We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometr...We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of Hölder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.展开更多
We analyze fluorescence due to oxidizing activity of DNA in neutrophils of peripheral blood in the large populations ~104 - 105 of cells. Fluorescence is registered by flow cytometry method. Spatial resolution is abou...We analyze fluorescence due to oxidizing activity of DNA in neutrophils of peripheral blood in the large populations ~104 - 105 of cells. Fluorescence is registered by flow cytometry method. Spatial resolution is about a few nanometers for varied complex three-dimensional (3D) DNA nanostructures of all non-coding and coding parts of DNA. It’s shown that oxidative activity of all 3D DNA in the full set of chromosomes inside cells is defined by new standards for complex networks of “exponentially small worlds”, with more dense packing than in the well known networks of “small worlds”. Analysis of various blood samples in vivo and during medical treatment shown that only two classes of Good and Bad Networks of DNA for a good and a bad health existed. This division is defined by any network to one from two classes of “n” or “s” shaped curves for typical deviations and from straight line in perfect networks of “exponentially small worlds”, as for two types of hysteresis curves at phase transitions or at switching of bistability. These deviations coincide with two types of positive and negative trends of changing fractal dimension by changing the scales of multi-scale networks of fluorescing DNA. These trends give the overall assessments of human immunity, including hidden and unidentified diseases, and as a sum of all kinds of health and illness of given person, from the point of view the inner life of neutrophils, living in different parts of human body in given time. Characteristics of deviations associated with type, level and complexity of illness in the dependence on展开更多
This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna.The access time or hitting time H(i,j)is the expected number of steps before node j is visite...This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna.The access time or hitting time H(i,j)is the expected number of steps before node j is visited,starting from node i.The eigentime of G is the expectation of H(i,j)for all i,j∈G.Classical eigenvalue method let H(i,i)=0.However,when studying the random walk behavior of electrons in fractal networks corresponding to fractal antennas,it is nec-essary to consider the time when electrons leave a certain node and first return to that node(self return time).This paper adopts two research methods-the eigenvalue method based on spectral theory and the Markov chain method based on stochastic process theory-to obtain the modified in-trinsic time,and demonstrates through an example that the difference between the classical intrin-sic time and the modified intrinsic time is precisely due to the self return time.This paper shows the applications of fractal networks in modern communications.The research results are expected to provide a theoretical basis for the design and performance optimization of fractal antennas.展开更多
Oriented attachment can be used as a good synthetic route to make highly anisotropic nanostructures including nanorod,nanowire,nanoplate,and nanosheets.In a typical growth of anisotropic nanostructures,coalescence and...Oriented attachment can be used as a good synthetic route to make highly anisotropic nanostructures including nanorod,nanowire,nanoplate,and nanosheets.In a typical growth of anisotropic nanostructures,coalescence and reshaping after attachment make dense nanostructures.In this report,we show the formation of Ag sheets having fractal network by oriented attachment at low reaction temperature of 30℃.The synthesized Ag sheets exhibited good crystalline nature despite of their network structure and low synthetic temperature.We also investigated the effect of reaction conditions for the formation of the Ag sheets.In addition,using the Ag sheets as a sacrificial template,we could make hollow Au sheets via galvanic replacement.展开更多
Symmetrical relationships between humans and their environment have been referred to as an extension of symmetries in the human geographical system and have drawn great attention.This paper explored the symmetry betwe...Symmetrical relationships between humans and their environment have been referred to as an extension of symmetries in the human geographical system and have drawn great attention.This paper explored the symmetry between physical and human systems through fractal analysis of the road and drainage networks in Wuling mountainous area.We found that both the road and drainage networks reflect weak clustering distributions.The evolution of the road network shared a significant self-organizing composition,while the drainage network showed obvious double fraetal characteristics.The geometric fractal dimension of the road network was larger than that of the drainage network.In addition,when assigned a weight relating to hierarchy or length,neither the road network nor drainage network showed a fractal property.These findings indicated that the fractal evolution of the road network shared certain similarities with fractal distribution of the drainage network.The symmetry between the two systems resulted from an interactive process of destroying symmetry at the lower order and reconstructing symmetry at the higher order.The relationships between the fractal dimensions of the rural-urban road network,the drainage network andthe urban system indicated that the development of this area was to achieve the symmetrical isomorphism of physical-human geographical systems.展开更多
The generation method of three-dimensional fractal discrete fracture network(FDFN)based on multiplicative cascade process was developed.The complex multi-scale fracture system in shale after fracturing was characteriz...The generation method of three-dimensional fractal discrete fracture network(FDFN)based on multiplicative cascade process was developed.The complex multi-scale fracture system in shale after fracturing was characterized by coupling the artificial fracture model and the natural fracture model.Based on an assisted history matching(AHM)using multiple-proxy-based Markov chain Monte Carlo algorithm(MCMC),an embedded discrete fracture modeling(EDFM)incorporated with reservoir simulator was used to predict productivity of shale gas well.When using the natural fracture generation method,the distribution of natural fracture network can be controlled by fractal parameters,and the natural fracture network generated coupling with artificial fractures can characterize the complex system of different-scale fractures in shale after fracturing.The EDFM,with fewer grids and less computation time consumption,can characterize the attributes of natural fractures and artificial fractures flexibly,and simulate the details of mass transfer between matrix cells and fractures while reducing computation significantly.The combination of AMH and EDFM can lower the uncertainty of reservoir and fracture parameters,and realize effective inversion of key reservoir and fracture parameters and the productivity forecast of shale gas wells.Application demonstrates the results from the proposed productivity prediction model integrating FDFN,EDFM and AHM have high credibility.展开更多
Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner li...Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner link between rock mass destruction phenomena caused by mining and nonlinear science was revealed. There are numerous cracks in natural rock mass. The cracks’ distribution is irregular and is of statistical fractal structure. Self-organizational nonlinear evolution of the inner structure flaws leads to the rock mass destruction with external force. The evolution includes single fault’s fractal development, formation and evolution of fractal crack network and coordination of fractal crack network, etc. The law of fractal crack network’s evolution was introduced, at the same time, the coordination of fractal crack network was analyzed. Finally, based on coordination the principal equation of mining-caused subsidence of structural rock mass was established and its steady-state solution and unsteady-state solution were found.展开更多
Image compression consists of two main parts: encoding and decoding. One of the important problems of the fractal theory is the long encoding implementation time, which hindered the acceptance of fractal image compres...Image compression consists of two main parts: encoding and decoding. One of the important problems of the fractal theory is the long encoding implementation time, which hindered the acceptance of fractal image compression as a practical method. The long encoding time results from the need to perform a large number of domain-range matches, the total encoding time is the product of the number of matches and the time to perform each match. In order to improve encoding speed, a hybrid method combining features extraction and self-organization network has been provided, which is based on the feature extraction approach the comparison pixels by pixels between the feature of range blocks and domains blocks. The efficiency of the new method was been proved by examples.展开更多
Based on the Ising spin, the phase transition on fractal scale-free networks with tree-like skeletons is studied, where the loops are generated by local links. The degree distribution of the tree-like skeleton satisfi...Based on the Ising spin, the phase transition on fractal scale-free networks with tree-like skeletons is studied, where the loops are generated by local links. The degree distribution of the tree-like skeleton satisfies the power-law form P（k）～ k^-δ.It is found that when δ≥3, the renormalized scale-free network will have the same degree distribution as the original network. For a special case of δ = 4.5, a ferromagnetic to paramagnetic transition is found and the critical temperature is determined by the box-covering renormalization method. By keeping the structure of the fractal scale-free network constant, the numerical relationship between the critical temperature and the network size is found, which is the form of power law.展开更多
Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mo...Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks （MSNs） are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.展开更多
The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal co...The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.展开更多
Clustering algorithms in feature space are important methods in image segmentation. The choice of the effective feature parameters and the construction of the clustering method are key problems encountered with cluste...Clustering algorithms in feature space are important methods in image segmentation. The choice of the effective feature parameters and the construction of the clustering method are key problems encountered with clustering algorithms. In this paper, the multifractal dimensions are chosen as the segmentation feature parameters which are extracted from original image and wavelet-transformed image. SOM (Self-Organizing Map) network is applied to cluster the segmentation feature parameters. The experiment shows that the performance of the presented algorithm is very good.展开更多
Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we prop...Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we propose the FractalNet-LSTM model,which combines fractal convolutional units with recurrent long short-term memory(LSTM)layers to model time series efficiently.To test the effectiveness of the model,data with complex structures and patterns,in particular,with seasonal and cyclical effects,were used.To better demonstrate the obtained results and the formed conclusions,the model performance was shown on the datasets of electricity consumption,sunspot activity,and Spotify stock price.The result showed that the proposed model outperforms traditional approaches at medium forecasting horizons and demonstrates high accuracy for data with long-term and cyclical dependencies.However,for financial data with high volatility,the model’s efficiency decreases at long forecasting horizons,indicating the need for further adaptation.The findings suggest further adaptation.The findings suggest that integrating fractal properties into neural network architecture improves the accuracy of time series forecasting and can be useful for developing more accurate and reliable forecasting systems in various industries.展开更多
Electrochemical techniques and fractal theory were employed to study the corrosion behaviors and pits distribution characteristics on the corroded surfaces of 304 stainless steel exposed in FeCl3 solution. Fractal fea...Electrochemical techniques and fractal theory were employed to study the corrosion behaviors and pits distribution characteristics on the corroded surfaces of 304 stainless steel exposed in FeCl3 solution. Fractal features of pits distribution over the corroded surfaces were observed and described by the fractal dimension. A 5-8-2 back-propagation （BP） artificial neural network model for the diagnoses of the pitting corrosion rate and pits deepness of 304 stainless steel under various conditions was developed by considering the fractal dimension as a key parameter for describing the pitting corrosion characteristics. The predicted results are well in agreement with the experimental data of pitting corrosion rate and pit deepness. The max relative errors between their experimental and simulation data are 6.69% and 4.62%, respectively.展开更多
The geological conditions of the Pingdingshan coal mining group were used to construct a physical model used to study the distribution and evolution of mining induced cracks in the overburden strata.Digital graphics t...The geological conditions of the Pingdingshan coal mining group were used to construct a physical model used to study the distribution and evolution of mining induced cracks in the overburden strata.Digital graphics technology and fractal theory are introduced to characterize the distribution and growth of the mining induced fractures in the overburden strata of an inclined coal seam.A relationship between fractal dimension of the fracture network and the pressure in the overburden strata is suggested.Mining induced fractures spread dynamically to the mining face and up into the roof as the length of advance increases.Moreover,the fractal dimension of the fracture network increases with increased mining length,in general,but decreases during a period from overburden strata separation until the main roof collapses.It is a1so shown that overburden strata pressure plays an important role in the evolution of mining induced fractures and that the fractal dimension of the fractures increases with the pressure of the overburden.展开更多
The back-propagation neural （BPN） network was proposed to model the relationship between the parameters of the dieless draw- ing process and the microstrecmres of the QSi3-1 silicon bronze alloy. Combined with image...The back-propagation neural （BPN） network was proposed to model the relationship between the parameters of the dieless draw- ing process and the microstrecmres of the QSi3-1 silicon bronze alloy. Combined with image processing techniques, grain sizes and grain-boundary morphologies were respectively determined by the quantitative metallographic method and the flactal theory. The outcomes obtained show that the deformed microstructures exhibit typical fractal features, and the boundaries can be characterized quantitatively by ffactal dimensions. With the temperature of 600-800℃ and the drawing speed of 0.67-1.00 mm-s-1, either a lower temperature or a higher speed will cause a smaller grain size together with an elevated fractal dimension. The developed model can be capable for forecasting the microstructure evolution with a minimum error. The average relative errors between the predicted results and the experimental values of grain size and fractal dimension are 3.9% and 0.9%, respectively.展开更多
Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals...Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.展开更多
Grain shape of the hot deforming alloy is an important of material. The fractal theory was applied to analyze index to character the microstructure and performance the recrystallized microstructure of Ti-15-3 alloy af...Grain shape of the hot deforming alloy is an important of material. The fractal theory was applied to analyze index to character the microstructure and performance the recrystallized microstructure of Ti-15-3 alloy after hot deformation and solution treatment. The fractal dimensions of recrystallized grains were calculated by slit island method. The influence of processing parameters on fractal dimension and grain size was studied, It has been shown that the shapes of recrystallized grain boundaries are self-similar, and the fractal dimension varies from 1 to 2. With increasing deformation degree and strain rate or decreasing deformation temperature, the fractal dimension of grain boundaries increased and the grain size decreased. So the fractal dimension could characterize the grain shape and size. A neural network model was trained to predict the fractal dimension of recrystallized microstructure and the result is in excellent agreement with the experimental data.展开更多
文摘We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of Hölder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.
文摘We analyze fluorescence due to oxidizing activity of DNA in neutrophils of peripheral blood in the large populations ~104 - 105 of cells. Fluorescence is registered by flow cytometry method. Spatial resolution is about a few nanometers for varied complex three-dimensional (3D) DNA nanostructures of all non-coding and coding parts of DNA. It’s shown that oxidative activity of all 3D DNA in the full set of chromosomes inside cells is defined by new standards for complex networks of “exponentially small worlds”, with more dense packing than in the well known networks of “small worlds”. Analysis of various blood samples in vivo and during medical treatment shown that only two classes of Good and Bad Networks of DNA for a good and a bad health existed. This division is defined by any network to one from two classes of “n” or “s” shaped curves for typical deviations and from straight line in perfect networks of “exponentially small worlds”, as for two types of hysteresis curves at phase transitions or at switching of bistability. These deviations coincide with two types of positive and negative trends of changing fractal dimension by changing the scales of multi-scale networks of fluorescing DNA. These trends give the overall assessments of human immunity, including hidden and unidentified diseases, and as a sum of all kinds of health and illness of given person, from the point of view the inner life of neutrophils, living in different parts of human body in given time. Characteristics of deviations associated with type, level and complexity of illness in the dependence on
基金supported by the Young Talent Fund of Association for Science and Technology in Shaanxi,China,un-der grant No.20230513.
文摘This paper studies the eigentime and related issues in the fractal network corresponding to the Sierpiński fractal antenna.The access time or hitting time H(i,j)is the expected number of steps before node j is visited,starting from node i.The eigentime of G is the expectation of H(i,j)for all i,j∈G.Classical eigenvalue method let H(i,i)=0.However,when studying the random walk behavior of electrons in fractal networks corresponding to fractal antennas,it is nec-essary to consider the time when electrons leave a certain node and first return to that node(self return time).This paper adopts two research methods-the eigenvalue method based on spectral theory and the Markov chain method based on stochastic process theory-to obtain the modified in-trinsic time,and demonstrates through an example that the difference between the classical intrin-sic time and the modified intrinsic time is precisely due to the self return time.This paper shows the applications of fractal networks in modern communications.The research results are expected to provide a theoretical basis for the design and performance optimization of fractal antennas.
基金This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science,ICT,&Future Planning(2014R1A5A1009799)by a National Research Foundation of Korea grant funded by the Korean government(MSIP)(NRF-2015R1C1A1A01054109 and NRF-2016M3D1A1021140).
文摘Oriented attachment can be used as a good synthetic route to make highly anisotropic nanostructures including nanorod,nanowire,nanoplate,and nanosheets.In a typical growth of anisotropic nanostructures,coalescence and reshaping after attachment make dense nanostructures.In this report,we show the formation of Ag sheets having fractal network by oriented attachment at low reaction temperature of 30℃.The synthesized Ag sheets exhibited good crystalline nature despite of their network structure and low synthetic temperature.We also investigated the effect of reaction conditions for the formation of the Ag sheets.In addition,using the Ag sheets as a sacrificial template,we could make hollow Au sheets via galvanic replacement.
基金supported by the National Natural Science Foundation of China project(Grant Nos.41201130,41101361,and 41371183)
文摘Symmetrical relationships between humans and their environment have been referred to as an extension of symmetries in the human geographical system and have drawn great attention.This paper explored the symmetry between physical and human systems through fractal analysis of the road and drainage networks in Wuling mountainous area.We found that both the road and drainage networks reflect weak clustering distributions.The evolution of the road network shared a significant self-organizing composition,while the drainage network showed obvious double fraetal characteristics.The geometric fractal dimension of the road network was larger than that of the drainage network.In addition,when assigned a weight relating to hierarchy or length,neither the road network nor drainage network showed a fractal property.These findings indicated that the fractal evolution of the road network shared certain similarities with fractal distribution of the drainage network.The symmetry between the two systems resulted from an interactive process of destroying symmetry at the lower order and reconstructing symmetry at the higher order.The relationships between the fractal dimensions of the rural-urban road network,the drainage network andthe urban system indicated that the development of this area was to achieve the symmetrical isomorphism of physical-human geographical systems.
基金Supported by the National Science and Technology Major Project(2017ZX05063-005)Science and Technology Development Project of PetroChina Research Institute of Petroleum Exploration and Development(YGJ2019-12-04)。
文摘The generation method of three-dimensional fractal discrete fracture network(FDFN)based on multiplicative cascade process was developed.The complex multi-scale fracture system in shale after fracturing was characterized by coupling the artificial fracture model and the natural fracture model.Based on an assisted history matching(AHM)using multiple-proxy-based Markov chain Monte Carlo algorithm(MCMC),an embedded discrete fracture modeling(EDFM)incorporated with reservoir simulator was used to predict productivity of shale gas well.When using the natural fracture generation method,the distribution of natural fracture network can be controlled by fractal parameters,and the natural fracture network generated coupling with artificial fractures can characterize the complex system of different-scale fractures in shale after fracturing.The EDFM,with fewer grids and less computation time consumption,can characterize the attributes of natural fractures and artificial fractures flexibly,and simulate the details of mass transfer between matrix cells and fractures while reducing computation significantly.The combination of AMH and EDFM can lower the uncertainty of reservoir and fracture parameters,and realize effective inversion of key reservoir and fracture parameters and the productivity forecast of shale gas wells.Application demonstrates the results from the proposed productivity prediction model integrating FDFN,EDFM and AHM have high credibility.
基金Foundatinitem Project(50274044) supported by the National Natural Science Foundation of China .
文摘Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner link between rock mass destruction phenomena caused by mining and nonlinear science was revealed. There are numerous cracks in natural rock mass. The cracks’ distribution is irregular and is of statistical fractal structure. Self-organizational nonlinear evolution of the inner structure flaws leads to the rock mass destruction with external force. The evolution includes single fault’s fractal development, formation and evolution of fractal crack network and coordination of fractal crack network, etc. The law of fractal crack network’s evolution was introduced, at the same time, the coordination of fractal crack network was analyzed. Finally, based on coordination the principal equation of mining-caused subsidence of structural rock mass was established and its steady-state solution and unsteady-state solution were found.
文摘Image compression consists of two main parts: encoding and decoding. One of the important problems of the fractal theory is the long encoding implementation time, which hindered the acceptance of fractal image compression as a practical method. The long encoding time results from the need to perform a large number of domain-range matches, the total encoding time is the product of the number of matches and the time to perform each match. In order to improve encoding speed, a hybrid method combining features extraction and self-organization network has been provided, which is based on the feature extraction approach the comparison pixels by pixels between the feature of range blocks and domains blocks. The efficiency of the new method was been proved by examples.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2014EL002)
文摘Based on the Ising spin, the phase transition on fractal scale-free networks with tree-like skeletons is studied, where the loops are generated by local links. The degree distribution of the tree-like skeleton satisfies the power-law form P（k）～ k^-δ.It is found that when δ≥3, the renormalized scale-free network will have the same degree distribution as the original network. For a special case of δ = 4.5, a ferromagnetic to paramagnetic transition is found and the critical temperature is determined by the box-covering renormalization method. By keeping the structure of the fractal scale-free network constant, the numerical relationship between the critical temperature and the network size is found, which is the form of power law.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61501217,61363015,61501218 and 61262020the Natural Science Foundation of Jiangxi Province under Grant No 20142BAB206026
文摘Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks （MSNs） are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.
基金supported by National Natural Science Foundation of China(No.51674279)China Postdoctoral Science Foundation(No.2016M602227)a grant from National Science and Technology Major Project(No.2017ZX05049-006)
文摘The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.
文摘Clustering algorithms in feature space are important methods in image segmentation. The choice of the effective feature parameters and the construction of the clustering method are key problems encountered with clustering algorithms. In this paper, the multifractal dimensions are chosen as the segmentation feature parameters which are extracted from original image and wavelet-transformed image. SOM (Self-Organizing Map) network is applied to cluster the segmentation feature parameters. The experiment shows that the performance of the presented algorithm is very good.
文摘Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we propose the FractalNet-LSTM model,which combines fractal convolutional units with recurrent long short-term memory(LSTM)layers to model time series efficiently.To test the effectiveness of the model,data with complex structures and patterns,in particular,with seasonal and cyclical effects,were used.To better demonstrate the obtained results and the formed conclusions,the model performance was shown on the datasets of electricity consumption,sunspot activity,and Spotify stock price.The result showed that the proposed model outperforms traditional approaches at medium forecasting horizons and demonstrates high accuracy for data with long-term and cyclical dependencies.However,for financial data with high volatility,the model’s efficiency decreases at long forecasting horizons,indicating the need for further adaptation.The findings suggest further adaptation.The findings suggest that integrating fractal properties into neural network architecture improves the accuracy of time series forecasting and can be useful for developing more accurate and reliable forecasting systems in various industries.
基金the Natural Science Foundation of Liaoning Province (No.972210)
文摘Electrochemical techniques and fractal theory were employed to study the corrosion behaviors and pits distribution characteristics on the corroded surfaces of 304 stainless steel exposed in FeCl3 solution. Fractal features of pits distribution over the corroded surfaces were observed and described by the fractal dimension. A 5-8-2 back-propagation （BP） artificial neural network model for the diagnoses of the pitting corrosion rate and pits deepness of 304 stainless steel under various conditions was developed by considering the fractal dimension as a key parameter for describing the pitting corrosion characteristics. The predicted results are well in agreement with the experimental data of pitting corrosion rate and pit deepness. The max relative errors between their experimental and simulation data are 6.69% and 4.62%, respectively.
基金the financial support from the State Key Basic Research Program of China(No.2011CB201201)
文摘The geological conditions of the Pingdingshan coal mining group were used to construct a physical model used to study the distribution and evolution of mining induced cracks in the overburden strata.Digital graphics technology and fractal theory are introduced to characterize the distribution and growth of the mining induced fractures in the overburden strata of an inclined coal seam.A relationship between fractal dimension of the fracture network and the pressure in the overburden strata is suggested.Mining induced fractures spread dynamically to the mining face and up into the roof as the length of advance increases.Moreover,the fractal dimension of the fracture network increases with increased mining length,in general,but decreases during a period from overburden strata separation until the main roof collapses.It is a1so shown that overburden strata pressure plays an important role in the evolution of mining induced fractures and that the fractal dimension of the fractures increases with the pressure of the overburden.
基金supported by the National Basic Research Priorities Program of China (No.2006CB605200)the National Natu-ral Science Foundation of China (Nos.50674008 and 50634010)+1 种基金the Program for New Century Excellent Talents in Chinese Universities (No.NCET-06-0083)the Foundation of State Key Laboratory for Advanced Metals and Materials (No.2008Z-15)
文摘The back-propagation neural （BPN） network was proposed to model the relationship between the parameters of the dieless draw- ing process and the microstrecmres of the QSi3-1 silicon bronze alloy. Combined with image processing techniques, grain sizes and grain-boundary morphologies were respectively determined by the quantitative metallographic method and the flactal theory. The outcomes obtained show that the deformed microstructures exhibit typical fractal features, and the boundaries can be characterized quantitatively by ffactal dimensions. With the temperature of 600-800℃ and the drawing speed of 0.67-1.00 mm-s-1, either a lower temperature or a higher speed will cause a smaller grain size together with an elevated fractal dimension. The developed model can be capable for forecasting the microstructure evolution with a minimum error. The average relative errors between the predicted results and the experimental values of grain size and fractal dimension are 3.9% and 0.9%, respectively.
文摘Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.
基金supported by the National Natural Science Foundation of China under grant No.50405020.
文摘Grain shape of the hot deforming alloy is an important of material. The fractal theory was applied to analyze index to character the microstructure and performance the recrystallized microstructure of Ti-15-3 alloy after hot deformation and solution treatment. The fractal dimensions of recrystallized grains were calculated by slit island method. The influence of processing parameters on fractal dimension and grain size was studied, It has been shown that the shapes of recrystallized grain boundaries are self-similar, and the fractal dimension varies from 1 to 2. With increasing deformation degree and strain rate or decreasing deformation temperature, the fractal dimension of grain boundaries increased and the grain size decreased. So the fractal dimension could characterize the grain shape and size. A neural network model was trained to predict the fractal dimension of recrystallized microstructure and the result is in excellent agreement with the experimental data.
