检索结果-内蒙古大学图书馆

Multifractal temporally weighted detrended partial cross-correlation analysis to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Li, Bao-Gen Ling, Dian-Yi Yu, Zu-Guo Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China School of Electrical Engineering and Computer Science Queensland University of Technology GPO Box 2434 BrisbaneQ4001 Australia

When common factors strongly influence two cross-correlated time series recorded in complex natural and social systems, the results will be biased if we use multifractal detrended cross-correlation analysis (MF-DXA) without considering these common factors. Based on multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) proposed by our group and multifractal partial cross-correlation analysis (MF-DPXA) proposed by Qian et al., we propose a new method-multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA) to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors in this paper. We use MF-TWDPCCA to characterize the intrinsic cross-correlations between the two simultaneously recorded time series by removing the effects of other potential time series. To test the performance of MF-TWDPCCA, we apply it, MF-TWXDFA and MF-DPXA on simulated series. Numerical tests on artificially simulated series demonstrate that MF-TWDPCCA can accurately detect the intrinsic cross-correlations for two simultaneously recorded series. To further show the utility of MF-TWDPCCA, we apply it on time series from stock markets and find that there exists significantly multifractal power-law cross-correlation between stock returns. A new partial cross-correlation coefficient is defined to quantify the level of intrinsic cross-correlation between two time series. Copyright © 2020, The Authors. All rights reserved.

关键词： Fractals

Fractal and complex network analyses of protein molecular dynamics

学校读者我要写书评

暂无评论

Physica A: Statistical Mechanics and its Applications 2014年 416卷 21-32页

作者： Yuan-Wu Zhou Jin-Long Liu Zu-Guo Yu Zhi-Qin Zhao Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China Civil Construction Engineering Department Guangxi University of Science and Technology Liuzhou 545006 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h ( q ) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h ( 2 ) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H ≈ 0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h ( 2 ) of MF-DFA on the time series, exponent λ of the exponential degree distribution and fractal dimension d B of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈 h ( 2 ) 〉 (from MF-DFA on time series) and 〈 d B 〉 of the converted HVGs for different energy, pressure and volume.

关键词： Protein molecular dynamics Multifractal detrended fluctuation analysis Horizontal visibility graph Fractal analysis Degree distribution

Correlating the Structure and Optical Absorption Properties of Au76（SR）44 Cluster

学校读者我要写书评

暂无评论

Correlating the Structure and Optical Absorption Properties ...

第九届计算纳米科学与新能源材料国际研讨会

作者： Zhongyun Ma P.Wang G.Zhou J.Tang H.Li Y.Pei Department of Chemistry Key Laboratory of Environmentally Friendly Chemistry and Applications of Ministry of EducationXiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied MathematicsXiangtan University School of Materials Science and Engineering Central South University

The atomic structure of recently synthesized thiolate-protected Au cluster is theoretically predicted via a simple structural rule summarized from the crystal structures of thiolate-protected Au（SR）, Au（SR） and Au（SR） clusters. We find that the Au（SR）（N = 7） and recently reported Au（SR）（N = 4）, Au（SR）（N = 3）, Au（SR）（N = 2） and Au（SR）（N = 1） belong to a family of homologous Au（SR） cluster whose Au-cores follow one-dimensional polytetrahedral growth pathway. The Au（SR） cluster is predicted to contain an anisotropic face-centered cubic（FCC） Au-core, which can be viewed as combination of two helical tetrahedra-Au4 chains and is remarkably different from the well-known spherical Au-core in ligand protected gold clusters in the size region of 1-2 nm. The intense near infrared（NIR） absorption of Au（SR） is attributed to the synergistic effect of anisotropic Au-core structure and ligand protections. A plausible cluster-to-cluster transformation mechanism is further suggested.

关键词： thiolated-protected gold nanocluster Au76SR44 face-centered cubic near infrared adsorption

Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Zhang, Juan Zhao, Wenjie Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Hunan First Normal University Hunan Changsha410205 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This paper studies the solution existence of the continuous-time algebraic Riccati equation (CARE). We formulate the CARE as two constrained polynomial optimization problems, and then use Lasserre's hierarchy of semi-definite relaxations to solve them. Compared to the existing work, our approaches can obtain the exact positive semi-definite solution of the CARE when the coefficient matrices are symmetric. Moreover, our methods can detect the nonexistence of the positive semi-definite solution for the CARE. Numerical examples show that our approaches are effective compared to the existing methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

High-accurate and efficient numerical algorithms for the self-consistent field theory of liquid-crystalline polymers

学校读者我要写书评

暂无评论

arXiv 2024年

作者： He, Zhijuan Jiang, Kai Tan, Liwei Wang, Xin 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 Hunan Xiangtan411105 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China

Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT encompass efficiently solving plenty of six dimensional partial differential equations (PDEs), precisely determining the subtle energy difference among self-assembled structures, and developing effective iterative methods for nonlinear SCF iteration. To address these challenges, this work introduces a suite of high-order and efficient numerical methods tailored for SCFT of liquid-crystalline polymers. These methods include various advaced PDE solvers, an improved Anderson iteration algorithm to accelerate SCFT calculations, and an optimization technique of adjusting the computational domain during the SCF iterations. Extensive numerical tests demonstrate the efficiency of the proposed methods. Based on these algorithms, we further explore the self-assembly behavior of liquid crystalline polymers through simulations in four, five, and six dimensions, uncovering intricate three-dimensional spatial structures. Copyright © 2024, The Authors. All rights reserved.

关键词： Crystalline materials

High-Accurate and Eﬀicient Numerical Algorithms for the Self-Consistent Field Theory of Liquid-Crystalline Polymers

学校读者我要写书评

暂无评论

SSRN

SSRN 2024年

作者： Tan, Liwei He, Zhijuan Wang, Xin Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China

In this paper, we develop and investigate numerical methods for the self-consistent field theory (SCFT) of liquid crystalline polymers. Both the Flory-Huggins interaction potential and the Maier-Saupe orientational interaction are considered, enabling simultaneous exploration of microphase separation and liquid crystalline order in these systems. The main challenge in numerically solving this complex system lies in solving 6-dimensional (3D spatial + 2D orientation + 1D time) partial differential equations and performing nonlinear iterations to optimize the fields. We present ten numerical algorithms for solving high-dimensional PDEs and give an evaluation criterion of choosing the most appropriate PDE solver both from theoretical and numerical performance. Results demonstrate that coupling the fourth-order Runge-Kutta scheme with Fourier pseudo-spectral methods and spherical harmonic transformations is superior compared to other algorithms. We develop two nonlinear iteration schemes, alternating direction iteration method and Anderson mixing method, and design an adaptive technique to enhance the stability of the Anderson mixing method. Moreover, the cascadic multi-level (CML) technique further accelerates the SCFT computation when applied to these iteration methods. Meanwhile, an approach to optimize the computational domain is developed. To demonstrate the power of our approaches, we investigate the self-assembled behaviors of flexible-semiflexible diblock copolymers in 4, 5, 6-dimensional simulations. Numerical results illustrate the eﬀiciency of our proposed method. © 2024, The Authors. All rights reserved.

关键词： Mixing

Quasiperiodic Symmetric Tilt FCC Grain Boundaries

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Zou, Wenwen Zhang, Juan Xu, Jie Jiang, Kai 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 Hunan Xiangtan411105 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we investigate [110] symmetric tilt FCC grain boundaries (GBs) by a recently developed approach for quasiperiodic interfaces using the Landau-Brazovskii model. On special tilt angles associated with quadratic algebraic numbers, quasiperiodic GBs exhibit generalized Fibonacci substitution rules. The transition mechanism from quasiperiodic GBs to periodic GBs is explored through sphere offsets and spectral coalescence. We also propose an accurate method to calculate the GB energy for arbitrary tilt angle and analyze the factors affecting the GB energy. The revealing GB energy change is continue along with tilt angle except periodic GBs. © 2024, CC BY-NC-SA.

关键词： Grain boundaries

On the vanishing dissipation limit for the incompressible MHD equations on bounded domains

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Duan, Qin Xiao, Yuelong Xin, Zhouping Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University China College of Mathematics and Statistics Shenzhen University China Institute of Mathematical Sciences Chinese University of Hong Kong Hong Kong

In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field fulfills a Navier-slip condition, while the magnetic field satisfies the insulating condition. It is shown that the initial-boundary problem has a global weak solution for a general smooth domain. More importantly, for a flat domain, we establish the uniform local well-posedness of the strong solution with higher order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD as the dissipation tends to zero. Copyright © 2020, The Authors. All rights reserved.

关键词： Initial value problems

Sinc-Chebyshev collocation method for a class of fractional diffusion-wave equations

学校读者我要写书评

暂无评论

The Scientific World Journal

The Scientific World Journal 2014年第1期2014卷 143983页

作者： Mao, Zhi Xiao, Aiguo Yu, Zuguo Shi, Long Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China Mathematics and Information Engineering Department Tongren University Tongren Guizhou 554300 China

This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. © 2014 Zhi Mao et al.

关键词：