT enunciated the uncertainty of the length of a coastline in his paper "How long is the coastline of Britain?" published in Science in 1967. The fractal concept was presented for the first time in t...MANDELBROT enunciated the uncertainty of the length of a coastline in his paper "How long is the coastline of Britain?" published in Science in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated by the box-counting method,the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China′s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China′s Mainland,and it does not vary with the changes of series of square grids,the fractal dimensions of the mountains of China′s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China′s Mainland vary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China′s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension,and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China′s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China′s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension,and ensure that the fractal studies would be scientific.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
To give a better understanding of the morphological features of rock fracture surfaces within the framework of fractal geometry, the fractal characters of the rough surfaces in rock are analyzed according to the vario...To give a better understanding of the morphological features of rock fracture surfaces within the framework of fractal geometry, the fractal characters of the rough surfaces in rock are analyzed according to the variogram method. The study elaborates the significance of the geometric parameters-fractal dimension D and the intercept A on a log-log plot to the surface structure. Investigation extends to the anisotropy and heterogeneity of rock fracture surfaces, and the scale effect on the fractal estimation. The present study indicates that fractal dimension alone may not be sufficient to characterize the surface roughness of rock Joints. A reliable estimation should take into account the combination of D and A.展开更多
文摘Experiments were performed to study the pitting corrosion morphology of 304 stainless steel exposed to FeCl 3 environments and SEM micrographs of the pitting corrosion morphology were obtained. The image processing technique combining with the fractal method was employed to analyze these pitting corrosion images and the self-similarity of pits morphology was observed. It indicates that fractal characteristics exist in pitting corrosion of 304 stainless steel. The self-similarity and complexity of the pitting morphology phenomenon were described in terms of fractal dimension which can also be an important parameter related to characterize pitting morphology qualitatively and quantitatively.
文摘Fractal theory was applied to a preliminary discussion of the fractal character and formation mechanism of the coastline of the bedrock coast of China on the basis of GIS (Geographical Information System). Some significant conclusions were drawn:(1) The fractal dimensions of the coastline and linear structures of Liaodong Peninsula are 1.0093 and 1.0246 respectively, those of Shandong Peninsula are 1.019 and 1.021 respectively, etc.(2) The fractal dimensions of coastlines of Liaodong Peninsula, Shandong Peninsula, Zhejiang and Fujian-Guangdong tend to increase with the spatial change from north to south.(3)The regional linear structures(including faults)control the basic trends and fractal dimensions of coastlines as a whole in the regions of the bedrock coast of China:the more the controlling effect of linear structures, the smaller the fractal dimensions of coastlines.(4)The substantial constituents of coast and biologic function both play an important role in affecting the fractal dimensions of coastlines of Liaodong Peninsula, Shandong Peninsula, Zhejiang, Fujian-Guangdong and Taiwan Island.
基金Under the auspices of the National Natural Science Foundation of China(No.40301002) and the Key Program of the National Natural Science Foundation of China(No.40335046)
文摘MANDELBROT enunciated the uncertainty of the length of a coastline in his paper "How long is the coastline of Britain?" published in Science in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated by the box-counting method,the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China′s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China′s Mainland,and it does not vary with the changes of series of square grids,the fractal dimensions of the mountains of China′s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China′s Mainland vary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China′s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension,and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China′s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China′s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension,and ensure that the fractal studies would be scientific.
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.
文摘To give a better understanding of the morphological features of rock fracture surfaces within the framework of fractal geometry, the fractal characters of the rough surfaces in rock are analyzed according to the variogram method. The study elaborates the significance of the geometric parameters-fractal dimension D and the intercept A on a log-log plot to the surface structure. Investigation extends to the anisotropy and heterogeneity of rock fracture surfaces, and the scale effect on the fractal estimation. The present study indicates that fractal dimension alone may not be sufficient to characterize the surface roughness of rock Joints. A reliable estimation should take into account the combination of D and A.
