Based on the characteristics of the internal structure of closed-cell aluminum foam, this paper attempts to illus- trate the process of reconstructing the internal structures of closed-cell aluminum foam in Monte-Carl...Based on the characteristics of the internal structure of closed-cell aluminum foam, this paper attempts to illus- trate the process of reconstructing the internal structures of closed-cell aluminum foam in Monte-Carlo method and the fractal characteristics of the reconstructed model. Furthermore, Binary Array Method is proposed by analyzing the reconstructed model and the thermal conductivity model of closed-cell aluminum foam is established. At the same time, the thermal conductivity of the foam materials with different porosity is calculated by Binary Array Method, and the calculated value coincides with the experimental results in the reference, which proves the correctness of these methods.展开更多
The optical recording of three-dimensional(3-D)reconstruction of CA1 pyramidal cells wasderived from the studies on the CA1 region of the hippocampus in adult male Wistar rats.The recordingwas produced by the Confocal...The optical recording of three-dimensional(3-D)reconstruction of CA1 pyramidal cells wasderived from the studies on the CA1 region of the hippocampus in adult male Wistar rats.The recordingwas produced by the Confocal Laser Scan Microscope(LSM-10).The attemption was to outline themorphological neural network of CA1 pyramidal cells organization,following the trail of axo-dendritic connec-tions in 3-D spatial distributions among neurons.The fractal structure of neurons with their dendritic andaxonal trees using fractal algorithm was noticed,and 2—18 simulated cells were obtained using PC-486 comput-er.The simulational cells are similar in morphology to the natural CA1 hippocampal pyramidal cells.There-fore,the exploitation of an advanced neurohistological research technique combining optical recording of theLSM-10 and computer simulation of fractal structure can provide the quantitative fractal structural basis forchaosic dynamics of brain.展开更多
Based on the Fermat’s Last Theorem and the Po, P1 projections from the 4th space coordinate to the time variable for Po and to the remaining 3D space variables for P1, the carbon 12 nucleus is shown explicitly as giv...Based on the Fermat’s Last Theorem and the Po, P1 projections from the 4th space coordinate to the time variable for Po and to the remaining 3D space variables for P1, the carbon 12 nucleus is shown explicitly as given by the hard-sphere dense packing model that also satisfies the Gell-Mann standard model. It is through these that C12 is a vital element in all biomaterials, and all proteins as well as the Nitrogenous bases in DNAs, are of hexagon geometric structures. Furthermore, the unique presence of a 3D × 1D space void within the C12 nucleus provides for the monopole Boson field tunneling to occur, giving rise to the enormous variety spectra in the DNA of life forms. In addition, on the surface of the bio cells, the carbon valence band p electron excitation into the empty conduction band separated by a bandgap G, can result in HTC Excitonic induced superconductivity binding gaps from the Excitonic spectra, which match part of those of the DNA and thus produce the self-grow mechanism of numerous different cells in a life form.展开更多
The characterization of reinforcement in 15% SiC particles reinforced AI matrix composites processed by powder metallurgy route was studied by statistical method. During the analysis, a new approach for the estimation...The characterization of reinforcement in 15% SiC particles reinforced AI matrix composites processed by powder metallurgy route was studied by statistical method. During the analysis, a new approach for the estimation of the characterization of reinforcement was presented. The mathematic software MATLAB was used to calculate the area and perimeter of reinforcement, in which the image processing technique was applied. Based on the calculation, the fractal dimension, shape factor, reinforcement size distribution and reinforcement distribution were investigated. The results show that the reinforcement shape is similar to rectangle; the reinforcement size distribution is broad with the＇ range of 1-12 μm; the topography of reinforcement is smooth; and the reinforcement distribution is inhomogeneous. Furthermore, the cell model based on the statistical characterization was established and tested.展开更多
Diffusion of microbe plays an important role in microbial restoration of soil and groundwater.For saturated soil,a membrane cell was designed to measure the effective diffusion coefficient.In this study,the theory of ...Diffusion of microbe plays an important role in microbial restoration of soil and groundwater.For saturated soil,a membrane cell was designed to measure the effective diffusion coefficient.In this study,the theory of fractal dimension was also used to calculate the cell constant of bacteria and the tortuosity factor of soil membrane.In the experiment of KCl diffusion,cell constant of KCl was directly calculated.In the second experiment the model of fractal dimension was used and the cell constant of microbe diffusion was obtained.Using the model of fractal dimension,tortuosity factor was also deduced.The effective diffusion coefficient of bacteria was obtained.展开更多
The previous study implies that the fractional operator may stem from the motion in fractal space or the motion of fractal structure abstracted from biological systems.This study is devoted to answering another essent...The previous study implies that the fractional operator may stem from the motion in fractal space or the motion of fractal structure abstracted from biological systems.This study is devoted to answering another essential question,i.e.,what determines the order of the fractional operator in fractal structure?This paper generalizes the concept of the fractal cell defined in the previous paper,explores the tree-like and net-like fractal structures with higher-order topology,abstracts two classes of higherorder fractal operators,and derives the algebraic equations satisfied by the fractal operators to answer this question.It is proved that the solutions of the algebraic equations for fractal operators are deterministically related to the fractional-time operators that are usually of fractional orders.By the Vieta theorem,the relation between the solutions of algebraic equations for fractal operators and the physical-component operators is clarified,and the duality constraints between them are revealed.The solutions of the fractal operators show that the topological invariants of the fractal cells are one of the essential factors in determining the fractional orders.A conjecture on the specific order of the fractional-time operator in fractal structure is proposed.展开更多
In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and me...In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and measured by means of a new-type 3D laser scanning system.Based on geographic information system(GIS)technique,the fracture surfaces were 3D visualized and reestablished.According to GIS 3D statistics,the geometrical characteristics of fracture surfaces under different breakage conditions were analyzed,and then based on fractal theory,the change laws of fractal dimension of fracture surfaces were discussed under the conditions of different cell pressures and initial water contents of rock.Furthermore,the relationships between characteristics of fracture surface and mechanical properties of rock were discussed.The results indicate that cell pressure,initial water content,and mechanical parameters of rock are the important factors to influence on the geometrical characteristics of fracture surface.The research provides a new experimental method for quantitative study on the fracture characteristics of various materials under different breakage conditions.展开更多
文摘Based on the characteristics of the internal structure of closed-cell aluminum foam, this paper attempts to illus- trate the process of reconstructing the internal structures of closed-cell aluminum foam in Monte-Carlo method and the fractal characteristics of the reconstructed model. Furthermore, Binary Array Method is proposed by analyzing the reconstructed model and the thermal conductivity model of closed-cell aluminum foam is established. At the same time, the thermal conductivity of the foam materials with different porosity is calculated by Binary Array Method, and the calculated value coincides with the experimental results in the reference, which proves the correctness of these methods.
基金the National Natural Science Foundation of ChinaLaboratory of Visual Information Processing,Institute of Biophysics,Chinese Academy of Sciences
文摘The optical recording of three-dimensional(3-D)reconstruction of CA1 pyramidal cells wasderived from the studies on the CA1 region of the hippocampus in adult male Wistar rats.The recordingwas produced by the Confocal Laser Scan Microscope(LSM-10).The attemption was to outline themorphological neural network of CA1 pyramidal cells organization,following the trail of axo-dendritic connec-tions in 3-D spatial distributions among neurons.The fractal structure of neurons with their dendritic andaxonal trees using fractal algorithm was noticed,and 2—18 simulated cells were obtained using PC-486 comput-er.The simulational cells are similar in morphology to the natural CA1 hippocampal pyramidal cells.There-fore,the exploitation of an advanced neurohistological research technique combining optical recording of theLSM-10 and computer simulation of fractal structure can provide the quantitative fractal structural basis forchaosic dynamics of brain.
文摘Based on the Fermat’s Last Theorem and the Po, P1 projections from the 4th space coordinate to the time variable for Po and to the remaining 3D space variables for P1, the carbon 12 nucleus is shown explicitly as given by the hard-sphere dense packing model that also satisfies the Gell-Mann standard model. It is through these that C12 is a vital element in all biomaterials, and all proteins as well as the Nitrogenous bases in DNAs, are of hexagon geometric structures. Furthermore, the unique presence of a 3D × 1D space void within the C12 nucleus provides for the monopole Boson field tunneling to occur, giving rise to the enormous variety spectra in the DNA of life forms. In addition, on the surface of the bio cells, the carbon valence band p electron excitation into the empty conduction band separated by a bandgap G, can result in HTC Excitonic induced superconductivity binding gaps from the Excitonic spectra, which match part of those of the DNA and thus produce the self-grow mechanism of numerous different cells in a life form.
文摘The characterization of reinforcement in 15% SiC particles reinforced AI matrix composites processed by powder metallurgy route was studied by statistical method. During the analysis, a new approach for the estimation of the characterization of reinforcement was presented. The mathematic software MATLAB was used to calculate the area and perimeter of reinforcement, in which the image processing technique was applied. Based on the calculation, the fractal dimension, shape factor, reinforcement size distribution and reinforcement distribution were investigated. The results show that the reinforcement shape is similar to rectangle; the reinforcement size distribution is broad with the＇ range of 1-12 μm; the topography of reinforcement is smooth; and the reinforcement distribution is inhomogeneous. Furthermore, the cell model based on the statistical characterization was established and tested.
文摘Diffusion of microbe plays an important role in microbial restoration of soil and groundwater.For saturated soil,a membrane cell was designed to measure the effective diffusion coefficient.In this study,the theory of fractal dimension was also used to calculate the cell constant of bacteria and the tortuosity factor of soil membrane.In the experiment of KCl diffusion,cell constant of KCl was directly calculated.In the second experiment the model of fractal dimension was used and the cell constant of microbe diffusion was obtained.Using the model of fractal dimension,tortuosity factor was also deduced.The effective diffusion coefficient of bacteria was obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.12050001,and 11672150).
文摘The previous study implies that the fractional operator may stem from the motion in fractal space or the motion of fractal structure abstracted from biological systems.This study is devoted to answering another essential question,i.e.,what determines the order of the fractional operator in fractal structure?This paper generalizes the concept of the fractal cell defined in the previous paper,explores the tree-like and net-like fractal structures with higher-order topology,abstracts two classes of higherorder fractal operators,and derives the algebraic equations satisfied by the fractal operators to answer this question.It is proved that the solutions of the algebraic equations for fractal operators are deterministically related to the fractional-time operators that are usually of fractional orders.By the Vieta theorem,the relation between the solutions of algebraic equations for fractal operators and the physical-component operators is clarified,and the duality constraints between them are revealed.The solutions of the fractal operators show that the topological invariants of the fractal cells are one of the essential factors in determining the fractional orders.A conjecture on the specific order of the fractional-time operator in fractal structure is proposed.
文摘In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and measured by means of a new-type 3D laser scanning system.Based on geographic information system(GIS)technique,the fracture surfaces were 3D visualized and reestablished.According to GIS 3D statistics,the geometrical characteristics of fracture surfaces under different breakage conditions were analyzed,and then based on fractal theory,the change laws of fractal dimension of fracture surfaces were discussed under the conditions of different cell pressures and initial water contents of rock.Furthermore,the relationships between characteristics of fracture surface and mechanical properties of rock were discussed.The results indicate that cell pressure,initial water content,and mechanical parameters of rock are the important factors to influence on the geometrical characteristics of fracture surface.The research provides a new experimental method for quantitative study on the fracture characteristics of various materials under different breakage conditions.
