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Lower Bounds for Eigenvalues of the Stokes Operator

Advances in Applied Mathematics and Mechanics 2013年第1期5卷 1-18页

作者： Jun Hu Yunqing Huang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China

In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconformin... 详细信息

关键词： Lower bound eigenvalue Stokes operator

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A directed continuous time random walk model with jump length depending on waiting time

The Scientific World Journal

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The Scientific World Journal 2014年第1期2014卷 182508页

作者： Shi, Long Yu, Zuguo Mao, Zhi Xiao, Aiguo 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 Institute of Mathematics and Physics Central South University of Forest and Technology Changsha Hunan 410004 China School of Mathematical Sciences Queensland University of Technology Brisbane QLD 4001 G.P.O. Box 2434 Australia

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P (x, t) of finding the walker at position x at time t is completely determined by the Laplace transform of the probability density function (t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived. © 2014 Long Shi et al.

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The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations

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Journal of Statistical Mechanics: Theory and Experiment 2014年第12期2014卷

作者： Shi, Long Yu, Zu-Guo Huang, Hai-Lan Mao, Zhi Xiao, Ai-Guo Hunan Key Laboratory for Computation and Simulation in Science Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Science Central South University of Forest and Technology Changsha Hunan 410004 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of a time variable and a negative power function of an α-stable random variable. The effect of parameters in the subordinators on the subordinated process is discussed. By suitable variable substitutions and the Laplace transform technique, the corresponding fractional Fokker-Planck-type equations are derived. We also compute their mean square displacements in a free force field. By choosing suitable ranges of parameters, the resulting subordinated processes may be subdiffusive, normal diffusive or superdiffusive. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

关键词： diffusion

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Discovery of New Metastable Patterns in Diblock Copolymers

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Communications in computational Physics 2013年第7期14卷 443-460页

作者： Kai Jiang Chu Wang Yunqing Huang Pingwen Zhang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871P.R.China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105P.R.China

The ordered patterns formed bymicrophase-separated block copolymer systems demonstrate periodic symmetry,and all periodic structures belong to one of 230 space *** on this fact,a strategy of estimating the initial values of self-consistent field theory to discover ordered patterns of block copolymers is *** particular,the initial period of the computational box is estimated by the Landau-Brazovskii model as *** planting the strategy into the whole-space discrete method,several new metastable patterns are discovered in diblock copolymers.

关键词： Metastable patterns diblock copolymers self-consistent field theory(SCFT) space group theory initial values

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Supercloseness of the Divergence-Free Finite Element Solutions on Rectangular Grids

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Communications in Mathematics and Statistics 2013年第2期1卷 143-162页

作者： Yunqing Huang Shangyou Zhang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

By the standard theory,the stable Qk+1,k−Qk,k+1/Qdck divergence-free element converges with the optimal order of approximation for the Stokes equations,but only order k for the velocity in H1-norm and the pressure in *** is due to one polynomial degree less in y direction for the first component of velocity,which is a Qk+1,k polynomial of x and *** this manuscript,we will show by supercloseness of the divergence free element that the order of convergence is truly k+1,for both velocity and *** special solutions(if the interpolation is also divergence-free),a two-order supercloseness is shown to *** tests are provided confirming the accuracy of the theory.

关键词： Mixed finite element Stokes equations Divergence-free element Quadrilateral element Rectangular grids Supercloseness Superconvergence

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High-fidelity fast quantum driving in nonlinear systems

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Physical Review A 2014年第1期89卷 012123-012123页

作者： F. Q. Dou L. B. Fu J. Liu Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province College of Physics and Electronic Engineering Northwest Normal University Lanzhou 730070 China School of Physics Beijing Institute of Technology Beijing 100081 China National Laboratory of Science and Technology on Computation Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China Key Laboratory of High Energy Density Physics Simulation (HEDPS) Center for Applied Physics and Technology Peking University Beijing 100084 China

We investigate high-fidelity quantum driving in a nonlinear two-level system and find that nonlinear atomic interaction can break the speed limit of the linear model. We show that repulsive atomic interaction can decrease the minimal time requested for reaching target state even to zero, while attractive atomic interaction tends to increase the minimal time. There exists a critical attractive interaction beyond which the target state cannot be reached with high fidelity. Possible experimental observation of the nonlinear effects using a Bose-Einstein condensate in an accelerating optical lattice is discussed.

关键词： QUANTUM states NONLINEAR systems ATOMIC interactions SPEED limits LINEAR models (Statistics) OPTICAL lattices

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Multifractal analyses of daily rainfall time series in Pearl River basin of China

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Physica A: Statistical Mechanics and its Applications 2014年 405卷 193-202页

作者： Zu-Guo Yu Yee Leung Yongqin David Chen Qiang Zhang Vo Anh Yu Zhou 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 School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia Department of Geography and Resource Management The Chinese University of Hong Kong Hong Kong China Institute of Environment Energy and Sustainability The Chinese University of Hong Kong Hong Kong China Department of Water Resources and Environment Sun Yat-sen University Guangzhou 510275 China Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education Institute Sun Yat-sen University Guangzhou 510275 China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K ( q ) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter H from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h ( 2 ) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K ( 2 ) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

关键词： Daily rainfall time series Multifractal property Universal multifractal model Multifractal detrended fluctuation analysis

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Recent progress in quantifying substituent effects

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science China Chemistry 2013年第7期56卷 883-910页

作者： CAO ChenZhong WU YaXin Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Key Laboratory of QSAR/QSPR of Hunan Provincial University School of Chemistry and Chemical Engineering Hunan University of Science and Technology School of Chemistry and Chemical Engineering University of South China

This paper summarizes significant progress in quantifying organic substituent effects in the last 20 years. The main content is as follows：（1） The principle of electronegativity equalization has gained wide acceptance, and has been used to calculate the intramolecular charge distribution and inductive effect of groups. A valence electrons equalization method was proposed to compute the molecular electronegativity on the basis of geometric mean method, harmonic mean method, and weighted mean method. This new calculation method further extended the application of the principle of electronegativity equalization. （2） A scale method was established for experimentally determining the electrophilic and nucleophilic ability of reagents, in which benzhydryliumions and quinone methides were taken as the reference compounds, and the research field was extended to the gas phase conditions, organometallic reaction and radicals system. Moreover, the nucleophilicity parameters N and electro- philicity parameters E for a series of reagents were obtained. The definition and quantitative expression of electrophilicity in- dex co and nucleophilicity index co were proposed theoretically, and the correlation between the parameters from experimental determination and the indexes from theoretical calculation was also investigated. （3） The polarizability effect parameter was initially calculated by empirical method and further developed by quantum chemistry method. Recently, the polarizability ef- fect index of alkyl （PEI） and groups （PEIx） were proposed by statistical method, and got wide applications in explaining and estimating gas-phase acidity and basicity, ionization energy, enthalpy of formation, bond energy, reaction rate, water solubility and chromatographic retention for organic compounds. （4） The excited-state substituent constant Crcc obtained directly from the UV absorption energy data of substituted benzenes, is different from the polar constants in molecular ground state an

关键词： substituent effect electronic effect steric effect molecular equalized electronegativity electrophilicity index nucleo-philicity index polarizability effect parameter excited-state substituent constant steric shielding effect

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The improved Hagedorn wavepacket method for semiclassical Schrödinger equation

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International Journal of Modeling, simulation, and Scientific Computing 2014年第4期5卷

作者： Xueyang Li Aiguo Xiao 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 P. R. China

The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation. In this paper, a new semi-discretization in space is obtained by wavepacket operator. In a sense, such semi-discretization is equivalent to the Hagedorn wavepacket method, but this discretization is more intuitive to show the advantages of wavepacket methods. Moreover, we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation. The improved algorithms are of the Gauss–Hermite spectral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation. And for the given accuracy, the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation. The superiority is shown by the error estimation and numerical experiments.

关键词： High oscillation semiclassical Schrödinger equation Hagedorn wavepacket multi-time-step method Magnus-expansion

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Adaptive mesh refinement and superconvergence for two-dimensional interface problems

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SIAM Journal on Scientific Computing 2014年第4期36卷 A1478-A1499页

作者： Wei, Huayi Chen, Long Huang, Yunqing Zheng, Bin Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Lab. of Intelligent Comp. and Info. Proc. Comp. Min. of Educ. School of Math. and Computational Sci. Xiangtan University Xiangtan Hunan 411105 China Department of Mathematics University of California at Irvine Irvine 92697 CA United States Northwest National Lab Richland 99352 WA United States

Adaptive mesh refinement and the Börgers algorithm are combined to generate a body-fitted mesh which can resolve the interface with fine geometric details. Standard linear finite element method based on such body-fitted meshes is applied to the elliptic interface problem and proven to be superclose to the linear interpolation of the exact solution. Based on this superconvergence result, a maximal norm error estimate of order one and half is obtained without using the discrete maximum principle. The data structure and meshing algorithms, including local refinement and coarsening, are very simple. In particular, no tree structure is needed. An efficient solver for solving the resulting linear algebraic systems is also developed and shown be robust with respect to both the problem size and the jump of the diffusion coefficients. © 2014 Society for Industrial and Applied Mathematics.

关键词： Adaptive mesh refinement Body-fitted mesh Superconvergence

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