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.

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 fractional percolation equation(FPE) with the Dirichlet and fractional boundary conditions.The stability and convergence are discussed for two special cases, i.e., a continued seepage 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.

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.

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.

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.

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.

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.

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.

PERCOLATION TRANSITION IN ELECTRORHEOLOGICAL FLUIDS

The electric conductivity, dynamic modulus and yield stress of the developed electrorheolo-gical fluid (ERF) are measured at different volume fraction and different electric field strengthusing a modified Rheometrics Mechanical Spectrometer (Model 605). The percolation theory isintroduced to explain electrorheological effect and found that the ERF′s have the similarpercolated network structure as that of other ordinary suspensions with a critical volume fractionvalue independent of electric field strength. A master curve of dimensionless modulus againstdimensionless volume fraction is obtained. which shows that the essence of ER phenomenonactually is one kind of the second ofder phase transition.

ON THE RANDOM-ORIENTED PERCOLATION

Let Ld=(Zd, Ed) be the d-dimensional lattice, suppose that each edge of Ld be oriented in a random direction, i.e., each edge being independently oriented positive direction along the coordinate axises with probability p and negative direction otherwise. Let Pp be the percolation measure, η(p) be the probability that there exists an infinite oriented path from the origin. This paper first proves η(p) θ(p) for d 2 and 1/2 p 1, where θ(p) is the percolation probability of bond model; then, as corollaries, the author gets η(1/2) = 0 for d = 2 and dc(1/2) = 2, where dc(1/2) = sup{d: η(1/2) = 0}. Next, based on BK Inequality for arbitrary events in percolation (see[2]), two inequalities are proved, which can be used as FKG Inequality in many cases (note that FKG Inequality is absent for Random-Oriented model). Finally, the author proves the uniqueness of infinite cluster and a theorem on geometry of the infinite cluster (similar to theorem (6.127) in [1] for bond percolation).

The Insulator-to-Conductor Transition in Sulphonated Poly(Phenylene Oxide)Polymer membranes:Percolation Theory Approach

In this paper the percolation theory is employed to study the insulator-to-conductortransition in sulphonated poly（phenylene oxide）（SPPO） polymer membranes.The membranes withdifferent sulphonation degree were prepared and infrared characterized.The transition thresholdwas calculated by the experimental data of membrane conductivities and the coordination numberwas thus estimated.The functional group-SO3H distribution in the membrane was evaluated inaccordance with the calculations and showed a non-random dispersion on the microscopic scale.

HIGH-Tc SUPERCONDUCTIVITY AND PERCOLATION

On microscopic and microstructural lev-els,the relations between high Tc superconduc-tivity and percolation have been discussed.On themicroscopic level,the critical oxygen concentra-tion in YBa2Cu307 with Tc around 90 K hasbeen obtained in terms of percolation.On themicrostruclural level,the percolation considera-tions have provided,usefully theoretical basisfor materials design of metal/high-Tc super-conducting phase（nonmetal）composites.

Percolation of Mobile Individuals on Weighted Scale-Free Networks

The percolation-like phase transition of mobile individuals is studied on weighted scale-free(WSF)networks,in which the maximum occupancy at each node is one individual(i.e.hard core interaction)and individuals can move to neighbor void node.Especially,the condition for the existence of a spanning cluster of individuals(a connected cluster of neighbor nodes occupied by individuals that span the entire systems)is investigated and it is found that there exists a critical value of weight coupling parameter𝛽βc,above which the density threshold of individuals is zero and below which the density threshold is larger than zero for WSF networks in the thermodynamic limit N→∞.Furthermore,the finite size scaling analysis show that for certain value𝛽β,the percolation transition of mobile individuals on a WSF network belongs to the same universality class of regular random graph percolation.

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.

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.

Electric conductivity and percolation threshold research of Cu-Cu_2O cermet

Cu-Cu2O cermets were prepared via hot pressing（HP） or in situ reduction hot pressing （ISPHP）. The results of electric conductivity tests show that the percolation threshold of the cermet, which is prepared by HP, is lower than that of cermet prepared by ISRHP. The electric conductivity and the percolation threshold depend on four influencing factors: the content, the size, the shape and the distribution of Cu phase. The electric conductivity decreases with the increase of Cu particle size, and decrease of the aspect ratio of Cu particle. The more even the Cu phase distribution, the higher the electric conductivity of the cermets.

Influence of Percolation Patterns and Soil Copper Concentration on Copper Uptake,and Growth and Yield with Copper-Polluted Stratified Paddy Fields

Copper(Cu)was designated as a specific substance in the Agricultural Land Soil Pollution Prevention Act in Japan.It has been known that high Cu concentrations in soil layers reduce rice crop production and thus agricultural practices such as soil dressing have been applied to minimize the damages to crops by copper pollution.In this study,authors investigated the effects of percolation patterns of the under-plowsole and subsoil on growth and yield,and copper uptake of paddy rice.Six stratified paddy field models were constructed to conduct the growth tests under the condition in which the percolation patterns of the under-plowsole and subsoil were in an open and closed system.These models have a plow layer(10 cm thickness)and upper-plowsole(2.5 cm thickness)made with 12.5 cm-thickness of non-polluted soil dressing(3.7 mgCu?kg-1)and an underlying 15 cm-thickness of polluted under-plowsole(7.5 cm thickness)and subsoil whose Cu concentration was higher or lower than Japanese safety standard(approximately 100 mgCu?kg-1,150 mgCu?kg-1 and 500 mgCu?kg-1,respectively).During the tests,a constant water-ponding system was adopted,and mid-summer drainage was not done.As a result,Cu concentrations of the rice grains were 5%significantly higher in the open system percolation models regardless of the original amount of Cu in the under-plowsole and subsoil.On the other hand,authors did not recognize any significant differences in growth and yield of rice plants among the models.Authors concluded that the Cu concentrations in rice plants are affected by percolation patterns of polluted plowsole and subsoil even though they are covered with non-polluted soil dressing layers.

Effects of puddling on percolation and rice yields in rainfed lowland paddy cultivation: Case study in Khammouane province, central Laos

We investigated the effects of puddling on percolation and rice yields in rainfed lowland paddy cultivation. We selected a study village in Khammouane province, central Laos, and set up non-puddling and puddling plots from high to low positions. Even when puddling was conducted carefully, the ponding water in the plots disappeared in the case of little rainfall. Further, percolatifons during the later periods of rice growth increased drastically. Therefore, it is difficult to overcome drought stresses only by conducting puddling. We also compared the water conditions in the non-puddling and puddling plots. In the puddling plots at high position and low position along a stream, the number of days without ponding water in the puddling plots was less than that in the non-puddling field in July, suggesting the possibility of a different transplanting date. We tried to estimate the effects of transplanting date on the rice yields and found that transplanting 15 days earlier leads to an increase of 0.5 t/ha in the rice yields. Moreover, the profits from the increased yields exceed the puddling costs considerably, leading to a definite increase in income. Because the transplanting date has no effects in the fields with high ground water, puddling is effective in paddy fields where ponding does not occur to a significant degree.

Liquid Pre-Freezing Percolation Transition to Equilibrium Crystal-in-Liquid Mesophase

Pre-freezing anomalies are explained by a percolation transition that delineates the existence of a pure equilibrium liquid state above the temperature of 1st-order freezing to the stable crystal phase. The precursor to percolation transitions are hetero-phase fluctuations that give rise to molecular clusters of an otherwise unstable state in the stable host phase. In-keeping with the Ostwald’s step rule, clusters of a crystalline state, closest in stability to the liquid, are the predominant structures in pre-freezing hetero-phase fluctuations. Evidence from changes in properties that depend upon density and energy fluctuations suggests embryonic nano-crystallites diverge in size and space at a percolation threshold, whence a colloidal-like equilibrium is stabilized by negative surface tension. Below this transition temperature, both crystal and liquid states percolate the phase volume in an equilibrium state of dispersed coexistence. We obtain a preliminary estimate of the prefreezing percolation line for water determined from higher-order discontinuities in Gibbs energy that derivatives the isothermal rigidity [(dp/dρ)T] and isochoric heat capacity [(dU/dT)v] respectively. The percolation temperature varies only slightly with pressure from 51.5°C at 0.1 MPa to around 60°C at 100 MPa. We conjecture that the predominant dispersed crystal structure is a tetrahedral ice, which is the closest of the higher-density ices (II to XV) to liquid water in configurational energy. Inspection of thermodynamic and transport properties of liquid argon also indicate the existence of a similar prefreezing percolation transition at ambient pressures (0.1 MPa) around 90 K, ~6% above the triple point (84 K). These findings account for many anomalous properties of equilibrium and supercooled liquids generally, and also explain Kauzmann’s “paradox” at a “glass” transition.