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.

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.

A Study on Numerical Calculation Method of Small Cluster Density in Percolation Model

Percolation theory deals with the numbers and properties of the clusters formed in the different occupation probability. In this Paper, we study the calculation method of small clusters. We calcu-lated the small cluster density of 1, 2 and 3 in the percolation model with the exact method and the numerical method. The results of the two methods are very close, which can be verified by each other. We find that the cluster density of all three kinds of small clusters reaches the highest value when the occupation probability is between 0.1 and 0.2. It is very difficult to get the analytical formula for the exact method when the cluster area is relatively large (such as the area is more than 50), so we can get the density value of the cluster by numerical method. We find that the time required calculating the cluster density is proportional to the percolation area, which is indepen-dent of the cluster size and the occupation probability.

Extracting energetic disorder in organic solar cells using percolation models

The energetic disorder𝜎describes the energy state distribution in organic semiconducting materials.In organic solar cells(OSCs),energetic disorder is an important parameter for evaluating the charge transport behavior,and it is strongly correlated with the device performance.Thus far,a widely used approach for extracting energetic disorder values in OSCs is the Gaussian disorder model(GDM),in which the disorder values can be extracted by fitting the slope of lnμ∼1-T2,where𝜇is the charge mobility and𝑇is the temperature.Herein,we demonstrate the potential of the percolation approach to evaluate the energetic disorder values in OSCs and compare them with the data obtained using the GDM approach.Two typical non-fullerene acceptor(NFA)-based bulk heterojunction(BHJ)films,with PTB7-Th:ITIC and PM6:Y6,were selected as the model systems.When the percolation models were adopted in the two BHJ films,the energetic disorder values extracted from the Grünewald/Thomas and Nenashev percolation models gave similar results for electron transport in the PTB7-Th:ITIC and PM6:Y6 BHJ films.This work successfully demonstrates the feasibility of microresistance analysis in BHJ systems and the application potential of the percolation model for extracting energetic disorders in OSCs.

Simultaneous analysis of three-dimensional percolation models

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, 2013, 87（5）： 052107], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker finite-size corrections and are more sensitive to the deviation from percolation threshold Pc, and thus provide a powerful means for determining Pc. We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus significantly improved estimates of Pc are obtained.

Quantum to classical crossover under dephasing effects in a two-dimensional percolation model

Scaling theory predicts complete localization in d = 2 in quantum systems belonging to the orthogonal class(i.e., with timereversal symmetry and spin-rotation symmetry). The conductance g behaves as g^exp(-L/l) with system size L and localization length l in the strong disorder limit. However, classical systems can always have metallic states in which Ohm’s law shows a constant g in d=2. We study a two-dimensional quantum percolation model by controlling dephasing effects. The numerical investigation of g aims at simulating a quantum-to-classical percolation evolution. An unexpected metallic phase, where g increases with L, generates immense interest before the system becomes completely classical. Furthermore, the analysis of the scaling plot of g indicates a metal-insulator crossover.

Four Types of Percolation Transitions in the Cluster Aggregation Network Model

We study the percolation transition in a one-species cluster aggregation network model, in which the parameter α describes the suppression on the cluster sizes. It is found that the model can exhibit four types of percolation transitions, two continuous percolation transitions and two discontinuous ones. Continuous and discontinuous percolation transitions can be distinguished from each other by the largest single jump. Two types of continuous percolation transitions show different behaviors in the time gap. Two types of discontinuous percolation transitions are different in the time evolution of the cluster size distribution. Moreover, we also find that the time gap may also be a measure to distinguish different discontinuous percolations in this model.

Shear-induced particle segregation in binary mixtures:Verification of a percolation theory

Granular materials composed of different-sized grains may experience undesired segregation.Segregation is detrimental for a lot of industries because it leads to an increase in production costs and wastes.For these reasons,the segregation phenomena have been intensively studied in the last decades,and a lot of models have been provided by many researchers.However,these models are mainly based on empirical relations rather than physical considerations.This paper aims to confirm the main assumptions made by Volpato,Tirapelle,and Santomaso(2020)in their percolation theory by means of DEM simulations.The simulated geometry is a tilting shear box filled with few tracer particles in a bed of coarser sized grains,and simulations are performed for a range of tilting frequencies and size ratios.The results provide meaningful insight on the mathematical model parameters and allow us to say that the percolation theory relies on physically consistent assumptions.