The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The...The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.展开更多
The sedimentary rock has a very complex pore structure. Since the middle of the1980s, researches into pore space structure of sandstone show that the pore space ofsedimentary rock has statistical fractal or self-simil...The sedimentary rock has a very complex pore structure. Since the middle of the1980s, researches into pore space structure of sandstone show that the pore space ofsedimentary rock has statistical fractal or self-similar structure. In July 1991, we discovered the triangular porous clusters with regular nestedstructure developed all over the cements in an outcrop sandstone sample from Tuhaarea by SEM. The discovery not only shows a visible and positive evidence of fractalstructure, but also indicates an example of regular fractal in sandstone.展开更多
A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpi...A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11171201)
文摘The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.
文摘The sedimentary rock has a very complex pore structure. Since the middle of the1980s, researches into pore space structure of sandstone show that the pore space ofsedimentary rock has statistical fractal or self-similar structure. In July 1991, we discovered the triangular porous clusters with regular nestedstructure developed all over the cements in an outcrop sandstone sample from Tuhaarea by SEM. The discovery not only shows a visible and positive evidence of fractalstructure, but also indicates an example of regular fractal in sandstone.
基金Supported by Visiting Scholar Foundation of Key Laboratory.inUniversity
文摘A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.
