STUDY OF PHASE BOUNDARIES FOR SITE-BOND PERCOLATION

Relations of phase boundaries and phase region for site-bond percolation are given.It can be seen from the simulation of Monte Carlo that the relations describe the site-bond percolation process much better than others practically.

Phase behavior and percolation in an equilibrium system of symmetrically interacting Janus disks on the triangular lattice

A Janus particle has two distinct areas on its surface.Denoting the two areas as P(patch)and N(nonpatch),when two particles come close to each other,the strength of the PP interaction is usually different from that of the NN interaction.Recently the interplay between a rotational-symmetry-breaking continuous phase transition and percolation has been explored for an equilibrium system of asymmetrically interacting(i.e.,attractive PP interaction,zero NN and PN interactions)Janus disks on the triangular lattice.By Monte Carlo simulation and finite-size scaling analysis,in this work we study an equilibrium system of symmetrically interacting(i.e.,attractive PP and NN interactions with the same strength,zero PN interaction)Janus disks on the same lattice.By definition,the phase diagram in the T-θplane is symmetric for systems with patch sizesθbelow and above 90°.We determine the phase diagram and compare it with that of the asymmetric system.Similar to the latter system,for 60°<θ<90°,a rotational-symmetry-breaking continuous phase transition and an anisotropic percolation transition are found in the symmetric system,though the transition points in the two systems are quite different.Phase crossover curves are found to be different,e.g.,a continuous varying crossover line extends betweenθ=0°and 90°for the symmetric model;and in the range 0°<θ≤30°,along the crossover lines of the two models,the trends of 1/T vs.θare opposite in the two systems.We understand the latter by analytically solving the models with two particles in 0°<θ≤30°.These results are helpful for understanding close-packed systems of Janus disks with more complex interactions.

Percolation transitions in edge-coupled interdependent networks with directed dependency links

We propose a model of edge-coupled interdependent networks with directed dependency links(EINDDLs)and develop the theoretical analysis framework of this model based on the self-consistent probabilities method.The phase transition behaviors and parameter thresholds of this model under random attacks are analyzed theoretically on both random regular(RR)networks and Erd¨os-Renyi(ER)networks,and computer simulations are performed to verify the results.In this EINDDL model,a fractionβof connectivity links within network B depends on network A and a fraction(1-β)of connectivity links within network A depends on network B.It is found that randomly removing a fraction(1-p)of connectivity links in network A at the initial state,network A exhibits different types of phase transitions(first order,second order and hybrid).Network B is rarely affected by cascading failure whenβis small,and network B will gradually converge from the first-order to the second-order phase transition asβincreases.We present the critical values ofβfor the phase change process of networks A and B,and give the critical values of p andβfor network B at the critical point of collapse.Furthermore,a cascading prevention strategy is proposed.The findings are of great significance for understanding the robustness of EINDDLs.

SITE-BOND PERCOLATION AND PHASE TRANSITION IN DILUTED MAGNETIC SYSTEM

The phase boundary relationship for site-bond percolation is established by generalizingthe universal relationships in pure bond percolation and pure site percolation, and the phasetransition in diluted magnetic system is studied. By using the Potts model, the phase bound-ary relationship for ferromagnetic-paramagnetic and antiferromagnetic-paramagnetic transi-tions is derived. The method adopted in this paper is convenient, simple and accurate.Especially, it has a clearer physical meaning.

段家河流域泥石流发育的渗流(Percolation)模型

在观察资料的基础上,提出了泥石流发育的渗流(Percolation)模型。由类比得到泥石流爆发的临界值P_c=d/(Z(d-1)),其中d是欧氏空间维数,z是配位数。根据广义Fibonacci数列,得到临界状态时的分形维数D_t(p,q)=In N/2ln,其中p、q是与人类活动、环境因素有关的参数.用以上结果对段家河流域的泥石流的发生作了理论分析。

Percolation on networks with dependence links

As a classical model of statistical physics, the percolation theory provides a powerful approach to analyze the network structure and dynamics. Recently, to model the relations among interacting agents beyond the connection of the networked system, the concept of dependence link is proposed to represent the dependence relationship of agents. These studies suggest that the percolation properties of these networks differ greatly from those of the ordinary networks. In particular, unlike the well known continuous transition on the ordinary networks, the percolation transitions on these networks are discontinuous. Moreover, these networks are more fragile for a broader degree distribution, which is opposite to the famous results for the ordinary networks. In this article, we give a summary of the theoretical approaches to study the percolation process on networks with inter- and inner-dependence links, and review the recent advances in this field, focusing on the topology and robustness of such networks.

Research on the nonlinear spherical percolation model with quadratic pressure gradient and its percolation characteristics

For bottom water reservoir and the reservoir with a thick oil formation, there exists partial penetration completion well and when the well products the oil flow in the porous media takes on spherical percolation. The nonlinear spheri-cal flow equation with the quadratic gradient term is deduced in detail based on the mass conservation principle, and then it is found that the linear percolation is the approximation and simplification of nonlinear percolation. The nonlinear spherical percolation physical and mathematical model under different external boundaries is established, considering the ef-fect of wellbore storage. By variable substitu-tion, the flow equation is linearized, then the Laplace space analytic solution under different external boundaries is obtained and the real space solution is also gotten by use of the nu-merical inversion, so the pressure and the pressure derivative bi-logarithmic nonlinear spherical percolation type curves are drawn up at last. The characteristics of the nonlinear spherical percolation are analyzed, and it is found that the new nonlinear percolation type curves are evidently different from linear per-colation type curves in shape and characteris-tics, the pressure curve and pressure derivative curve of nonlinear percolation deviate from those of linear percolation. The theoretical off-set of the pressure and the pressure derivative between the linear and the nonlinear solution are analyzed, and it is also found that the in-fluence of the quadratic pressure gradient is very distinct, especially for the low permeabil-ity and heavy oil reservoirs. The influence of the non-linear term upon the spreading of pressure is very distinct on the process of percolation, and the nonlinear percolation law stands for the actual oil percolation law in res-ervoir, therefore the research on nonlinear per-colation theory should be strengthened and reinforced.

Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.

Percolation Model of Graphite-modified Asphalt Concrete

The addition of graphite powder in conventional asphalt mixture can produced asp halt concrete with excellent electrical performance. Percolation theor y was employed to discuss the relation between the conductivity and graphite con tent of graphite-modified asphalt concrete. It was found that the results of pe rcolation model are consistent with experimental values. The percolation thresho ld of graphite-modified asphalt concrete is 10.94% graphite content account for the total volume of the binder phase consisting of asphalt and graphite. The cr itical exponent is 3.16, beyond the range of 1.6-2.1 for the standard lattice c ontinuous percolation problem. Its reason is that the tunnel conduction mec hanism originates near the critical percent content, which causes this system to be not universal. Tunnel mechanism is demonstrated by the nonlinear voltage-cu rrent characteristic near percolation threshold.The percolation model is able to well predict the formation and development of conductive network in graphite- modified asphalt concrete.

A Novel Method for Preparing Polyurethane Based Conductive Composites with Low Percolation Threshold

A novel method for preparing conductive carbon black fllled polymer composites with low percolation threshold from polyurethane emulsion are reported in this paper. The experimental results indicate that with a rise in carbon black concentration the insulator-conductor transition in the emulsion blended composites occurs at 0.8-1.4vol%. In contrast, the solution blended composites exhibit drastic increase in conductivity at conducting filler fraction as high as 12.3-13.3vol%. It is demonstrated that the composites microstructure rather than chemical structure of the matrix polymer predominantly determines the electrical conduction performance of the composites.

Research on percolation model and criticality of seismicity

Making use of modern nonlinear physics theory and earthquake focus theory, combined with seismicity characteristics, the percolation model of earthquake activity is given in this paper. We take the seismogenic process of alarge earthquake as a phase transition process of percolation and apply the renormalization method to phase transition of percolation. The critical property of the system, which is like percolation probability exponential andcorrelative length exponential, etc, can be calculated under the fixed point as which in the renormalization transformation infinite correlative length in percolation phase transition is taken. The percolation phase transition process of two large earthquakes, which are Haicheng and Tangshan event occurred in 1975 and 1976 respectively, hasbeen discussed by means of seismicity data before and after two shocks.

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.

Continuum percolation of porous media via random packing of overlapping cube-like particles

The pore configuration in porous medium is assumed to be the randomly distributed cube-like particles which can overlap each other in the periodic cubic domain, and the impact of particle characteristics on the percolation property of these cube-like particle packing systems is analyzed.Firstly, by combining the percolation models and finite-size scaling analysis, three numerical parameters(i.e., percolation transition width △L, local percolation threshold ψ_c(L), and correlation length exponent v) for the cube-like particle systems with shape parameter s in[1.0, +∞] are derived successively. Then, based on the relation between the percolation thresholdψ_c in infinite space and the local percolation threshold ψ_c(L), the corresponding ψ_c with s in[1.0, +∞] are further determined. It is shown from the study that the characteristics of cube-like particles have significant influence on the global percolation threshold ψ_c of the particle packing systems. As the parameter s increases from 1.0 to +∞, the percolation threshold ψ_c will go down persistently. When the surface of cube-like particles is cubical and spherical, respectively, the minimum and maximum thresholds ψ_c,min and ψ_c,max are obtained.

Carbon materials with quasi-graphene layers:The dielectric,percolation properties and the electronic transport mechanism

We investigate the dielectric properties of multi-walled carbon nanotubes（MWCNTs） and graphite filling in SiO2 with the filling concentration of 2-20 wt.% in the frequency range of 10 ^2-10^ 7 Hz.MWCNTs and graphite have general electrical properties and percolation phenomena owing to their quasi-structure made up of graphene layers.Both permittivity ε and conductivity σ exhibit jumps around the percolation threshold.Variations of dielectric properties of the composites are in agreement with the percolation theory.All the percolation phenomena are determined by hopping and migrating electrons,which are attributed to the special electronic transport mechanism of the fillers in the composites.However,the twin-percolation phenomenon exists when the concentration of MWCNTs is between 5-10 wt.% and 15-20 wt.% in the MWCNTs/SiO2 composites,while in the graphite/SiO2 composites,there is only one percolation phenomenon in the graphite concentration of 10-15 wt.%.The unique twin-percolation phenomenon of MWCNTs/SiO2 is described and attributed to the electronic transfer mechanism,especially the network effect of MWCNTs in the composites.The network formation plays an essential role in determining the second percolation threshold of MWCNTs/SiO2.

Research on Percolation Network and Physical Properties of Graphite/Antimony Composites

The microstructure, friction and wear behaviour of graphite preform and graphite/antimony composites are analysed based on the percolation theory of hydrodynamics to investigate the relationship between the percolation net- work and physical properties of graphite/antimony composites. The result shows that there are two important factors to enhance friction and wear behaviour of graphite/antimony composites at high temperature: 1) the formation of the pore network in the preform, which is called the first percolation and 2) the optimization of infiltration method in the process of infiltrating antimony, which is called the second percolation. By adding some pyrolysate and controlling the roasting process, perfect net pores and sub-micron percolation microstructure may be formed in the graphite preform. By con- trolling the infiltration process, the saturation of molten antimony infiltrating into perfect pores can be optimized.

Percolation analysis of large-scale wireless balloon networks

Recent advancements in wireless technology have tested Wireless Balloon Networks (WBNs) as an ideal solution for the provision of internet facilities in deprived and challenging areas. A few high profile companies, such as Google, Space Data Inc., etc., have already made news by initiating projects based on high-altitude WBNs in order to provide internet facilities in remote areas. Unfortunately, the technical details have mainly been kept confidential so far. In this paper, we attempt to analyze the percolation properties of large-scale WBNs, considering both homogenous and heterogenous wireless nodes. In order to do so, we modeled a WBN as a large-scale random network where the path-loss models of homogenous and heterogenous WBNs were reduced to GDM (Gilbert's Disk Model) and RGDM (Random Gilbert's Disk Model), respectively. The bounds of the critical density regime were derived for both percolation models. Additionally, this paper implemented an experimental test bed for the WBN percolation model. Consequently, the findings of this research may prove crucial in estimating critical network properties.

Effect of Percolation Pattern on Yields and Accumulation of Copper and Cadmium in the Rice Plants with Soil Dressing Models

A greenhouse experiment was conducted using stratified paddy field models, which were prepared by polluted soil with 12.5 cm soil dressing. The paddy models were assembled with open and closed percolation system to focus the effect of percolation pattern on accumulation of cupper （Cu） and cadmium （Cd） in rice plants in contaminated paddy filed with soil dressing models. Percolation pattern has significant effect on soil environment, especially redox potential that may influence mobilization of Cd, Cu and other elements. In open system percolation models, the plowsole and subsoil were in oxidative condition （600 mV）, whereas reduction condition （-200 mV） was measured in closed system percolation models. Accumulations of Cu and Cd in all parts of rice plants （roots, grains, stems and leaves） were found higher in an open system percolation with the paddy field model comparatively than in a closed system percolation. The soil redox （Eh） condition influenced by the percolation pattern might be one of the main factors for uptake and accumulation of Cu and Cd in rice plants. The plant height and stem number were found lower in open system percolation comparatively to closed system percolation. In the yields section, the average panicle length, number of panicle and rice grain/hill and weight of grain/hill were lower in open system percolation than the closed system percolation.

Determination of a Pore Structure Parameter of Porous Media by Analysis of Percolation Network Model

According to the simulation of nitrogen sorption process in porous media with three-dimensional network model, and the analysis for such a process with percolation theory, a new method is proposed to determine a pore structure parameter--mean coordination number of pore network, which represents the connectivity among a great number of pores. Here the 'chamber-throat' model and the Weibull distribution are used to describe the pore geometry and the pore size distribution respectively. This method is based on the scaling law of percolation theory after both effects of sorption thermodynamics and pore size on the sorption hysteresis loops are considered. The results show that it is an effective procedure to calculate the mean coordination number for micro- and meso-porous media.

Development of an Ontology-Based Knowledge Network by Interconnecting Soil/Water Concepts/Properties, Derived from Standards Methods and Published Scientific References Outlining Infiltration/Percolation Process of Contaminated Water

The present work deals with the development of an Ontology-Based Knowledge Network of soil/water physicochemical & biological properties (soil/water concepts), derived from ASTM Standard Methods (ASTMi,n) and relevant scientific/applicable references (published papers—PPi,n) to fill up/bridge the gap of the information science between cited Standards and infiltration discipline conceptual vocabulary providing accordingly a dedicated/internal Knowledge Base (KB). This attempt constitutes an innovative approach, since it is based on externalizing domain knowledge in the form of Ontology-Based Knowledge Networks, incorporating standardized methodology in soil engineering. The ontology soil/water concepts (semantics) of the developed network correspond to soil/water physicochemical & biological properties, classified in seven different generations that are distinguished/located in infiltration/percolation process of contaminated water through soil porous media. The interconnections with arcs between corresponding concepts/properties among the consecutive generations are defined by the relationship of dependent and independent variables. All these interconnections are documented according to the below three ways: 1) dependent and independent variables interconnected by using the logical operator “depends on” quoting existent explicit functions and equations;2) dependent and independent variables interconnected by using the logical operator “depends on” quoting produced implicit functions, according to Rayleigh’s method of indices;3) dependent and independent variables interconnected by using the logical operator “related to” based on a logical dependence among the examined nodes-concepts-variables. The aforementioned approach provides significant advantages to semantic web developers and web users by means of prompt knowledge navigation, tracking, retrieval and usage.

Effects of the Percolation Patterns and the Thickness of Soil Dressing on Reducing Cadmium Uptake and and Yields of Rice Plants （Oryza Sativa L.）

The objective of this study is to clarify the effects of the thickness of soil dressing, the percolation patterns of plowsole and subsoil on reducing cadmium （Cd） uptake, and growth and yields of rice plants. Six stratified paddy field models, three patterns of soil dressing layer and two percolation patterns were used for the experiments. These models had 12.5 cm, 15.0 cm and 25.0 cm thickness of soil dressing layer and 15 cm thickness of underlying polluted soil layer, whose Cd concentration was about 1.81 mg·kg^-1. As a result Cd concentration of brown rice was lower than 0.04 mg·kg^-1 for the models with the close system percolation, while that in the open system percolation models were lower than 0.17 mg.kgl.When the thickness of soil dressing became lower, Cd concentrations with the open system percolation models showed significantly higher values than those of the other models （5% of significant level）. But any significant difference was not found in the growth and yield among these models. As above mentioned, it was found that Cd concentration in rice grains was affected by the thickness of soil dressing and percolation patterns.