基于解耦差分泽尼克待定系数法的二维横向剪切波面重建算法

横向剪切干涉术是一种自参考干涉计量技术,其原理是被检测波前与其自身被剪开的波前之间在重叠范围内相干涉,由干涉图得到两相互剪切波前的波前差,通过波面重建算法得到待测波面.在波面重建算法中,泽尼克待定系数法是其中的一种.分析了横向剪切干涉技术的测量原理;提出了一种新的基于解耦差分泽尼克待定系数法的二维横向剪切波面重建算法....     

分形物体转动惯量的计算

由分形物体的自相似性、转动惯量的量纲和平行轴定理,分别计算并得到分形三角形、分形正方体、分形四面体和科赫雪花的转动惯量.     

基于径向基神经网络预测的混沌时间序列嵌入维数估计方法

根据Takens定理,研究了混沌时间序列相空间重构嵌入维数的选取问题.提出了基于径向基函数神经网络预测模型性能的嵌入维数估计方法,即根据嵌入维数与混沌时间序列预测模型性能的变化关系来确定嵌入维数.通过对几种典型混沌动力学系统的数值验证,结果表明该方法能够确定出合适的相空间重构嵌入维数. 关键词： 混沌 相空间重构 嵌入维数 预测     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

电化学沉积金属铜的分形枝晶生长控制与性能

 以CuSO_{4/sub>为前驱体,HCl为添加剂,采用电化学沉积方法,在室温条件下制得了μm级、面心立方结构分形铜的枝状晶体,研究了铜离子浓度、硫酸浓度、电流密度、沉积时间、氯离子浓度等实验参数对分形枝状铜晶体尺寸、结构的影响。结果表明：硫酸的浓度对铜沉积物结构无明显影响;随着Cu^{2+/sup>浓度的不断增大,铜沉积物的分形效果越来越明显;增大电流密度（0.4～1.6 A·cm-2/sup>）,铜沉积物由致密向多分枝的开放型转变;延长沉积时间（大于等于5 min）,可获得含大量次级分枝铜的晶体;适当增加盐酸用量（0.05～0.20 mol/L）,铜沉积物枝晶尺寸显著减小。最后讨论了分形枝晶铜在碱性条件下氧化甲醇的电化学性能。}}     

Shape effect on the size and dimension dependent order-disorder transition temperatures of bimetallic alloys

Chemically ordered bimetallic nanocrystals may be promising candidates for the future magnetic-storage applications. In order to theoretically understand the order-disorder transition in nanoscale, a model based on the previous result for the size and dimension dependent melting temperature is developed to describe the effects of sizes, shapes and dimensions on order-disorder transition temperatures (T_OD) of bimetallic alloys. The results show that T_OD drops as size decreases, shape factor increases and dimension decreases. Also, the shape effect on T_OD cannot be neglected. Among these effects on T_OD, size is the strongest, while shape is the weakest. All these conclusions have been compared and confirmed by the recent simulations and experiments.     

High‐throughput data dimension reduction via seeded canonical correlation analysis

Canonical correlation analysis (CCA) is one of popular statistical methodologies in multivariate analysis, especially, in studying relation of two sets of variables. However, if sample sizes are smaller than the maximum of the dimensions of two sets of variables, it is not plausible to construct canonical coefficient matrices due to failure of inverting sample covariance matrices. In this article, we develop a two step procedure of CCA implemented in such situation. For this, seeded dimension reduction is adapted into CCA. Numerical studies confirm the approach, and two real data analyses are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

AIFS—A Tool for Biomorphic Fractal Modeling

A considerable class of fractal sets can be represented by using the attractors of Iterated Function Systems (Barnsley, 1988), with affine contractive mappings of a metric space . The modeling capabilities of such systems are heavily limited however. For example, it is not easy to predict the location of the attractor nor its global shape. Then, Iterated Systems are not affinely invariant (affine mappings of the elements of the system do not result in affine image of its attractor). In this paper a new setting, the affine invariant Iterated Function System is described in such a way that it removes the mentioned shortcomings and can be used for shape-predictable modeling of fractal based forms. The stress is put on modeling of biological forms and their atributes such as: continuous deformation of the attractor in desired way (like in growing), branching (plants, vascular or alveolar network), gradual changing of fractal dimension from smooth to space-filling fractals. The last is useful for creating images of tissues in different stages of development, symmetry, gradual transformation from one to another form, etc. The fractal images obtained by AIFS are merely to gain resemblance to bio-forms.     

An Iterative Method of Point Mapping under Cell Reference for the Global Analysis: Theory and a Multiscale Reference Technique

In iterative method of Point Mapping under Cell Reference, a cell co-ordinate system, called cell reference, is built to identify the subregions (cells) in the state space. When the cell reference is equipped with the so-called characteristic functions, it can work as an inspector or a recorder to derive the local dynamics of the subregions from the information provided by the trajectories passing through them. This method can retain the accuracy of the Point Mapping Method but greatly reduce the computational work. In this paper, the theoretic basis for this method is first discussed and a multiscale reference technique is then devised which can select an optimal cell reference and make the method more practicable. Finally, an example for application is presented. It is shown that the present method cannot only accurately and efficiently depict the basins of attraction of a dynamical system but also potentially detect other characteristics of the system.