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High-fidelity fast quantum driving in nonlinear systems

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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Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method

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Applied Mathematics 2013年第1期4卷 113-118页

作者： Yin Yang College of Civil Engineering and Mechanics Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.

关键词： Legendre Pseudo-Spectral Method Multi-Order Fractional Differential Equations Caputo Derivative

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Parametric symplectic partitioned Runge–Kutta methods with energy-preserving properties for Hamiltonian systems

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Computer Physics Communications 2013年第2期184卷 303-310页

作者： Dongling Wang Aiguo Xiao Xueyang Li School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 PR China

Based on W -transformation, some parametric symplectic partitioned Runge–Kutta (PRK) methods depending on a real parameter α are developed. For α = 0 , the corresponding methods become the usual PRK methods, including Radau IA – I A ¯ and Lobatto IIIA – IIIB methods as examples. For any α ≠ 0 , the corresponding methods are symplectic and there exists a value α ∗ such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results.

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Fractional variational integrators for fractional Euler–Lagrange equations with holonomic constraints

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Communications in Nonlinear science and Numerical simulation 2013年第4期18卷 905-914页

作者： Dongling Wang Aiguo Xiao School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 PR China

In this paper, the fractional variational integrators developed by Wang and Xiao (2012) [28] are extended to the fractional Euler–Lagrange (E–L) equations with holonomic constraints. The corresponding fractional discrete E–L equations are derived, and their local convergence is discussed. Some fractional variational integrators are presented. The suggested methods are shown to be efficient by some numerical examples.

关键词： Fractional variational integrators Fractional Euler–Lagrange equations Holonomic constraints

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Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation

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science CHINA Mathematics 2013年第12期56卷 2615-2630页

作者： HUANG YunQing SU YiFan WEI HuaYi YI NianYu Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China

Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features. Defining an appropriate metric tensor and designing an efficient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology. In this paper, we are concerned with the natural metric tensor for use in anisotropic mesh generation for anisotropic elliptic problems. We provide an algorithm to generate anisotropic meshes under the given metric tensor. We show that the inverse of the anisotropic diffusion matrix of the anisotropic elliptic problem is a natural metric tensor for the anisotropic mesh generation in three aspects: better discrete algebraic systems, more accurate finite element solution and superconvergence on the mesh nodes. Various numerical examples demonstrating the effectiveness are presented.

关键词： anisotropic mesh metric tensor superconvergence anisotropic elliptic equation

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Superconvergence for General Convex Optimal Control Problems Governed by Semilinear Parabolic Equations

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International Scholarly Research Notices 2014年第1期2014卷

作者： Yongquan Dai Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of Mathematics Xiangtan University Xiangtan Hunan 411105 *** School of Mathematical Sciences South China Normal University Guangzhou Guangdong 510631 ***

We will investigate the superconvergence for the semidiscrete finite element approximation of distributed convex optimal control problems governed by semilinear parabolic equations. The state and costate are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We present the superconvergence analysis for both the control variable and the state variables.

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