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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

arXiv

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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

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Multicontinuum homogenization for coupled flow and transport equations

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Journal of computational and Applied Mathematics 2026年 471卷

作者： Dmitry Ammosov Jian Huang Wing Tat Leung Buzheng Shan Computational Technologies & Artificial Intelligence North-Eastern Federal University Yakutsk 677980 Russia School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 Hunan China Department of Mathematics City University of Hong Kong Hong Kong Department of Mathematics Texas A&M University College Station TX 77843 USA

In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and formulate novel coupled constraint cell problems to capture the multiscale property, where oversampled regions are utilized to avoid boundary effects. Assuming the smoothness of macroscopic variables, we obtain a multicontinuum system composed of macroscopic elliptic equations and convection–diffusion–reaction equations with homogenized effective properties. Finally, we present numerical results for various coefficient fields and boundary conditions to validate our proposed algorithm.

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Energy-Efficient Virtual Machine Placement in Data Centers Via Accelerated Genetic Algorithm with Improved Fitness computation

SSRN

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SSRN 2021年

作者： Hormozi, Elham Hu, Shuwen Ding, Zhe Tian, Yu-Chu Wang, You-Gan Yu, Zu-Guo Zhang, Weizhe School of Computer Science Queensland University of Technology GPO Box 2434 BrisbaneQLD4001 Australia School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQLD4001 Australia Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China School of Cyberspace Science Harbin Institute of Technology Harbin China Cyberspace Security Research Center Peng Cheng Laboratory Shenzhen China Queensland University of Technology

Energy efficiency basically refers to how effectively energy can be utilised or consumed by any virtualised data centre giving cloud administrations. Since Genetic Algorithm (GA) is an acceptable method to solve the VM placement problem, this research formulates the Virtual Machine (VM) placement problem as a constrained optimisation problem. A considerable amount of residual resources is available for each new VM allocation, however they are distributed across multiple active PMs, rendering them inefficient. Our research focuses on improving a data centre’s energy and time efficiency by devising a technique to decrease PM’s residual resources and make them more valuable. As the most time consuming element of a GA is calculating the fitness function, this paper presents a new fitness function to simplify the fitness function calculation in GA. The results are compared to the standard GA and First Fit Decreasing (FFD) algorithm. The findings reveals a 8% energy savings for our GA compared to FFD and a 66% reduction in our GA execution time compared to the standard GA for virtualised data centres. The simulation experiments are conducted on small-, medium- and large-scale of the google data centre to demonstrate the effectiveness of our GA. © 2021, The Authors. All rights reserved.

关键词： Energy efficiency

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Piecewise divergence-free nonconforming virtual elements for stokes problem in any dimensions

arXiv

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arXiv 2020年

作者： Wei, Huayi Huang, Xuehai Li, Ao Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Mathematics Shanghai University of Finance and Economics Shanghai200433 China

Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming virtual element method is proposed for Stokes problem. A detailed and rigorous error analysis is presented for the discrete method. An important property in the analysis is that the local energy projector commutes with the divergence operator. With the help of a divergence-free interpolation operator onto a generalized Raviart-Thomas element space, a pressure-robust nonconforming virtual element method is developed by simply modifying the right hand side of the previous discretization. A reduced virtual element method is also discussed. Numerical results are provided to verify the theoretical *** Codes 76D07, 65N12, 65N22, 65N30 Copyright © 2020, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Numerical homogenization of elastoplastic deformations of composite material with small proportion of inclusions 4

Numerical homogenization of elastoplastic deformations of co...

引用

4th International Conference on Supercomputer Technologies of Mathematical Modelling, SCTeMM 2019

作者： Sivtsev, Petr V. Kolesov, Aleksandr E. Zakharov, Petr E. Yang, Ying Research Laboratory multiscale Matheatical Modeling and Computing Ammosov North-Eastern Federal University Belinskogo 58 Yakutsk677000 Russia Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China

Numerical simulation of the stress-strain state of a composite material may be difficult due to large computational complexity associated with a grid resolution of a large number of inclusions. To overcome the problem one may use the homogenization method. But for material with plastic properties, proper modeling of yield stress and hardening may be overcomplicated. In this work we use some simplification associated with a small proportion of inclusions and restriction of stress values by matrix material strength. As model problem, we use deformation of concrete deep beam reinforced with steel or basalt fiber inclusions. For the numerical solution, the finite element method was applied using the FEniCS computing platform. © Published under licence by IOP Publishing Ltd.

关键词： Homogenization method

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Particle Scale Numerical simulation on Momentum and Heat Transfer of Two Tandem Spheroids:an IB-LBM Study

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1497-1526页

作者： Chunhai Ke Shi Shu Hao Zhang Haizhuan Yuan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105HunanChina School of Metallurgy Northeastern UniversityShenyang 110819LiaoningChina

The cold fluid flowing over two hot spheroids placed in a tandem arrangement was numerically studied via a GPU-based immersed boundary-lattice Boltzmann method(IB-LBM)*** drag coefficient and average Nusselt number of both the two spheroids were obtained with the main influencing factors *** validate the IB-LBM model,several numerical case studies containing one and two spheres were firstly conducted to reach the good agreement with the previously reported ***,a number of simulations were further carried out which were designed by changing the particle aspect ratio(1.0≤Ar≤4.0)and inter particle distance(1.5≤ι≤7.0,whereι=L/D,D stands for the volume-equivalent sphere diameter)as well as the Reynolds number(10≤Re≤200).Their influence on the momentum and heat transfer characteristics between the solid and fluid phases was fully *** results show that,for all the considered Reynolds numbers and aspect ratios,the individual and total drag coefficients and average Nusselt number increase with the inter particle *** inter particle distance has greater influence on the drag coefficient and average Nusselt number of the trailing particle than the leading *** drag coefficient and average Nusselt number of the trailing particle are far less than the leading one under the same working *** prediction correlations for the drag coefficient and average Nusselt number of both the two spheroids were established with low *** last,the influence of the relative incidence angles between the two tandem spheroids on the momentum and heat transfer was *** is shown that the relative incidence angles play significant roles due to the change of the frontal area of the leading spheroid with these angles.

关键词： Drag coefficient average Nusselt number IB-LBM spheroids inter particle distance relative incidence angle

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

arXiv

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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

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Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation

arXiv

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arXiv 2019年

作者： Dai, Xinjie Xiao, Aiguo Bu, Weiping School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates to include all the cases of Abel-type singular kernels. Firstly, the existence, uniqueness and continuous dependence on the initial value of the true solution under local Lipschitz condition and linear growth condition are derived in detail. Secondly, the Euler–Maruyama method is developed for solving numerically the equation, and then its strong convergence is proven under the same conditions as the well-posedness. Moreover, we obtain the accurate convergence rate of this method under global Lipschitz condition and linear growth condition. In particular, the Euler–Maruyama method can reach strong first-order superconvergence when α = 1. Finally, several numerical tests are reported for verification of the theoretical *** Codes 65C30, 65C20, 65L05, 65L20 Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

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Space-time finite element method for the distributed-order time fractional reaction diffusion equations

Space-time finite element method for the distributed-order t...

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第十六届全国微分方程数值方法暨第十三届全国仿真算法学术会议

作者： Weiping Bu School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityHunan 411105China

In this paper,we propose a space-time finite element method for the distributed-order time fractional reaction diffusion equations(DOTFRDEs).

关键词： Distributed-order reaction diffusion equation space-time finite element method graded time mesh well-posedness error estimate sum-of-exponentials approximation

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Numerical methods for the mass-conserved Ohta-Kawasaki equation

arXiv

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arXiv 2019年

作者： Zhang, Juan Li, Shifeng Jiang, Kai School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

In this paper, we propose a numerical method to solve the mass-conserved Ohta-Kawasaki equation with finite element discretization. An unconditional stable convex splitting scheme is applied to time approximation. The Newton method and its variant are used to address the implicitly nonlinear term. We rigorously analyze the convergence of the Newton iteration methods. Theoretical results demonstrate that two Newton iteration methods have the same convergence rate, and the Newton method has a smaller convergent factor than the variant one. To reduce the condition number of discretized linear system, we design two efficient block preconditioners and analyze their spectral distribution. Finally, we offer numerical examples to support the theoretical analysis and indicate the efficiency of the proposed numerical methods for the mass-conserved Ohta-Kawasaki equation. Copyright © 2019, The Authors. All rights reserved.

关键词： Newton-Raphson method

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