A simple and practical method to calculate the fractal dimension （FD） of amicron＇s projective surface profile based on fractal theory is proposed. Taking AI（OH）3 material particles as an example, the scanning ele...A simple and practical method to calculate the fractal dimension （FD） of amicron＇s projective surface profile based on fractal theory is proposed. Taking AI（OH）3 material particles as an example, the scanning electron microscope （SEM） photos of particles were processed using an image.processing software （IPS） Photoshop. Taking the pixel as a fixed yardstick with the enlargement of the size of the particle image, the box-dimension and circumference-area （C-S） methods were used to calculate the FD of the surface profile of the particle. The FD of 1.2623 of the classic Koch curve is obtained, which approximates the true value of 1.2628. The complexities of the object＇s boundary and surface micro-topography are simulated successfully by a generator method.展开更多
Using fractal dimension to reflect and simulate urban morphology are two applications of fractal theory in city geography. As the only consistent description of a fractal, fractal dimension plays an important role in ...Using fractal dimension to reflect and simulate urban morphology are two applications of fractal theory in city geography. As the only consistent description of a fractal, fractal dimension plays an important role in describing the basic features of fractals. Just like other fractals, our cities have similar characteristics. Fractal dimension to some extent is regarded as an indicator of urban expansion, and it may change with urban morphology in different time and space. Based on the Geographic Information System (GIS), taking Wuhan city as a test area, the fractal dimensions of different land use were calculated, and a linear regression equation was established to analyze the relationship between fractal dimension and residential areas. Then the author used fractal dimension to simulate the urban boundary which is an important part of urban mor-phology. A mid-point subdivision fractal generator is needed in the simulation process, and the shape of the generator is determined by fractal dimension. According to the fractal theory, fractal boundaries in different scales have self-similarity and they have the same fractal dimensions. Based on this fact, the simulation method the author used could quantitatively keep the similarity of configuration of the urban boundaries.展开更多
Araneiforms are spider-like ground patterns that are widespread in the southern polar regions of Mars.A gas erosion process driven by the seasonal sublimation of CO_(2)ice was proposed as an explanation for their form...Araneiforms are spider-like ground patterns that are widespread in the southern polar regions of Mars.A gas erosion process driven by the seasonal sublimation of CO_(2)ice was proposed as an explanation for their formation,which cannot occur on Earth due to the high climatic temperature.In this study,we propose an alternative mechanism that attrib-utes the araneiform formation to the erosion of upwelling salt water from the subsurface,relying on the identification of the first terrestrial analog found in a playa of the Qaidam Basin on the northern Tibetan Plateau.Morphological analysis indicates that the structures in the Qaidam Basin have fractal features comparable to araneiforms on Mars.A numerical model is developed to investigate the araneiform formation driven by the water-diffusion mechanism.The simulation res-ults indicate that the water-diffusion process,under varying ground conditions,may be responsible for the diverse aranei-form morphologies observed on both Earth and Mars.Our numerical simulations also demonstrate that the orientations of the saltwater diffusion networks are controlled by pre-existing polygonal cracks,which is consistent with observations of araneiforms on Mars and Earth.Our study thus suggests that a saltwater-related origin of the araneiform is possible and has significant implications for water searches on Mars.展开更多
The influences of fractal pore structure in coal reservoir on coalbed methane(CBM) migration were analyzed in detail by coupling theoretical models and numerical methods.Different types of fractals were generated base...The influences of fractal pore structure in coal reservoir on coalbed methane(CBM) migration were analyzed in detail by coupling theoretical models and numerical methods.Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures.Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method(LBM).Based on the coupled method,porosity(ф),fractal dimension of pore structure(Db),pore size range(rmin,rmax) and other parameters were systematically analyzed for their influences on the permeability(ф) of fractal porous medium.The results indicate that:① the channels connected by pores with the maximum size(rmax) dominate the permeability,approximating in the quadratic law;② the greater the ratio of r max and r min is,the higher is;③ the relationship between D b and follows a negative power law model,and breaks into two segments at the position where Db ≌2.5.Based on the results above,a predicting model of fractal porous medium permeability was proposed,formulated as k=cfrnmax,where C and n(approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure.In addition,the equivalence of the new proposed model for porous medium and the Kozeny-Carman model k=Crn was verified at Db =2.0.展开更多
基金Project 50474003 supported by the National Natural Science Foundation of China
文摘A simple and practical method to calculate the fractal dimension （FD） of amicron＇s projective surface profile based on fractal theory is proposed. Taking AI（OH）3 material particles as an example, the scanning electron microscope （SEM） photos of particles were processed using an image.processing software （IPS） Photoshop. Taking the pixel as a fixed yardstick with the enlargement of the size of the particle image, the box-dimension and circumference-area （C-S） methods were used to calculate the FD of the surface profile of the particle. The FD of 1.2623 of the classic Koch curve is obtained, which approximates the true value of 1.2628. The complexities of the object＇s boundary and surface micro-topography are simulated successfully by a generator method.
基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘Using fractal dimension to reflect and simulate urban morphology are two applications of fractal theory in city geography. As the only consistent description of a fractal, fractal dimension plays an important role in describing the basic features of fractals. Just like other fractals, our cities have similar characteristics. Fractal dimension to some extent is regarded as an indicator of urban expansion, and it may change with urban morphology in different time and space. Based on the Geographic Information System (GIS), taking Wuhan city as a test area, the fractal dimensions of different land use were calculated, and a linear regression equation was established to analyze the relationship between fractal dimension and residential areas. Then the author used fractal dimension to simulate the urban boundary which is an important part of urban mor-phology. A mid-point subdivision fractal generator is needed in the simulation process, and the shape of the generator is determined by fractal dimension. According to the fractal theory, fractal boundaries in different scales have self-similarity and they have the same fractal dimensions. Based on this fact, the simulation method the author used could quantitatively keep the similarity of configuration of the urban boundaries.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB41000000)the Fundamental Research Funds for the Central Universities(WK2080000144)。
文摘Araneiforms are spider-like ground patterns that are widespread in the southern polar regions of Mars.A gas erosion process driven by the seasonal sublimation of CO_(2)ice was proposed as an explanation for their formation,which cannot occur on Earth due to the high climatic temperature.In this study,we propose an alternative mechanism that attrib-utes the araneiform formation to the erosion of upwelling salt water from the subsurface,relying on the identification of the first terrestrial analog found in a playa of the Qaidam Basin on the northern Tibetan Plateau.Morphological analysis indicates that the structures in the Qaidam Basin have fractal features comparable to araneiforms on Mars.A numerical model is developed to investigate the araneiform formation driven by the water-diffusion mechanism.The simulation res-ults indicate that the water-diffusion process,under varying ground conditions,may be responsible for the diverse aranei-form morphologies observed on both Earth and Mars.Our numerical simulations also demonstrate that the orientations of the saltwater diffusion networks are controlled by pre-existing polygonal cracks,which is consistent with observations of araneiforms on Mars and Earth.Our study thus suggests that a saltwater-related origin of the araneiform is possible and has significant implications for water searches on Mars.
基金supported by National Natural Science Foundation of China(Grant Nos.41102093&41072153)CBM Union Foundation of Shanxi Province (Grant No.2012012002)Doctoral Scientific Foundation of Henan Polytechnic University(Grant No.648706)
文摘The influences of fractal pore structure in coal reservoir on coalbed methane(CBM) migration were analyzed in detail by coupling theoretical models and numerical methods.Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures.Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method(LBM).Based on the coupled method,porosity(ф),fractal dimension of pore structure(Db),pore size range(rmin,rmax) and other parameters were systematically analyzed for their influences on the permeability(ф) of fractal porous medium.The results indicate that:① the channels connected by pores with the maximum size(rmax) dominate the permeability,approximating in the quadratic law;② the greater the ratio of r max and r min is,the higher is;③ the relationship between D b and follows a negative power law model,and breaks into two segments at the position where Db ≌2.5.Based on the results above,a predicting model of fractal porous medium permeability was proposed,formulated as k=cfrnmax,where C and n(approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure.In addition,the equivalence of the new proposed model for porous medium and the Kozeny-Carman model k=Crn was verified at Db =2.0.
