This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intens...This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.展开更多
A certain type of self-affine curves can be transferred into fractal functions. The upper bound of fractal dimensions of the Weyl-Marchaud derivative of these functions has been investigated, and further questions hav...A certain type of self-affine curves can be transferred into fractal functions. The upper bound of fractal dimensions of the Weyl-Marchaud derivative of these functions has been investigated, and further questions have been put forwarded.展开更多
The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each l...The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.展开更多
We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theor...We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering,by letting them have the same maximum value and half-width,and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained.The previous results in the two extreme cases are included in the results of this paper.In the simulational verification,we propose a method for the generation of self-affine fractal random surfaces,using the square-root of Fourier transform of the correlation function of the surface height.The simulated results conform well with the theory.展开更多
In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-S...In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-Stieltjes measures are given.展开更多
The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D valu...The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same展开更多
The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on <span style="white-space:nowrap;">μ&l...The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on <span style="white-space:nowrap;">μ<sub>M,D</sub><sub> </sub>is to estimate the number of orthogonal exponentials in L<sup>2</sup><span style="white-space:normal;">(μ<sub>M,D<span style="white-space:normal;">)</sub>. In the present paper, we establish some relations inside the zero set <img src="Edit_2196df81-d10f-4105-a2a9-779f454a56c3.png" width="55" height="23" alt="" /> by the Fourier transform of the self-affine measure μ<sub>M,D</sub>. Based on these facts, we show that μ<sub>M,D</sub> is a non-spectral measure<sub> </sub>and there exist at most 4 mutually orthogonal exponential functions in <em style="white-space:normal;"><em style="white-space:normal;">L<sup style="white-space:normal;">2</sup><span style="white-space:normal;">(<span style="white-space:normal;"><em style="white-space:normal;">μ<sub>M,D)</sub>, where the number 4 is the best possible. This extends several known conclusions.展开更多
Biot theory research has been extended to the multi-scale heterogeneity in actual rocks. Focused on laboratory frequency bandwidth studies, we discuss the relationships between double-porosity and BISQ wave equations,...Biot theory research has been extended to the multi-scale heterogeneity in actual rocks. Focused on laboratory frequency bandwidth studies, we discuss the relationships between double-porosity and BISQ wave equations, analytically derive the degeneration method for double-porosity＇s return to BISQ, and give three necessary conditions which the degeneration must satisfy. By introducing dynamic permeability and tortuosity theory, a full set of dynamic double-porosity wave equations are derived. A narrow band approximation is made to simplify the numerical simulation for dynamic double-porosity wavefields. Finally, the pseudo-spectral method is used for wave simulation within the laboratory frequency band （50 kHz）. Numerical results have proved the feasibility for dynamic double-porosity＇s description of squirt flow and the validity of the quasi-static approximation method.展开更多
Based on the extreme value theory, self-affinity, and scale invariance, we studied the temporal and spatial relationship and the variation of water level and established a model of Gumbel-Pareto distribution for desig...Based on the extreme value theory, self-affinity, and scale invariance, we studied the temporal and spatial relationship and the variation of water level and established a model of Gumbel-Pareto distribution for designed flood calculation. The model includes the previous extreme value models, the over-threshold data, and the fractal features shared by previous extreme value models. The model was simplified into a logarithmic normal distribution and a Pareto distribution for specific parameter values, and was used to calculate the designed flood values for the Shanghai Wusong Station in 100- and 1 000-year return periods. The calculated results show that the value of the designed flood height calculated in the Gumbel-Pareto distribution is between those in the Gumbel and Pearson-Ⅲ distributions. The designed flood values in the 100- and 1 000-year return periods of the model were 0.03% and 0.11% lower, respectively, than the Gumbel distribution and 0.06% and 1.54% higher, respectively, than the Pearson-Ⅲ distribution. Compared to the traditional model based solely on extreme probability, the Gumbel-Pareto distribution model could better describe the probabilistic characteristics of extreme marine elements and better use the data.展开更多
In this paper, we propose a new method to estimate the wave height of a specifi c return period based on the Hurst rule and a self-affi ne fractal formula. A detailed description of our proposed model is presented in ...In this paper, we propose a new method to estimate the wave height of a specifi c return period based on the Hurst rule and a self-affi ne fractal formula. A detailed description of our proposed model is presented in this paper. We use the proposed model to analyze wave height data recorded along the coast of Chaolian Island from 1963 to 1989. The results show that the performance of our proposed model in estimating design wave heights is superior to traditional models.展开更多
In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. T...In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.展开更多
As mass transport mechanisms,the spreading and mixing(dilution) processes of miscible contaminated compounds are fundamental to understanding reactive transport behaviors and transverse dispersion.In this study,the sp...As mass transport mechanisms,the spreading and mixing(dilution) processes of miscible contaminated compounds are fundamental to understanding reactive transport behaviors and transverse dispersion.In this study,the spreading and dilution processes of a miscible contaminated compound in a three-dimensional self-affine rough fracture were simulated with the coupled lattice Boltzmann method(LBM).Moment analysis and the Shannon entropy(dilution index) were employed to analyze the spreading and mixing processes,respectively.The corresponding results showed that the spreading process was anisotropic due to the heterogeneous aperture distribution.A compound was transported faster in a large aperture region than in a small aperture region due to the occurrence of preferential flow.Both the spreading and mixing processes were highly dependent on the fluid flow velocity and molecular diffusion.The calculated results of the dilution index showed that increasing the fluid flow velocity and molecular diffusion coefficient led to a higher increasing rate of the dilution index.展开更多
The strength of rock structures strongly depends inter alia on surface irregularities of rock joints. These irregularities are characterized by a coefficient of joint roughness. For its estimation, visual comparison i...The strength of rock structures strongly depends inter alia on surface irregularities of rock joints. These irregularities are characterized by a coefficient of joint roughness. For its estimation, visual comparison is often used. This is rather a subjective method, therefore, fully computerized image recognition procedures were proposed. However, many of them contain imperfections, some of them even mathematical nonsenses and their application can be very dangerous in technical practice. In this paper, we recommend mathematically correct method of fully automatic estimation of the joint roughness coefficient. This method requires only the Barton profiles as a standard.展开更多
Dynamical fluctuation of target evaporated black particles is investigated in both forward and backward hemispheres within the framework of multi-dimensional factorial moment methodology using the brilliant concept of...Dynamical fluctuation of target evaporated black particles is investigated in both forward and backward hemispheres within the framework of multi-dimensional factorial moment methodology using the brilliant concept of the Hurst exponent. We analyse the black particles emitted in ^32S-AgBr interactions at 200AGeV and it is evident that the dynamical fluctuation in the backward hemisphere is self-affine. In the forward hemisphere, dynamical fluctuation is self-similar but not self-affine. However, study indicates that the fluctuation in the forward hemisphere is more pronounced than that in backward hemisphere.展开更多
In this paper we calculate the local fractal dimension values D of the self-affine feature of earthquake time series by RMS (root-mean-square) error method, and express the fractal dimensionality by the normalized cor...In this paper we calculate the local fractal dimension values D of the self-affine feature of earthquake time series by RMS (root-mean-square) error method, and express the fractal dimensionality by the normalized correlation coefficient R. The fractal dimension values are given for earthquakes occurred in Tangshan, Haicheng, Songpan, Longling, Changshu, I.iyang in China and its vicinity by the moving scanning method with different magnitude thresholds and the fixed-window length (100 events). The results show the D values are characterized by decreasing, continued low level in values or by decreasing first and then increasing before moderate earthquakes.展开更多
The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spe...The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.展开更多
The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measu...The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measures have some surprising connections with a number of areas in mathematics, and have been received much attention in recent years. In the present paper, we shall determine the spectrality and non-spectrality of a class of self-aiffine measures with decomposable digit sets. We present a method to deal with such case, and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.展开更多
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
Modeling the real contact area plays a key role in every tribological process,such as friction,adhesion,and wear.Contact between two solids does not necessarily occur everywhere within the apparent contact area.Consid...Modeling the real contact area plays a key role in every tribological process,such as friction,adhesion,and wear.Contact between two solids does not necessarily occur everywhere within the apparent contact area.Considering the multiscale nature of roughness,Persson proposed a theory of contact mechanics for a soft and smooth solid in contact with a rigid rough surface.In this theory,he assumed that the vertical displacement on the soft surface could be approximated by the height profile of the substrate surface.Although this assumption gives an accurate pressure distribution at the interface for complete contact,when no gap exists between two surfaces,it results in an overestimation of elastic energy stored in the material for partial contact,which typically occurs in many practical applications.This issue was later addressed by Persson by including a correction factor obtained from the comparison of the theoretical results with molecular dynamics simulation.This paper proposes a different approach to correct the overestimation of vertical displacement in Persson’s contact theory for rough surfaces with self-affine fractal properties.The results are compared with the correction factor proposed by Persson.The main advantage of the proposed method is that it uses physical parameters such as the surface roughness characteristics,material properties,sliding velocity,and normal load to correct the model.This method is also implemented in the theory of rubber friction.The results of the corrected friction model are compared with experiments.The results confirm that the modified model predicts the friction coefficient as a function of sliding velocity more accurately than the original model.展开更多
By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we exten...By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 69978012）, and by the National Key Basic Research Special Foundation （NKBRSF） of China （Grant No G1999075200）.
文摘This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.
基金Supported by 2009QX06 TPLAUSTNSFC (10571084)Math model Foundation of CZU2008
文摘A certain type of self-affine curves can be transferred into fractal functions. The upper bound of fractal dimensions of the Weyl-Marchaud derivative of these functions has been investigated, and further questions have been put forwarded.
基金This research is partly supported by NNSF of China (60204001) the Youth Chengguang Project of Science and Technology of Wuhan City (20025001002)
文摘The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.
文摘We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering,by letting them have the same maximum value and half-width,and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained.The previous results in the two extreme cases are included in the results of this paper.In the simulational verification,we propose a method for the generation of self-affine fractal random surfaces,using the square-root of Fourier transform of the correlation function of the surface height.The simulated results conform well with the theory.
文摘In this paper,some conditions which assure the compactly supported refinable distributions supported on a self-affine tile to be Lebesgue-Stieltjes measures or absolutely continuous measures with respect to Lebesgue-Stieltjes measures are given.
文摘The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same
文摘The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on <span style="white-space:nowrap;">μ<sub>M,D</sub><sub> </sub>is to estimate the number of orthogonal exponentials in L<sup>2</sup><span style="white-space:normal;">(μ<sub>M,D<span style="white-space:normal;">)</sub>. In the present paper, we establish some relations inside the zero set <img src="Edit_2196df81-d10f-4105-a2a9-779f454a56c3.png" width="55" height="23" alt="" /> by the Fourier transform of the self-affine measure μ<sub>M,D</sub>. Based on these facts, we show that μ<sub>M,D</sub> is a non-spectral measure<sub> </sub>and there exist at most 4 mutually orthogonal exponential functions in <em style="white-space:normal;"><em style="white-space:normal;">L<sup style="white-space:normal;">2</sup><span style="white-space:normal;">(<span style="white-space:normal;"><em style="white-space:normal;">μ<sub>M,D)</sub>, where the number 4 is the best possible. This extends several known conclusions.
基金supported by the National Basic Research Program of China (973 Program, 2007CB209505)the International Cooperative Project of the Ministry of Science and Technology of China (2006DFB62030)
文摘Biot theory research has been extended to the multi-scale heterogeneity in actual rocks. Focused on laboratory frequency bandwidth studies, we discuss the relationships between double-porosity and BISQ wave equations, analytically derive the degeneration method for double-porosity＇s return to BISQ, and give three necessary conditions which the degeneration must satisfy. By introducing dynamic permeability and tortuosity theory, a full set of dynamic double-porosity wave equations are derived. A narrow band approximation is made to simplify the numerical simulation for dynamic double-porosity wavefields. Finally, the pseudo-spectral method is used for wave simulation within the laboratory frequency band （50 kHz）. Numerical results have proved the feasibility for dynamic double-porosity＇s description of squirt flow and the validity of the quasi-static approximation method.
基金Supported by the NSFC-Shandong Joint Fund "Study on the DisasterCausing Mechanism and Disaster Prevention Countermeasures of MultiSource Storm Surges"(No.U1706226)the Program of Promotion Plan for Postgraduates’Educational Quality "Paying More Attention to the Study on the Cultivation Mode of Mathematical Modeling for Engineering Postgraduates"(No.HDJG18007)
文摘Based on the extreme value theory, self-affinity, and scale invariance, we studied the temporal and spatial relationship and the variation of water level and established a model of Gumbel-Pareto distribution for designed flood calculation. The model includes the previous extreme value models, the over-threshold data, and the fractal features shared by previous extreme value models. The model was simplified into a logarithmic normal distribution and a Pareto distribution for specific parameter values, and was used to calculate the designed flood values for the Shanghai Wusong Station in 100- and 1 000-year return periods. The calculated results show that the value of the designed flood height calculated in the Gumbel-Pareto distribution is between those in the Gumbel and Pearson-Ⅲ distributions. The designed flood values in the 100- and 1 000-year return periods of the model were 0.03% and 0.11% lower, respectively, than the Gumbel distribution and 0.06% and 1.54% higher, respectively, than the Pearson-Ⅲ distribution. Compared to the traditional model based solely on extreme probability, the Gumbel-Pareto distribution model could better describe the probabilistic characteristics of extreme marine elements and better use the data.
基金Supported by the National Natural Science Foundation of China’s“Study on Multi-objective Four-layer Nested Probability Model(MOFLNPM)and its Application to Risk Assessment for Coastal Engineering”(No.51379195)the Shandong Province Natural Science“Study on the Risk Assessments and Statistical Analysis of Marine Engineering based on Multi-target Three-level Nested Statistical Model”(No.ZR2013EEM034)+1 种基金the National Natural Science Foundation of China(No.41476078)the Science Research Program of Zhejiang Province(No.2015C34013)
文摘In this paper, we propose a new method to estimate the wave height of a specifi c return period based on the Hurst rule and a self-affi ne fractal formula. A detailed description of our proposed model is presented in this paper. We use the proposed model to analyze wave height data recorded along the coast of Chaolian Island from 1963 to 1989. The results show that the performance of our proposed model in estimating design wave heights is superior to traditional models.
基金supported by the National Natural Science Foundation of China(Grants No.51079043,41172204,and 51109139)the Natural Science Foundation of Jiangsu Province(Grant No.BK2011110)
文摘In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.
基金supported by the National Natural Science Foundation of China(Grant No.41602239)the Natural Science Foundation of Jiangsu Province(Grant No.BK20160861)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.2016B05514)the International Postdoctoral Exchange Fellowship Program from the Office of China Postdoctoral Council(Grant No.20150048)the"333 Project"of Jiangsu Province(Grant No.BRA2015305)
文摘As mass transport mechanisms,the spreading and mixing(dilution) processes of miscible contaminated compounds are fundamental to understanding reactive transport behaviors and transverse dispersion.In this study,the spreading and dilution processes of a miscible contaminated compound in a three-dimensional self-affine rough fracture were simulated with the coupled lattice Boltzmann method(LBM).Moment analysis and the Shannon entropy(dilution index) were employed to analyze the spreading and mixing processes,respectively.The corresponding results showed that the spreading process was anisotropic due to the heterogeneous aperture distribution.A compound was transported faster in a large aperture region than in a small aperture region due to the occurrence of preferential flow.Both the spreading and mixing processes were highly dependent on the fluid flow velocity and molecular diffusion.The calculated results of the dilution index showed that increasing the fluid flow velocity and molecular diffusion coefficient led to a higher increasing rate of the dilution index.
基金The Project LO1202 by financial means from the Ministry of Education, Youth ； Sports under the National Sustainability Programme I
文摘The strength of rock structures strongly depends inter alia on surface irregularities of rock joints. These irregularities are characterized by a coefficient of joint roughness. For its estimation, visual comparison is often used. This is rather a subjective method, therefore, fully computerized image recognition procedures were proposed. However, many of them contain imperfections, some of them even mathematical nonsenses and their application can be very dangerous in technical practice. In this paper, we recommend mathematically correct method of fully automatic estimation of the joint roughness coefficient. This method requires only the Barton profiles as a standard.
文摘Dynamical fluctuation of target evaporated black particles is investigated in both forward and backward hemispheres within the framework of multi-dimensional factorial moment methodology using the brilliant concept of the Hurst exponent. We analyse the black particles emitted in ^32S-AgBr interactions at 200AGeV and it is evident that the dynamical fluctuation in the backward hemisphere is self-affine. In the forward hemisphere, dynamical fluctuation is self-similar but not self-affine. However, study indicates that the fluctuation in the forward hemisphere is more pronounced than that in backward hemisphere.
文摘In this paper we calculate the local fractal dimension values D of the self-affine feature of earthquake time series by RMS (root-mean-square) error method, and express the fractal dimensionality by the normalized correlation coefficient R. The fractal dimension values are given for earthquakes occurred in Tangshan, Haicheng, Songpan, Longling, Changshu, I.iyang in China and its vicinity by the moving scanning method with different magnitude thresholds and the fixed-window length (100 events). The results show the D values are characterized by decreasing, continued low level in values or by decreasing first and then increasing before moderate earthquakes.
基金supported by the Key Project of Chinese Ministry of Education(Grant No. 108117)National Natural Science Foundation of China (Grant No. 10871123,61071066,11171201)
文摘The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.
基金supported by National Natural Science Foundation of China (Grant Nos.10871123,11171201)
文摘The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measures have some surprising connections with a number of areas in mathematics, and have been received much attention in recent years. In the present paper, we shall determine the spectrality and non-spectrality of a class of self-aiffine measures with decomposable digit sets. We present a method to deal with such case, and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.
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Modeling the real contact area plays a key role in every tribological process,such as friction,adhesion,and wear.Contact between two solids does not necessarily occur everywhere within the apparent contact area.Considering the multiscale nature of roughness,Persson proposed a theory of contact mechanics for a soft and smooth solid in contact with a rigid rough surface.In this theory,he assumed that the vertical displacement on the soft surface could be approximated by the height profile of the substrate surface.Although this assumption gives an accurate pressure distribution at the interface for complete contact,when no gap exists between two surfaces,it results in an overestimation of elastic energy stored in the material for partial contact,which typically occurs in many practical applications.This issue was later addressed by Persson by including a correction factor obtained from the comparison of the theoretical results with molecular dynamics simulation.This paper proposes a different approach to correct the overestimation of vertical displacement in Persson’s contact theory for rough surfaces with self-affine fractal properties.The results are compared with the correction factor proposed by Persson.The main advantage of the proposed method is that it uses physical parameters such as the surface roughness characteristics,material properties,sliding velocity,and normal load to correct the model.This method is also implemented in the theory of rubber friction.The results of the corrected friction model are compared with experiments.The results confirm that the modified model predicts the friction coefficient as a function of sliding velocity more accurately than the original model.
文摘By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.
