After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
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
Plants respond to drought stress with different physical manners, such as morphology and color of leaves. Thus, plants can be considered as a sort of living-sensors for monitoring dynamic of soil water content or the ...Plants respond to drought stress with different physical manners, such as morphology and color of leaves. Thus, plants can be considered as a sort of living-sensors for monitoring dynamic of soil water content or the stored water in plant body. Because of difficulty to identify the early wilting symptom of plants from the results in 2D (two-dimension) space, this paper presented a preliminary study with 3D (three-dimension)-based image, in which a laser scanner was used for achieving the morphological information of zucchini (Cucurbita pepo) leaves. Moreover, a leaf wilting index (DLWIF) was defined by fractal dimension. The experiment consisted of phase-1 for observing the temporal variation of DLWIF and phase-2 for the validation of this index. During the experiment, air temperature, luminous intensity, and volumetric soil water contents (VSWC) were simultaneously recorded over time. The results of both phases fitted the bisector (line: 1:1) with R2=0.903 and REMS=0.155. More significantly, the influence of VSWC with three levels (0.22, 0.30, and 0.36 cm3 cm-3) on the response of plant samples to drought stress was observed from separated traces of DLWIF. In brief, two conclusions have been made: (i) the laser scanner is an effective tool for the non-contact detection of morphological wilting of plants, and (ii) defined DLWIF can be a promising indicator for a category of plants like zucchini.展开更多
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
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.
基金the Chinese-German Center for Scientific Promotion (Chinesisch-Deutsches Zentrum für Wissenschaftsfrderung) under the Project of Sino-German Research Group (GZ494)the Beijing Municipal Education Commission for Building Scientific Research and Scientific Research Base (2008BJKY01)+1 种基金the German Academic Exchange Service (DAAD),and China Scholarship Council (CSC) for enhancing our cooperationthe International Cooperation Fund of Ministry of Science and Technology, China (2010DFA34670)
文摘Plants respond to drought stress with different physical manners, such as morphology and color of leaves. Thus, plants can be considered as a sort of living-sensors for monitoring dynamic of soil water content or the stored water in plant body. Because of difficulty to identify the early wilting symptom of plants from the results in 2D (two-dimension) space, this paper presented a preliminary study with 3D (three-dimension)-based image, in which a laser scanner was used for achieving the morphological information of zucchini (Cucurbita pepo) leaves. Moreover, a leaf wilting index (DLWIF) was defined by fractal dimension. The experiment consisted of phase-1 for observing the temporal variation of DLWIF and phase-2 for the validation of this index. During the experiment, air temperature, luminous intensity, and volumetric soil water contents (VSWC) were simultaneously recorded over time. The results of both phases fitted the bisector (line: 1:1) with R2=0.903 and REMS=0.155. More significantly, the influence of VSWC with three levels (0.22, 0.30, and 0.36 cm3 cm-3) on the response of plant samples to drought stress was observed from separated traces of DLWIF. In brief, two conclusions have been made: (i) the laser scanner is an effective tool for the non-contact detection of morphological wilting of plants, and (ii) defined DLWIF can be a promising indicator for a category of plants like zucchini.