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.     

Renormalization group analysis of the global properties of a strange attractor

This paper considers the circle map at the special point: the one at which there is a trajectory with a golden mean winding number and at which the map just fails to be invertable at one point on the circle. The invariant density of this trajectory has fractal properties. Previous work has suggested that the global behavior of this fractal can be effectively analyzed using a kind of partition function formalism to generate anf versus curve. In this paper the partition function is obtained by using a renormalization group approach.     

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.     

MgO声子散射曲线和热力学特性的第一原理研究

利用从头算场论结合局域密度近似和Troullier-Martins赝势,计算了MgO的声子散射曲线和热力学特性.计算结果和所有的有效实验值进行了比较,发现理论计算结果和实验结果吻合的很好.     

Existence of periodic solutions and closed invariant curves in a class of discrete-time cellular neural networks

This paper discusses the dynamical behavior of excitatory-inhibitory discrete-time cellular neural networks (DTCNNs) with piecewise linear output functions. Our analysis shows that such DTCNNs have periodic solutions and closed invariant curves, and all their solutions, except for fixed points, eventually stay on the closed invariant curves. Moreover, these results are also illustrated by examples and figures. These results demonstrate that excitatory-inhibitory DTCNNs can exhibit permanent nonlinear oscillations. Moreover, such DTCNNs with permanent nonlinear oscillations may be chosen arbitrarily to close a DTCNN satisfying the SP-Condition which ensures the complete stability of DTCNNs. Thus, this work indicates that the SP-Condition on complete stability is not robust.     

偏心环形开放台球中粒子逃逸动力学的分形性质

二维台球体系因为能够体现混沌现象的基本特征且数值运算相对简单,从而成为研究微观体系混沌动力学的理想模型,近年来一直广受关注.本文研究非同心的环形开放台球中粒子逃逸的混沌动力学性质,它体现了与初条件密切相关的奇异性.采用简化的盒计数 (box-counting)算法,计算了分形维数,结果定量地反映了粒子逃逸前与环壁碰撞次数随粒子入射角变化的函数关系.其中,特别关注环形台球的偏心率对体系混沌性质的影响.     

等离子喷涂层原生性孔隙几何结构的分形及统计特性

孔隙是等离子喷涂涂层原生性结构, 对涂层的耐磨损、耐腐蚀、耐高温等性能具有显著影响, 是涂层参数优化的重要指标之一. 因此, 对涂层孔隙结构特征参数的全面表征对于更加精确地评价涂层质量具有重要意义. 本文将概率统计方法、分形方法与数字图像分析技术相结合, 研究了等离子喷涂涂层原生性孔隙数量、形态、尺寸及其分布等结构特征参数表征方法及孔隙的成形机理. 首先通过改变喷涂功率得到不同孔隙状态的Fe基合金涂层, 随后采用数字图像分析技术对涂层截面孔隙的扫描电子显微形貌图进行处理, 最后通过Weibull统计模型分析了孔隙周长及面积的尺寸分布特征, 并利用基于分形思想的面积-周长幂率研究了孔隙不规则形态的定量表征方法. 在实验过程中, 为了分析涂层孔隙的成形机理, 采用Spraywatch在线监测喷涂粒子的飞行状态. 结果表明: 分形维数能够表征孔隙的不规则形态, 分形维数越大, 孔隙面积越大或边界形态越复杂, 并且其与孔隙的成形机理之间存在良好的映射关系; 孔隙面积及周长的尺寸分布均服从明显的两项Weibull分布特征, 孔隙尺寸较小时, 形状参数β 较大, 而孔隙尺寸较大时, 则反之; 喷涂功率对孔隙尺寸的聚集特点产生不同程度的影响, 随着喷涂功率的增加, 粒子的融化状态逐渐改善, 孔隙的尺寸明显降低; 而当孔隙面积(周长)小于特征值时, 相同尺寸的孔隙概率密度值则越来越接近, 说明孔隙功率的变化对小尺寸孔隙出现的概率影响较小.     

Exact treatment of mode locking for a piecewise linear map

A piecewise linear map with one discontinuity is studied by analytic means in the two-dimensional parameter space. When the slope of the map is less than unity, periodic orbits are present, and we give the precise symbolic dynamic classification of these. The localization of the periodic domains in parameter space is given by closed expressions. The winding number forms a devil's terrace, a two-dimensional function whose cross sections are complete devils's staircases. In such a cross section the complementary set to the periodic intervals is a Cantor set with dimensionD=0.     

The dimension spectrum of some dynamical systems

We analyze the dimension spectrum previously introduced and measured experimentally by Jensen, Kadanoff, and Libchaber. Using large-deviation theory, we prove, for some invariant measures of expanding Markov maps, that the Hausdorff dimensionf() of the set on which the measure has a singularity is a well-defined, concave, and regular function. In particular, we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number. We also show in these particular cases that the functionf is universal.     

Universal multifractal properties of circle maps from the point of view of critical phenomena I. Phenomenology

The strange attractor for maps of the circle at criticality has been shown to be characterized by a remarkable infinite set of exponents. This characterization by an infinite set of exponents has become known as the multifractal approach. The present paper reformulates the multifractal properties of the strange attractor in a way more akin to critical phenomena. This new approach allows one to study the universal properties of both the critical point and of its vicinity within the same framework, and it allows universal properties to be extracted from experimental data in a straightforward manner. Obtaining Feigenbaum's scaling function from the experimental data is, by contrast, much more difficult. In addition to the infinite set of exponents, universal amplitude ratios here appear naturally. To study the crossover region near criticality, a correlation time, which plays a role analogous to the correlation length in critical phenomena, is introduced. This new approach is based on the introduction of a joint probability distribution for the positive integer moments of the closest-return distances. This joint probability distribution is physically motivated by the large fluctuations of the multifractal moments with respect to the choice of origin. The joint probability distribution has scaling properties analogous to those of the free energy close to a critical point.     

Optimum design of photoresist thickness for 90-nm critical dimension based on ArF laser lithography

In this work,a 90-nm critical dimension(CD) technological process in an ArF laser lithography system is simulated,and the swing curves of the CD linewidth changing with photoresist thickness are obtained in the absence and presence of bottom antireflection coating(BARC).By analysing the simulation result,it can be found that in the absence of BARC the CD swing curve effect is much bigger than that in the presence of BARC.So,the BARC should be needed for the 90-nm CD manufacture.The optimum resist thickness for 90-nm CD in the presence of BARC is obtained,and the optimizing process in this work can be used for reference in practice.     

Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.     

Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map

The spectrum and eigenfunctions of the Frobenius-Perron operator induced by the tent map are discussed in detail. Special attention is paid to the case where the critical point of the map lies on an aperiodic trajectory and the differences from maps with a periodic critical trajectory are stressed. It is shown that the relevant eigenvalues of the spectrum are not sensitive to the aperiodicity of the critical trajectory. All other parts of the spectrum and all eigenfunctions in particular are changed drastically if the critical trajectory becomes aperiodic. The intimate connection between the point spectrum and the kneading invariant is established and the critical slowing down as well as the band splitting are a consequence of its properties. The structure of the infinite sequence of null spaces and its implications on the spectrum of the operator are discussed. It is shown that any initial distributionP(0,x) of bounded variation can be projected uniquely onto the eigenfunctions of the relevant eigenvalues and that the time dependence ofP(n, x) is determined by this expansion up to an errorO( ⁿ). From this the stationary and the asymptotic behavior of the correlation function x(n) x can be derived exactly.