特殊钻石型等级晶格上S4模型的临界性质

应用实空间重整化群和累积展开的方法,研究了外场中特殊钻石型等级晶格上S4模型的相变和临界性质,求出了系统的临界点和临界指数. 结果表明,此系统除了存在一个Gauss不动点外,还存在一个Wilson-Fisher不动点,与该等级晶格上的Gauss模型相比较,系统的临界指数发生了变化.     

特殊钻石型等级晶格上S4模型的临界性质

应用实空间重整化群和累积展开的方法，研究了外场中特殊钻石型等级晶格上S⁴模型的相变和临界性质，求出了系统的临界点和临界指数. 结果表明，此系统除了存在一个Gauss不动点外，还存在一个Wilson-Fisher不动点，与该等级晶格上的Gauss模型相比较，系统的临界指数发生了变化. 关键词： 钻石型等级晶格 4模型')" href="#">S⁴模型 重整化群 临界性质     

截断误差诱导阵发混沌与拓展维

进一步研究过焦系统，找到了截断误差诱导阵发混沌的直接实验证据.实验显示，过焦系统的数字解呈现开关阵发混沌的特征，分析解仅是一个简单极限序列；影子效应支配系统演化；截断误差的累计误差是演化轨道的影子距离，影子距离随系统逼近不动点增加，随系统远离不动点减少，增加量与减少量统计上相等；在非双曲不动点的邻域内，存在一个阈值，当累计误差超过该阈值时，影子效应失灵，系统从吸引相跳到排斥相.一种合理的猜测是在非双曲不动点局域截断误差可以诱导出新维度——拓展维. 关键词： 开关阵发混沌 截断误差 过焦系统 拓展维     

移动环境下网络病毒传播模型及其稳定性研究

考虑网络节点的随机移动, 基于平均场理论 提出一个移动环境下网络病毒传播的数学模型, 利用微分动力学系统理论研究了病毒传播行为. 研究表明, 当病毒基本再生数R₀ ≤ 1时, 网络中病毒逐渐消除, 系统的无病毒平衡点全局渐进稳定; 当R₀ > 1时, 网络中病毒持续存在, 系统的地方病平衡点全局渐进稳定.通过仿真验证了所得结论的正确性.     

密度泛函理论对CdnTen（1≤n≤12）团簇结构与性质的研究

采用基于密度泛函理论的DMol3软件包对CdnTen（1≤n≤12）团簇的几何结构进行优化,并对其能量、频率以及电子性质进行模拟分析. 结果表明,团簇CdnTen（1≤n≤12）与团簇CdnSen（1≤n≤12）具有相似的最低能量结构：当n=1～3时,团簇的最低能量结构是平面结构;当n=4～12时,团簇的最低能量结构可以看成是由Cd2Te2和Cd3Te3团簇的最低能量结构组成的三维笼状结构;当n=12时,Cd12Te12团簇的最低能量结构为一个完美的球壳. 随着团簇尺寸的增大,转移的电荷逐渐增加,转移的电荷量有达到块体中电荷值的趋势. 团簇的总能量二阶有限差分,平均结合能以及能隙都显示团簇的幻数为Cd3Te3,Cd6Te6 和Cd9Te9.     

密度泛函理论对Cd_nTe_n(1≤n≤12)团簇结构与性质的研究

采用基于密度泛函理论的DMol 3软件包对CdnTen(1≤n≤12)团簇的几何结构进行优化,并对其能量、频率以及电子性质进行模拟分析.结果表明,团簇CdnTen(1≤n≤12)与团簇CdnSen(1≤n≤12)具有相似的最低能量结构:当n=1～3时,团簇的最低能量结构是平面结构;当n=4～12时,团簇的最低能量结构可以看成是由Cd2Te2和Cd3Te3团簇的最低能量结构组成的三维笼状结构;当n=12时,Cd12Te12团簇的最低能量结构为一个完美的球壳.随着团簇尺寸的增大,转移的电荷逐渐增加,转移的电荷量有达到块体中电荷值的趋势.团簇的总能量二阶有限差分,平均结合能以及能隙都显示团簇的幻数为Cd3Te3,Cd6Te6和Cd9Te9.     

湍流热对流Prandtl数效应的数值研究

本文采用直接数值模拟的并行直接求解方法,计算了Ra=10~(10),0.05≤Pr≤20的系列Prandtl(Pr)数二维湍流热对流.通过流动显示技术,讨论了Pr数对羽流形态和大尺度环流结构的影响.在Ra=10~(10)时,随着Pr数减小,羽流的运动和分布表现出更强的湍流性质,较高Pr数的羽流则表现出较强的规律性,当Pr4.3时,流场中存在明显的大尺度环流和角涡结构.不同Pr数的温度边界层厚度差异不大,并随Pr数存在标度率变化关系.当Pr数较低时,系统的传热Nusselt(Nu)数随着Pr数增加而增加,当Pr数较高时,Nu数随Pr数的变化不敏感.靠近底板处速度脉动随Pr数有显著的变化,Pr数越低速度波动越剧烈.通过底板中心位置水平脉动速度和平均场水平速度最大值给出的雷诺数Re_((u))和Re_(U_(max)),两种Re数随Pr数的变化满足同一标度律,为Re～Pr~(-0.81).     

不同温度下团簇生长的Monte Carlo模拟

引入基底表面束缚能、最近邻粒子间的耦合能以及应力场,对粒子扩散势垒进行修正,采用Monte Carlo方法对不同温度下薄膜生长过程进行模拟研究.结果表明,当400 K≤T ≤ 480 K,所得团簇的平均分支宽度基本保持不变,其值近似为单粒子直径.当500 K≤T ≤ 680 K,团簇分支宽度随着温度的升高而逐渐增大至约4个粒子.随着温度的继续升高,由于粒子较高的活跃性而无法凝聚形成大团簇,团簇包含粒子数的平均值小于2.还研究了不同温度下团簇在生长过程中的形貌演化过程以及团簇数变化规律.     

负P表示非经典光场的信息熵

G.S.Agarwal and K.Tara发现了一个具有负P表示的非经典光场,而此前发现非经典光场的P表示都是奇异的.本文研究了这类负P表示光场的信息熵随场参数m和平均光子数的关系.结果显示,负P表示的非经典光场的Wehrl熵随着场参数m的增大而减小;而当平均光子数增大时,Wehrl熵亦随其增大而减小.同时本文用数值计算的方法研究了负P表示光场的Shannon熵与平均光子数的关系.发现当场参数m一定时,Shannon熵随着平均光子数的增大反而愈来愈小.以上结果表明,当场参数m一定时,随着平均光子数的增大,负P表示光场的非经典性增强;当平均光子数一定时,随着场参数m的增大,负P表示光场的非经典性亦越来越强.这是因为,当m 趋于零时,该光场则演化为经典的热光场;当平均光子数趋于无穷时,该光场则变为Fock态光场.     

倾斜多孔介质方腔内纳米流体自然对流的格子Boltzmann方法模拟

利用格子玻尔兹曼方法 (lattice Boltzmann method, LBM) 对倾斜多孔介质方腔内 Al_2O_3-H_2O 纳米流体的自然对流进行数值模拟, 考虑了孔隙率 (0.3 ≤?≤ 0.9)、瑞利数 (10~3 ≤ Ra ≤ 10~6)、纳米颗粒体积分数(0 ≤ ? ≤ 0.04) 和倾斜角 (0°≤γ≤ 120°) 等因素的影响, 研究了正弦温度分布边界条件下倾斜多孔介质方腔内纳米流体的自然对流传热机理. 结果表明: 若?和γ保持不变时, 随着 Ra 数的增大, 热壁面处的平均努塞尔数 (Nu_(ave) 数) 呈现出先减小后增大的趋势; 对于给定的 Ra 数, 当γ = 0°时, 随着孔隙率的增大, 热壁面处Nu_(ave) 数逐渐增大, 当γ = 40°, 80°和 120°时, Nuave 数在?= 0.7 左右时达到最大值; 若?和 Ra 数保持不变, 当γ = 40°时, 方腔内的自然对流换热效率最强, 当γ = 80°时热壁面自然对流换热效率被削弱. 最后, 研究了纳米颗粒体积份数的影响, 当方腔施加一定倾角时, 热壁面处的 Nuave 数随着纳米颗粒体积分数的增大而增大.     

The Gaussian Model on the Inhomogeneous Fractal Lattices

The decimation real-space renormalization group and spin-rescaling methods are applied to the study of phase transition of the Gaussian model on fractal lattices. It is found that the critical point K^* equals b/2 ( b is the distribution constant of Gaussian model) on nonbranching Koch curves. For inhomogeneous fractal lattices, it is proposed that the b is replaced with b_qi (qi is the coordination number of the site i) and satisfies a certain relation b_qi/b_qj = q_i/q_j. Under this supposition we find that the critical point of the Gaussian model on a branching Koch curve can be expressed uniquely as K^* = b_qi/q_i.     

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.     

Critical Percolation Probabilities for the Next-Nearest-Neighbouring Site Problems on Sierpinski Carpets

In this paper, we compute the next-nearest-neighbouring site percolation (Connections exist not only between nearest-neighbouring sites, but also between next-nearest-neigh bouring sites.) probabilities PC on the two-dimensional Sierpinski carpets, using the translationaldilation method and Monte Carlo technique. We obtain a relation among PC, fractal dimensionality D and connectivity Q. For the family of carpets with central cutouts,(1 - P_c)/(1 - P_c^s) = (D - 1)^1.60, where P_c^s = 0.41, the critical percolation probability for the next-nearest-neighbouring site problem on square lattice. As D reaches 2, P_c = P_c^s = 0.41, which is in agreement with the critical percolation probability on 2-d square lattices with . next-nearest-neigh bouring interactions.     

A Complete Renormalization Group Trajectory Between Two Fixed Points

We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.     

Sierpinski 地毯上S4模型的临界特性

通过键移动重整化群的方法, 分析了Sierpinski 地毯上S⁴模型的临界行为, 得到了系统的临界点. 由得到的结果可知, 本系统不仅有一个高斯不动点, 而且还存在着一个Wilson Fisher不动点, 把它与Sierpinski 地毯上的高斯模型相互对比, 发现本系统的临界点变化很大. 这说明这两个系统隶属于两个不同的普适类.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

d-Dimensional Kinetic S4 Model

A single-spin transitional critical dynamics based on the Glauber theory is used to investigate the d-dimensional kinetic S⁴ model. We derive the fundamental dynamical equations by a cumulant expansion, and then, a one-dirnensional model is treated. We obtain approximately the local magnetization and equal-time spin-pair correlation function, in which the terms of k₃ and the higher orders are ignored (corresponding to high-temperature cutoff). These are finally extended to d-dimensional case. In addition, we obtain the critical point k_c of d-dimensional S⁴ model, and give a relation satisfied by the dynamic critical exponent Z and the correlation length critical exponent ν.     

Critical slowing down of the Gaussian spin system on diamond—type hierarchical lattices

Based on the single-spin transition critical dynamics, we have investigated the critical slowing down of the Gaussian spin model situated on the fractal family of diamond-type hierarchical lattices. We calculate the dynamical critical exponent z and the correlation-length critical exponent ν using the dynamical decimation renormalization-group technique. The result, together with some earlier ones, suggests us to conclude that on a wide range of geometries, zν=1 is the general relationship, while the two exponents depend on the specific structure. However, we have investigated for various lattices in an earlier paper, the system studied in this paper shows highly universal z=1/ν=2 independent of the structure and the dimensionality.     

Continuum limit of finite temperature λφ3 from lattice Monte Carlo

The φ₃⁴ model at finite temperature is simulated on the lattice. For fixed N_t we compute the transition line for N_s → ∞ by means of finite size scaling techniques. The crossings of a renormalization group trajectory with the transition lines of increasing N_t give a well-defined limit for the critical temperature in the continuum. By considering different RG trajectories, we compute T^c/g as a function of the renormalized parameters.