动力系统时间延迟重构变换的行为

利用延迟重构变换的雅可比行列式,分析了动力系统重构中的拓朴性质。讨论了延迟时间的选择和重构变量本身的条件稳定性对重构拓朴的影响。利用条件Lyapunov指数分析了重构变量本身的好坏。文中以强迫Brusselator系统为例进行了讨论     

高精度TVD有限差分格式的自由梯度条件

1自由流条件守恒性气动方程组的高精度TVD有限差分格式一般通过使用通量限制器加入非线性的人工粘性来构成。在曲线坐标系中，通量限制器比较的两个因子与各自所在单元的界面雅可比转换行列式相关。为了消除畸变网格单元界面雅可比转换行列式的变化对通量限制器比较结果的影响，本文提出了高精度TVD格式的自由梯度性质，并分别就Osher和HartenTVD格式讨论了同时满足自由流和自由梯度的度量张量计算方法，使高精度TVD格式在畸变网格上得以实现。任意曲线坐标系中守恒型二维欧拉方程表示为其中，E、F为笛卡尔坐标系中的通量；J为坐标变…     

广义动量算符和雅可比行列式

本文导出了正交曲线坐标系下广义动量算符与雅可比行列式的关系．并利用所导出的公式算出了几个较常见的正交曲线坐标系下广义动量算符的明显形式．     

CMYK防伪印刷微镜阵列

以印刷微镜的反射亮度、反射稳定性和CMYK颜色模式为基础,建立了一种新型的CMYK印刷微镜结构模型。利用微镜表面函数的雅可比行列式和梯度函数,对模型的表面反射亮度和稳定性进行了分析评价。结果表明:该结构模型表面函数的雅可比行列式近似为0,梯度函数随坐标变化而变化。因此,此结构模型表面的反射光具有足够大的亮度和稳定性,适用于创建基于位置和角度变化来改变光变图案反射密度的光学防伪效果。设计了一幅由不同CMYK印刷微镜组成的防伪光变图案,模拟了该防伪图案的印刷微镜阵列结构。     

用雅可俾函数行列式指导热力学关系

一 、引言1.在本文提出的方法中要用到: 1.雅可俾函数行列式的三个主要性质[1]。设 x=x(u,v) y=y(u,v) u=u(s, t)v=v(s, t)雅可俾函数行列式定义为J的性质如下:令 2.对化学性质没有变化的均匀系,有下面四个麦克斯韦关系[2] 二、方法和例证 1、在热力学关系中只含有体系状态参量T、p、V、S时,首先将偏微分关系写成雅可俾函数行列式的形式,然后乘以D(x,y)/D(x,y),而其中变量(x,y)对绝热过程是o,V)或…。p)对共他过程是(T,D戍iT,P｝。最后利用雅可饶函数行列式的性质和麦克斯韦莱系,即可得到所需要的热力学关系。、_、;_-。。 例如,我们要…     

利用二阶雅可比行列式确定二维重构系统的延迟时间

提出了二阶雅可比行列式的第一极值来确定二维重构系统的延迟时间，它比用互信息函数第一极小确定延迟时间等方法，可以给出更多信息，文中以强迫Ｂｒｕｓｓｅｌａｔｏｒ方程系统的为例进行了讨论。     

三阶非线性聚合物光波导研究

以三阶克尔型非线性波导为例,利用雅可比椭圆函数的特性,定义了一种新颖的雅可比椭圆余切振幅函数,以此建立了类似线性的在非线性条件下的色散关系,使形式简化、物理意义清晰。并利用这一关系分析了该情况下的模式特性和场特性。     

散射振幅的广义Regge表示

本文建立了Resse表示的一般形式其中P_l^(μ,ν)(z)为雅可比函数。我们比较详细地研究了它与普通Regge表示的关系。在附录中讨论了雅可比函数的若干性质。     

常用数学工具在热力学关系式证明中的应用

对热力学中常用的数学工具如多元函数的导数及其全微分、雅可比行列式、勒让德变换、复合函数求导等进行了简单介绍,并由热力学基本规律出发,在充分分析基本热力学关系式特点的基础上,较系统地归纳出6种解决热力学关系式证明的方法,对每一种方法都给出了适用的要点,并以典型例题进行了说明.     

随机扰动优化和多模型融合的目标密度非线性重建

针对高能闪光X射线图像线性重建结果受系统模糊影响的问题,提出一种随机扰动优化和多模型融合的非线性重建算法.构建非线性正向模型并推导相应的雅可比矩阵形式,结合贝叶斯理论考虑该反演问题的求解及不确定量化,引入基于弱信息先验的超参数构建非线性分层贝叶斯模型.通过加速求解随机扰动的优化问题对条件分布进行采样,结合雅可比矩阵投影...     

Markov transition probability-based network from time series for characterizing experimental two-phase flow

We generate a directed weighted complex network by a method based on Markov transition probability to represent an experimental two-phase flow. We first systematically carry out gas-liquid two-phase flow experiments for measuring the time series of flow signals. Then we construct directed weighted complex networks from various time series in terms of a network generation method based on Markov transition probability. We find that the generated network inherits the main features of the time series in the network structure. In particular, the networks from time series with different dynamics exhibit distinct topological properties. Finally, we construct two-phase flow directed weighted networks from experimental signals and associate the dynamic behavior of gas-liquid two-phase flow with the topological statistics of the generated networks. The results suggest that the topological statistics of two-phase flow networks allow quantitative characterization of the dynamic flow behavior in the transitions among different gas-liquid flow patterns.     

Generation of singular beams in uniaxial crystals

The process of generation and transformation of the structure of singular beams both coherent and incoherent, in a crystal-polarization compensator-polarizer system is studied. It is shown that this system can transform the topological charge of the initial beam. The value of the transformed charge depends both on the structure of the initial beam and on its polarization. The initial singular beams, transferring topological multipoles, are shown to acquire unique properties after passing through the system. This system, in particular, makes it possible to control the position of bound optical vortices and the magnitudes of their angular momenta, which may find practical application in devices for trapping, transportation, and mutual arrangement of microparticles.     

Complex network from pseudoperiodic time series: topology versus dynamics

We construct complex networks from pseudoperiodic time series, with each cycle represented by a single node in the network. We investigate the statistical properties of these networks for various time series and find that time series with different dynamics exhibit distinct topological structures. Specifically, noisy periodic signals correspond to random networks, and chaotic time series generate networks that exhibit small world and scale free features. We show that this distinction in topological structure results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor. Standard measures of structure in complex networks can therefore be applied to distinguish different dynamic regimes in time series. Application to human electrocardiograms shows that such statistical properties are able to differentiate between the sinus rhythm cardiograms of healthy volunteers and those of coronary care patients.     

基于条件熵扩维的多变量混沌时间序列相空间重构

提出一种多变量混沌时间序列相空间重构的条件熵扩维方法.首先使用互信息法求解每个变量的时间延迟,其次按条件熵最大原则逐步扩展相空间的嵌入维数,使得重构坐标从低维到高维的转换保持较强的独立性,最终的重构相空间具有较低的冗余度,为多变量时间序列的预测构造了有效的模型输入向量.通过对几个经典多变量混沌时间序列进行数值实验,结果表明该方法比单变量预测和已有多变量预测方法具有更好的预测效果,说明了该重构方法的有效性. 关键词： 多变量混沌时间序列 相空间重构 条件熵 神经网络预测     

First-principles study of the topological surface states of α-Sn(111)

α-Sn is on the boundary of a couple of distinct topological phases. It will transform into a topological insulator under a suitable strain. However, a clear picture of its topological surface states (TSSs) is still lacking. Here we perform first-principles calculations on the electronic structure of α-Sn(111) surface to identify its TSSs and reveal their properties. The results show that the presence of valence band reorganizes the TSSs in the inverted sp gap into two Dirac cones. The lower one is in the valence band continuum; the upper one resides in the gap between the valence and conduction bands. We also demonstrate the transformation of the surface states by switching on or off of strain and/or spin-orbit coupling. Without spin-orbit coupling, only the TSSs associated with the lower Dirac cone survive, and they are spin unpolarized. The results are useful for understanding and engineering the topological properties of α-Sn.     

Topological causality analysis of horizontal gas-liquid flows based on cross map of phase spaces

Nonlinear systems are always characterized by the interactions between constituents which yield data in the form of time series. Exploration of the causality between the times series is beneficial for understanding the dynamics of the system. We introduce a topological causality method to explore the dynamics of horizontal gas-liquid flows. First, the principle of the topological causality algorithm is illustrated and validated using the Lorenz system and transfer entropy. Then, we conducted an experiment of gas-liquid flows in a horizontal pipe, during which a wire-mesh sensor (WMS) was used to capture the flow structures. The WMS data at different time frames are embedded in high-dimension phase spaces. Through building a cross map between coupled phase spaces, a cross map smoothness was employed to derive the topological causality index. The causality index enables us to understand the mechanism of the flow pattern transition and the intrinsic dynamics of the transient gas-liquid flows.     

Conditional independence graph for nonlinear time series and its application to international financial markets

Conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series, which extend the graphical modeling approach based on partial correlation. The vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series. The conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure. Furthermore, a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence. The efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations. Finally, we show how the method can be applied to international financial markets to investigate the nonlinear independence structure.     

声学蜂窝结构中的拓扑角态

高阶拓扑绝缘体是近年来发现的一类具有特殊拓扑相的新型拓扑绝缘体,目前已在光学、声学等多种经典波系统中实现.本文采用数值模拟方法研究了一种二维声学蜂窝结构,通过调节胞内和胞间耦合波导管,使体能带发生反转诱导拓扑相变,进而利用拓扑相构建出声学二阶拓扑绝缘体.蜂窝结构的拓扑性质可以用量子化的四极矩Q_ij表征,当Q_ij=0时,系统是平庸的;而当Q_ij=1/2时,系统是拓扑的.基于该蜂窝结构,分别研究了六边形和三角形结构的声学高阶态,在两种构型的蜂窝结构中均观测到了孤立的零维角态,研究结果表明只有存在钝角的六边形结构对缺陷具有鲁棒性,受拓扑保护.本文的拓扑角态丰富了高阶拓扑绝缘体的研究,同时可为紧凑声学系统中的鲁棒限制声提供一条新途径.