Dimer percolation and jamming on simple cubic lattice

We consider site percolation of dimers (“needles”) on simple cubic lattice. The percolation threshold is estimated as p_c ^perc ≈ 0.2555 ± 0.0001. The jamming threshold is estimated as p_c ^jamm = 0.799 ± 0.002.     

含椭球包体多相复合介质电导率的有效介质理论

本文应用有效介质理论(EMT),研究含椭球包体的多相复合介质中的导电性。建议用各向异性因子m估计非均匀系统的局域各向异性,并给出一个计算此情况下有效电导率张量的公式。对于椭球包体取向完全无序的介质,建议以介质的几何结构因子I_i(i=χ,y,z)估计组成包体的颗粒之间的近场效应。研究表明,结构因子I_i与包体的退极化因子n_i(i=χ,y,z)之间存在简单的关系。EMT的计算结果表明,抻长的椭球包体(b/α≈0.2)和压扁的椭球包体((b/α≈7—8)是导致渗流阈值对c₁^*=0.17的两种主要几何结构。初步的理论分析表明,由这两种几何形状产生渗流的共同机制是在介质中形成“无穷”长的链状集团。     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Cu-MgF2复合纳米金属陶瓷薄膜的电导特性研究

用射频磁控共溅射法制备了Cu体积分数分别为10%，15%，20%和30%的Cu-MgF₂复 合金属陶 瓷薄膜.用x射线衍射、x射线光电子能谱和变温四引线技术对薄膜的微结构、组分及电导特 性进行了测试分析.微结构分析表明：制备的Cu-MgF₂复合薄膜由fcc-Cu晶态纳 米微粒镶嵌 于主要为非晶态的MgF₂陶瓷基体中构成，Cu晶粒的平均晶粒尺寸随组分增加从1 1.9nm增 至17.8nm.50—300K温度范围内的电导测试结果表明：当Cu体积 关键词： 2复合纳米金属陶瓷膜')" href="#">Cu-MgF₂复合纳米金属陶瓷膜 微结构 组分 电导特性 激活能 渗透阈     

Effect of particle size of graphites on electrical conductivity of graphite/polymer composite

The effect of particle size of graphite particles on the dispersion state of graphite particles and electrical conductivity of graphite/low-density polyethylene (LDPE) composites is investigated. Graphite particles which have plate-like and spherical shapes and mean particle sizes of 2.1 to 82.6 μm are used. Scanning electron microscopy observation showed that graphite particles are not aggregated and ordered along the direction of mixing-roll in the polymer matrix. X-ray diffraction measurements show that crystallite size of the (110) plane of polyethylene crystal and the crystallinity are significantly affected by the particle size of graphite particles. These results were interpreted as due to the orientation of PE crystallites. The electrical conductivity of composites changes discontinuously at the critical volume fraction of particles, Ø_c. The Ø_c values given by the percolation equation increase with decreasing of the particle size of graphites. The plate-like graphite particles with a mean particle size of 2.1 μm could induce conductivity at Ø_c of 0.135. The values of Ø_c increased linearly with increasing of the mean particle sizes of the plate-like graphites. The value of Ø_c of spherical graphite particle is the largest value, 0.292, in all specimens.     

Influence of the shape of inclusions on the percolation thresholds in 2D models of composites

The influence of the shape of inclusions on the conductivity of composites, including critical concentration N _c (percolation threshold), is considered using 2D models as an example. A relationship between constant N _I , which characterizes effective conductivity ?? _e for low concentrations N of inclusions and percolation threshold N _c is established.     

Metal-insulator transition and superconductivity in SnAr films

We studied the conductivity and superconducting transition temperature T_c of SnAr films. The films were prepared by condensing the SnAr mixture on a sapphire substrate held at 5 K. A plot of the conductivity as a function of Sn concentration shows a metal-insulator transition which agrees with a percolation model consisting of Sn clusters embedded in solid Ar. A drop of T_c is observed below the percolation threshold.     

Crossover scaling,correlation function and connectivity in dilute low temperature ferromagnets

For quenched dilute ferromagnets with a fractionp of spins (nearest neighbor exchange energyJ) and a fraction 1 —p of randomly distributed nonmagnetic atoms, a crossover assumption similar to tricritical scaling theory relates the critical exponents of zero temperature percolation theory to the low temperature critical amplitudes and exponents near the critical lineT _c (p)>0. For example, the specific heat amplitude nearT _c (p) is found to vanish, the susceptibility amplitude is found to diverge forT _c (p →p _c ) → 0. (Typically,p _c =20%.) AtT=0 the spin-spin correlation function is argued from a droplet picture to obey scaling homogeneity but (at fixed distance) not to vary like the energy; instead it varies as const + (p _c —p)^2β +? for fixed small distances. A generalization of the correlation function to finite temperatures nearT _c (p) allows to estimate the number of effective percolation channels connecting two sites in the infinite (percolating) network forp>p _c ; this in turn gives, via a dynamical scaling argument, a good approximation for theT=0 percolation exponent 1.6 in the conductivity of random three-dimensional resistor networks. This channel approximation also givesΦ=2 for the crossover exponent; i.e. exp(?2J/kT _c (p)) is an analytic function ofp nearp=p _c . An appendix shows that cluster-cluster correlations atT=0 (excluded volume effects) are responsible for the difference between percolation exponents and the (pure) Ising exponents atT _c (p=1).     

Scaling assumption for lattice animals in percolation theory

A scaling assumption for the numberg _ns of different cluster configurations with perimeters and sizen leads to the desired cluster numbers near the percolation threshold. The perimeter distribution function has a mean square width proportional ton for largen. The relation between the average perimeter and the cluster sizen for percolation has three different forms atp _c, belowp _c, and abovep _c and is closely related to the shape of the cluster size distribution.     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

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.     

磁性颗粒复合体磁渗流区矫顽力异常的研究

制备了MnZn铁氧体/SiO₂颗粒复合体.研究了磁性颗粒复合体的有效磁导率μ、 比磁化强度σ以及矫顽力H_c随磁性颗粒含量的变化.研究发现，在MnZn铁氧体体积百分含 量为90%—98%的区域，复合体的有效磁导率μ的变化速率发生突变，出现磁渗流现象，从实验得到的体系磁渗流阈值V_c=97.9%.在磁渗流区，矫顽力表现出异常行为.结果表明 ，这种异常行为与复合体微观结构有着密切关系.在磁渗流前，矫顽力H_c的变化主要来 源于磁 关键词： 颗粒复合体 磁渗流 矫顽力     

An alternative proof of some percolation threshold (p c ) using the idea of self-organized criticality

Summary By means of a well-developed method in self-organized criticality, we can obtain the lower bound for the percolation threshold (p _c) of the corresponding site percolation problem. In some special cases, we have proved that such lower bounds are indeed the percolation thresholds. We can reproduce some well-known percolation thresholds of various lattices including the Cayley trees and Kock curves in this framework.     

Relationship between the parting limit for de-alloying and a particular geometric high-density site percolation threshold

The parting limit or de-alloying threshold for electrolytic dissolution of the more reactive component from a homogeneous fcc binary alloy is usually between 50 and 60 at%. The system that has been most studied, dissolution of Ag from Ag–Au, shows a parting limit close to 55 at% Ag. Here, Kinetic Monte Carlo (KMC) simulations of ‘Ag–Au’ alloys and geometric percolation modeling are used to study the relationship between this parting limit and the high-density site percolation thresholds p _c(m) for an fcc lattice, subject to the rule that atoms with coordination greater than nine are prevented from dissolution. The value of p _c(9) is calculated from geometric considerations to be 59.97 ± 0.03%. In comparison, using KMC simulations with no surface diffusion and no dissolution allowed for ‘Ag’ atoms with more than nine total neighbors, the parting limit is found to be slightly lower (58.4 ± 0.1%). This slight discrepancy is explained by consideration of the local atomic configurations of ‘Ag’ atoms – a few of these configurations satisfy the percolation requirement but do not sustain de-alloying, while a larger number show the converse behavior. There is still, however, an underlying relationship between the parting limit and the percolation threshold, because being at p _c(9) guarantees a percolation path in which successive ‘Ag’ atoms share at least one other ‘Ag’ neighbor. With realistic kinetics of surface diffusion for ‘Au’, the parting limit drops to 54.7 ± 0.3% because a few otherwise inaccessible dissolution paths are opened up by surface diffusion of ‘Au’.     

The Critical Point of k-Clique Percolation in the Erdős–Rényi Graph

Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdős–Rényi graph. When the probability p of two nodes being connected is above a certain threshold p _c (k), the complete subgraphs of size k (the k-cliques) are organized into a giant cluster. By making some assumptions that are expected to be valid below the threshold, we determine the average size of the k-clique percolation clusters, using a generating function formalism. From the divergence of this average size we then derive an analytic expression for the critical linking probability p _c (k).     

Long-range connections, quantum magnets and dilute contact processes

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold p_c of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at p_c. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied.     

Note on the asymptotic decay of the numbers of percolation clusters

Renormalization group principles are used to argue that the Kunz-Souillard exponents are valid for all concentrations away from the percolation threshold, i.e. that the average numbers n_s of clusters containing s sites each decay as log n_s ∝ -sζ (s → ∞, p fixed), with ζ = 1 for all p below p_c, and ζ = 1 - 1/d for all p above p_c in d dimensions.     

Metal-Filled Epoxy Composites: Mechanical Properties and Electrical/Thermal Conductivity

Abstract

The mechanical properties and the electrical and thermal conductivity of composites based on an epoxy polymer (EP) filled with dispersed copper (Cu) and nickel (Ni) were studied. It was shown that the electrical conductivity of the composites demonstrated percolation behavior with the values of the percolation threshold being 9.9 and 4.0?vol.% for the EP-Cu and EP-Ni composites, respectively. Using the Lichtenecker model, the thermal conductivity of the dispersed metal phase in the composites, λ_f, was estimated as being 35?W/mK for Cu powder and 13?W/mK for Ni powder. It was shown that introduction of the filler in EP led to a decrease in the intensity of the mechanical loss tangent (tan δ) peak that was caused by the existence of an immobilized polymer layer around the filler particles which did not contribute to mechanical losses. Using several models the thickness of this layer, ΔR, was estimated. The concept of an “excluded volume” of the polymer, V_ex, i.e. the volume of the immobilized polymer layer, which does not depend on the particle size and is determined solely by the value of the interaction parameter, B, was proposed.     

Classical and quantum percolation phenomena and controlling them in eutectic semiconductor-superconductor compositions

Experimental data on the conduction of heterogeneous systems have been traditionally interpreted in the context of the theory of percolation phenomena taking into account the relative threshold volume fraction η_C ≈ 0.16) of the high-conductivity phase. This work is concerned with the conduction of eutectic compositions semiconductor-normal metal at T > T _c (the classical limit) and semiconductor-superconductor at T < T _c (the quantum limit) obtained at various material growth rates; these materials contain metal particles as oriented whiskers in semiconducting matrices. The paper presents spatial and energy models of discrete, finite, and infinite clusters that well explain classical and quantum percolation conductivities. Depending on the growth rate of eutectic compositions, their classical and quantum conductivities can manifest themselves at arbitrary percolation thresholds η_p (0 < η_p ≤ η_c). It is shown that the density of whiskers, the distances between them, their diameters, and the critical supercurrent density per whisker can be controlled by varying the rate of composition growth.