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 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
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
Fractal networks are widely applied in the field of heat and mass transfer. As one of the important parts of the fractal network, Y-shaped structure definitely has a significant impact on the performance of the whole ...Fractal networks are widely applied in the field of heat and mass transfer. As one of the important parts of the fractal network, Y-shaped structure definitely has a significant impact on the performance of the whole network. In this paper, the analytical relationship between Y-shaped microchannel geometry and its capillary flow time is established through theoretical analysis with mass continuity equation and Navier-Stokes(N-S) equations.The result reveals that the capillary flow time increases with the increase of the topology length and bifurcation angle of the Y-shaped microchannel, but decreases with the increase of the channel width.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
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.
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 National Natural Science Foundation of China(No.51375169)
文摘Fractal networks are widely applied in the field of heat and mass transfer. As one of the important parts of the fractal network, Y-shaped structure definitely has a significant impact on the performance of the whole network. In this paper, the analytical relationship between Y-shaped microchannel geometry and its capillary flow time is established through theoretical analysis with mass continuity equation and Navier-Stokes(N-S) equations.The result reveals that the capillary flow time increases with the increase of the topology length and bifurcation angle of the Y-shaped microchannel, but decreases with the increase of the channel width.
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.
