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...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.展开更多
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 phas...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.展开更多
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 perco...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. CO<sub>2</sub>, H<sub>2</sub>O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)<sub>T</sub>, between gaseous and liquid states along any isotherm from critical (T<sub>c</sub>) to Boyle (T<sub>B</sub>) 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 = ρ<sub>rs</sub>(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)<sub>T</sub> = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρ<sub>BW</sub>(T) = 2ρ<sub>PA</sub>(T) = 3ρ<sub>PB</sub>(T) = 3ρ<sub>RS</sub>(T)/2 for T T<sub>B</sub>. These simple relationships arise, because the higher virial coefficients (b<sub>n</sub>, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T T<sub>B</sub>)<sub> </sub>within the gas phase. The Boyle-work line (p/ρ<sub>BW</sub>)<sub>T</sub> is related exactly at lower densities as T → T<sub>B</sub>, and accurately for liquid densities, by ρ<sub>BW</sub>(T) = −(b<sub>2</sub>/b<sub>3</sub>)<sub>T</sub>. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρ<sub>RS</sub>(0) = (2/3)ρ<sub>BW</sub>(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below T<sub>B</sub> are obtainable from b<sub>2</sub>(T). A BW-line ground-state crystal density ρ<sub>BW</sub>(0) can be defined by the pair potential minimum. The Ar<sub>2</sub> pair potential, ∅ij</sub>(r<sub>ij</sub>) determines b<sub>2</sub>(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 ∅<sub>ij</sub>(r<sub>ij</sub>) for all fluid states, without any adjustable parameters.展开更多
半导电屏蔽材料是制造高压电缆的关键组分,但仍存在电阻率高及其稳定性差难题。基于此,该文提出构筑双逾渗网络结构思路,选择乙烯-丙烯酸丁酯共聚物(ethylene-butyl acrylate copolymer,EBA)和低密度聚乙烯(low density polyethylene,LD...半导电屏蔽材料是制造高压电缆的关键组分,但仍存在电阻率高及其稳定性差难题。基于此,该文提出构筑双逾渗网络结构思路,选择乙烯-丙烯酸丁酯共聚物(ethylene-butyl acrylate copolymer,EBA)和低密度聚乙烯(low density polyethylene,LDPE)作为基体、导电炭黑(conductive carbon black,CB)作为导电填料制备半导电屏蔽材料,系统研究半导电屏蔽材料结构演变规律,评价半导电屏蔽材料结晶行为、电学性能、力学性能、表面光洁度等关键性能。实验结果表明:EBA与LDPE质量比为6:4时,半导电屏蔽材料内部形成双逾渗导电网络结构,相比于常规分布结构,其23和90℃的体积电阻率分别降低46.7%和74.4%,对应的正温度系数(positive temperature coefficient,PTC)降低52.1%,表明具有良好的电阻率稳定性。此外,该半导电屏蔽材料还具有优异的力学性能和表面光洁度。该结果可为高压电缆半导电屏蔽材料开发提供一定理论基础与数据支撑。展开更多
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 ...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.展开更多
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 conn...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.展开更多
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...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.展开更多
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 a...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.展开更多
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 i...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11905001)。
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.61973118,51741902,11761033,12075088,and 11835003)Project in JiangXi Province Department of Science and Technology(Grant Nos.20212BBE51010 and 20182BCB22009)the Natural Science Foundation of Zhejiang Province(Grant No.Y22F035316)。
文摘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.
文摘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. CO<sub>2</sub>, H<sub>2</sub>O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)<sub>T</sub>, between gaseous and liquid states along any isotherm from critical (T<sub>c</sub>) to Boyle (T<sub>B</sub>) 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 = ρ<sub>rs</sub>(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)<sub>T</sub> = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρ<sub>BW</sub>(T) = 2ρ<sub>PA</sub>(T) = 3ρ<sub>PB</sub>(T) = 3ρ<sub>RS</sub>(T)/2 for T T<sub>B</sub>. These simple relationships arise, because the higher virial coefficients (b<sub>n</sub>, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T T<sub>B</sub>)<sub> </sub>within the gas phase. The Boyle-work line (p/ρ<sub>BW</sub>)<sub>T</sub> is related exactly at lower densities as T → T<sub>B</sub>, and accurately for liquid densities, by ρ<sub>BW</sub>(T) = −(b<sub>2</sub>/b<sub>3</sub>)<sub>T</sub>. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρ<sub>RS</sub>(0) = (2/3)ρ<sub>BW</sub>(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below T<sub>B</sub> are obtainable from b<sub>2</sub>(T). A BW-line ground-state crystal density ρ<sub>BW</sub>(0) can be defined by the pair potential minimum. The Ar<sub>2</sub> pair potential, ∅ij</sub>(r<sub>ij</sub>) determines b<sub>2</sub>(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 ∅<sub>ij</sub>(r<sub>ij</sub>) for all fluid states, without any adjustable parameters.
文摘半导电屏蔽材料是制造高压电缆的关键组分,但仍存在电阻率高及其稳定性差难题。基于此,该文提出构筑双逾渗网络结构思路,选择乙烯-丙烯酸丁酯共聚物(ethylene-butyl acrylate copolymer,EBA)和低密度聚乙烯(low density polyethylene,LDPE)作为基体、导电炭黑(conductive carbon black,CB)作为导电填料制备半导电屏蔽材料,系统研究半导电屏蔽材料结构演变规律,评价半导电屏蔽材料结晶行为、电学性能、力学性能、表面光洁度等关键性能。实验结果表明:EBA与LDPE质量比为6:4时,半导电屏蔽材料内部形成双逾渗导电网络结构,相比于常规分布结构,其23和90℃的体积电阻率分别降低46.7%和74.4%,对应的正温度系数(positive temperature coefficient,PTC)降低52.1%,表明具有良好的电阻率稳定性。此外,该半导电屏蔽材料还具有优异的力学性能和表面光洁度。该结果可为高压电缆半导电屏蔽材料开发提供一定理论基础与数据支撑。
基金supported by the National Natural Science Foundation of China(Nos.11171193 and11371229)the Natural Science Foundation of Shandong Province(No.ZR2014AM033)the Science and Technology Development Project of Shandong Province(No.2012GGB01198)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11275186 and 91024026)
文摘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.
文摘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.
基金Funded by the Outstanding Youth Foundation of Hubei Province of China (No.2004ABB019)
文摘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.
文摘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.
