分形聚集逾渗性质的计算机模拟

提出3种模型——小尺寸随机逐次成核生长模型和二维及三维代代聚集生长模型,在不同的近邻条件下和不同尺寸的网格中,通过蒙特卡罗模拟,系统地研究了一维、二维和三维分形聚集的逾渗性质.计算结果显示,分形聚集的逾渗阈值仅取决于空间维数和近邻条件,与模型的网格大小无关,是分形系统固有的临界属性;生长概率等于逾渗阈值时,聚集体可以无限生长并保持分形维数恒定,此时的分形维数只是空间维数的线性函数.     

Monte Carlo重整化群方法计算逾渗模型的临界指数

本文运用Ｍｏｎｔｅ Ｃａｒｌｏ重整化群方法计算了点逾渗中次近邻正方格子的导通阈值和临界指数，得出与最近领正方格子属于同一普适类的结论。     

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     

磁性纳米颗粒膜的微磁学模拟

用微磁学方法对磁性纳米颗粒膜的磁特性进行了模拟，采用的模型是由122个磁性纳米颗粒组成的面心立方(fcc)结构体系.结果表明：在该体系中，偶极相互作用对体系的静态磁结构的影响显著，而交换相互作用的影响表现不明显.在此基础上，本文还采用有效媒质理论计算分析了磁性合金颗粒不同体积比时颗粒膜的磁谱和表征电磁参量发生显著变化的逾渗现象和逾渗阈值.并完成了对高磁损耗磁性纳米颗粒膜的材料设计. 关键词： 微磁学 纳米颗粒膜 逾渗阈值 磁导率 材料设计     

确定动力学流行病模型阈值的一种方法

采用六方格子上的动力学流行病模型描述流体凝固过程,根据流体中所含杂质粒子与固态粒子间的短程推斥作用,导出了被陷杂质粒子与固态粒子的密度比方程.并得到方程所含的两个变量χ与r之间有如下关系:当r为有限值时,分形生长局限于该区域 r无解时,集团可无限生长,在平面上形成较密集集团,维数Db→2 仅当r的解为∞时,分形生长可无限进行,该点χ即为阈值χc.由此,得到六方格子上阈值χc≈0655,与计算机模拟结果相符合,大于四方格子的结果χc(s)(∞)=0560±0005. 关键词：     

元胞方法与蒙特卡洛方法相结合的薄膜生长过程模拟

利用仿真方法从原子尺度研究薄膜生长过程是当前薄膜研究领域的热点. 目前, 仿真方法主要在纳米尺度模型实现, 时空需求很大. 针对这一问题, 本文提出元胞和蒙特卡洛相结合的模拟方法, 实现对微米尺度模型薄膜生长过程的模拟. 利用元胞方法来实现模型表示以及演化计算, 从而降低对内存空间的要求, 提高计算效率, 并使用蒙特卡洛方法计算粒子的扩散概率. 通过对氮化硅薄膜生长过程进行具体研究, 将模拟结果与实际实验结果和分子动力学演化结果进行表面形貌和成分的比较, 验证了该方法的有效性.     

裂隙多孔介质双重逾渗模型的算法实现

简要介绍基于孔隙逾渗和裂隙逾渗叠加的双重逾渗模型,阐述模型的原理、算法及其实现过程.初步研究模型的分形特性,认为分形维数D是能够衡量模型连通性的重要参数.最后探讨模型的蒙特卡洛数值计算方法,兼顾计算精度与计算耗时,提出可操作的计算规模.     

炭黑橡胶复合材料导热逾渗行为

研究了导电炭黑40b2填充天然橡胶复合材料的导热性能和力学性能随炭黑体积分数的变化规律,并采用扫描电子显微镜观察了炭黑橡胶体系内部的炭黑分布状况.结果表明,导热性能随炭黑体积分数的变化规律存在类似于导电逾渗现象的导热逾渗现象,逾渗阈值在8.3%～13.63%之间.在逾渗阈值之后,复合材料的拉伸强度下降.炭黑橡胶复合材料...     

栅氧化层介质经时击穿的逾渗模型

在研究了MOSFET栅氧化层介质经时击穿物理机制的基础上，提出了氧化层击穿的逾渗模型.认为氧化层的击穿是E′心和氧空位等深能级缺陷产生与积累，并最终形成电导逾渗通路的结果.指出在电场作用下，氧化层中产生深能级缺陷，缺陷形成定域态，定域态的体积与外加电场有关.随着应力时间的增长，氧化层中的缺陷浓度增大，定域态之间的距离缩小.当定域态之间的距离缩小到一个阈值时，定域态之间通过相互交叠形成逾渗通路，形成扩展态能级，漏电流开始急剧增大，氧化层击穿. 关键词： 栅氧化层 TDDB 逾渗 模型     

叶顶间隙尺度的不确定性对压气机性能影响的CFD模拟

本文研究了转子叶顶间隙尺度的不确定性对某轴流压气机的气动性能的影响。采用非嵌入式概率配置点法模拟间隙尺度不确定性在流场中的传播。先以二维随机方腔流动为模型,通过与蒙特卡洛模拟进行对比对非嵌入式概率配置点法进行验证。验证后采用该不确定性方法模拟了当叶顶间隙大小服从Beta分布时气动性能及流场参数的变化。     

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.     

Two-dimensional site-bond percolation as an example of a self-averaging system

The Harris-Aharony criterion for a static model predicts that if a specific heat exponent α>0, then this model does not exhibit self-averaging. In the two-dimensional percolation model, the index α= ?1/2. This means that, in accordance with the Harris-Aharony criterion, the model can exhibit self-averaging properties. We study numerically the relative variances R _M and R _χ for the probability M of a site belonging to the “infinite” (maximum) cluster and for the mean finite-cluster size χ. It was shown that two-dimensional site-bond percolation on the square lattice, where the bonds play the role of the impurity and the sites play the role of the statistical ensemble over which the averaging is performed, exhibits self-averaging properties.     

Site-bond percolation problems

We study a percolation process in which both sites and bonds are randomly blocked, independent of each other. In the Bethe lattice, the exact solution for the percolation threshold is found to be a hyperbola in thex-p plane, wherex andp are the respective probabilities of each site and bond being unblocked. Percolation threshold for a square and a simple cubic lattice is obtained by computer simulation. We also present a result obtained by a real-space renormalization group technique for the square lattice.     

The influence of inhomogeneous properties of a system on the percolation process in two-dimensional space

The percolation process in a two-dimensional inhomogeneous lattice is studied by the Monte Carlo method. The inhomogeneous lattice is simulated by a random distribution of inhomogeneities differing in size and number. The influence of inhomogeneities on the parameters (critical concentration, average number of sites in finite clusters, percolation probability, critical exponents, and fractal dimension of an infinite cluster) characterizing the percolation in the system is analyzed. It is demonstrated that all these parameters essentially depend on the linear size of inhomogeneities and their relative area.     

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.     

Universal crossing probabilities and incipient spanning clusters in directed percolation

Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the system is strongly anisotropic, the shape dependence in space-time enters through the effective aspect ratio r _eff = ct/L ^z, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for isotropic percolation, we also obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture. Received 10 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: turban@lpm.u-nancy.fr RID="b" ID="b"UMR CNRS 7556     

Iterated Fully Coordinated Percolation on a Square Lattice

We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also occupied. Repeating this site selection process again yields the iterated fully coordinated percolation model. Our results show a large enhancement in the size of highly connected regions after each iteration (from ordinary to fully coordinated and then to iterated fully coordinated percolation); enhancements that are much larger than an extension of correlations by an extra lattice constant might suggest. We also study the universality among the three problems by determining the corresponding static and dynamic critical exponents. Specifically, a new method to directly calculate the walk dimension, d _w , using finite size scaling applied to normal mode analysis is used. This method is applicable to any geometry and requires significantly less computation than previously known calculations to determine d _w .     

Comparison of theoretical and experimental 3He desorption behaviour of titanium tritide films

Helium-3 formed by tritium radioactive decay from tritide layer desorbs at room temperature slowly in a first step, more strongly afterwards. A helium-3 desorption model has been established, based on the positions of He-3 atom and trapping sites in the γ tritide lattice, CaF₂ type, supposed in a perfect state. Theoretical desorption curves as a function of time or helium concentration in the layer has been computed, for metal tritide or deutero-tritide layers. Experimental curves, for a wide tritium concentration range, are given here in the case of titanium layers. They show good agreement with theoretical curves for appropriate parameter values, up to a helium/titanium atomic ratio of 0.25 to 0.30. For higher helium concentrations, rapid helium desorption can be explained by gas bubble growth and percolation, and mechanical degradation of the layer: at this stage, the theoretical model does not apply.     

Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.