Modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system

A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

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.

1/f-noise in a Pt-film percolation system deposited on random fractal substrates

A dc method for measuring the critical exponent of the 1/f-noise spectral density in metallic film percolation system is developed. The power-law behavior of the 1/f-noise in a lower-resistivity rough Pt-film percolation system deposited on fracture surface (with self-affine structure) of α-Al2O3 ceramics is systematically studied by using this new method. The result indicates that the hopping conductivity effect of this rough system is much stronger than that of the regular flat film percolation system.

MWCNTs/SiO2 Composite System:Carrier Transmission,Twin-Percolation and Dielectric Properties

We synthesize composite systems of multi-wall carbon nanotubes(MWCNTs)/SiO_(2) by using the sol−gel method.The dielectric properties of the systems with different-concentration MWCNTs are studied.In our MWCNTs/SiO_(2) inorganic systems,the twin−percolation phenomenon exists when the concentrations of MWCNTs are 5–10%and 15–20%.The permittivity and conductivity have jumping changes.The twin−percolation phenomenon is attributed to the special transfer mechanism of MWCNTs in the system,determined by hopping and migrating electrons.Variations of dielectric properties and conductance of the MWCNTs/SiO_(2) systems are conformed to the percolation theory.The special percolation phenomenon and electric properties of MWCNTs/SiO_(2) can help us comprehend the conductivity mechanism of the MWCNTs/SiO2 systems effectively,and promote the development of a high performance function composite system.

In situ infiltration-precipitation processes in some rock systems

We carry out a chemical treatment(acidization or basification)of typical rock specimens in-situ,and characterize the emerging pattern resulting from the infil-tration-precipitation scenario.Galena and limestone sam-ples were treated with sulfuric acid,while pyrite was reacted with sodium hydroxide.Various infiltration tech-niques were employed,after selection of the most feasible method for each rock separately.The patterns of anglesite(PbSO_(4)),anhydrite(CaSO_(4))and goethite(FeOOH)depo-sition presented different alteration modes of the bare rock textures.Among the three deposited minerals,only the anhydrite(CaSO_(4))displayed a band stratification.The formation of a Liesegang pattern in the rock of highest porosity indicates a plausible correlation between the band formation and a minimum porosity requirement.A banded rock of compact texture could then be formed by a cementation mechanism,governing the long time evolution of the rock.

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.

大鼠骨髓单个核细胞诱导扩增为内皮祖细胞的细胞分离方法、接种数目、培养瓶包被条件

目的筛选大鼠骨髓单个核细胞(BMMNCs)诱导扩增为内皮祖细胞(BM-EPCs)的细胞分离方法、接种数目、培养瓶包被条件,构建一个高效、高产量、高纯度的骨髓来源BM-EPCs分离培养诱导扩增方法。方法取2周龄雄性SD大鼠,脱颈处死后分离大鼠双侧胫骨和股骨,收集骨髓细胞悬液。配制30%、50%、60%和70%浓度的Percoll细胞分离液,通过Percoll密度梯度离心法分离出大鼠BMMNCs种子细胞,并计算活细胞比例。将获得的BMMNCs分为1×10^(5)、5×10^(5)、1×10^(6)、2.5×10^(6)、5×10^(6)、1×10^(7)六个组别,分别接种于25 cm^(2)无菌培养瓶中,培养7 d后镜下观察各组细胞集落形成数目,并计算每10^(6)细胞的集落形成数。运用Graphpad prism9.5软件进行Logistic拟合曲线,根据相关系数R^(2)确定相关性,根据其P值将有统计学差异的接种数目纳入范围,随后使用R语言编程定义计算函数,根据已知种子细胞总数及相关性函数限制下,通过迭代寻找最佳的BMMNCs细胞接种数目。分别配制20、50、100 nmol/L浓度的人纤连蛋白(FN)溶液,以不添加FN的空白溶液为对照,分别包被空白培养瓶2、6、12、24 h,将收集的48 h未贴壁BMMNCs接种于FN包被的各培养瓶中,静置培养3 d后计算各组集落形成数目,确定FN包被的最佳浓度与时间。接种48 h未贴壁BMMNCs于25 cm^(2)培养瓶底,使用EGM-2完全培养基定向诱导,于显微镜下观察集落形成及诱导扩增进程。取培养14 d的BM-EPCs,分别采用双阳性染色法和流式细胞术鉴定BM-EPCs的纯度。结果使用Percoll分离法可把BMMNCs细胞清晰的分为5层,其中30%与50%Percoll细胞分离层之间为BMMNCs活细胞比率最高。BMMNCs的最优接种数目为2.5×10^(6)个。以50 nmol/L的FN溶液包被24 h或以100 nmol/L的FN溶液包被6 h皆可有效促进细胞集落形成。细胞接种7 d后获得形态良好的铺路石样细胞并建立生长优势,表明BMMNCs已经诱导成为形态良好的BM-EPCs。Dil-Ac-LDL/FITC-UEA-1双阳性细胞占比为91.89%±5.77%,CD31+KDR阳性率为90.73%±0.61%、CD14阳性率为0.53%±0.17%、CD45阳性率0.77%±0.34%,说明获得的BM-EPCs纯度良好。结论大鼠BMMNCs诱导扩增为BM-EPCs过程中,可使用Percoll密度梯度离心法分离BMMNCs,BMMNCs的最优细胞接种数目为2.5×10^(6)个,细胞培养瓶包被条件为以50 nmol/L的FN溶液包被24 h或以100 nmol/L的FN溶液包被6 h,分离培养诱导获得的BM-EPCs形态和纯度均良好。

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.

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO2, H2O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)T, between gaseous and liquid states along any isotherm from critical (Tc) to Boyle (TB) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρrs(T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ)T = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρBW(T) = 2ρPA(T) = 3ρPB(T) = 3ρRS(T)/2 for T TB. These simple relationships arise, because the higher virial coefficients (bn, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T TB) within the gas phase. The Boyle-work line (p/ρBW)T is related exactly at lower densities as T → TB, and accurately for liquid densities, by ρBW(T) = −(b2/b3)T. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρRS(0) = (2/3)ρBW(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below TB are obtainable from b2(T). A BW-line ground-state crystal density ρBW(0) can be defined by the pair potential minimum. The Ar2 pair potential, ∅ij(rij) determines b2(T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from ∅ij(rij) for all fluid states, without any adjustable parameters.

INVESTIGATION OF STRUCTURE AND PROPERTIES FOR POLYMER SYSTEMS BASED ON DYNAMIC RHEOLOGICAL APPROACHES

The dynamic rheological measurements have been a preferred approach to the characterization of the structure and properties for multi-component or multi-phase polymer systems,due to its sensitive response to changes of structure for these heterogeneous polymers.In the present article,recent progresses in the studies on dynamic rheology for heterogeneous polymer systems including polymeric composites filled with inorganic particles,thermo-oxidized polyolefins,phase- separated polymeric blends and functional polymers with the scaling and percolation behavior are reviewed,mainly depending on the results by the authors' group.By means of rheological measurements,not only some new fingerprints responsible for the evolution of morphology and structure concerning these polymer systems are obtained,the corresponding results are also significant for the design and preparation of novel polymer-based composites and functional materials.

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 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.

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.

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.

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.

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.

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.

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.