基于逾渗理论的非晶合金屈服行为研究

从非晶合金的微观结构出发,基于处理强无序和具有随机几何结构系统常用的理论方法——逾渗理论来描述非晶合金剪切屈服时的塑性流变.为了更好地理解非晶合金剪切带萌生时的临界问题,结合已有的"自由体积(free volume)模型"和"剪切转变区(shear transformation zone)模型",建立了非晶合金剪切转变的逾渗模型.以Cu_(25)Zr_(75)二元非晶合金为例,计算了在剪切转变区内易发生塑性流动的原子团簇剪切失稳的逾渗阈值,并粗略估算了这些原子团簇的大小.研究发现,剪切失稳的逾渗阈值与临界约化自由体积浓度(x_c～2.4%)有着相似的特性,不同之处在于其值与自由体积的分散度有着密切联系.研究结果作为非晶合金的韧脆转变问题提供了新思路.     

二维孔隙裂隙双重介质逾渗规律研究

在孔隙介质逾渗理论的基础上，将另外一个非常重要的渗透通道——裂隙引入到介质的逾渗研究中，提出了更为普遍的孔隙裂隙双重介质的逾渗研究方法.通过对二维平面孔隙裂隙双重介质的数值计算，得到了孔隙裂隙双重介质三个重要参数：孔隙率，裂隙分形维数、裂隙数量分布初值与逾渗概率的关系，给出了孔隙裂隙双重介质逾渗阈值的数学表达式，揭示了孔隙裂隙双重介质的逾渗规律. 关键词： 孔隙 裂隙 双重介质 逾渗 逾渗阈值     

含随机裂纹网络孔隙材料渗透率的逾渗模型研究

采用逾渗理论对含随机裂纹网络的孔隙材料渗透性进行研究. 开裂孔隙材料渗透率的影响因素包括裂纹网络的几何特征、孔隙材料本体渗透率以及裂纹开度, 本文使用连续区逾渗理论模型建立了渗透率的标度律. 对于裂纹网络的几何特征, 本文基于连续区逾渗理论并考虑裂纹网络的分形特征提出了有限区域内二维随机裂纹网络的连通度定义; 对随机裂纹网络的几何分析表明, 随机裂纹局部团簇效应会降低裂纹网络的整体连通性, 随机裂纹网络的标度指数并非经典逾渗理论给出的固定值, 而是随着网络的分形维数的减小而增大. 本文在网络连通度和主裂纹团的曲折度的基础上, 提出了开裂孔隙材料渗透率标度律的解析表达, K=K₀(K_m,b)(ρ-ρ_c)^μ, 分别考虑了裂纹网络的几何逾渗特征 (ρ-ρ_c)^μ、孔隙材料渗透率K_m 以及裂纹开度比b; 对有限区域含有随机裂纹网络的孔隙材料渗透过程的有限元模拟表明, K₀ 在裂纹逾渗阈值附近与b呈指数关系, 但当裂纹的局部渗透率与K_m比值高于10⁶ 后, 开度比b对渗透率不再有影响.     

Ag-MgF2复合纳米金属陶瓷薄膜的渗透阈研究

介绍了几种计算纳米金属颗粒镶嵌于陶瓷基体中而形成的复合纳米金属陶瓷薄膜渗透阈的理论方法，分析了理论方法中所运用模型的特点及其精度.并将Landauer有效介质理论和Priou渗透阈理论应用于Ag-MgF₂复合纳米金属陶瓷薄膜的渗透阈计算，所得值分别为0.08和0.14(Ag的体积分数)，按Priou渗透阈理论计算的结果与实验结果相符.最后讨论了影响复合金属陶瓷薄膜体系渗透阈的主要因素. 关键词： 2复合纳米金属陶瓷薄膜')" href="#">Ag-MgF₂复合纳米金属陶瓷薄膜 渗透阈理论 渗透阈     

Monte Carlo studies of percolation phenomena for a simple cubic lattice

The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates forp _c (0.3115±0.0005), (0.41±0.01), (1.6±0.1), and(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average surface area for clusters of sizek is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizesk is found to have an exponential tail for large values ofk forP <p _c. Forp >p _c there is too much scatter in the data to draw firm conclusions about the size distribution.Work supported in part by USAFOSR Grant #73-2430B and by ERDA #E(11-1)-3077.     

基于有向渗流理论的关联微博转发网络信息传播研究

微博网络的快速性、爆发性和时效性, 以及用户复杂的行为模式, 使得研究其信息传播模型及影响因素成为网络舆情的热点方向. 利用压缩映射定理, 分析不动点迭代过程的收敛条件, 得到有向网络信息传播过程的渗流阈值和巨出向分支的数值解法; 通过可变同配系数生成模型, 分析关联特征对信息传播的影响; 最后利用微博转发网络数据进行仿真对比实验. 结果表明: 虽然四类关联特征同时体现出同配、异配特征, 但信息传播结果更多受入度-入度相关性、入度-出度相关性影响; 通过删除少量节点的方法, 提取边同配比例, 验证大部分节点的四类关联特征呈现一致性.     

基于生成函数方法的现实网络座键渗流建模

基于生成函数方法针对现实网络构建座键渗流模型, 并应用于4种有代表性的具体网络, 检验其对关键渗流指标估计的精确程度, 讨论模型估计误差成因, 同时给出其简单应用。所得现实网络渗流模型可应用于估计各类现实网络承受点边打击之后的连通状态, 也可以用来评估现实网络的整体抗毁程度。该模型处理过程简单, 预测结果精度与信息传播算法的结果精度相比可以被接受, 其计算用时则远低于信息传播算法, 具备很好的应用潜力。     

Correlation lengths for oriented percolation

Oriented percolation has two correlation lengths, one in the space and one in the time direction. In this paper we define these quantities for the two-dimensional model in terms of the exponential decay of suitably chosen quantities, and study the relationship between the various definitions. The definitions are used in a companion paper to prove inequalities between critical exponents.     

No directed fractal percolation in zero area

We consider the fractal percolation process on the unit square with fixed decimation parameterN and level-dependent retention parameters {p _k}; that is, for allk ⩾ 1, at thek th stage every retained square of side lengthN ¹⁻ k is partitioned intoN ² congruent subsquares, and each of these is retained with probabilityp _k. independent of all others. We show that if Π_k p _k =0 (i.e., if the area of the limiting set vanishes a.s.), then a.s. the limiting set contains no directed crossings of the unit square (a directed crossing is a path that crosses the unit square from left to right, and moves only up, down, and to the right).     

Bootstrap percolation in a polluted environment

Let a low densityp of sites on the lattice Z² be occupied, remove a proportionq of them, and call the remaining sites empty. Then update this configuration in discrete time by iteration of the following synchronous rule: an empty site becomes occupied by contact with at least two occupied nearest neighbors, while occupied and removed sites nerver change their states. Ifq/p ² is large most sites remain unoccupied forever, while ifq/p ² is small, this dynamics eventually makes most sites occupied. This demonstrates how sensitive the usual bootstrap percolation rule (theq=0 case) is to the pollution of space.     

On the Fractal dimension and correlations in percolation theory

We discuss the fractal dimension of the infinite cluster at the percolation threshold. Using sealing theory and renormalization group we present an explicit expression for the two-point correlation function within percolation clusters. The fractal dimension is given by direct integration of this function.See especially Ref. 1 for a discussion of the general aspects of percolation.     

On the universality of geometrical and transport exponents of rigidity percolation

We develop a three-parameter position-space renormalization group method and investigate the universality of geometrical and transport exponents of rigidity (vector) percolation in two dimensions. To do this, we study site-bond percolation in which sites and bonds are randomly and independently occupied with probabilitiess andb, respectively. The global flow diagram of the renormalization transformation is obtained which shows that thegeometrical exponents of the rigid clusters in both site and bond percolation belong to the same universality class, and possibly that of random (scalar) percolation. However, if we use the same renormalization transformation to calculate the critical exponents of the elastic moduli of the system in bond and site percolation, we find them to be very different (although the corresponding values of the correlation length exponent are the same). This indicates that the critical exponent of the elastic moduli of rigidity percolation may not be universal, which is consistent with some of the recent numerical simulations.     

Optical percolation in ceramics assisted by porous clusters

We investigated optical transparency in ceramics assisted by disordered porous clusters. The structure and statistical properties of three-dimensional (3D) well porous ceramics is studied. Theoretical model based on the percolation theory and numerical simulations are applied to interpret the observed phase transition from an optically opaque state to a transparent state. The porous ceramic samples were fabricated by the technique of slurry casting. The transmission of optical radiation (optical percolation) over the entire porous samples is observed since the critical concentration of porosity was exceeded. We explain this effect by the rising of the spanning cluster inside of the porous structure that produces a network of porous voids. Our experimental results are in good agreement with the numerical simulations.     

Covering by random intervals and one-dimensional continuum percolation

A brief historical introduction is given to the problem of covering a line by random overlapping intervals. The problem for equal intervals was first solved by Whitworth in the 1890s. A brief resume is given of his solution. The advantages of the present author's approach, which uses a Poisson process, are outlined, and a solution is derived by Laplace transforms. The method of Hammersley for dealing with a stochastic distribution of intervals is described, and a solution can still be derived by Laplace transforms. The asymptotic behavior as the line becomes long is calculated and is related to the one-dimensional continuum percolation problem. It is shown that as long as the mean interval size is finite, the probability of complete coverage decays exponentially, so that the critical percolation probabilityp _c =1. However, as soon as the mean interval size becomes infinite, the critical percolation probabilityp _c switches to 0. This is in accord with previous results for a lattice model by Chinese workers, but differs from those of Schulman. A possible reason for the discrepancy is a difference in boundary conditions.On sabbatical leave from Physics Department, Bar Ilan University, Ramat Gan, Israel.     

Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].     

Probabilistic bootstrap percolation

In bootstrap percolation, sites are occupied with probabilityp, but those with less thanm occupied first neighbors are removed. This culling process is repeated until a stable configuration (all occupied sites have at leastm occupied first neighbors or the whole lattice is empty) is achieved. Formm ₁ the transition is first order, while form<m ₁ it is second order, withm-dependent exponents. In probabilistic bootstrap percolation, sites have probabilityr or (1–r) of beingm- orm-sites, respectively (m-sites are those which need at leastm occupied first neighbors to remain occupied). We have studied the model on Bethe lattices, where an exact solution is available. Form=2 andm=3, the transition changes from second to first order atr ₁=1/2, and the exponent is different forr<1/2,r=1/2, andr>1/2. The same qualitative behavior is found form=1 andm=3. On the other hand, form=1 andm=2 the transition is always second order, with the same exponents ofm=1, for any value ofr>0. We found, form=z–1 andm=z, wherez is the coordination number of the lattice, thatp _c=1 for a value ofr which depends onz, but is always above zero. Finally, we argue that, for bootstrap percolation on real lattices, the exponents and form=2 andm=1 are equal, for dimensions below 6.On leave from Universidade Federal de Santa Catarina, Depto. de Fisica, 88049, Florianópolis, SC, Brazil     

Precision calculation of elasticity for percolation

Monte Carlo transfer matrix evaluation of the elastic constants at the percolation threshold of the random-bond honeycomb lattice, with widths of up to 96 and lengths of about two million lattice constants (roughly 200 hours CDC Cyber 205 vector computer time) gave a critical exponentT=3.96±0.04 with a logarithmic correction term. This exponent agrees well with the scaling hypothesisT=t+2v=3.97, relatingT to the two-dimensional conductivity exponent.We thank G. Güntherodt, B. I. Halperin, B. Hillebrands, and S. Roux for discussions, and the SFB 125 for support. This research was supported at Tel Aviv University in part by a grant from The Israel Academy of Sciences.     

A percolation approach to the Kauffman model

A study is made of the spreading of damage in the random but deterministic Kauffman model on the square lattice with the spreading from one edge of the lattice. The critical value of the parameterp _c above which the system becomes chaotic is found to bep _c0.298. The possibility of suppression of the chaotic phase by noise is also studied. It is found that forpp _c, an extremely large noise levelg>0.99 is required, if possible at all.On leave from Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Proof of Straley's argument for bootstrap percolation

We prove thatP _c =1 for bootstrap percolation with large void instabilities (in particular, ifm=3 on the square lattice).