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Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

Journal of Geophysical Research: Space Physics 2014年第9期119卷 7577-7586页

作者： Yu, Zu-Guo Anh, Vo Eastes, Richard Hunan Key Laboratory for Computation and Simulation in Science and Engineering Ministry of Education Xiangtan University Xiangtan Hunan China School of Mathematical Sciences Queensland University of Technology Brisbane QLD Australia Florida Space Institute University of Central Florida Orlando FL United States

This paper identifies some scaling relationships between solar activity and geomagnetic activity. We examine the scaling properties of hourly data for two geomagnetic indices (a_p and AE), two solar indices (solar X-rays X_l and solar flux F10.7), and two inner heliospheric indices (ion density Ni and flow speed Vs) over the period 1995-2001 by the universal multifractal approach and the traditional multifractal analysis. We found that the universal multifractal model (UMM) provides a good fit to the empirical K(q) and τ(q) curves of these time series. The estimated values of the Lévy index α in the UMM indicate that multifractality exists in the time series for a_p, AE, X_l, and Ni, while those for F10.7 and Vs are monofractal. The estimated values of the nonconservation parameter H of this model confirm that these time series are conservative which indicate that the mean value of the process is constant for varying resolution. Additionally, the multifractal K(q) and τ(q) curves, and the estimated values of the sparseness parameter C₁ of the UMM indicate that there are three pairs of indices displaying similar scaling properties, namely a_p and X_l, AE and Ni, and F10.7 and Vs. The similarity in the scaling properties of pairs (a_p,X_l) and (AE,Ni) suggests that a_p and X_l, AE and Ni are better correlated - in terms of scaling - than previous thought, respectively. But our results still cannot be used to advance forecasting of a_p and AE by X_l and Ni, respectively, due to some reasons. key Points The scaling properties of the geomagnetic and the solar indices are examinedThe results suggest that multifractality exists in a_p, AE, Xl, and ion densityThe scaling similarity of the a_p and Xl data suggests flare-storm dependence ©2014. American Geophysical Union. All Rights Reserved.

关键词： geomagnetic indices multifractal analysis scaling property solar indices universal multifractal model

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Finite element methods for fractional diffusion equations

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International Journal of Modeling, simulation, and Scientific Computing 2020年第4期11卷 32-52页

作者： Yue Zhao Chen Shen Min Qu Weiping Bu Yifa Tang LSEC ICMSECAcademy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190P.R.China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 P.R.China School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan 411105P.R.China

Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast *** paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion ***,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm.

关键词： Fractional diffusion equation finite element method regularity theory well-posedness fast algorithm.

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Spring pair method of finding saddle points using the minimum energy path as a compass

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Physical Review E 2024年第6期110卷 064123-064123页

作者： Gang Cui Kai Jiang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan 411105 China

Finding index-1 saddle points is crucial for understanding phase transitions. In this work, we propose a simple yet efficient approach, the spring pair method (SPM), to accurately locate saddle points. Without requiring the Hessian information, the SPM evolves a single pair of spring-coupled particles on an energy surface. By designing complementary drifting and climbing dynamics based on gradient decomposition, the spring pair converges onto the minimum energy path (MEP) and spontaneously aligns its orientation with the MEP tangent, providing a reliable ascent direction for efficient convergence to saddle points. The SPM fundamentally differs from traditional surface walking methods that rely on the eigenvectors of the Hessian, which may deviate from the MEP tangent and potentially lead to convergence failure or undesired saddle points. The efficiency of the SPM for finding saddle points is verified by ample examples, including Lennard-Jones clusters, Morse clusters, water clusters, and the Landau energy functional involving quasicrystal phase transitions.

关键词： Lennard-Jones potential

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Watchdog from academia: Do academic independent directors matter for financial statement fraud?

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International Review of Economics & Finance 2025年

作者： Shigang Wen Jianping Li Chuangxia Huang Xiaoqian Zhu School of Management Guangdong University of Technology Guangzhou 510520 China School of Economics and Management University of Chinese Academy of Sciences Beijing 100190 China MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS Beijing 100190 China School of Mathematics and Statistics Changsha University of Science and Technology Changsha 410114 Hunan China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha 410114 Hunan China

We examine whether academic independent directors affect financial statement fraud. Using a sample of independent directors’ academic experience data for Chinese public firms, we find a significantly negative relation between academic independent directors and financial statement fraud. This finding is robust after applying various methods to address potential endogeneity concerns. Further analyses suggest that the negative relation between academic independent directors and financial statement fraud is more pronounced when academic independent directors are professors and possess accounting and technological expertise, sit on audit committees, compensation committees, multiple boards, and have relatively low-level compensation. In addition, the negative relation is stronger for non-state-owned firms and firms audited by small auditors. Overall, our findings suggest that academic independent directors are watchdogs for financial statement fraud.

关键词： academic independent director financial statement fraud corporate governance board committee professor compensation

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Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods

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Advances in Applied Mathematics and Mechanics 2009年第6期1卷 830-844页

作者： Yanping Chen Peng Luan Zuliang Lu School of Mathematical Science South China Normal UniversityGuangzhou 510631GuangdongChina Mathematics Teaching and Research Group Sanshui Experimental High School of Zhongshan UniversityFoshan 528145GuangdongChina Hunan Key Lab for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina

In this paper,we present an efficient method of two-grid scheme for the approximation of two-dimensional nonlinear parabolic equations using an expanded mixed finite element *** use two Newton iterations on the fine grid in our ***,we solve an original nonlinear problem on the coarse nonlinear grid,then we use Newton iterations on the fine grid *** two-grid idea is from Xu's work[SIAM ***.,33(1996),pp.1759–1777]on standard finite *** also obtain the error estimates for the algorithms of the two-grid *** is shown that the algorithm achieve asymptotically optimal approximation rate with the two-grid methods as long as the mesh sizes satisfy h=O(H^((4k+1)/(k+1))).

关键词： Nonlinear parabolic equations two-grid scheme expanded mixed finite element methods Gronwall’s Lemma

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SATURATION AND RELIABLE HIERARCHICAL A POSTERIORI MORLEY FINITE ELEMENT ERROR CONTROL

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Journal of computational Mathematics 2018年第6期36卷 833-844页

作者： Carsten Carstensen Dietmar Gallistl Yunqing Huang Humboldt-Universitat zu Berlin Institut fiir Mathematik Unter den Linden 6 10099 Berlin Germany Department of Applied Mathematics University of Twente P.O. Box 217 7500 AE Enschede Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering Xiangtan University Xiangtan 411105 China

This paper proves the saturation assumption for the nonconforming Morley finite ele- ment discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle. This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.

关键词： Saturation Hierarchical error estimation Finite element Nonconforming Biharmonie Morley Kirchhoff plate Crouzeix-Raviart

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Effects of substituent and solvent on the UV absorption energy of 4,4'-disubstituted stilbenes

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science China Chemistry 2011年第2期54卷 1735-1744页

作者： CAO ChenZhong CHEN GuanFan WU YaXin Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Hunan Provincial University Key Laboratory of QSAR/QSPRSchool of Chemistry and Chemical EngineeringHunan University of Science and TechnologyXiangtan 411201China

Twenty five samples of 4,4'-disubstituted stilbene derivatives were synthesized, and their UV absorption max wavelengths were determined in over 10 kinds of solvents including cyclohexane, ether, chloroform, acetonitrile and ethanol, in which 242 experimental data were recorded. The effects of substituents and solvents on the energy of their UV absorption max wavelengths were discussed. The research results showed: the energy of UV absorption max wavelengths of 4,4'-disubstituted stilbenes was mainly affected by their intramolecular structure (substituent effect) in a given solvent, that is, the energy is dominated by both of excited-state substituent parameter o-~c and polar substituent constant crp. While their energy was dominated by the substituent effect and solvent effect in different kinds of solvents. An equation quantifying the energy of UV absorption max wavelengths of 4,4'-disubstituted stilbenes was developed. In addition, it is found that the n-octanol/water partition coefficient (logP) is more effective than the solvatochromic dye (ET(30)) in scaling the solvent effect. The equation employed the parameter logP has a better correlation and more specific physical meaning. Further, the energies of UV absorption max wavelengths of some reported compounds were predicted by the obtained equation, which are in agreement with their experimental values.

关键词： 4,4'-disubstituted stilbene UV absorption energy excited-state substituent parameter solvent effect

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A DISCONTINUOUS GALERKIN METHOD FOR THE FOURTH-ORDER CURL PROBLEM

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Journal of computational Mathematics 2012年第6期30卷 565-578页

作者： Qingguo Hong Jun Hu Shi Shu Jinchao Xu School of Mathematical Science Peking University Beijing 100871 China LMAM and School of Mathematical Science Peking University Beijing 100871 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China Department of Mathematics Pennsylvania State University University Park PA 16802 USA

In this paper, we present a discontinuous Galerkin （DG） method based on the N@d@lec finite element space for solving a fourth-order curl equation arising from a magnetohy- drodynamics model on a 3-dimensional bounded Lipschitz polyhedron. We show that the method has an optimal error estimate for a model problem involving a fourth-order curl operator. Furthermore, some numerical results in 2 dimensions are presented to verify the theoretical results.

关键词： Fourth-order curl problem DG method Nedelec finite element space Errorestimate.

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A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

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Numerical Mathematics(Theory,Methods and Applications) 2023年第3期16卷 597-621页

作者： Yedan Shen Ting Wang Jie Zhou Guanghui Hu School of Mathematics and Information Science Guangzhou UniversityGuangzhouChina Faculty of Science and Technology University of MacaoMacao SARChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanChina School of Mathematical Computational Sciences Xiangtan UniversityXiangtanChina Zhuhai UM Science&Technology Research Institute ZhuhaiChina Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications University of MacaoMacao SARChina

In[Dai et al.,***.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et al.,EAJAM.13(2)(2023)]for further improving the numerical *** this paper,a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham ***,the convergence,the asymptotic stability,as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works,while spatially,the convergence of the h-adaptive mesh method is demonstrated following[Chen et al.,***.12(2014)],with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham *** examples confirm the theoretical results very well.

关键词： Kohn-Sham density functional theory gradient flow model structure-preserving linear scheme convergence analysis

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Analysis theory of random energy of train derailment in wind

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science China(Physics,Mechanics & Astronomy) 2010年第4期53卷 751-757页

作者： CHEN RuiLin 1,2,3 , ZENG QingYuan 3 , HUANG YunQing 1 , XIANG Jun 3 , WEN Ying 3 , GUO XiaoGang 2 , YIN ChangJun 2 , DONG Hui 2 & ZHAO Gang 4 1 hunan key laboratory for computation and simulation in science and engineering, Xiangtan University, Xiangtan 411105, China 2 School of Civil engineering & Mechanics, Xiangtan University, Xiangtan 411105, China 3 School of Civil Architecture, Central South University, Changsha 410075, China 4 AMEC, Toronto M5A5G7, Canada 1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China2. School of Civil Engineering & Mechanics Xiangtan University Xiangtan 411105 China3. School of Civil Architecture Central South University Changsha 410075 China4. AMEC Toronto M5A5G7 Canada

Based on the analysis theory of random energy of train derailment, an analysis theory of random energy of train derailment in wind is suggested. Two methods are proposed -the time domain method and the frequency domain method of analysis theory of random energy of train derailment in wind. The curves of σ pw -v under various wind speeds are obtained through the computation. The original curve of σ p -v is expanded, which turns the analysis theory of random energy of train derailment into the all-weather theory. Train derailment condition has been established under wind action. The first and second criterions of train derailment have been proposed in light of wind action. The analysis of train derailment cases at home or abroad is made, in- cluding the first analysis of Xinjiang train derailment case encountered 13-level of gale, which explained the inevitability of train derailment. The analysis theory of random energy of train derailment in wind shows its validity and accuracy. The input energy σ pw of the transverse vibration of train-track(bridge)-wind system is linked to train speed. With the establishment of the analysis theory of random energy of train derailment in wind, It is likely to initiate an all-weather speed limit map for a train or any high-speed train.

关键词： train derailment analysis theory of random energy of train derailment analysis theory of random energy of train de- railment in wind train derailment condition in wind the criterion of train derailment in wind train derailment case

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