Study on the phase transition of the fractal scale-free networks

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.

Fractal Analysis of Mobile Social Networks

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.

A smart productivity evaluation method for shale gas wells based on 3D fractal fracture network model

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.

Hierarchically structured 2D silver sheets with fractal network

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.

Influence of the Unit Y-Shaped Microchannel Geometry on the Capillary Flow

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.