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Discontinuous transition between Zundel and eigen for H5O2^+

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Chinese Physics B 2020年第8期29卷 54-58页

作者：王恩栋朱倍恩高嶷 Key Laboratory of Interfacial Physics and Technology Shanghai Institute of Applied PhysicsChinese Academy of SciencesShanghai 201800China Zhangjiang Laboratory Shanghai Advanced Research InstituteChinese Academy of SciencesShanghai 201210China

The hydrated-proton structure is critical for understanding the proton transport in ***,whether the hydrated proton adopts Zundel or eigen structure in solution has been highly debated in the past several *** experimental techniques cannot directly visualize the dynamic structures in situ,while the available theoretical results on the infrared(IR)spectrum derived from current configurational models cannot fully reproduce the experimental results and thus are unable to provide their precise *** this work,using H5O2^+ as a model,we performed first-principles calculations to demonstrate that both the structural feature and the IR frequency of proton stretching,characteristics to discern the Zundel or eigen structures,evolve discontinuously with the change of the O–O distance.A simple formula was introduced to discriminate the Zundel,Zundel-like,and eigen-like *** work arouses new perspectives to understand the proton hydration in water.

关键词： eigen Zundel infrared absorption ab initio calculations

eigen theory of elastic mechanics for anisotropic solids

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中国有色金属学会会刊：英文版 2000年第2期10卷 217-219页

作者：郭少华中南工业大学湖南长沙

eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standard space, and the modal equilibrium equation and the modal harmony equation under mechanical space were obtained. Based on them and the modal Hooke’s law, a new system of the fundamental equation of elastic mechanics is given. The advantages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy and anisotropy, both force method and displacement method, both force boundary and displacement boundary; the number of stress functions is equal to that of the anisotropic subspaces, which avoids the man made mistakes; the solution of stress field or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matter how complicated the anisotropy of solids may be, the complete solutions can be obtained.

关键词： anisotropic solid elastic mechanics eigen form standard space

eigen elastic mechanics and its variation principle

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中国有色金属学会会刊：英文版 2001年第2期11卷 281-282页

作者： GUO Shao-hua 郭少华 College of Resources Environment and Civil Engineering Central South University

The fundamental equations and the corresponding boundary condition of elastic mechanics under mechanical representation are given by using the conception of eigen space and elastic variation principle. It is proved theoretically that the solution of anisotropic elastic mechanics consists of modal ones, which are obtained respectively from the modal equation of the different subspaces. A simple application is also given.

关键词： anisotropy eigen elastic mechanics variation principle modal equation

Condensation of eigen microstate in statistical ensemble and phase transition

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Science China(Physics,Mechanics & Astronomy) 2019年第9期62卷 41-48页

作者： GaoKe Hu Teng Liu MaoXin Liu Wei Chen XiaoSong Chen Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China School of Systems Science Beijing Normal UniversityBeijing 100875China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China State Key Laboratory of Multiphase Complex Systems Institute of Process EngineeringChinese Academy of SciencesBeijing 100190China State Key Laboratory of Information Photonics and Optical Communications & School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China

In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.

关键词： statistical ensemble eigen microstate condensation phase transition finite-size scaling

eigen-Space Decomposition(ESD)Method for the Design of Internal Model Controller(IMC)from Noisy Input and Output Plant Data

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Journal of China Textile University(English Edition) 1999年第4期16卷 13-16页

作者：吴国海华建兴

A novel approach to design Internal Model Controller(IMC)is proposed in this paper directly from measuredinput and output plant data,which are assumed to becontaminated by measurement *** order to avoidthe complicated structure-identification problem inmost cases,two Finite Impulse Response(FIR)modelsare taken to represent the plant model and the internalmodel controller *** account of mea-surement noise both in the plant input and its output,anESD based Total Least Squares(TLS)solution is appliedfor the unbiased identification of the plant model and itsinverse model,the latter constitutes the internal modelcontroller according to the principle that the internalmodel controller approximates the inverse dynamics ofthe plant *** are given for a testifica-tion.

关键词： Internal model control total least squares eigen - space decomposition parameter estimation identification

On Exact Determination of eigen Vectors

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Advances in Linear Algebra & Matrix Theory 2015年第2期5卷 46-53页

作者： Raghuram Prasad Dasaradhi V. V. Haragopal Department of Mathematics Osmania University Hyderabad India Department of Statistics Osmania University Hyderabad India

In this article, we determine the eigen values and eigen vectors of a square matrix by a new approach. This considers all the roots with their multiplicities are known, using only the simple matrix multiplication of a... 详细信息

关键词： Characteristic Equation Minimal Polynomia eigen Values eigen Vectors Vander Monde Matrices Jordan Reduction

基于eigen和OpenCV的图像算法加速

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微型机与应用 2017年第24期36卷 40-43页

作者：舒畅秦肖臻华中科技大学自动化学院湖北武汉430074

OpenCV作为一款免费、开源的计算机视觉库已广泛应用于图像处理的各种项目开发中。在算法实现中,高性能的线性代数运算库能提升算法的执行效率和算法实现灵活性。介绍了eigen线性代数运算库,并在矩阵运算效率上与OpenCV进行了比较。以基... 详细信息

OpenCV作为一款免费、开源的计算机视觉库已广泛应用于图像处理的各种项目开发中。在算法实现中,高性能的线性代数运算库能提升算法的执行效率和算法实现灵活性。介绍了eigen线性代数运算库,并在矩阵运算效率上与OpenCV进行了比较。以基于SVD分解的图像压缩算法为例,将eigen和OpenCV进行联合编程并给出了主要代码。

关键词： OpenCV eigen 图像处理算法加速