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Superconvergence and L^(∞)-Error Estimates of RT1Mixed Methods for Semilinear Elliptic Control Problems with an Integral Constraint

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Numerical Mathematics(Theory,Methods and Applications) 2012年第3期5卷 423-446页

作者： Yanping Chen Tianliang Hou School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina

In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral *** state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear *** derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant ***,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear ***,some numerical examples are given to demonstrate the theoretical results.

关键词： Semilinear elliptic equations optimal control problems superconvergence L∞-error estimates mixed finite element methods postprocessing

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An Iterative Two-Grid Method of A Finite Element PML Approximation for the Two Dimensional Maxwell Problem

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Advances in Applied Mathematics and Mechanics 2012年第2期4卷 175-189页

作者： Chunmei Liu Shi Shu Yunqing Huang Liuqiang Zhong Junxian Wang Hunan Key Laboratory for Computation&Simulation in Science and Engineering and Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education Xiangtan UniversityHunan 411105China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

In this paper,we propose an iterative two-grid method for the edge finite element discretizations(a saddle-point system)of Perfectly Matched Layer(PML)equations to the Maxwell scattering problem in two ***,we use a fine space to solve a discrete saddle-point system of H(grad)variational problems,denoted by auxiliary system ***,we use a coarse space to solve the original saddle-point ***,we use a fine space again to solve a discrete H(curl)-elliptic variational problems,denoted by auxiliary system ***,we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system *** we essentially transform the original problem in a fine space to a corresponding(but much smaller)problem on a coarse space,due to the fact that the above two preconditioners are efficient and *** with some existing iterative methods for solving saddle-point systems,such as PMinres,numerical experiments show the competitive performance of our iterative two-grid method.

关键词： Maxwell scattering edge finite element PML iterative two-grid method

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Crystal Structures and Spectroscopy of Anti-2,4-bis(3-R-phenyl)pentane-2,4-diols (R = Me, SMe)

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Chinese Journal of Structural Chemistry 2012年第12期31卷 1713-1720页

作者：焦银春曹晨忠赵小林 School of Chemistry and Chemical Engineering Central South University School of Chemistry and Chemical Engineering Hunan University of Science and Technology Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Hunan University of Science and Technology Hunan Provincial University Key Laboratory of QSAR/QSPR

Two anti-2,4-bis（3-R-phenyl）pentane-2,4-diols （1, R = Me; 2, R = SMe） have been synthesized and were characterized by X-ray diffraction, IR and UV spectra. X-ray diffractions indicate that intra- and intermolecular hydrogen bonding interactions form one-dimensional （ID） ribbons. The adjacent infinite I D ribbons result in 3D supramolecular structures. The dihedral angles between every two benzene rings in the two diols are 31.61（12） and 31.80（7）°, respectively. UV absorption spectra of the title compounds were recorded in MeOH, C2H5OH, CH3CN, n-BuOH and cyclohexane solvents with different dielectric constants.

关键词： crystal structure hydrogen bonds UV absorption solvent effect

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Mathematical simulation of Cloaking Metamaterial Structures

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Advances in Applied Mathematics and Mechanics 2012年第1期4卷 93-101页

作者： Jichun Li Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China Department of Mathematical Sciences University of Nevada Las VegasLas VegasNevada 89154-4020USA

In this paper we present a rigorous derivation of the material parameters for both the cylinder and rectangle cloaking *** results using these material parameters are presented to demonstrate the cloaking effect.

关键词： Maxwell’s equations metamaterial finite element method cloaking structures

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Crystal structures and theoretical investigation of anti-/syn-2,4-diphenylpentane-and 2,4-di-p-tolylpentane-2,4-diols

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Journal of Central South University 2012年第5期19卷 1219-1225页

2,4-diphenylpentane- and 2,4-di-p-tolylpentane-2,4-diols were investigated employing experimental and density functional theory （DFT） method at B3LYP/6-31G （d） level. The structure of syn-2,4-di-p-tolylpentane-2,4-diol （2b） was characterized by X-ray diffraction and compared with the crystal structures of anti- and syn-2,4-diphenylpentane-2,4-diols （la and lb）. X-ray diffraction indicates that inter and intra-molecular hydrogen bonds are formed in the crystal structures. There is n-n staking interaction in lb and 2b. Good linear correlations and similar results are found between the experimental 1H and 13C NMR chemical shifts （6~exp） and GIAO （Gauge Independent Atomic Orbital） method calculated magnetic isotropic shielding tensors （acalc）. HOMO and LUMO molecular orbitals were calculated at the same levels with the different results. UV-vis absorption spectra of the compounds were recorded in EtOH, MeCN, n-BuOH and cyclohexane with different dielectric constants. It is found that the solvent effect is obvious when e is 24.85（EtOH）, 35.69（MeCN） and it is weak when e is decreased to 17.33（n-BuOH）, 1.18 （cyclohexane）.

关键词： X-ray crystallography hydrogen bonds nuclear magnetic resonance （NMR） density function theory （DFT） UV-visabsorption solvent effect

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Formation of N-body polymer molecules through generalized stimulated Raman adiabatic passage

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Physical Review A 2013年第4期87卷 043631-043631页

作者： Fu-quan Dou Li-bin Fu Jie Liu 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 Center for Applied Physics and Technology Peking University Beijing 100084 China

We investigate the creation of stable homonuclear and heteronuclear N-body polymer molecules from ultracold atoms via a generalized stimulated Raman adiabatic passage scheme. The atom-molecule dark-state solutions for the system are obtained and are found to satisfy universal algebraic equations. We discuss the linear instability and the adiabatic fidelity of the dark state. We also explore the effects of the interparticle interactions, the atomic number of the polymer, and external field parameters on the conversion process.

关键词： DARK states (Quantum optics) ADIABATIC processes MANY-body problem ATOMS ALGEBRAIC equations ATOMIC number

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Amyloid-β peptide (1-42) aggregation induced by copper ions under acidic conditions

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生物化学与生物物理学报（英文版） 2013年第7期45卷 570-577页

作者： Yannan Bin Xia Li Yonghui He Shu Chen Juan Xiang Institute of Surface Analysis and Biosensing College of Chemistry and Chemical Engineering Central South University Changsha 410083 China Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education of China School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan 411201 China Institute of Surface Analysis and Biosensing College of Chemistry and Chemical Engineering Central South University Changsha 410083 China Institute of Surface Analysis and Biosensing College of Chemistry and Chemical Engineering Central South University Changsha 410083 China Key Laboratory of Resources Chemistry of Nonferrous Metals Ministry of Education Central South University Changsha 410083 China

It is well known that the aggregation of amyloid-β peptide (Aβ) induced by Cu2+ is related to incubation time, solution pH, and temperature. In this work, the aggregation of Aβ1–42 in the presence of Cu2+ under acidic conditions was studied at different incubation time and temperature (e.g. 25 and 37°C). Incubation temperature, pH, and the presence of Cu2+ in Aβ solution were confirmed to alter the morphology of aggregation (fibrils or amorphous aggregates), and the morphology is pivotal for Aβ neurotoxicity and Alzheimer disease (AD) development. The results of atomic force microscopy (AFM) indicated that the formation of Aβ fibrous morphology is preferred at lower pH, but Cu2+ induced the formation of amorphous aggregates. The aggregation rate of Aβ was increased with the elevation of temperature. These results were further confirmed by fluorescence spectroscopy and circular dichroism spectroscopy and it was found that the formation of β-sheet structure was inhibited by Cu2+ binding to Aβ. The result was consistent with AFM observation and the fibrillation process was restrained. We believe that the local charge state in hydrophilic domain of Aβ may play a dominant role in the aggregate morphology due to the strong steric hindrance. This research will be valuable for understanding of Aβ toxicity in AD.

关键词： amyloid-β peptide copper ions atomic force microscopy acidic pH morphology

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Enthalpies Estimation of Formation of Monosubstituted Alkanes by Interaction Potential Index

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Chinese Journal of Chemical Physics 2012年第2期25卷 153-160,I0003页

作者： Ya-xin Wu Chen-zhong Cao Hua Yuan School of Chemistry and Chemical Engineering Central South UniversityChangsha 410083China School of Chemistry and Chemical Engineering Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of EducationHunan University of Science and Technologyand Hunan Provincial University Key Laboratory of QSAR/QSPRXiangtan 411201China

The interaction potential index IPI（X） of 16 Br, C1, I, NO2, CN, CHO, COOH, CH3, CH： kinds of substituents X （X---OH, SH, NH2, ：CH2, C-CH, Ph, COCH3, COOCH3） were proposed, which are derived from the experimental enthalpies of formation △fHФ （g） values of monosubstituted straight-chain alkanes. Based on the IPI（X） and polarizability effect index, a simple and effective model was constructed to estimate the △fHФ （g） values of monosubstituted alkanes RX （including the branched derivatives）. The present model takes into account not only the contributions of the alkyl R and the substituent X, but also the contribution of the interaction between R and X. Its stability and prediction ability was confirmed by the results of leave-one-out method. Compared with previous reported studies, the obtained equation can be used to estimate enthalpies of formation for much more kinds of monosubstituted alkanes with less parameters. Thus, it is recommended for the calculation of the △fHФ（g） for the RX.

关键词： Interaction potential index Substituent Monosubstituted alkane Enthalpy offormation Polarizability effect index

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A two-dimensional numerical wave flume based on SA-MPLS method

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Acta Oceanologica Sinica 2012年第3期31卷 18-30页

作者： HUANG Xiaoyun LI Shaowu State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin 300072China School of Hydraulic Engineering Changsha University of Science and TechnologyChangsha410114China Water&Sediment Science and Water Hazard Prevention Hunan Provincial Key Laboratory Changsha University of Science and TechnologyChangsha 410114China

A spatially adaptive (SA) two-dimensional (2-D) numerical wave flume is presented based on the quadtree mesh system,in which a new multiple particle level set (MPLS) method is proposed to solve the problem of interface tracking,in which common intersection may be traversed by multiple *** using the adaptive mesh technique and the MPLS method,mesh resolution is updated automatically with time according to flow characteristics in the modeling process with higher resolution around the free surface and the solid boundary and lower resolution in less important *** model has good performance in saving computer memory and CPU time and is validated by computational examples of small amplitude wave,second-order Stokes wave and cnoidal *** results also indicate that standing wave and wave overtopping are also reasonably simulated by the model.

关键词： spatially adaptive quadtree mesh system multiple particle level set method numerical wave flume

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Error estimates of triangular mixed finite element methods for quasilinear optimal control problems

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Frontiers of Mathematics in China 2012年第3期7卷 397-413页

作者： Yanping CHEN Zuliang LU Ruyi GUO School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China College of Civil Engineering and Mechanics Xiangtan UniversityXiangtan 411105China School of Mathematics and Statistics China Three Gorges UniversityChongqing 404000China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105China

The goal of this paper is to study a mixed finite element approximation of the general convex optimal control problems governed by quasilinear elliptic partial differential equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a priori error estimates both for the state variables and the control variable. Finally, some numerical examples are given to demonstrate the theoretical results.

关键词： A priori error estimate quasilinear elliptic equation generalconvex optimal control problem triangular mixed finite element method

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